0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.23 % Computer : n023.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:02:10 CDT 2018 0.02/0.23 % CPUTime : 0.96/1.13 ============================== Prover9 =============================== 0.96/1.13 Prover9 (32) version 2009-11A, November 2009. 0.96/1.13 Process 8148 was started by sandbox2 on n023.star.cs.uiowa.edu, 0.96/1.13 Sat Jul 14 06:02:10 2018 0.96/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8020_n023.star.cs.uiowa.edu". 0.96/1.13 ============================== end of head =========================== 0.96/1.13 0.96/1.13 ============================== INPUT ================================= 0.96/1.13 0.96/1.13 % Reading from file /tmp/Prover9_8020_n023.star.cs.uiowa.edu 0.96/1.13 0.96/1.13 set(prolog_style_variables). 0.96/1.13 set(auto2). 0.96/1.13 % set(auto2) -> set(auto). 0.96/1.13 % set(auto) -> set(auto_inference). 0.96/1.13 % set(auto) -> set(auto_setup). 0.96/1.13 % set(auto_setup) -> set(predicate_elim). 0.96/1.13 % set(auto_setup) -> assign(eq_defs, unfold). 0.96/1.13 % set(auto) -> set(auto_limits). 0.96/1.13 % set(auto_limits) -> assign(max_weight, "100.000"). 0.96/1.13 % set(auto_limits) -> assign(sos_limit, 20000). 0.96/1.13 % set(auto) -> set(auto_denials). 0.96/1.13 % set(auto) -> set(auto_process). 0.96/1.13 % set(auto2) -> assign(new_constants, 1). 0.96/1.13 % set(auto2) -> assign(fold_denial_max, 3). 0.96/1.13 % set(auto2) -> assign(max_weight, "200.000"). 0.96/1.13 % set(auto2) -> assign(max_hours, 1). 0.96/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.96/1.13 % set(auto2) -> assign(max_seconds, 0). 0.96/1.13 % set(auto2) -> assign(max_minutes, 5). 0.96/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.96/1.13 % set(auto2) -> set(sort_initial_sos). 0.96/1.13 % set(auto2) -> assign(sos_limit, -1). 0.96/1.13 % set(auto2) -> assign(lrs_ticks, 3000). 0.96/1.13 % set(auto2) -> assign(max_megs, 400). 0.96/1.13 % set(auto2) -> assign(stats, some). 0.96/1.13 % set(auto2) -> clear(echo_input). 0.96/1.13 % set(auto2) -> set(quiet). 0.96/1.13 % set(auto2) -> clear(print_initial_clauses). 0.96/1.13 % set(auto2) -> clear(print_given). 0.96/1.13 assign(lrs_ticks,-1). 0.96/1.13 assign(sos_limit,10000). 0.96/1.13 assign(order,kbo). 0.96/1.13 set(lex_order_vars). 0.96/1.13 clear(print_given). 0.96/1.13 0.96/1.13 % formulas(sos). % not echoed (523 formulas) 0.96/1.13 0.96/1.13 ============================== end of input ========================== 0.96/1.13 0.96/1.13 % From the command line: assign(max_seconds, 300). 0.96/1.13 0.96/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.96/1.13 0.96/1.13 % Formulas that are not ordinary clauses: 0.96/1.13 1 (all V_aa_2 all V_A_2 all T_a (hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_aa_2)) <-> V_aa_2 = c_List_Olist_ONil(T_a) | (exists B_a exists B_l (hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),B_l)) & hBOOL(hAPP(V_A_2,B_a)) & hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) = V_aa_2)))) # label(fact_listsp_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 2 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 3 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 4 (all V_A_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2)))) # label(fact_lists_ONil) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 5 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (V_m != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 6 (all V_n_2 all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olexn(T_a,V_r_2,V_n_2))) -> V_n_2 = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2) & V_n_2 = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2))) # label(fact_lexn__length) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 7 (all V_Pa_2 all T_a c_List_OtakeWhile(T_a,V_Pa_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 8 (all V_Q all V_P all T_b all T_a hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 9 (all V_y_2 all V_x_2 all V_u_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_ba_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))))) # label(fact_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 10 (all V_ca_2 all V_ba_2 all V_aa_2 all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),V_r_2)))))) # label(fact_transD) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 11 (all V_xs_2 all T_a (c_List_Olist_ONil(T_a) = c_List_Orotate1(T_a,V_xs_2) <-> V_xs_2 = c_List_Olist_ONil(T_a))) # label(fact_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 12 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 != V_n_2)) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 13 (all T_a all V_ys_2 all V_xs_2 ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> c_List_Onth(T_a,V_xs_2,B_i) = c_List_Onth(T_a,V_ys_2,B_i))) & c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2) <-> V_xs_2 = V_ys_2)) # label(fact_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 14 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 15 (all V_S_2 all V_R_2 all T_b all T_a (V_R_2 = V_S_2 <-> hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2))) # label(fact_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 16 (all V_C_2 all V_B_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x),hAPP(V_C_2,B_x)))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2)))) # label(fact_Pi__mono) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 17 (all V_r_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))))) # label(fact_lists__accD) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 18 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 19 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) -> hBOOL(hAPP(hAPP(V_f_2,V_aa_2),V_ba_2)))) # label(fact_splitD) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 20 (all V_y_2 all V_x_2 (V_y_2 = V_x_2 | -hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 21 (all V_xs_2 all V_Pa_2 all T_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> -hBOOL(hAPP(V_Pa_2,c_List_Onth(T_a,V_xs_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2))))))) # label(fact_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 22 (all V_xs all T_a all V_ys ((V_ys != c_List_Olist_ONil(T_a) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys))) & (c_List_Olist_ONil(T_a) = V_ys -> c_List_Obutlast(T_a,V_xs) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))))) # label(fact_butlast__append) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 23 (all V_xs_2 all V_Pa_2 all T_a hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_a,V_Pa_2,V_xs_2)) = V_xs_2) # label(fact_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 24 (all T_b all T_a all V_B_2 all V_y_2 all V_x_2 all V_A_2 (hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2))))) # label(fact_inf2I) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 25 (all V_A_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))))) # label(fact_append__in__lists__conv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 26 (all V_r_2 all T_b all V_aa_2 all T_a ((exists B_y hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))))) # label(fact_Domain__iff) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 27 (all V_xs_2 all V_x_2 all V_zs_2 all V_ys_2 all T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) <-> (exists B_ys_H (hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2)) | c_List_Olist_ONil(T_a) = V_ys_2 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2)) # label(fact_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 28 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 29 (all V_xs_2 all T_a all V_Pa_2 all V_j_2 ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_j_2) -> hBOOL(hAPP(V_Pa_2,c_List_Onth(T_a,V_xs_2,B_i))))) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)))))) # label(fact_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 30 (all V_ys_2 all V_xs_2 all T_a (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) <-> c_List_Olist_ONil(T_a) = V_ys_2)) # label(fact_append__self__conv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 31 (all V_p_2 all V_g_2 all T_e all T_d all V_f_2 all T_a all T_c all T_b hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2))) # label(fact_split__twice) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 32 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & -c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 33 (all V_x_2 all V_r_2 all V_v_2 all V_u_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))))) # label(fact_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 34 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b != V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 35 (all V_g_2 all V_f_2 all T_b all V_A_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_g_2,V_aa_2))) # label(fact_override__on__apply__in) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 36 (all V_f_2 all V_y_2 all V_x_2 all T_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omeasure(T_a,V_f_2))))) # label(fact_in__measure) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 37 (all V_Pa_2 all T_a c_List_Olist_ONil(T_a) = c_List_OdropWhile(T_a,V_Pa_2,c_List_Olist_ONil(T_a))) # label(fact_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 38 (all V_r_2 all V_aa_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downwards__aux) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 39 (all V_ba_2 all V_aa_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2))))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 40 (all T_a all V_xs (c_List_Olist_ONil(T_a) != V_xs -> (c_List_Odistinct(T_a,V_xs) -> c_List_Odistinct(T_a,c_List_Obutlast(T_a,V_xs))))) # label(fact_distinct__butlast) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 41 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 42 (all V_y_2 all V_x_2 all V_Q_2 all V_Pa_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_predicate2D) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 43 (all V_L_2 all V_y_2 all V_x_2 (V_y_2 != V_x_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_above__Lin) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 44 (all V_fs_2 all T_a all V_y_2 all V_x_2 all 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)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))))) # label(fact_measures__less) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 45 (all V_r_2 all T_b all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Relation_ORange(T_b,T_a,V_r_2))) -> -(all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_ba_2)),V_r_2))))) # label(fact_RangeE) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 46 (all T_a all V_B_2 all V_x_2 all 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))))) # label(fact_inf1I) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 47 (all V_x_2 all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))))) # label(fact_listrel1I2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 48 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Olattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Olattice) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 49 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> V_B_2 = V_A_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 50 (all V_y_2 all V_x_2 all V_S_2 all V_R_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2))))) # label(fact_inf__Int__eq2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 51 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 52 (all V_b_H all V_a_H all V_b all V_a all T_b all T_a (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) -> -(V_a_H = V_a -> V_b_H != V_b))) # label(fact_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 53 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 54 (all T_b all T_a all V_ba_2 all V_aa_2 all V_f_2 (hBOOL(hAPP(hAPP(V_f_2,V_aa_2),V_ba_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))))) # label(fact_splitI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 55 (all V_r_2 all V_ys_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2)))) # label(fact_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 56 (all V_xs_2 all V_x_2 all V_f_2 all T_a all T_b hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) # label(fact_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 57 (all V_r_2 all V_xs_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2)))) # label(fact_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 58 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 59 (all V_zs all V_xs all V_ys all V_xs1 all V_x all T_a (V_ys = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) -> (hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) = V_xs -> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)))) # label(fact_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 60 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 61 (all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),B_x)) & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x),c_Arrow__Order__Mirabelle_OLin)))))) # label(fact_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 62 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 63 (all V_xs_2 all V_Pa_2 all T_a all V_j_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2))) -> c_List_Onth(T_a,c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2),V_j_2) = c_List_Onth(T_a,V_xs_2,V_j_2))) # label(fact_takeWhile__nth) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 64 (all V_A_2 all V_g_2 all T_c all V_f_2 all T_a all T_b c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2),V_A_2) = c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_c,T_b,V_g_2,V_A_2))) # label(fact_image__image) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 65 (all V_Q_2 all T_a all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 66 (all V_B_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 67 (all V_r_2 all V_x_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2)))) # label(fact_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 68 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))) # label(fact_inf__apply) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 69 (all V_B_2 all V_A_2 all T_a (V_B_2 = V_A_2 | c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 70 (all V_s_2 all V_r_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) <-> V_a_H_2 = V_aa_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2)) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2)))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 71 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 72 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_B_2)))))) # label(fact_extensional__subset) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 73 (all V_zs all V_ys all V_xs all T_a hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs)) # label(fact_append__assoc) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 74 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 75 (all V_xs_2 all V_Pa_2 all T_a all V_j_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OdropWhile(T_a,V_Pa_2,V_xs_2))) -> c_List_Onth(T_a,c_List_OdropWhile(T_a,V_Pa_2,V_xs_2),V_j_2) = c_List_Onth(T_a,V_xs_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)))))) # label(fact_dropWhile__nth) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 76 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 77 (all V_list_H_2 all V_a_H_2 all V_list_2 all V_aa_2 all T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) <-> V_a_H_2 = V_aa_2 & V_list_H_2 = V_list_2)) # label(fact_list_Oinject) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 78 (all V_xs_2 all V_Pa_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OdropWhile(T_a,V_Pa_2,V_xs_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2))) # label(fact_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 79 (all V_ca_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 80 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 81 (all V_ys_2 all V_x_2 all V_xs_2 all T_a (c_List_Obutlast(T_a,V_ys_2) = V_xs_2 & c_List_Olast(T_a,V_ys_2) = V_x_2 & V_ys_2 != c_List_Olist_ONil(T_a) <-> hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2)) # label(fact_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 82 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),c_List_Olistrel(T_a,V_r_2),c_List_Olistrel(T_a,V_s_2)))) # label(fact_listrel__mono) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 83 (all V_x all T_a all V_xs ((c_List_Olist_ONil(T_a) != V_xs -> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))) & (c_List_Olist_ONil(T_a) = V_xs -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)))) # label(fact_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 84 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 85 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) | V_x_2 = V_y_2 <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 86 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 87 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> ((all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 88 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (-c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 89 (all T_a c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 90 (all T_b all V_f_2 all V_ba_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hAPP(V_f_2,V_x_2) = V_ba_2 -> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))))) # label(fact_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 91 (all T_a all V_xs (c_List_Olist_ONil(T_a) != V_xs -> hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs)) # label(fact_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 92 (all V_ys_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2)))))) # label(fact_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 93 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_n_2 = V_m_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 94 (all V_r_2 all T_b all T_a ((all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) -> B_y = B_z)))) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2))) # label(fact_single__valuedI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 95 (all V_r_2 all V_xs_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_listrel__rtrancl__refl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 96 (all V_us all V_ys all V_zs all V_xs1 all V_xs all T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs -> (hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) = V_ys -> hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)))) # label(fact_append__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 97 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 98 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_y != V_x -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 99 (all V_aa_2 all V_r_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downward) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 100 (all V_f_2 all T_a all T_b c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a)) # label(fact_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 101 (all V_list_2 all V_aa_2 all V_f2_2 all V_f1_2 all T_b all T_a hAPP(hAPP(V_f2_2,V_aa_2),V_list_2) = c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_aa_2),V_list_2))) # label(fact_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 102 (all V_ba_2 all V_aa_2 all V_f_2 all T_a all T_c all T_b hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f_2,V_aa_2),V_ba_2)) # label(fact_split__conv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 103 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Relation_ORange(T_a,T_b,V_r_2))))) # label(fact_RangeI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 104 (all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 105 (all V_ca_2 all V_z_2 all T_c all T_b all T_a all V_p_2 ((all B_a all B_b (V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) -> hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))))) -> hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_ca_2),V_p_2))))) # label(fact_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 106 (all T_a all V_A_2 all T_b all V_x_2 all V_f_2 all V_ba_2 (hAPP(V_f_2,V_x_2) = V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))))) # label(fact_image__eqI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 107 (all V_A_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) & V_y_2 = V_x_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))))) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 108 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)))) # label(fact_image__Int__subset) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 109 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption]. 0.96/1.13 110 (all V_Q_2 all T_b all T_a all V_y_2 all V_x_2 all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2,V_Q_2) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 111 (all V_A_2 all V_xs_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))))) # label(fact_Cons__in__lists__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 112 (all V_y all V_x all 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)))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 113 (all V_xs_2 all T_a ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> (all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> (B_i != B_j -> c_List_Onth(T_a,V_xs_2,B_j) != c_List_Onth(T_a,V_xs_2,B_i)))))) <-> c_List_Odistinct(T_a,V_xs_2))) # label(fact_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 114 (all V_ba_2 all V_aa_2 all V_ca_2 all T_a all T_c all T_b hAPP(hAPP(V_ca_2,V_aa_2),V_ba_2) = hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2))) # label(fact_internal__split__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 115 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))))) # label(fact_restrict__in__funcset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 116 (all V_ys all V_xs all V_x all T_a hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))) # label(fact_append__Cons) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 117 (all V_ba_2 all V_aa_2 all V_f1_2 all T_a all T_c all T_b hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2))) # label(fact_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 118 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 119 (all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) -> c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2))) # label(fact_listrel__eq__len) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 120 (all V_A_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))))) # label(fact_funcset__id) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 121 (all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) <-> V_x_2 = V_y_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 122 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_less__infI1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 123 (all T_c all T_b all T_a c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) = c_Product__Type_Ointernal__split(T_a,T_b,T_c)) # label(fact_internal__split__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 124 (all V_zs_2 all V_ys_2 all V_xs_2 all T_a (V_zs_2 = V_ys_2 <-> hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) # label(fact_same__append__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 125 (all V_va all V_v all T_a c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va)) # label(fact_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 126 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 127 (all V_ys all V_y all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) = c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys))) # label(fact_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 128 (all V_x_2 all V_Q_2 all V_Pa_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2) -> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 129 (all V_Pa_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 130 (all V_vs_2 all V_us_2 all V_r_2 all V_ys_2 all V_xs_2 all T_a (V_vs_2 = V_us_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) | V_ys_2 = V_xs_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))))) # label(fact_append__listrel1I) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 131 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2))))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 132 (all V_z all V_y all V_x all 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))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 133 (all V_A_2 all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_single__valued__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 134 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all V_x_2 all T_a (V_x_2 = V_y_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) & V_ys_2 = V_xs_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))))) # label(fact_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 135 (all V_r_2 all T_a c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))) # label(fact_listrel__rtrancl__eq__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 136 (all V_r_2 all V_y_2 all V_ba_2 all V_x_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_ba_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) <-> V_aa_2 = V_ba_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)))) # label(fact_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 137 (all V_L_2 all V_y_2 all V_x_2 (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_below__Lin) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 138 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 139 (all V_A_2 all T_a V_A_2 = c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_Domain__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 140 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Relation_Otrans(tc_List_Olist(T_a),c_List_Olexord(T_a,V_r_2)))) # label(fact_lexord__transI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 141 (all V_A_2 all T_a V_A_2 = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_Int__absorb) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 142 (all V_g_2 all V_f_2 all V_A_2 all T_c all T_b all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_f_2,V_g_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))) # label(fact_compose__extensional) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 143 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & V_x_2 != V_y_2 <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 144 (all V_fs_2 all T_a all V_y_2 all V_x_2 all V_f_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))))) # label(fact_measures__lesseq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 145 (all V_ys all V_xs all T_a (c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys) != c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs) -> V_ys != V_xs)) # label(fact_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 146 (all V_x_2 all V_r_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Relation_ORange(T_a,T_b,V_r_2))) <-> c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2))) # label(fact_RangeP__Range__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 147 (all V_r_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_aa_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))))))) # label(fact_acc_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 148 (all V_C_2 all V_B_2 all V_A_2 all 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)))) # label(fact_psubset__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 149 -(all B_c -c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_c),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))) # label(fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 150 (all V_B_2 all V_A_2 all V_l_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) -> hBOOL(hAPP(c_List_Olistsp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2))))) # label(fact_lists__IntI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 151 (all V_A_2 all T_a hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a)))) # label(fact_listsp_ONil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 152 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 153 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 154 (all V_y_2 all V_r_2 all T_a ((all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))))) # label(fact_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 0.97/1.13 155 (all V_r_2 all V_xs_2 all V_ys_2 all V_y_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) -> -(all B_y all B_ys (hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) = V_xs_2 -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2)))))))) # label(fact_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 156 (all V_fs_2 all V_f_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) & hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_x_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))))) # label(fact_in__measures_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 157 (all V_x_2 all V_B_2 all V_A_2 all 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))))) # label(fact_inf1E) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 158 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 159 (all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) != V_ca_2)))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 160 (all V_f_2 all T_c all V_A_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_aa_2),V_ba_2)),c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2),V_A_2))))) # label(fact_pair__imageI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 161 (all V_Pa_2 all V_xs_2 all T_a (c_List_Odistinct(T_a,V_xs_2) -> c_List_Odistinct(T_a,c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)))) # label(fact_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 162 (all V_xa_2 all V_x_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) <-> c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2))) # label(fact_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 163 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 164 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (V_y != V_x -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 165 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 166 (all V_t all V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) -> V_t != V_s)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 167 (all V_P all T_a V_P = hAPP(c_COMBI(T_a),V_P)) # label(help_c__COMBI__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 168 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 169 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 170 (all T_a all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_a) -> (c_List_Odistinct(T_a,V_xs_2) -> c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2)))) # label(fact_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 171 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)) # label(fact_Int__lower2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 172 (all V_f_2 all T_b all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)))) # label(fact_image__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 173 (all V_r_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) # label(fact_listrel1__rtrancl__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 174 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (V_z_2 != V_x_2 & (V_y_2 = V_z_2 -> V_y_2 != V_x_2) & (V_y_2 != V_z_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2))))) # label(fact_in__mktop) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 175 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_restrictI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 176 (all V_Fa_2 (c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))))))))) # label(fact_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 177 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2)))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 178 (all V_x all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,V_xs) = c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)))) # label(fact_last__ConsR) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 179 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 180 (all V_y_2 all V_x_2 all 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__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 181 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 ((V_x_2 != V_z_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))) & (V_z_2 = V_x_2 -> V_y_2 != V_x_2) & V_y_2 != V_z_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2))))) # label(fact_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 182 (all V_g_2 all V_f_2 all T_b all V_A_2 all V_aa_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2))) # label(fact_override__on__apply__notin) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 183 (all V_B_2 all V_A_2 all V_g_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_g_2 = c_FuncSet_Ocompose(T_a,T_a,T_b,V_A_2,V_g_2,c_FuncSet_Orestrict(T_a,T_a,c_COMBI(T_a),V_A_2))))) # label(fact_compose__Id) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 184 (all V_x all T_a c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) # label(fact_insert__Nil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 185 (all V_r_2 all T_a c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a))) # label(fact_listrelp_ONil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 186 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 187 (all V_ys_2 all V_xs_2 all T_a (c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) <-> V_xs_2 = c_List_Olist_ONil(T_a) & c_List_Olist_ONil(T_a) = V_ys_2)) # label(fact_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 188 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_a (c_Relation_Osingle__valued(T_a,T_a,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 189 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 190 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) -> (V_x_2 = V_y_2 <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2))))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 191 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs) # label(fact_not__Cons__self2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 192 (all V_x all V_xs all T_a c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs) # label(fact_butlast__snoc) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 193 (all V_y_2 all V_x_2 all 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__eq(T_a,V_x_2,V_y_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 194 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2))) # label(fact_funcset__image) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 195 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) = c_List_Olistsp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) # label(fact_lists__Int__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 196 (all V_xs_2 all T_a all V_x_2 all V_Pa_2 ((-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_Olist_ONil(T_a) = c_List_OtakeWhile(T_a,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) & (hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_a,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2))))) # label(fact_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 197 (all V_ca_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 198 (all V_r_2 all T_a ((all B_x hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))) <-> c_Nitpick_Orefl_H(T_a,V_r_2))) # label(fact_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 199 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 200 (all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_f_2 = c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2))) # label(fact_extensional__restrict) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 201 (all V_xs all T_a all V_ys (V_ys != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,V_ys) = c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)))) # label(fact_last__appendR) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 202 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) = hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2))) # label(fact_inf__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 203 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n)) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 204 (all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 205 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Relation_Otrans(tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)))) # label(fact_listrel__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 206 (all V_r_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2)))) # label(fact_listrel_ONil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 207 (all V_R_2 all T_a all V_y_2 all V_x_2 all V_f_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))))) # label(fact_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 208 (all V_y all V_x all 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)))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 209 (all V_f_2 all T_c all T_b all T_a hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2) # label(fact_split__eta) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 210 (all V_f2_2 all V_f1_2 all T_b all T_a V_f1_2 = c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b))) # label(fact_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 211 (all V_y_2 all V_x_2 all 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__eq(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 212 (all V_ys_2 all V_y_2 all V_xs_2 all V_Pa_2 all T_a (-hBOOL(hAPP(V_Pa_2,V_y_2)) & hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) = V_xs_2 <-> c_List_OdropWhile(T_a,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))) # label(fact_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 213 (all V_S_2 all V_R_2 all T_a (hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) <-> V_S_2 = V_R_2)) # label(fact_pred__equals__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 214 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 215 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 216 (all T_c all T_b all V_ba_2 all V_aa_2 all V_ca_2 all V_z_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_aa_2),V_ba_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)))))) # label(fact_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 217 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 218 (all T_a all V_ys all V_xs (V_xs = V_ys -> hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_xs)) # label(fact_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 219 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_f_2 = c_FuncSet_Ocompose(T_a,T_b,T_b,V_A_2,c_FuncSet_Orestrict(T_b,T_b,c_COMBI(T_b),V_B_2),V_f_2)))) # label(fact_Id__compose) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 220 (all V_ys_2 all V_xs_2 all T_a all V_y_2 all V_x_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) -> (c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) -> c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))))) # label(fact_listrelp_OCons) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 221 (all V_l_2 all V_xs_2 all T_a all V_x_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2) = c_List_OtakeWhile(T_a,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))))) # label(fact_takeWhile__tail) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 222 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 223 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 224 (all V_y all V_x all 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)))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 225 (all V_z all V_x all V_y all 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))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 226 (all V_C_2 all V_g_2 all T_c all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_c)),c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)),c_FuncSet_OPi(T_a,T_c,V_A_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a,V_C_2))))))) # label(fact_funcset__compose) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 227 (all V_r_2 all V_y_2 all V_x_2 all T_a (c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_y_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_x_2) & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))))) # label(fact_lexord__lex) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 228 (all V_r_2 all 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)) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 229 (all V_f_2 all T_b all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))))) # label(fact_imageI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 230 (all V_xs all V_x all T_b all T_a (c_List_Olist_ONil(T_a) = c_List_Orotate1(T_a,c_List_Olist_ONil(T_a)) & c_List_Orotate1(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))))) # label(fact_rotate__simps) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 231 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2)) -> V_y_2 = V_z_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 232 (all V_A_2 all T_a c_Relation_Otrans(T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_trans__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 233 (all V_B_2 all T_b all V_g_2 all V_f_2 all V_A_2 all T_a ((all B_w (hBOOL(hAPP(hAPP(c_member(T_a),B_w),V_A_2)) -> hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))))) # label(fact_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 234 (all V_p_2 all V_ca_2 all T_c all T_b all V_z_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),V_p_2))) -> -(all B_x all B_y (hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) = V_p_2 -> -hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))))))) # label(fact_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 235 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))))) # label(fact_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 236 (all V_x_2 all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 237 (all V_Q_2 all V_Pa_2 (-hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) | -hBOOL(V_Pa_2))) # label(help_c__fconj__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 238 (all V_r_2 all V_v_2 all V_u_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) -> ((all B_a -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2)))))) # label(fact_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 239 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)))) # label(fact_inf2D1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 240 (all V_Pa_2 all V_xs_2 all T_a (c_List_Odistinct(T_a,V_xs_2) -> c_List_Odistinct(T_a,c_List_OdropWhile(T_a,V_Pa_2,V_xs_2)))) # label(fact_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 241 (all V_Pa_2 (--hBOOL(V_Pa_2) | hBOOL(hAPP(c_fNot,V_Pa_2)))) # label(help_c__fNot__2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 242 (all V_c all V_a all V_b all 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))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 243 (all V_Q_2 all V_Pa_2 (hBOOL(V_Pa_2) | -hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)))) # label(help_c__fconj__2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 244 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)) -> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))))) # label(fact_curryD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 245 (all V_Y_2 all T_a c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2) # label(fact_image__ident) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 246 (all V_x all V_xs all T_a V_x = c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))) # label(fact_last__snoc) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 247 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 248 (all V_x all V_ys all V_xs all T_a (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs),c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys)) -> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) != V_xs)) # label(fact_impossible__Cons) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 249 (all V_B_2 all V_A_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_Int__greatest) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 250 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 251 (all V_x all T_a all V_xs (c_List_Olist_ONil(T_a) = V_xs -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x)) # label(fact_last__ConsL) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 252 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 253 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 254 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_ba_2 = V_aa_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Relation_OId__on(T_a,V_A_2)))))) # label(fact_Id__on__eqI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 255 (all V_c all V_b all V_a all 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))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 256 (all V_y_2 all V_R_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_a,V_R_2))) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))))) # label(fact_Not__Domain__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 257 (all V_r_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),c_List_Olistrel(T_a,V_r_2),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) # label(fact_listrel__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 258 (all V_Pa_2 all T_a c_List_Opartition(T_a,V_Pa_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))) # label(fact_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 259 (all V_ba_2 all V_r_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downwards) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 260 (all V_R_2 all T_a all V_y_2 all V_x_2 all 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)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))))) # label(fact_mlex__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 261 (all V_y_2 all V_x_2 all V_ca_2 all T_a all T_c all T_b hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))) # label(fact_curry__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 262 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),c_List_Olistrel1(T_a,V_r_2),c_List_Olistrel1(T_a,V_s_2)))) # label(fact_listrel1__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 263 (all V_ca_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 264 (all V_B_2 all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 265 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 266 (all V_r_2 all V_xs_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2)))) # label(fact_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 267 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Int__left__absorb) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 268 (all V_ys_2 all T_a all V_xs_2 (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) <-> c_List_Olist_ONil(T_a) = V_ys_2)) # label(fact_self__append__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 269 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 270 (all V_ys all T_a V_ys = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)) # label(fact_append__Nil) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 271 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_ba_2 = V_aa_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 272 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 273 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) = hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 274 (all V_zs_2 all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))))) # label(fact_listrel__rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 275 (all V_b all V_a (V_a != V_b -> (exists B_c c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),V_a),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),V_b),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_c),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))))) # label(fact_third__alt) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 276 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 277 (all V_xs_2 all T_a all V_x_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OdropWhile(T_a,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_Pa_2,V_xs_2)) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OdropWhile(T_a,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) # label(fact_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 278 (all V_a2_2 all V_a1_2 all V_A_2 all T_a (hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) & hBOOL(hAPP(V_A_2,V_a1_2)) <-> hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))))) # label(fact_listsp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 279 (all V_x all T_a all V_xs ((c_List_Olist_ONil(T_a) != V_xs -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)) & (V_xs = c_List_Olist_ONil(T_a) -> V_x = c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))))) # label(fact_last_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 280 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_y_2 = V_x_2))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 281 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(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)))) # label(fact_Range__Int__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 282 (all V_r_2 all T_a c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a))) # label(fact_listrelp_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 283 (all V_B_2 all T_b all V_A_2 all V_A_H_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2)))) # label(fact_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 284 (all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_listrel__reflcl__if__listrel1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 285 (all V_r_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) -> B_y = B_z)))))) # label(fact_single__valued__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 286 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) -> ((all B_x (V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),V_ys_2) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)))) -> -(all B_zs (hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),B_zs) = V_xs_2 -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_zs),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))))))) # label(fact_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 287 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 288 (all V_list_H all V_a_H all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a)) # label(fact_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 289 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_y = V_x -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 290 (all V_b all V_a all 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)))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 291 (all V_x_2 all V_B_2 all V_A_2 all 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_B_2,V_x_2)))) # label(fact_inf1D2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 292 (all V_r_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) -> c_List_Olist_ONil(T_a) = V_xs_2)) # label(fact_listrel__Nil2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 293 (all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))))) # label(fact_iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 294 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 295 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 296 (all V_Fa_2 ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))))))))) <-> c_Arrow__Order__Mirabelle_OIIA(V_Fa_2))) # label(fact_IIA__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 297 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 298 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 299 (all V_A_2 all V_f_2 all T_b all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))) # label(fact_restrict__extensional) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 300 (all V_ca_2 all T_c all T_b all T_a all V_q_2 all V_p_2 (V_q_2 = V_p_2 -> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2))) # label(fact_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 301 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d)))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 302 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 303 (all V_B_2 all V_l_2 all V_A_2 all T_a (hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) -> (hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) -> hBOOL(hAPP(c_List_Olistsp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)),V_l_2))))) # label(fact_listsp__infI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 304 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 305 (all V_C_2 all V_B_2 all V_A_2 all 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__eq(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)))) # label(fact_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 306 (all V_f_2 all T_c all T_b all T_a hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),c_Product__Type_Ocurry(T_a,T_b,T_c,V_f_2)) = V_f_2) # label(fact_split__curry) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 307 (all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> -(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_equalityE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 308 (all V_S_2 all V_R_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2))) # label(fact_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 309 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 310 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oaccp(T_a,V_R2_2),c_Wellfounded_Oaccp(T_a,V_R1_2)))) # label(fact_accp__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 311 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 312 (all V_A_2 all T_a V_A_2 = c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_Range__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 313 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 314 (all V_ys_2 all V_xs_2 all T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) <-> V_xs_2 = c_List_Olist_ONil(T_a) & V_ys_2 = c_List_Olist_ONil(T_a))) # label(fact_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 315 (all V_r_2 all V_aa_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 316 (all V_r_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_lists__accI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 317 (all V_xs_2 all T_a (c_List_Odistinct(T_a,c_List_Orotate1(T_a,V_xs_2)) <-> c_List_Odistinct(T_a,V_xs_2))) # label(fact_distinct1__rotate) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 318 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Int__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 319 (all V_zs_2 all V_xs_2 all V_ys_2 all T_a (V_zs_2 = V_ys_2 <-> hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2))) # label(fact_append__same__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 320 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2))))) # label(fact_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 321 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 322 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 323 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_PiE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 324 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 325 (all V_ba_2 all V_aa_2 all V_f_2 all T_a all T_c all T_b hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2),V_aa_2),V_ba_2)) # label(fact_curry__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 326 (all V_r_2 all V_zb_2 all V_za_2 all V_xb_2 all V_xa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(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))) -> (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_2) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2) -> -(all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(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)))))))) # label(fact_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 327 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))) # label(fact_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 328 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.14 329 (all V_r_2 all V_y_2 all V_ys_2 all V_x_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) <-> V_xs_2 = V_ys_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) | V_x_2 = V_y_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))))) # label(fact_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 330 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) -> -(hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> -hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))))) # label(fact_inf2E) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 331 (all V_B_2 all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 332 (all V_ca_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))))) # label(fact_psubsetD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 333 (all V_r_2 all V_ys_2 all V_xs_2 all T_a ((all B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_n,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),c_List_Onth(T_a,V_xs_2,B_n)),c_List_Onth(T_a,V_ys_2,B_n))),V_r_2)))) & c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))))) # label(fact_listrel__iff__nth) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 334 (all V_D_2 all V_h_2 all T_d all V_C_2 all V_g_2 all T_c all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,T_d)),V_h_2),c_FuncSet_OPi(T_c,T_d,V_C_2,c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c,V_D_2)))) -> c_FuncSet_Ocompose(T_a,T_b,T_d,V_A_2,c_FuncSet_Ocompose(T_b,T_c,T_d,V_B_2,V_h_2,V_g_2),V_f_2) = c_FuncSet_Ocompose(T_a,T_c,T_d,V_A_2,V_h_2,c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)))))) # label(fact_compose__assoc) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 335 (all V_g_2 all V_f_2 all T_b all V_A_2 all V_aa_2 all T_a ((hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> hAPP(V_g_2,V_aa_2) = c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2)) & (-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2,V_aa_2) = hAPP(V_f_2,V_aa_2)))) # label(fact_override__on__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 336 (all V_r_2 all V_p_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 337 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 338 (all V_ys_2 all V_xs_2 all V_A_2 all T_a (hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) <-> hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)))) # label(fact_append__in__listsp__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 339 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2,V_B_2),V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)))) # label(fact_inf2D2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 340 (all V_B_2 all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))))) # label(fact_IntI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 341 (all V_xs_2 all T_a all V_ys_2 (V_xs_2 = c_List_Olist_ONil(T_a) <-> hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2)) # label(fact_self__append__conv2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 342 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 343 (all V_r_2 all T_b all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))) -> -(all B_y -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2))))) # label(fact_DomainE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 344 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 345 (all V_a all V_b all 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)))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 346 (all V_ys_2 all V_vs_2 all V_us_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) -> (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2)) -> (hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2)) = V_ys_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))))))) # label(fact_listrel1I) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 347 (all V_x all T_a all V_xs V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) # label(fact_not__Cons__self) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 348 (all V_zs_2 all V_ys_2 all V_xs_2 all V_x_2 all T_a ((exists B_ys_H (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2))) | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 & V_ys_2 = c_List_Olist_ONil(T_a) <-> hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) # label(fact_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 349 (all V_r_2 all T_b all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ORange(T_b,T_a,V_r_2))) <-> (exists B_y hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_aa_2)),V_r_2))))) # label(fact_Range__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 350 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 351 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_z)),V_r_2)))))))) # label(fact_trans__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 352 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),c_List_Olistsp(T_a,V_A_2),c_List_Olistsp(T_a,V_B_2)))) # label(fact_listsp__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 353 (all V_Pa_2 (-hBOOL(hAPP(c_fNot,V_Pa_2)) | -hBOOL(V_Pa_2))) # label(help_c__fNot__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 354 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 355 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) <-> hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)))) # label(fact_listsp__conj__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 356 (all V_x_2 all V_B_2 all V_A_2 all 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)))) # label(fact_inf1D1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 357 (all V_f_2 all T_c all T_b all T_a c_Product__Type_Ocurry(T_a,T_b,T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)) = V_f_2) # label(fact_curry__split) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 358 (all V_r_2 all V_x_2 all T_a all V_y_2 ((exists B_b exists B_z hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) = V_y_2) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))))) # label(fact_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 359 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 360 (all V_i_2 all V_Fa_2 ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2))) <-> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2))) # label(fact_dictator__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 361 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 362 (all V_ba_2 all V_aa_2 all T_b all T_a all V_f_2 (hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) -> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)))) # label(fact_curryI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 363 (all V_r_2 all V_xs_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2)))) # label(fact_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 364 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 365 (all V_j_2 all V_i_2 all V_xs_2 all T_a (c_List_Odistinct(T_a,V_xs_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2)) -> (V_i_2 = V_j_2 <-> c_List_Onth(T_a,V_xs_2,V_j_2) = c_List_Onth(T_a,V_xs_2,V_i_2)))))) # label(fact_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 366 (all V_xs_2 all T_a c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_xs_2) = c_List_Orotate1(T_a,V_xs_2)) # label(fact_rotate1__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 367 (all T_a c_List_Odistinct(T_a,c_List_Olist_ONil(T_a))) # label(fact_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 368 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 369 (all V_ca_2 all V_r_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 370 (all V_s_2 all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> (c_Relation_Otrans(T_a,V_s_2) -> c_Relation_Otrans(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_trans__Int) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 371 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_y = V_x))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 372 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 373 (all V_g_2 all V_f_2 ((all B_x hAPP(V_g_2,B_x) = hAPP(V_f_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 374 (all V_z_2 all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_z_2)),c_List_Olexord(T_a,V_r_2))) -> (c_Relation_Otrans(T_a,V_r_2) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_z_2)),c_List_Olexord(T_a,V_r_2))))))) # label(fact_lexord__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 375 (all V_x all V_xs all T_a (c_List_Odistinct(T_a,V_xs) -> c_List_Odistinct(T_a,c_List_Oinsert(T_a,V_x,V_xs)))) # label(fact_distinct__insert) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 376 (all T_b all T_a all V_ba_2 all V_aa_2 all V_f1_2 (hBOOL(hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))))) # label(fact_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 377 (all V_r_2 all T_a c_Relation_Otrans(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_trans__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 378 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 379 (all V_r_2 all T_a ((all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_z)),V_r_2)))))) -> c_Relation_Otrans(T_a,V_r_2))) # label(fact_transI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 380 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 381 (all V_x all V_y all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_y))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 382 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) | V_n = V_m -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 383 (all V_ys_2 all V_xs_2 all T_a (V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) <-> V_xs_2 = c_List_Olist_ONil(T_a))) # label(fact_append__self__conv2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 384 (all V_aa_2 all V_r_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)))) <-> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)))) # label(fact_accp_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 385 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 386 (all V_ca_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))) -> -(-hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 387 (all V_c all V_b all V_a all 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))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 388 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 389 (all V_aa_2 all V_ba_2 all V_r_2 all T_a (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2)) -> (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))))) # label(fact_accp__downward) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 390 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (V_y_2 != V_x_2 & (V_aa_2 = V_y_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2))) & (V_aa_2 != V_y_2 -> (V_x_2 != V_aa_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))) & (V_aa_2 = V_x_2 -> V_y_2 = V_ba_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2)))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_aa_2),V_ba_2))))))) # label(fact_in__below) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 391 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_n = V_m))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 392 (all V_xs all T_a V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a))) # label(fact_append__Nil2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 393 (all V_f_2 all V_g_2 all V_A_2 all T_b all T_c all T_a c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2) = c_FuncSet_Orestrict(T_a,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_a),V_g_2),V_f_2),V_A_2)) # label(fact_compose__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 394 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) = hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2)) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 395 (all V_B_2 all V_A_2 all 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__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 396 (all V_xs_2 all V_r_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))))) # label(fact_Cons__acc__listrel1I) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 397 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 398 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 399 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),c_List_Olists(T_a,V_A_2),c_List_Olists(T_a,V_B_2)))) # label(fact_lists__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 400 (all V_xs all T_a all V_ys (c_List_Olist_ONil(T_a) = V_ys -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs))) # label(fact_last__appendL) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 401 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)))) # label(fact_acc__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 402 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 403 (all V_P_Ha_2 all V_Pa_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_a_H_2 != V_b_H_2 -> (V_b_H_2 != V_aa_2 -> (V_ba_2 != V_a_H_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2)))))))))))) # label(fact__C1_C) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 404 (all V_y_2 all V_x_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat)))))) # label(fact_in__measures_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 405 (all T_a all V_R_2 all V_y_2 all V_y_H_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 406 (all V_C_2 all V_g_2 all T_c all V_B_2 all V_A_2 all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_B_2 -> (V_C_2 = c_Set_Oimage(T_a,T_c,V_g_2,V_B_2) -> c_Set_Oimage(T_b,T_c,c_FuncSet_Ocompose(T_b,T_a,T_c,V_A_2,V_g_2,V_f_2),V_A_2) = V_C_2))) # label(fact_surj__compose) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 407 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(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_Pa_2,V_bx_2),V_by_2)) -> ((all B_a all B_b all B_aa all B_ba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba)),hAPP(hAPP(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_Pa_2,B_aa),B_ba)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)))))) # label(fact_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 408 (all V_xs all T_a c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_Orotate1(T_a,V_xs)) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs)) # label(fact_length__rotate1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 409 (all V_y_2 all V_x_2 all 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)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 410 (all V_r_2 all V_x_2 all T_a ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc_OaccI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 411 (all V_ys all V_x all V_xs all T_a c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs)) = V_x) # label(fact_nth__append__length) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 412 (all V_x_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) <-> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)))) # label(fact_accp__acc__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 413 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 414 (all T_b all T_a all V_Pa_2 ((all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (all B_a all B_b hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 415 (all V_x_2 all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))))) # label(fact_rtrancl__listrel1__ConsI1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 416 (all V_a4_2 all V_a2_2 all V_a3_2 all V_a1_2 all V_r_2 all T_a (c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) <-> c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)))) # label(fact_listrelp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 417 (all V_A_2 all T_a c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2))) # label(fact_Id__on__def_H) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 418 (all V_f_2 all V_g_2 all T_b all T_c all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(V_g_2,hAPP(V_f_2,V_x_2)) = hAPP(c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2),V_x_2))) # label(fact_compose__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 419 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_A_2)) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 420 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) | V_x = V_y)) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 421 (all V_A_2 all T_a all V_y_2 all V_x_2 (V_y_2 = V_x_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 422 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(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_Pa_2,V_ax_2),V_ay_2)) -> ((all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(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 all B_ba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)))))) # label(fact_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 423 (all V_n all V_m (V_n = V_m -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 424 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 425 (all V_B_2 all V_A_2 all T_a c_List_Olistsp(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),c_List_Olistsp(T_a,V_A_2),c_List_Olistsp(T_a,V_B_2))) # label(fact_listsp__inf__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 426 (all V_i_2 all V_Fa_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b (B_b != B_a -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))))))) -> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)))) # label(fact_dictatorI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 427 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_less__infI2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 428 (all V_xs_2 all V_x_2 all V_Pa_2 all T_a c_List_Opartition(T_a,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_Pa_2,V_xs_2))) # label(fact_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 429 (all T_b all T_a all V_ba_2 all V_aa_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> c_Predicate_ORangeP(T_a,T_b,V_r_2,V_ba_2))) # label(fact_RangeP_Ointros) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 430 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 431 (all V_y_2 all V_x_2 all V_r_2 all T_a ((all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) | B_b = B_a | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) | V_y_2 = V_x_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))))) # label(fact_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 432 (all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) -> c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2))) # label(fact_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 433 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 434 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_single__valued__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 435 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 436 (all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) -> -(all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) -> (all B_us all B_vs (hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) = V_xs_2 -> hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) != V_ys_2)))))) # label(fact_listrel1E) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 437 (all V_R2_2 all T_b all V_R1_2 all T_a (c_Relation_Otrans(T_a,V_R1_2) -> (c_Relation_Otrans(T_b,V_R2_2) -> c_Relation_Otrans(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_R1_2,V_R2_2))))) # label(fact_trans__lex__prod) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 438 (all V_list_H all V_a_H all T_a c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H)) # label(fact_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 439 (all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))))) # label(fact_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 440 (all V_ys_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))))) # label(fact_rtrancl__listrel1__ConsI2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 441 (all V_A_2 all V_f_2 all T_b all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) <-> (exists B_AA (V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA,V_A_2))))) # label(fact_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 442 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 443 (all V_r_2 all V_ys_2 all V_xs_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) -> ((all B_y (V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),V_xs_2) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_r_2)))) -> -(all B_zs (V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),B_zs)),c_List_Olistrel1(T_a,V_r_2)))))))) # label(fact_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 444 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(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)))) # label(fact_Domain__Int__subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 445 (all V_P_Ha_2 all V_Pa_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_b_H_2 != V_a_H_2 -> (V_aa_2 != V_b_H_2 -> (V_a_H_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_Ha_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_Ha_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_Ha_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))))))))))) # label(fact__C2_C) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 446 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 447 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 448 (all V_x_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) <-> hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)))) # label(fact_listsp__lists__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 449 (all V_xs all T_a c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs) # label(fact_splice__Nil2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 450 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 451 (all V_aa_2 all V_r_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(V_r_2,B_x),V_aa_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)))) <-> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)))) # label(fact_accp_Oequations) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 452 (all V_x_2 all V_S_2 all V_R_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2))))) # label(fact_inf__Int__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 453 (all V_A_2 all T_a hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a)))) # label(fact_listsp_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 454 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2))))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 455 (all V_r_2 all V_ys_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))))) # label(fact_rtrancl__listrel1__if__listrel) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 456 (all V_ca_2 all V_ba_2 all V_aa_2 all V_R_2 all T_c all T_b all T_a (hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_ca_2)) -> hBOOL(hAPP(hAPP(hAPP(V_R_2,V_aa_2),V_ba_2),V_ca_2)))) # label(fact_splitD_H) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 457 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b))))) # label(fact_le__infE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 458 (all V_B_2 all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 459 (all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2) = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 460 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 461 (all V_a2_2 all V_r_2 all T_b all T_a (c_Predicate_ORangeP(T_a,T_b,V_r_2,V_a2_2) <-> (exists B_a hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))))) # label(fact_RangeP_Oequations) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 462 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 463 (all V_Q_2 all V_Pa_2 (hBOOL(V_Q_2) | -hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)))) # label(help_c__fconj__3) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 464 (all V_r_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) -> c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_y_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_x_2))) # label(fact_rtrancl__listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 465 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2))) <-> (V_ba_2 = V_x_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))) & (V_x_2 != V_ba_2 -> (V_ba_2 != V_y_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))) & (V_y_2 = V_ba_2 -> V_x_2 = V_aa_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2)))) & V_x_2 != V_y_2)))) # label(fact_in__above) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 466 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) -> -(all B_x all B_xs (V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))))))) # label(fact_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 467 (all V_y_2 all V_ys_2 all V_x_2 all V_xs_2 all T_a (V_x_2 = V_y_2 & V_xs_2 = V_ys_2 <-> hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))) # label(fact_append1__eq__conv) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 468 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2),V_aa_2),V_ba_2)) -> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))))) # label(fact_curryE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 469 (all V_B_2 all V_A_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) -> -(hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 470 (all V_ba_2 all V_aa_2 all V_f1_2 all T_a all T_c all T_b c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2)) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 471 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) & V_B_2 != V_A_2 <-> c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 472 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 473 (all V_y all V_x (V_y != V_x -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 474 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Int__lower1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 475 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 476 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_Domain__mono) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 477 (all V_r_2 all V_xs_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) -> V_xs_2 = c_List_Olist_ONil(T_a))) # label(fact_listrel__Nil1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 478 (all V_A_2 all V_aa_2 all T_a ((exists B_a exists B_l (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) & V_aa_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l))) | c_List_Olist_ONil(T_a) = V_aa_2 <-> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_aa_2),c_List_Olists(T_a,V_A_2))))) # label(fact_lists_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 479 (all V_xs_2 all V_Pa_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a),c_List_OtakeWhile(T_a,V_Pa_2,V_xs_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2))) # label(fact_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 480 (all V_R_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) -> -(all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))))))) # label(fact_not__acc__down) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 481 (all V_A_2 all V_f_2 all T_b all V_z_2 all T_a ((exists B_x (V_z_2 = hAPP(V_f_2,B_x) & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))))) # label(fact_image__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 482 (all V_r_2 all V_y_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) <-> (exists B_a exists B_x hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) = V_y_2))) # label(fact_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 483 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_y = V_x)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 484 (all V_y_2 all V_x_2 all V_R_2 all T_b all T_a (c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)))) # label(fact_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 485 (all V_R_2 all V_Q_2 all V_Pa_2 all T_c all T_a all T_b hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) = hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_Pa_2),V_Q_2),V_R_2)) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 486 (all V_x_2 all V_r_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_b,V_r_2))) <-> c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2))) # label(fact_DomainP__Domain__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 487 (all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,V_L_2)),c_Arrow__Order__Mirabelle_OProf)))) # label(fact_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 488 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x) = V_x)) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 489 (all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 all T_b all T_a (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) <-> V_ba_2 = V_b_H_2 & V_a_H_2 = V_aa_2)) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 490 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))))) # label(fact_funcsetI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 491 (all T_b all T_a all V_ba_2 all V_aa_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> c_Predicate_ODomainP(T_a,T_b,V_r_2,V_aa_2))) # label(fact_DomainP_Ointros) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 492 (all V_xs all T_a all V_ys ((V_ys = c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)) & (c_List_Olist_ONil(T_a) != V_ys -> c_List_Olast(T_a,V_ys) = c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))))) # label(fact_last__append) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 493 (all V_r_2 all T_a ((all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))) <-> c_Relation_Oirrefl(T_a,V_r_2))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 494 (all V_y_2 all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (V_y_2 != V_x_2 -> (-hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)))))) # label(fact_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 495 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) & c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_xs_2) = c_Nat_Osize__class_Osize(tc_List_Olist(T_a),V_ys_2) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) & V_x_2 = V_y_2)) # label(fact_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 496 (all V_A_2 all V_f_2 all T_a all T_b c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = c_Set_Oimage(T_b,T_a,c_FuncSet_Orestrict(T_b,T_a,V_f_2,V_A_2),V_A_2)) # label(fact_image__restrict__eq) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 497 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) | V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 498 (all V_ts_2 all V_zs_2 all V_ys_2 all V_xs_2 all T_a ((exists B_us (hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) = V_xs_2 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 | hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) = V_ys_2 & V_zs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us))) <-> hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2))) # label(fact_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 499 (all V_ys all T_a V_ys = c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys)) # label(fact_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 500 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 501 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> -(all B_ys all B_y V_xs != hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),c_List_Olist_ONil(T_a)))))) # label(fact_rev__cases) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 502 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))))) # label(fact_DomainI) # label(axiom) # label(non_clause). [assumption]. 0.97/1.16 0.97/1.16 ============================== end of process non-clausal formulas === 0.97/1.16 0.97/1.16 ============================== PROCESS INITIAL CLAUSES =============== 0.97/1.16 0.97/1.16 ============================== PREDICATE ELIMINATION ================= 0.97/1.16 503 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 0.97/1.16 504 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf__commute) # label(axiom). [clausify(2)]. 0.97/1.16 505 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__greatest) # label(axiom). [clausify(28)]. 0.97/1.16 506 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf_Ocommute) # label(axiom). [clausify(58)]. 0.97/1.16 507 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__infI) # label(axiom). [clausify(62)]. 0.97/1.16 508 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__assoc) # label(axiom). [clausify(97)]. 0.97/1.16 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A). [resolve(503,a,504,a)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(503,a,505,a)]. 0.97/1.16 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(503,a,508,a)]. 0.97/1.16 509 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_less__infI1) # label(axiom). [clausify(122)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(509,a,503,a)]. 0.97/1.16 510 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__inf__iff) # label(axiom). [clausify(177)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(510,a,503,a)]. 0.97/1.16 511 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__inf__iff) # label(axiom). [clausify(177)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(511,a,503,a)]. 0.97/1.16 512 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__inf__iff) # label(axiom). [clausify(177)]. 0.97/1.16 513 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_le__infI1) # label(axiom). [clausify(186)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(513,a,503,a)]. 0.97/1.17 514 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_le__infI2) # label(axiom). [clausify(189)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(514,a,503,a)]. 0.97/1.17 515 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_inf__absorb1) # label(axiom). [clausify(295)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = A. [resolve(515,a,503,a)]. 0.97/1.17 516 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),c_Lattices_Osemilattice__inf__class_Oinf(A,C,E)) # label(fact_inf__mono) # label(axiom). [clausify(301)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,D)). [resolve(516,a,503,a)]. 0.97/1.17 517 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf__left__idem) # label(axiom). [clausify(302)]. 0.97/1.17 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B). [resolve(517,a,503,a)]. 0.97/1.17 518 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf__left__commute) # label(axiom). [clausify(313)]. 0.97/1.17 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C)). [resolve(518,a,503,a)]. 0.97/1.17 519 class_Lattices_Osemilattice__inf(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 0.97/1.17 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A). [resolve(519,a,504,a)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(519,a,505,a)]. 0.97/1.17 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)). [resolve(519,a,508,a)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),B). [resolve(519,a,509,a)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(519,a,510,a)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(519,a,511,a)]. 0.97/1.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),B). [resolve(519,a,513,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,C,A),B). [resolve(519,a,514,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) = A. [resolve(519,a,515,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,D)). [resolve(519,a,516,a)]. 0.97/1.18 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B). [resolve(519,a,517,a)]. 0.97/1.18 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,C)). [resolve(519,a,518,a)]. 0.97/1.18 520 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(372)]. 0.97/1.18 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,A) = A. [resolve(520,a,503,a)]. 0.97/1.18 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,A) = A. [resolve(520,a,519,a)]. 0.97/1.18 521 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) = B # label(fact_inf__absorb2) # label(axiom). [clausify(381)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A) = A. [resolve(521,a,503,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,B,A) = A. [resolve(521,a,519,a)]. 0.97/1.18 522 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf_Oleft__idem) # label(axiom). [clausify(388)]. 0.97/1.18 523 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(397)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C). [resolve(523,b,504,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(523,b,505,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),E) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)). [resolve(523,b,508,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),D). [resolve(523,b,509,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(523,b,510,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(523,b,511,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),D). [resolve(523,b,513,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),E,C),D). [resolve(523,b,514,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = C. [resolve(523,b,515,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,F)). [resolve(523,b,516,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D). [resolve(523,b,517,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,E)). [resolve(523,b,518,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,C) = C. [resolve(523,b,520,a)]. 0.97/1.18 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C) = C. [resolve(523,b,521,a)]. 0.97/1.18 524 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_less__infI2) # label(axiom). [clausify(427)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(524,a,503,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,C,A),B). [resolve(524,a,519,a)]. 0.97/1.18 Derived: -c_Orderings_Oord__class_Oless(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),E,C),D) | -class_Lattices_Olattice(B). [resolve(524,a,523,b)]. 0.97/1.18 525 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf_Oleft__commute) # label(axiom). [clausify(433)]. 0.97/1.18 526 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B) # label(fact_inf__le1) # label(axiom). [clausify(442)]. 0.97/1.18 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),A). [resolve(526,a,503,a)]. 0.97/1.18 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),A). [resolve(526,a,519,a)]. 0.97/1.18 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D),C) | -class_Lattices_Olattice(B). [resolve(526,a,523,b)]. 0.97/1.18 527 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf_Oassoc) # label(axiom). [clausify(450)]. 0.97/1.18 528 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__infE) # label(axiom). [clausify(457)]. 0.97/1.18 529 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__infE) # label(axiom). [clausify(457)]. 0.97/1.21 530 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != B | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__inf) # label(axiom). [clausify(459)]. 0.97/1.21 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(530,a,503,a)]. 0.97/1.21 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(530,a,519,a)]. 0.97/1.21 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D) != C | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -class_Lattices_Olattice(B). [resolve(530,a,523,b)]. 0.97/1.21 531 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__inf) # label(axiom). [clausify(459)]. 0.97/1.21 532 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf__idem) # label(axiom). [clausify(488)]. 0.97/1.21 533 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C) # label(fact_inf__le2) # label(axiom). [clausify(500)]. 0.97/1.21 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),B). [resolve(533,a,503,a)]. 0.97/1.21 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat,A,B),B). [resolve(533,a,519,a)]. 0.97/1.21 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D),D) | -class_Lattices_Olattice(B). [resolve(533,a,523,b)]. 0.97/1.21 534 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 535 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(fact_assms_I3_J) # label(axiom). [assumption]. 0.97/1.21 536 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f40(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 537 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f41(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 538 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(f40(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(f41(A),B))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 539 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(f40(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(f41(A),B))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 540 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(A,f41(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(A,f40(A)))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 541 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(A,f41(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(A)),f43(A))),hAPP(A,f40(A)))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 0.97/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))). [resolve(534,g,535,a)]. 0.97/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f40(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(534,g,536,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f41(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(534,g,537,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(534,g,538,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(534,g,539,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(534,g,540,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(534,g,541,c)]. 1.05/1.21 542 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))). [resolve(542,g,535,a)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f40(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(542,g,536,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f41(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(542,g,537,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(542,g,538,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(542,g,539,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(542,g,540,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(542,g,541,c)]. 1.05/1.21 543 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))). [resolve(543,g,535,a)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f40(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(543,g,536,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f41(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(543,g,537,b)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(543,g,538,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(543,g,539,c)]. 1.05/1.21 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(543,g,540,c)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(543,g,541,c)]. 1.05/1.22 544 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(296)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))). [resolve(544,g,535,a)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f40(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(544,g,536,b)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f41(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(544,g,537,b)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(544,g,538,c)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f40(E),F))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(f41(E),F))). [resolve(544,g,539,c)]. 1.05/1.22 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(544,g,540,c)]. 1.05/1.26 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f44(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f44(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f41(E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f42(E)),f43(E))),hAPP(E,f40(E)))). [resolve(544,g,541,c)]. 1.05/1.26 545 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 1.05/1.26 546 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(85)]. 1.05/1.26 547 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(85)]. 1.05/1.26 548 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(85)]. 1.05/1.26 549 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neqE) # label(axiom). [clausify(98)]. 1.05/1.27 550 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | B = C | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__cases) # label(axiom). [clausify(164)]. 1.05/1.27 551 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B = C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(180)]. 1.05/1.27 552 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | B != C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(180)]. 1.05/1.27 553 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(190)]. 1.05/1.27 554 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B = C | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(190)]. 1.05/1.27 555 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(193)]. 1.05/1.27 556 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(193)]. 1.05/1.27 557 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_leD) # label(axiom). [clausify(199)]. 1.05/1.27 558 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(211)]. 1.05/1.27 559 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(211)]. 1.05/1.27 560 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom). [clausify(276)]. 1.05/1.27 561 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(287)]. 1.05/1.27 562 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__leE) # label(axiom). [clausify(322)]. 1.05/1.27 563 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom). [clausify(385)]. 1.05/1.27 564 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(409)]. 1.05/1.27 565 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(409)]. 1.05/1.27 566 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(409)]. 1.05/1.27 567 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_linorder__less__linear) # label(axiom). [clausify(420)]. 1.05/1.27 568 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C != B | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(454)]. 1.05/1.27 569 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(454)]. 1.05/1.27 570 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_leI) # label(axiom). [clausify(462)]. 1.05/1.27 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(545,a,546,a)]. 1.05/1.27 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(545,a,547,a)]. 1.11/1.29 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | A = B. [resolve(545,a,551,a)]. 1.11/1.29 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | A != B. [resolve(545,a,552,a)]. 1.11/1.29 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(545,a,555,a)]. 1.11/1.29 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(545,a,556,a)]. 1.11/1.29 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(545,a,560,a)]. 1.11/1.29 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(545,a,566,a)]. 1.11/1.29 571 c_Arrow__Order__Mirabelle_Ounanimity(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f26(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_unanimity__def) # label(axiom). [clausify(176)]. 1.11/1.29 572 -c_Arrow__Order__Mirabelle_Ounanimity(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f25(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))) # label(fact_unanimity__def) # label(axiom). [clausify(176)]. 1.11/1.29 Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f26(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f25(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))). [resolve(571,a,572,a)]. 1.11/1.29 573 c_Arrow__Order__Mirabelle_Ounanimity(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f27(A)),f28(A))),hAPP(f26(A),B))) # label(fact_unanimity__def) # label(axiom). [clausify(176)]. 1.11/1.29 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f27(A)),f28(A))),hAPP(f26(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f25(A,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(573,a,572,a)]. 1.11/1.29 574 c_Arrow__Order__Mirabelle_Ounanimity(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f27(A)),f28(A))),hAPP(A,f26(A)))) # label(fact_unanimity__def) # label(axiom). [clausify(176)]. 1.11/1.35 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f27(A)),f28(A))),hAPP(A,f26(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f25(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))). [resolve(574,a,572,a)]. 1.11/1.35 575 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(fact_u) # label(axiom). [assumption]. 1.11/1.35 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B),C)),hAPP(A,f25(v_F,A,B,C)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B),C)),hAPP(v_F,A))). [resolve(575,a,572,a)]. 1.11/1.35 576 hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),C)) | -c_Nitpick_Orefl_H(A,C) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(198)]. 1.11/1.35 577 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f29(B,A)),f29(B,A))),B)) | c_Nitpick_Orefl_H(A,B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(198)]. 1.11/1.35 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),C)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f29(C,A)),f29(C,A))),C)). [resolve(576,b,577,b)]. 1.11/1.35 578 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | -c_Arrow__Order__Mirabelle_Odictator(B,C) # label(fact_dictator__def) # label(axiom). [clausify(360)]. 1.11/1.35 579 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f56(A,B)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(B,A) # label(fact_dictator__def) # label(axiom). [clausify(360)]. 1.11/1.35 580 hAPP(A,f56(B,A)) != hAPP(f56(B,A),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictator__def) # label(axiom). [clausify(360)]. 1.11/1.35 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f56(C,B)),c_Arrow__Order__Mirabelle_OProf)). [resolve(578,c,579,b)]. 1.11/1.35 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | hAPP(B,f56(C,B)) != hAPP(f56(C,B),C). [resolve(578,c,580,b)]. 1.11/1.36 581 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f75(B,A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(426)]. 1.11/1.36 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f75(B,A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B). [resolve(581,c,578,c)]. 1.11/1.36 582 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | f77(B,A) != f76(B,A) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(426)]. 1.11/1.36 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | f77(B,A) != f76(B,A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B). [resolve(582,c,578,c)]. 1.20/1.36 583 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f76(B,A)),f77(B,A))),hAPP(f75(B,A),B))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(426)]. 1.20/1.36 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f76(B,A)),f77(B,A))),hAPP(f75(B,A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B). [resolve(583,c,578,c)]. 1.20/1.36 584 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f76(B,A)),f77(B,A))),hAPP(A,f75(B,A)))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(426)]. 1.53/1.70 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f76(B,A)),f77(B,A))),hAPP(A,f75(B,A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B). [resolve(584,c,578,c)]. 1.53/1.70 585 c_FunDef_Oin__rel(A,B,C,D,E) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),D),E)),C)) # label(fact_in__rel__def) # label(axiom). [clausify(484)]. 1.53/1.70 586 -c_FunDef_Oin__rel(A,B,C,D,E) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),D),E)),C)) # label(fact_in__rel__def) # label(axiom). [clausify(484)]. 1.53/1.70 587 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),C)) | -c_Relation_Oirrefl(A,C) # label(fact_irrefl__def) # label(axiom). [clausify(493)]. 1.53/1.70 588 hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f99(B,A)),f99(B,A))),B)) | c_Relation_Oirrefl(A,B) # label(fact_irrefl__def) # label(axiom). [clausify(493)]. 1.53/1.70 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),C)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f99(C,A)),f99(C,A))),C)). [resolve(587,b,588,b)]. 1.53/1.70 1.53/1.70 ============================== end predicate elimination ============= 1.53/1.70 1.53/1.70 Auto_denials: (non-Horn, no changes). 1.53/1.70 1.53/1.70 Term ordering decisions: 1.53/1.70 Function symbol KB weights: tc_Arrow__Order__Mirabelle_Oalt=1. tc_HOL_Obool=1. tc_Nat_Onat=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. c_Arrow__Order__Mirabelle_OLin=1. v_F=1. c_Arrow__Order__Mirabelle_Obelow=1. v_b____=1. c_fconj=1. v_a____=1. c_fequal=1. v_P____=1. v_P_H____=1. v_c____=1. c_fNot=1. c1=1. hAPP=1. tc_prod=1. tc_fun=1. c_Product__Type_OPair=1. c_List_Olistrel1=1. c_Transitive__Closure_Ortrancl=1. c_Nat_Osize__class_Osize=1. c_List_Olistsp=1. c_List_Olistrel=1. c_List_Olists=1. c_Wellfounded_Oacc=1. c_List_Olexord=1. c_List_Olast=1. c_Wellfounded_Oaccp=1. c_List_Obutlast=1. c_List_Olex=1. c_Relation_OId__on=1. c_List_Omeasures=1. c_List_Orotate1=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Wellfounded_Omeasure=1. c_If=1. f9=1. f16=1. f17=1. f29=1. f34=1. f51=1. f52=1. f53=1. f56=1. f57=1. f58=1. f59=1. f60=1. f75=1. f76=1. f77=1. f99=1. f101=1. f102=1. c_member=1. tc_List_Olist=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_List_Olist_ONil=1. c_COMBI=1. f26=1. f27=1. f28=1. f40=1. f41=1. f42=1. f43=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_COMBB=1. c_COMBC=1. c_Product__Type_Oprod_Oprod__case=1. c_COMBK=1. c_List_Onth=1. c_List_OtakeWhile=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Groups_Oplus__class_Oplus=1. c_Relation_ODomain=1. c_List_OdropWhile=1. c_Relation_ORange=1. c_COMBS=1. c_FuncSet_Oextensional=1. c_List_Osplice=1. c_List_Opartition=1. c_List_Oinsert=1. c_List_Olexn=1. c_Product__Type_Ointernal__split=1. c_Wellfounded_Omlex__prod=1. f1=1. f2=1. f3=1. f11=1. f12=1. f13=1. f19=1. f20=1. f23=1. f35=1. f36=1. f37=1. f61=1. f67=1. f68=1. f69=1. f70=1. f88=1. f92=1. f93=1. f94=1. f96=1. f97=1. c_FuncSet_OPi=1. c_Set_Oimage=1. c_FuncSet_Orestrict=1. c_Product__Type_Ocurry=1. c_Wellfounded_Olex__prod=1. c_List_Omaps=1. c_Recdef_Osame__fst=1. f5=1. f7=1. f8=1. f10=1. f25=1. f47=1. f48=1. f50=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f89=1. c_List_Olist_Olist__case=1. c_Product__Type_Oprod_Oprod__rec=1. f4=1. f6=1. f18=1. f21=1. f22=1. f24=1. f33=1. f38=1. f39=1. f44=1. f49=1. f54=1. f55=1. f84=1. f85=1. f86=1. f90=1. f91=1. f95=1. f98=1. f100=1. c_FuncSet_Ocompose=1. c_Fun_Ooverride__on=1. f14=1. f15=1. f30=1. f31=1. f32=1. f62=1. f87=1. f45=1. f46=1. f63=1. f64=1. f65=1. f66=1. f71=1. f72=1. f73=1. f74=1. 2.63/2.87 2.63/2.87 ============================== end of process initial clauses ======== 2.63/2.87 2.63/2.87 ============================== CLAUSES FOR SEARCH ==================== 2.63/2.87 2.63/2.87 ============================== end of clauses for search ============= 2.63/2.87 2.63/2.87 ============================== SEARCH ================================ 2.63/2.87 2.63/2.87 % Starting search at 0.62 seconds. 2.63/2.87 2.63/2.87 Low Water (keep): wt=103.000, iters=3605 2.63/2.87 2.63/2.87 Low Water (keep): wt=87.000, iters=3515 2.63/2.87 2.63/2.87 Low Water (keep): wt=86.000, iters=3510 2.63/2.87 2.63/2.87 Low Water (keep): wt=74.000, iters=3370 2.63/2.87 2.63/2.87 Low Water (keep): wt=71.000, iters=3443 2.63/2.87 2.63/2.87 Low Water (keep): wt=66.000, iters=3400 2.63/2.87 2.63/2.87 Low Water (keep): wt=63.000, iters=3362 2.63/2.87 2.63/2.87 Low Water (keep): wt=59.000, iters=3427 2.63/2.87 2.63/2.87 Low Water (keep): wt=56.000, iters=3372 2.63/2.87 2.63/2.87 ============================== PROOF ================================= 2.63/2.87 % SZS status Theorem 2.63/2.87 % SZS output start Refutation 2.63/2.87 2.63/2.87 % Proof 1 at 1.77 (+ 0.02) seconds. 2.63/2.87 % Length of proof is 9. 2.63/2.87 % Level of proof is 3. 2.63/2.87 % Maximum clause weight is 18.000. 2.63/2.87 % Given clauses 441. 2.63/2.87 2.63/2.87 167 (all V_P all T_a V_P = hAPP(c_COMBI(T_a),V_P)) # label(help_c__COMBI__1) # label(axiom) # label(non_clause). [assumption]. 2.63/2.87 191 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs) # label(fact_not__Cons__self2) # label(axiom) # label(non_clause). [assumption]. 2.63/2.87 394 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) = hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2)) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption]. 2.63/2.87 818 hAPP(c_COMBI(A),B) = B # label(help_c__COMBI__1) # label(axiom). [clausify(167)]. 2.63/2.87 856 hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C # label(fact_not__Cons__self2) # label(axiom). [clausify(191)]. 2.63/2.87 1103 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)) # label(help_c__COMBS__1) # label(axiom). [clausify(394)]. 2.63/2.87 5251 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),c_COMBI(E)),F) = hAPP(hAPP(D,F),F). [para(818(a,1),1103(a,2,2))]. 2.63/2.87 5272 hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F) != hAPP(E,F). [para(1103(a,2),856(a,1))]. 2.63/2.87 5273 $F. [resolve(5272,a,5251,a(flip))]. 2.63/2.87 2.63/2.87 % SZS output end Refutation 2.63/2.87 ============================== end of proof ========================== 2.63/2.87 2.63/2.87 ============================== STATISTICS ============================ 2.63/2.87 2.63/2.87 Given=441. Generated=7759. Kept=4625. proofs=1. 2.63/2.87 Usable=428. Sos=3829. Demods=153. Limbo=167, Disabled=1122. Hints=0. 2.63/2.87 Megabytes=38.13. 2.63/2.87 User_CPU=1.77, System_CPU=0.02, Wall_clock=2. 2.63/2.87 2.63/2.87 ============================== end of statistics ===================== 2.63/2.87 2.63/2.87 ============================== end of search ========================= 2.63/2.87 2.63/2.87 THEOREM PROVED 2.63/2.87 % SZS status Theorem 2.63/2.87 2.63/2.87 Exiting with 1 proof. 2.63/2.87 2.63/2.87 Process 8148 exit (max_proofs) Sat Jul 14 06:02:12 2018 2.63/2.87 Prover9 interrupted 2.63/2.87 EOF