0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n015.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 180 0.13/0.35 % DateTime : Thu Aug 29 17:33:52 EDT 2019 0.13/0.35 % CPUTime : 1.25/1.58 ============================== Prover9 =============================== 1.25/1.58 Prover9 (32) version 2009-11A, November 2009. 1.25/1.58 Process 18689 was started by sandbox2 on n015.cluster.edu, 1.25/1.58 Thu Aug 29 17:33:53 2019 1.25/1.58 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_18536_n015.cluster.edu". 1.25/1.58 ============================== end of head =========================== 1.25/1.58 1.25/1.58 ============================== INPUT ================================= 1.25/1.58 1.25/1.58 % Reading from file /tmp/Prover9_18536_n015.cluster.edu 1.25/1.58 1.25/1.58 set(prolog_style_variables). 1.25/1.58 set(auto2). 1.25/1.58 % set(auto2) -> set(auto). 1.25/1.58 % set(auto) -> set(auto_inference). 1.25/1.58 % set(auto) -> set(auto_setup). 1.25/1.58 % set(auto_setup) -> set(predicate_elim). 1.25/1.58 % set(auto_setup) -> assign(eq_defs, unfold). 1.25/1.58 % set(auto) -> set(auto_limits). 1.25/1.58 % set(auto_limits) -> assign(max_weight, "100.000"). 1.25/1.58 % set(auto_limits) -> assign(sos_limit, 20000). 1.25/1.58 % set(auto) -> set(auto_denials). 1.25/1.58 % set(auto) -> set(auto_process). 1.25/1.58 % set(auto2) -> assign(new_constants, 1). 1.25/1.58 % set(auto2) -> assign(fold_denial_max, 3). 1.25/1.58 % set(auto2) -> assign(max_weight, "200.000"). 1.25/1.58 % set(auto2) -> assign(max_hours, 1). 1.25/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.25/1.58 % set(auto2) -> assign(max_seconds, 0). 1.25/1.58 % set(auto2) -> assign(max_minutes, 5). 1.25/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.25/1.58 % set(auto2) -> set(sort_initial_sos). 1.25/1.58 % set(auto2) -> assign(sos_limit, -1). 1.25/1.58 % set(auto2) -> assign(lrs_ticks, 3000). 1.25/1.58 % set(auto2) -> assign(max_megs, 400). 1.25/1.58 % set(auto2) -> assign(stats, some). 1.25/1.58 % set(auto2) -> clear(echo_input). 1.25/1.58 % set(auto2) -> set(quiet). 1.25/1.58 % set(auto2) -> clear(print_initial_clauses). 1.25/1.58 % set(auto2) -> clear(print_given). 1.25/1.58 assign(lrs_ticks,-1). 1.25/1.58 assign(sos_limit,10000). 1.25/1.58 assign(order,kbo). 1.25/1.58 set(lex_order_vars). 1.25/1.58 clear(print_given). 1.25/1.58 1.25/1.58 % formulas(sos). % not echoed (535 formulas) 1.25/1.58 1.25/1.58 ============================== end of input ========================== 1.25/1.58 1.25/1.58 % From the command line: assign(max_seconds, 180). 1.25/1.58 1.25/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.25/1.58 1.25/1.58 % Formulas that are not ordinary clauses: 1.25/1.58 1 (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_H),V_b_H) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) -> -(V_a = V_a_H -> V_b != V_b_H))) # label(fact_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 2 (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]. 1.25/1.58 3 (all T_b all T_a all V_S_2 (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != V_S_2 -> c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) = c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_extensional__funcset__empty__range) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 4 (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_Otrancl(T_a,V_R_2))) -> (exists 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_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),B_z)),V_R_2)))))) # label(fact_tranclD) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 5 (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)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclicI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 6 (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]. 1.25/1.58 7 (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_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 8 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) # label(fact_sup__assoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 9 (all V_y_2 all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_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)),V_L_2)))))) # label(fact_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 10 (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_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) & V_aa_2 != V_ba_2 | V_ba_2 = V_aa_2)) # label(fact_rtranclD) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 11 (all V_A_2 all T_a V_A_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 12 (all V_C_2 all V_B_2 all V_A_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2))),c_Product__Type_OSigma(T_a,T_b,V_B_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2)))) # label(fact_Times__Int__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 13 (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]. 1.25/1.58 14 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(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]. 1.25/1.58 15 (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_Groups_Ominus__class_Ominus(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_DiffE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 16 (all V_r_2 all V_A_2 all T_a (c_Relation_Ototal__on(T_a,V_A_2,V_r_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) -> (B_xa != B_x -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),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_xa)),V_r_2))))))))) # label(fact_total__on__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 17 (all V_A_2 all T_a V_A_2 = hAPP(hAPP(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]. 1.25/1.58 18 (all V_x_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 19 (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(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_y_2),V_z_2)),c_Transitive__Closure_Otrancl(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_Otrancl(T_a,V_r_2)))))) # label(fact_rtrancl__trancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 20 (all V_A_2 all V_B_2 all V_ca_2 all T_a ((-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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnCI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 21 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 22 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 23 (all V_A_2 all V_C_2 all V_B_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))) # label(fact_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.58 24 (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(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(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_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)),hAPP(hAPP(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]. 1.25/1.59 25 (all V_B_2 all V_A_2 all T_a (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) -> B_x != B_xa)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 26 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) # label(fact_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 27 (all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,V_L_2)),c_Arrow__Order__Mirabelle_OProf)))) # label(fact_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 28 (all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 29 (all V_S_2 all V_R_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))))) # label(fact_in__rtrancl__UnI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 30 (all V_x_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))) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b)))) # label(fact_extensional__arb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 31 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_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_x_2 = V_ba_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))) & (V_x_2 != V_ba_2 -> (V_y_2 != V_ba_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_aa_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_aa_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_Oabove(V_L_2,V_aa_2,V_ba_2))))))) # label(fact_in__above) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 32 (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]. 1.25/1.59 33 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(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]. 1.25/1.59 34 (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]. 1.25/1.59 35 (all V_A_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2)) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 36 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))) # label(fact_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 37 (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]. 1.25/1.59 38 (all V_aa_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) -> V_ba_2 = V_aa_2)) # label(fact_singletonE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 39 (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]. 1.25/1.59 40 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y),V_x))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 41 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2))) <-> (V_z_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))) & (V_x_2 = V_z_2 -> V_x_2 != V_y_2) & V_y_2 != V_z_2)) # label(fact_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 42 (all V_r_2 all T_a c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ODomain(T_a,T_a,V_r_2)) # label(fact_trancl__domain) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 43 (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_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]. 1.25/1.59 44 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 45 (all V_B_2 all V_aa_2 all V_A_2 all T_a c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 46 (all V_ca_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))) -> -(-hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 47 (all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 48 (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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_UnE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 49 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_PiE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 50 (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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Un__upper2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 51 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) -> (-hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(V_B_2,V_x_2))))) # label(fact_sup1E) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 52 (all V_B_2 all V_ba_2 all V_A_2 all V_aa_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,c_Set_Oinsert(T_a,V_aa_2,V_A_2),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,c_Set_Oinsert(T_b,V_ba_2,V_B_2))) = c_Set_Oinsert(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,c_Set_Oinsert(T_b,V_ba_2,V_B_2)))),c_Product__Type_OSigma(T_a,T_b,c_Set_Oinsert(T_a,V_aa_2,V_A_2),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2))))) # label(fact_insert__times__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 53 (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_a____),v_b____)),hAPP(v_P____,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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____))))) # label(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 54 (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(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2))) # label(fact_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 55 (all V_r_2 all T_a all T_b (c_Relation_ORange(T_b,T_a,V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)))) # label(fact_Range__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 56 (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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(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]. 1.25/1.59 57 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_g_2 = V_f_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 58 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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]. 1.25/1.59 59 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))))) # label(fact_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 60 (all V_A_2 all T_b all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) = c_Product__Type_OSigma(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_Sigma__empty2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 61 (all V_A_2 all T_a c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2) # label(fact_Range__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 62 (all V_r_2 all V_ba_2 all V_aa_2 all T_a all T_b c_Set_Oinsert(T_a,V_ba_2,c_Relation_ORange(T_b,T_a,V_r_2)) = c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_aa_2),V_ba_2),V_r_2))) # label(fact_Range__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 63 (all V_B_2 all V_ba_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)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_aa_2))) -> 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)),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2)))))) # label(fact_SigmaI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 64 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 65 (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]. 1.25/1.59 66 (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) -> hAPP(hAPP(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]. 1.25/1.59 67 (all V_B_2 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)),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_aa_2))))) # label(fact_mem__Sigma__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 68 (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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 69 (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]. 1.25/1.59 70 (all V_B_2 all V_A_2 all T_b all V_C_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) -> (c_Product__Type_OSigma(T_b,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b,V_C_2)) = c_Product__Type_OSigma(T_b,T_a,V_B_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b,V_C_2)) <-> V_B_2 = V_A_2))) # label(fact_Times__eq__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 71 (all V_B_2 all V_A_2 all T_b all V_C_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),c_Product__Type_OSigma(T_b,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b,V_C_2)),c_Product__Type_OSigma(T_b,T_a,V_B_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b,V_C_2)))))) # label(fact_Times__subset__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 72 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 73 (all V_B_2 all V_C_2 all V_aa_2 all T_a ((-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_B_2)),V_C_2)) & (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) -> c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_B_2)),V_C_2)))) # label(fact_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 74 (all V_A_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2)) # label(fact_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 75 (all T_a all V_B_2 all V_A_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) <-> V_A_2 = V_B_2)) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 76 (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]. 1.25/1.59 77 (all T_a c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a)) # label(fact_rtrancl__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 78 (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_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_za_2),V_zb_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]. 1.25/1.59 79 (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_A_2 = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 80 (all V_aa_2 all V_D_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_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2),c_Set_Oinsert(T_a,V_aa_2,V_D_2)))) # label(fact_insert__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 81 (all V_x_2 all V_A_2 all V_y_2 all T_a (V_x_2 = V_y_2 | hBOOL(hAPP(V_A_2,V_x_2)) <-> hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 82 (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) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 83 (all V_x_2 all T_b all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Obot__class_Obot(T_a) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2))) # label(fact_bot__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 84 (all V_D_2 all V_B_2 all T_b 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) -> ((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_D_2,B_x)))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2),c_Product__Type_OSigma(T_a,T_b,V_C_2,V_D_2))))) # label(fact_Sigma__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 85 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))))) # label(fact_le__supI2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 86 (all V_B_2 all V_A_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) -> (V_B_2 = V_A_2 <-> c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2))))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 87 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 88 (all T_a c_Relation_OField(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Field__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 89 (all V_d_2 all V_ca_2 all V_ba_2 all V_aa_2 all T_a (V_d_2 = V_ba_2 & V_ca_2 = V_aa_2 | V_d_2 = V_aa_2 & V_ca_2 = V_ba_2 <-> c_Set_Oinsert(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Set_Oinsert(T_a,V_ca_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 90 (all V_Pa_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(V_Pa_2,V_ba_2)) -> ((all B_y 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_z),V_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(V_Pa_2,B_z)) -> hBOOL(hAPP(V_Pa_2,B_y)))))) -> hBOOL(hAPP(V_Pa_2,V_aa_2)))))) # label(fact_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 91 (all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_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_x)),V_r_2)))) & c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))))) # label(fact_refl__on__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 92 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) # label(fact_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 93 (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(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]. 1.25/1.59 94 (all V_ba_2 all V_aa_2 all T_a (V_aa_2 = V_ba_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(T_a))))) # label(fact_pair__in__Id__conv) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 95 (all V_R_2 all V_y_2 all V_x_2 all T_a (V_y_2 = V_x_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_Transitive__Closure_Otrancl(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))))) # label(fact_rtrancl__eq__or__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 96 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_sup__ge2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 97 (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]. 1.25/1.59 98 (all V_y_2 all V_f_2 all T_b all T_a all V_x_2 all V_z_2 (V_z_2 != V_x_2 -> hAPP(V_f_2,V_z_2) = hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2))) # label(fact_fun__upd__other) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 99 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Orderings_Obot__class_Obot(T_a) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x))) # label(fact_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 100 (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,hAPP(hAPP(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_z_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 101 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(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),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_acyclic__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 102 (all V_y_2 all V_x_2 all V_ca_2 all T_a all T_c all T_b 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]. 1.25/1.59 103 (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)),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_Otrancl(T_a,V_R_2)))))) # label(fact_r__r__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 104 (all V_A_2 all T_a all V_y_2 all V_x_2 (V_x_2 = V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 105 (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]. 1.25/1.59 106 (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) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2)) # label(fact_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 107 (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]. 1.25/1.59 108 (all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Un__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.59 109 (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]. 1.25/1.59 110 (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_ba_2 != V_aa_2 -> (V_b_H_2 != V_a_H_2 -> (V_aa_2 != V_b_H_2 -> (V_ba_2 != V_a_H_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_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_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_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_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__C2_C) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 111 (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_y_2 = V_x_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 112 (all V_a2_2 all V_r_2 all T_b all T_a ((exists B_a hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))) <-> c_Predicate_ORangeP(T_a,T_b,V_r_2,V_a2_2))) # label(fact_RangeP_Oequations) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 113 (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]. 1.25/1.60 114 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(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]. 1.25/1.60 115 (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(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]. 1.25/1.60 116 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Orderings_Obot__class_Obot(T_a) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)))) # label(fact_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 117 (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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnI1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 118 (all T_b all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) # label(fact_Domain__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 119 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 120 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_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)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_refl__onD1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 121 (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]. 1.25/1.60 122 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) -> (V_ba_2 != V_aa_2 -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 123 (all V_s_2 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),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2)))))) # label(fact_trancl__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 124 (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_Otrancl(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)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_trancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 125 (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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) # label(fact_rtrancl__Un__subset) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 126 (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_Otrancl(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_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__rtrancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 127 (all V_Fa_2 all V_R_2 all T_b all T_a (c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2) <-> (all B_f all B_g all B_x ((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),B_x)),V_R_2)) -> hAPP(B_g,B_z) = hAPP(B_f,B_z))) -> hAPP(hAPP(V_Fa_2,B_g),B_x) = hAPP(hAPP(V_Fa_2,B_f),B_x))))) # label(fact_adm__wf__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 128 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_a,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(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_refl__on__Int) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 129 (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_Otrancl(T_a,V_r_2)))))) # label(fact_rtrancl__into__trancl1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 130 (all V_B_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) # label(fact_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 131 (all T_a all T_b c_Relation_ORange(T_b,T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Range__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 132 (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_a != B_b -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))))))) -> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)))) # label(fact_dictatorI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 133 (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]. 1.25/1.60 134 (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_A_2 = V_B_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 135 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_trancl__rtrancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 136 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) = hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2))) # label(fact_sup__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 137 (all V_Pa_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(V_Pa_2,V_aa_2)) -> ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),c_Transitive__Closure_Ortrancl(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_y),B_z)),V_r_2)) -> (hBOOL(hAPP(V_Pa_2,B_y)) -> hBOOL(hAPP(V_Pa_2,B_z))))))) -> hBOOL(hAPP(V_Pa_2,V_ba_2)))))) # label(fact_rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 138 (all V_aa_2 all V_r_2 all T_a hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2))) # label(fact_rtranclp_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 139 (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]. 1.25/1.60 140 (all V_A_2 all T_a ((exists B_x hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))) <-> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 141 (all T_a all V_A_2 all V_x_2 all V_B_2 ((-hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(V_A_2,V_x_2))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1CI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 142 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Un__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 143 (all V_Q_2 all V_Pa_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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_Pa_2),V_Q_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_ba_2)),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2))) -> (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),B_x)),V_Q_2)) -> B_x = B_y)))) -> 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_Pa_2)))))) # label(fact_rtrancl__Un__separator__converseE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 144 (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]. 1.25/1.60 145 (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]. 1.25/1.60 146 (all V_r_2 all T_b all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ODomain(T_a,T_b,V_r_2) <-> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) = V_r_2)) # label(fact_Domain__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 147 (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_a____),v_b____)),hAPP(v_P____,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))))) # label(fact_iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 148 (all V_Pa_2 (-hBOOL(V_Pa_2) | -hBOOL(hAPP(c_fNot,V_Pa_2)))) # label(help_c__fNot__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 149 (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]. 1.25/1.60 150 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)))) # label(fact_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 151 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_a,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_refl__on__Un) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 152 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 153 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(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]. 1.25/1.60 154 (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_Otrancl(T_a,V_r_2))))) # label(fact_r__into__trancl_H) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 155 (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_y = V_x)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 156 (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]. 1.25/1.60 157 (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]. 1.25/1.60 158 (all V_T_2 all V_S_2 all T_b all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)),c_FuncSet_OPi(T_a,T_b,V_S_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_T_2))),c_FuncSet_Oextensional(T_a,T_b,V_S_2)) = c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2)) # label(fact_extensional__funcset__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 159 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a (c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2,V_a2_2) <-> (exists B_g ((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_a1_2)),V_R_2)) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(B_g,B_z)))) & V_a2_2 = hAPP(hAPP(V_Fa_2,B_g),V_a1_2))))) # label(fact_wfrec__rel_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 160 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__assoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 161 (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),hAPP(hAPP(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]. 1.25/1.60 162 (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]. 1.25/1.60 163 (all V_T_2 all T_b all T_a c_FuncSet_Oextensional__funcset(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_T_2) = c_Set_Oinsert(tc_fun(T_a,T_b),c_COMBK(T_b,T_a,c_HOL_Oundefined(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) # label(fact_extensional__funcset__empty__domain) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 164 (all V_Q all V_P all T_b all T_a V_P = hAPP(c_COMBK(T_a,T_b,V_P),V_Q)) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 165 (all V_r_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Relation_ODomain(T_a,T_a,V_r_2)),c_Relation_ORange(T_a,T_a,V_r_2)) = c_Relation_OField(T_a,V_r_2)) # label(fact_Field__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 166 (all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 167 (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(hAPP(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]. 1.25/1.60 168 (all V_B_2 all V_A_2 all T_b all T_a ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) & c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(V_B_2,B_x))) <-> c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) = c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) # label(fact_Pi__eq__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 169 (all V_B_2 all V_A_2 all V_ca_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> (all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) -> hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) != V_ca_2)))))) # label(fact_SigmaE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 170 (all V_B_2 all V_A_2 all T_b all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Relation_ODomain(T_a,T_b,V_A_2)),c_Relation_ODomain(T_a,T_b,V_B_2)) = c_Relation_ODomain(T_a,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Domain__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 171 (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]. 1.25/1.60 172 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(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]. 1.25/1.60 173 (all V_r_2 all T_a c_Transitive__Closure_Ortranclp(T_a,c_Transitive__Closure_Ortranclp(T_a,V_r_2)) = c_Transitive__Closure_Ortranclp(T_a,V_r_2)) # label(fact_rtranclp__idemp) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 174 (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]. 1.25/1.60 175 (all T_a all V_R_2 all V_y_2 all V_y_H_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 176 (all V_A_2 all V_y_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 177 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a))) # label(fact_reflcl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 178 (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(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_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)) & V_a_H_2 = V_aa_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_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))))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 179 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_sup__ge1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 180 (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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Un__upper1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 181 (all V_y_2 all V_x_2 (-hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 182 (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]. 1.25/1.60 183 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a))) # label(fact_rtrancl__reflcl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 184 (all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> (all B_x -hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))))) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 185 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 186 (all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x)) # label(fact_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 187 (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))) <-> (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))))) # label(fact_Domain__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 188 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_a (V_f_2 = c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2) <-> V_y_2 = hAPP(V_f_2,V_x_2))) # label(fact_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 189 (all V_B_2 all T_a all V_x_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1I1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 190 (all V_A_2 all V_C_2 all V_B_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2)) # label(fact_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 191 (all V_B_2 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)),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)))) # label(fact_SigmaD1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 192 (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_g_2,B_w) = hAPP(V_f_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]. 1.25/1.60 193 (all V_B_2 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)),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_aa_2))))) # label(fact_SigmaD2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 194 (all V_a3_2 all V_a1_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),V_a3_2)) <-> (exists B_b (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),B_b)) & hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2)))) | V_a1_2 = V_a3_2)) # label(fact_rtranclp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 195 (all V_A_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))) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))) -> V_ba_2 = V_aa_2 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_trancl__subset__Sigma__aux) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 196 (all T_a all T_b all V_y_2 all V_x_2 all V_f_2 (V_y_2 = hAPP(V_f_2,V_x_2) -> V_f_2 = c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2))) # label(fact_fun__upd__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 197 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(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]. 1.25/1.60 198 (all V_r_2 all V_ba_2 all V_aa_2 all T_a c_Relation_OField(T_a,c_Set_Oinsert(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)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Relation_OField(T_a,V_r_2))) # label(fact_Field__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 199 (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(c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2),V_x_2) = hAPP(V_g_2,hAPP(V_f_2,V_x_2)))) # label(fact_compose__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 200 (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]. 1.25/1.60 201 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> V_x = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x))) # label(fact_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 202 (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_A_2,V_B_2))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 203 (all T_2 all T_1 (class_Lattices_Odistrib__lattice(T_1) -> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 204 (all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 205 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_ba_2 != V_aa_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,V_L_2),V_aa_2),V_ba_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_x_2 = V_aa_2 -> V_y_2 = V_ba_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2)))) & (V_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_x_2 != V_y_2)))) # label(fact_in__below) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 206 (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]. 1.25/1.60 207 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_sup__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.60 208 (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) = 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]. 1.25/1.60 209 (all V_C_2 all V_B_2 all V_A_2 all T_b all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2))),c_Product__Type_OSigma(T_a,T_b,V_B_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2))) = c_Product__Type_OSigma(T_a,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_C_2))) # label(fact_Times__Un__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 210 (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),hAPP(hAPP(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]. 1.25/1.61 211 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y))) # label(fact_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 212 (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]. 1.25/1.61 213 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 214 (all V_x_2 all T_a c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2) # label(fact_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 215 (all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> V_a = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a))) # label(fact_sup_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 216 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) # label(fact_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 217 (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) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2)) # label(fact_Un__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 218 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 219 (all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(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]. 1.25/1.61 220 (all V_A_2 all T_a V_A_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) # label(fact_Un__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 221 (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)) -> hAPP(V_f_2,V_x_2) = hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2)) & (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b)))) # label(fact_restrict__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 222 (all V_g_2 all V_Fa_2 all T_b all V_R_2 all V_x_2 all T_a ((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)) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(V_g_2,B_z)))) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2,hAPP(hAPP(V_Fa_2,V_g_2),V_x_2)))) # label(fact_wfrec__rel_Ointros) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 223 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 224 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) # label(fact_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 225 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(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]. 1.25/1.61 226 (all V_x_2 all V_S_2 all V_R_2 all T_a (hBOOL(hAPP(hAPP(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),hAPP(hAPP(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]. 1.25/1.61 227 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_y_2),V_z_2)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_z_2))))) # label(fact_rtranclp__trans) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 228 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b),V_x))))) # label(fact_le__supI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 229 (all V_r_2 all V_z_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_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (V_z_2 != V_x_2 -> -(all B_y (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)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))))) # label(fact_converse__rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 230 (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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))))) # label(fact_Un__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 231 (all V_x_2 all T_a (hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 232 (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]. 1.25/1.61 233 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 234 (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_B_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),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2))) # label(fact_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 235 (all V_x_2 all V_T_2 all V_S_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__funcset(T_a,T_b,V_S_2,V_T_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_T_2))))) # label(fact_extensional__funcset__mem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 236 (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(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_sup__Un__eq2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 237 (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]. 1.25/1.61 238 (all V_r_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Product__Type_OSigma(T_a,T_a,c_Relation_OField(T_a,V_r_2),c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,c_Relation_OField(T_a,V_r_2))))) # label(fact_trancl__subset__Field2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 239 (all V_B_2 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)),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) -> -(hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_aa_2)))))) # label(fact_SigmaE2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 240 (all V_s_2 all V_r_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OField(T_a,V_r_2)),c_Relation_OField(T_a,V_s_2)) = c_Relation_OField(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))) # label(fact_Field__Un) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 241 (all V_Fa_2 (c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa)))))))))))) # label(fact_IIA__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 242 (all V_B_2 all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_A_2)),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 243 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) # label(fact_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 244 (all V_B_2 all V_C_2 all V_aa_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 245 (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]. 1.25/1.61 246 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_z_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2),V_z_2)))) # label(fact_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 247 (all V_z_2 all V_y_2 all V_x_2 all V_f_2 all T_b all T_a c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_z_2)) # label(fact_fun__upd__upd) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 248 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))))) # label(fact_le__supI1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 249 (all V_z all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(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_x) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z),V_x))))) # label(fact_sup__least) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 250 (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_z = B_y)))) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2))) # label(fact_single__valuedI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 251 (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]. 1.25/1.61 252 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__sup(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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d)))))) # label(fact_sup__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 253 (all V_aa_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_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_aa_2)),V_r_2))))) # label(fact_refl__onD) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 254 (all V_x_2 all V_r_2 all T_b all T_a (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(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_b,V_r_2))))) # label(fact_DomainP__Domain__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 255 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_aa_2 = V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 256 (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]. 1.25/1.61 257 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_OId__on(T_a,V_A_2),c_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2)))) # label(fact_Id__on__subset__Times) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 258 (all V_y_2 all V_x_2 all V_f_2 all T_a all T_b V_y_2 = hAPP(c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2),V_x_2)) # label(fact_fun__upd__same) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 259 (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]. 1.25/1.61 260 (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)) -> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = c_HOL_Oundefined(T_b)) & (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2) = hAPP(V_f_2,V_x_2)))) # label(fact_restrict__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 261 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2))) <-> V_x_2 != V_z_2 & (V_z_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_z_2 -> V_y_2 != V_x_2))) # label(fact_in__mktop) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 262 (all V_ba_2 all V_aa_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2))))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 263 (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]. 1.25/1.61 264 (all V_ba_2 all V_f_2 all T_b all T_a all V_aa_2 all V_x_2 ((V_aa_2 = V_x_2 -> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = V_ba_2) & (V_x_2 != V_aa_2 -> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2)))) # label(fact_fun__upd__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 265 (all V_x_2 all V_S_2 all V_f_2 all T_b all V_T_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_T_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_f_2),c_FuncSet_Oextensional__funcset(T_b,T_a,V_S_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_T_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_aa_2)),c_FuncSet_Oextensional__funcset(T_b,T_a,c_Set_Oinsert(T_b,V_x_2,V_S_2),V_T_2)))))) # label(fact_extensional__funcset__fun__upd__extends__rangeI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 266 (all V_x_2 all V_r_2 all T_a (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(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(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,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)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_accp__acc__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 267 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a (c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2,hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2)) <-> (exists B_g (hAPP(hAPP(V_Fa_2,B_g),V_a1_2) = hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_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_a1_2)),V_R_2)) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(B_g,B_z)))))))) # label(fact_wfrec__rel_Oequations) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 268 (all V_aa_2 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_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 269 (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]. 1.25/1.61 270 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) # label(fact_sup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 271 (all V_T_2 all V_f_2 all T_b all V_S_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional__funcset(T_a,T_b,c_Set_Oinsert(T_a,V_x_2,V_S_2),V_T_2))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,c_HOL_Oundefined(T_b))),c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2)))))) # label(fact_extensional__funcset__restrict__domain) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 272 (all V_f_2 all V_r_2 all T_b all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_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_Relation_Oinv__image(T_b,T_a,V_r_2,V_f_2))))) # label(fact_in__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 273 (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_Otrancl(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_Otrancl(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_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__trans) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 274 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 275 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x))) # label(fact_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 276 (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]. 1.25/1.61 277 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 278 (all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) = c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Id__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 279 (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]. 1.25/1.61 280 (all V_x_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 281 (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]. 1.25/1.61 282 (all V_x all V_y all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 283 (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,hAPP(hAPP(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]. 1.25/1.61 284 (all V_x all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b),V_x) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x))))) # label(fact_le__supE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 285 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b),V_x)))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 286 (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_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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 287 (all V_ba_2 all V_aa_2 all V_f_2 all T_b all T_a (hBOOL(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]. 1.25/1.61 288 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x)) # label(fact_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 289 (all V_Pa_2 all V_B_2 all V_A_2 all T_a ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x (hBOOL(hAPP(V_Pa_2,B_x)) & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)))) | (exists B_x (hBOOL(hAPP(V_Pa_2,B_x)) & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 290 (all V_r_2 all V_aa_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),V_aa_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 291 (all V_P all T_a hAPP(c_COMBI(T_a),V_P) = V_P) # label(help_c__COMBI__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 292 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a c_Set_Oinsert(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2)) = c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(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))) # label(fact_Domain__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 293 (all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x)) # label(fact_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 294 (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)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_x_2),V_y_2)))) # label(fact_r__into__rtranclp) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 295 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 296 (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_z = B_y)))))) # label(fact_single__valued__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 297 (all V_x all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a),V_x))) # label(fact_bot__least) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 298 (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]. 1.25/1.61 299 (all V_aa_2 all V_ba_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2)) -> (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2))))) # label(fact_accp__downwards__aux) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 300 (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_Otrancl(T_a,V_R_2))) -> (exists 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_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),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))))))) # label(fact_tranclD2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 301 (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),hAPP(hAPP(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]. 1.25/1.61 302 (all V_C_2 all V_B_2 all V_aa_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_B_2)),V_C_2) = c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.61 303 (all V_C_2 all V_J_2 all V_I_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_C_2)),c_Product__Type_OSigma(T_a,T_b,V_J_2,V_C_2))) # label(fact_Sigma__Int__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 304 (all V_i_2 all V_Fa_2 (c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2))))) # label(fact_dictator__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 305 (all V_x_2 all T_b all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Obot__class_Obot(T_a) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2))) # label(fact_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 306 (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,V_y_2) <-> V_x_2 = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2)))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 307 (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_B_2,V_A_2))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 308 (all V_Q_2 all V_Pa_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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_Pa_2),V_Q_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),V_aa_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_Pa_2))) -> (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_Q_2)) -> B_y = B_x)))) -> 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_Pa_2)))))) # label(fact_rtrancl__Un__separatorE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 309 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y),V_y))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 310 (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]. 1.25/1.62 311 (all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) = c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_trancl__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 312 (all V_y_2 all V_x_2 all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) <-> c_Orderings_Obot__class_Obot(T_a) = V_y_2 & c_Orderings_Obot__class_Obot(T_a) = V_x_2))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 313 (all V_x_2 all V_S_2 all V_f_2 all T_b all V_T_2 all V_y_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_T_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_f_2),c_FuncSet_Oextensional__funcset(T_b,T_a,V_S_2,V_T_2))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2)),c_FuncSet_Oextensional__funcset(T_b,T_a,c_Set_Oinsert(T_b,V_x_2,V_S_2),V_T_2)))))) # label(fact_extensional__funcset__extend__domainI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 314 (all V_Fa_2 all V_R_2 all T_b all T_a c_Recdef_Oadm__wf(T_a,T_b,V_R_2,hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(T_a,T_a),tc_fun(T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_b)),tc_fun(T_a,T_b),c_COMBS(T_a,T_a,T_b)),hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,tc_fun(T_a,T_b)),tc_fun(T_a,T_b),c_COMBB(tc_fun(T_a,T_b),tc_fun(T_a,T_b),T_a,V_Fa_2)),hAPP(hAPP(c_COMBC(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_fun(T_a,T_b))),c_Recdef_Ocut(T_a,T_b)),V_R_2)))),c_COMBI(T_a)))) # label(fact_adm__lemma) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 315 (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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____))))) # label(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 316 (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)) -> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x))))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 317 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_aa_2 = V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_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]. 1.25/1.62 318 (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]. 1.25/1.62 319 (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_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]. 1.25/1.62 320 (all V_g_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))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x))) -> V_f_2 = V_g_2)))) # label(fact_extensionalityI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 321 (all V_B_2 all T_b all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) = c_Product__Type_OSigma(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) # label(fact_Sigma__empty1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 322 (all V_B_2 all V_A_2 all V_I_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,V_I_2,hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_A_2)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_B_2))) # label(fact_Sigma__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 323 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 324 (all V_B_2 all V_aa_2 all T_a hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)))) # label(fact_insertI1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 325 (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(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]. 1.25/1.62 326 (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(T_a,tc_HOL_Obool),c_Relation_OField(T_a,V_r_2),c_Relation_OField(T_a,V_s_2)))) # label(fact_mono__Field) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 327 (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]. 1.25/1.62 328 (all V_y_2 all V_f_2 all T_b all T_a all V_x_2 all V_z_2 ((V_x_2 = V_z_2 -> V_y_2 = hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2)) & (V_x_2 != V_z_2 -> hAPP(V_f_2,V_z_2) = hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2)))) # label(fact_fun__upd__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 329 (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),hAPP(hAPP(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]. 1.25/1.62 330 (all V_aa_2 all T_a all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 331 (all V_r_2 all T_a c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_r_2),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot)),c_fequal))) = c_Transitive__Closure_Ortranclp(T_a,V_r_2)) # label(fact_rtranclp__r__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 332 (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,hAPP(hAPP(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]. 1.25/1.62 333 (all V_ca_2 all T_a -hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 334 (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]. 1.25/1.62 335 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Relation_Orefl__on(T_a,V_A_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)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))))) # label(fact_refl__onD2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 336 (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]. 1.25/1.62 337 (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]. 1.25/1.62 338 (all V_S_2 all V_R_2 all T_a c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),c_Transitive__Closure_Ortranclp(T_a,V_R_2)),c_Transitive__Closure_Ortranclp(T_a,V_S_2))) = c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R_2),V_S_2))) # label(fact_rtranclp__sup__rtranclp) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 339 (all V_ba_2 all V_aa_2 all V_r_2 all T_a (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) -> (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_aa_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2))))) # label(fact_accp__downwards) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 340 (all V_x_2 all V_T_2 all V_S_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__funcset(T_a,T_b,V_S_2,V_T_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_S_2)) -> hAPP(V_f_2,V_x_2) = c_HOL_Oundefined(T_b)))) # label(fact_extensional__funcset__arb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 341 (all T_2 all T_1 (class_Orderings_Obot(T_1) -> class_Orderings_Obot(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Obot) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 342 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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]. 1.25/1.62 343 (all V_ba_2 all V_B_2 all V_aa_2 all T_a ((-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) -> V_aa_2 = V_ba_2) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))))) # label(fact_insertCI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 344 (all V_f_2 all T_b all V_r_2 all V_x_2 all V_y_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_y_2),V_x_2)),V_r_2)) -> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2) = c_HOL_Oundefined(T_b)) & (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_x_2)),V_r_2)) -> hAPP(V_f_2,V_y_2) = hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2),V_y_2)))) # label(fact_cut__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 345 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_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),v_a____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) # label(fact_ac) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 346 (all V_R_2 all T_a c_Transitive__Closure_Ortranclp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R_2),c_fequal)) = c_Transitive__Closure_Ortranclp(T_a,V_R_2)) # label(fact_rtranclp__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 347 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d)))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 348 (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) -> V_y = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 349 (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_Otrancl(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_Otrancl(T_a,V_r_2)))))) # label(fact_Transitive__Closure_Otrancl__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 350 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x)) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 351 (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(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]. 1.25/1.62 352 (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) = 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))) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 353 (all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a))) # label(fact_single__valued__Id) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 354 (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]. 1.25/1.62 355 (all V_ba_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_A_2,c_Set_Oinsert(T_a,V_ba_2,V_B_2)))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 356 (all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 all T_b all T_a (V_b_H_2 = V_ba_2 & V_aa_2 = V_a_H_2 <-> hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2))) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 357 (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_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))))))) <-> c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2))) # label(fact_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 358 (all V_B_2 all V_A_2 all T_a (V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) & c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 359 (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]. 1.25/1.62 360 (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]. 1.25/1.62 361 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 362 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 363 (all V_S_2 all V_R_2 all T_a (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)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2,V_S_2))) # label(fact_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 364 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) = hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2))) # label(fact_sup__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 365 (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_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 366 (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]. 1.25/1.62 367 (all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x)) # label(fact_sup__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 368 (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_Otrancl(T_a,V_r_2)))))) # label(fact_rtrancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 369 (all V_C_2 all V_B_2 all V_A_2 all T_a (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 370 (all T_b all T_a all V_Pa_2 ((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)))) <-> (all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 371 (all V_x_2 all V_f_2 all T_b all T_a c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2) # label(fact_fun__upd__triv) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 372 (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_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_Relation_OId__on(T_a,V_A_2))))) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 373 (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]. 1.25/1.62 374 (all V_y all V_x 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__eq(T_a,V_x,V_y))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 375 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)))) # label(fact_ab) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 376 (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]. 1.25/1.62 377 (all V_xa_2 all V_x_2 all V_r_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_xa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) <-> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(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(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(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,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_rtranclp__rtrancl__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 378 (all V_A_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_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_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_x)),V_r_2)))) -> c_Relation_Orefl__on(T_a,V_A_2,V_r_2)))) # label(fact_refl__onI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 379 (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(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),V_x_2))) # label(fact_RangeP__Range__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 380 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 381 (all V_B_2 all V_A_2 all T_a all T_b c_Relation_ORange(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Relation_ORange(T_b,T_a,V_A_2)),c_Relation_ORange(T_b,T_a,V_B_2))) # label(fact_Range__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 382 (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_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_C_2)))) # label(fact_Un__least) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 383 (all V_r_2 all T_a c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2)) # label(fact_total__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 384 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2))) # label(fact_rtrancl__trancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 385 (all V_B_2 all V_A_2 all T_b all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = V_B_2 | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> c_Product__Type_OSigma(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) # label(fact_Times__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 386 (all V_g_2 all V_x_2 all V_r_2 all V_f_2 all T_b all T_a (hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_g_2),V_r_2),V_x_2) = hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_x_2) <-> (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)) -> hAPP(V_f_2,B_y) = hAPP(V_g_2,B_y))))) # label(fact_cuts__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 387 (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(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_sup2E) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 388 (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]. 1.25/1.62 389 (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]. 1.25/1.62 390 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))) # label(fact_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 391 (all V_A_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_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Product__Type_OSigma(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))))) # label(fact_trancl__subset__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 392 (all V_r_2 all T_a (c_Relation_Oirrefl(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),B_x)),V_r_2))))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 393 (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_aa_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl_Or__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 394 (all V_B_2 all T_a all V_A_2 (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) = V_A_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_less__by__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 395 (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]. 1.25/1.62 396 (all V_B_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 397 (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) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) <-> V_y_2 = V_x_2))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 398 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 399 (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]. 1.25/1.62 400 (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_Otrancl(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_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 401 (all V_B_2 all V_A_2 all T_a (V_B_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 402 (all V_ca_2 all V_ba_2 all V_aa_2 all V_r_2 all T_a (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ba_2)) -> (hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2))))) # label(fact_rtranclp_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 403 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 404 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 405 (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]. 1.25/1.62 406 (all V_B_2 all V_C_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_C_2)) -> c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a,V_aa_2,V_B_2)),V_C_2))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 407 (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(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]. 1.25/1.62 408 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) # label(fact_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 409 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(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__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 410 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x)) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 411 (all V_R_2 all V_Q_2 all V_Pa_2 all T_c all T_a all T_b hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 412 (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]. 1.25/1.62 413 (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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_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),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,B_i)),v_c____),v_b____)),v_b____),v_a____))))) # label(fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) # label(axiom) # label(non_clause). [assumption]. 1.25/1.62 414 (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]. 1.25/1.62 415 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(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]. 1.25/1.62 416 (all V_x_2 all V_Fa_2 all V_R_2 all T_a all T_b c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_Fa_2,V_x_2) = hAPP(hAPP(V_Fa_2,hAPP(hAPP(hAPP(c_Recdef_Ocut(T_b,T_a),c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_Fa_2)),V_R_2),V_x_2)),V_x_2)) # label(fact_Nitpick_Owf__wfrec_H__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 417 (all V_r_2 all T_a c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ORange(T_a,T_a,V_r_2)) # label(fact_trancl__range) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 418 (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_Relation_OId(T_a)))) # label(fact_IdI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 419 (all V_y_2 all V_x_2 all V_r_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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) <-> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),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(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(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,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)),c_fequal),V_x_2),V_y_2)))) # label(fact_reflcl__set__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 420 (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]. 1.25/1.63 421 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 422 (all V_B_2 all T_b all T_a 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(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_sup2I1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 423 (all V_ba_2 all V_aa_2 all T_a (c_Set_Oinsert(T_a,V_ba_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) -> V_aa_2 = V_ba_2)) # label(fact_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 424 (all V_y_2 all V_x_2 all V_R_2 all T_b all T_a (c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)))) # label(fact_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 425 (all V_C_2 all V_J_2 all V_I_2 all T_b all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_C_2)),c_Product__Type_OSigma(T_a,T_b,V_J_2,V_C_2)) = c_Product__Type_OSigma(T_a,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2),V_C_2)) # label(fact_Sigma__Un__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 426 (all T_a c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_refl__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 427 (all V_B_2 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 428 (all V_B_2 all V_A_2 all V_I_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,V_I_2,hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_A_2)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_B_2))) # label(fact_Sigma__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 429 (all V_S_2 all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))) # label(fact_rtrancl__Un__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 430 (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))) -> 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)) = V_g_2))) # label(fact_compose__Id) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 431 (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]. 1.25/1.63 432 (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__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]. 1.25/1.63 433 (all V_aa_2 all T_a -hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_emptyE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 434 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> V_x = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)))) # label(fact_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 435 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 436 (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) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 437 (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]. 1.25/1.63 438 (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]. 1.25/1.63 439 (all V_A_2 all T_a c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2))) # label(fact_refl__on__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 440 (all T_b all T_a c_FuncSet_Oextensional(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(tc_fun(T_a,T_b),c_COMBK(T_b,T_a,c_HOL_Oundefined(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) # label(fact_extensional__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 441 (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))) -> (V_ba_2 != V_aa_2 -> -(all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),B_y)),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),B_y),V_ba_2)),V_r_2))))))) # label(fact_rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 442 (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]. 1.25/1.63 443 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 444 (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]. 1.25/1.63 445 (all V_d_2 all V_ba_2 all V_m_2 all T_b all T_a all V_ca_2 all V_aa_2 (V_aa_2 != V_ca_2 -> c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_ca_2,V_d_2),V_aa_2,V_ba_2) = c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_aa_2,V_ba_2),V_ca_2,V_d_2))) # label(fact_fun__upd__twist) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 446 (all V_ba_2 all V_B_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))))) # label(fact_insertI2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 447 (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]. 1.25/1.63 448 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(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]. 1.25/1.63 449 (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_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2) = V_f_2)) # label(fact_extensional__restrict) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 450 (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]. 1.25/1.63 451 (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_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))) # label(fact_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 452 (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]. 1.25/1.63 453 (all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 454 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 455 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(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]. 1.25/1.63 456 (all V_A_2 all V_B_2 all V_ca_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnI2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 457 (all V_S_2 all V_R_2 all T_a (hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) <-> V_R_2 = V_S_2)) # label(fact_pred__equals__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 458 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))))) # label(fact_distrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 459 (all V_A_2 all T_a all V_x_2 all V_B_2 (hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1I2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 460 (all V_ca_2 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)) -> (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_ba_2),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_ca_2))))) # label(fact_converse__rtranclp__into__rtranclp) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 461 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 462 (all T_b all V_aa_2 all V_x_2 all T_a all B_f all B_R (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_aa_2)),B_R)) -> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),B_f),B_R),V_aa_2),V_x_2) = hAPP(B_f,V_x_2))) # label(fact_tfl__cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 463 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) | V_ba_2 = V_aa_2)) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 464 (all T_b all T_a all V_A_2 all V_y_2 all V_x_2 all V_B_2 ((-hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_sup2CI) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 465 (all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 466 (all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 467 (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]. 1.25/1.63 468 (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]. 1.25/1.63 469 (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__2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 470 (all V_B_2 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)))) # label(fact_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 471 (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_y_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))))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 472 (all V_C_2 all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 473 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 474 (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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b),V_x)))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 475 (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]. 1.25/1.63 476 (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_z_2 = V_y_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 477 (all V_f_2 all T_b all V_r_2 all V_aa_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_aa_2)),V_r_2)) -> hAPP(V_f_2,V_x_2) = hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),V_f_2),V_r_2),V_aa_2),V_x_2))) # label(fact_cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 478 (all V_r_2 all V_s_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_s_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Wellfounded_Oacyclic(T_a,V_r_2)))) # label(fact_acyclic__subset) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 479 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R_2,V_S_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_S_2,c_Transitive__Closure_Ortranclp(T_a,V_R_2)) -> c_Transitive__Closure_Ortranclp(T_a,V_S_2) = c_Transitive__Closure_Ortranclp(T_a,V_R_2)))) # label(fact_rtranclp__subset) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 480 (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) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))))) # label(fact_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 481 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))) # label(fact_sup__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 482 (all V_r_2 all V_x_2 all V_y_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))) & c_Wellfounded_Oacyclic(T_a,V_r_2) <-> c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2),V_r_2)))) # label(fact_acyclic__insert) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 483 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 484 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortranclp(T_a,V_r_2),c_Transitive__Closure_Ortranclp(T_a,V_s_2)))) # label(fact_rtranclp__mono) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 485 (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(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]. 1.25/1.63 486 (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]. 1.25/1.63 487 (all V_A_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Int__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 488 (all V_B_2 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) & (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Set_Oinsert(T_a,V_aa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))))) # label(fact_Int__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 489 (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]. 1.25/1.63 490 (all V_x_2 all V_S_2 all V_R_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) <-> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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)))) # label(fact_sup__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 491 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 492 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 493 (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]. 1.25/1.63 494 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))))) # label(fact_distrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 495 (all V_r_2 all T_a c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2)) # label(fact_trancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 496 (all V_B_2 all V_A_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 497 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 498 (all V_A_2 all T_b all T_a all V_y_2 all V_x_2 all V_B_2 (hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_sup2I2) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 499 (all V_aa_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) <-> V_aa_2 = V_ba_2)) # label(fact_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 500 (all V_ba_2 all V_aa_2 all V_f_2 all T_a all T_c all T_b c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2,V_aa_2,V_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2))) # label(fact_curry__conv) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 501 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))) # label(fact_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 502 (all V_aa_2 all V_r_2 all T_a hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_aa_2))) # label(fact_rtranclp_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 1.25/1.63 503 (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]. 1.25/1.63 504 -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))),v_a____)),v_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),v_b____),v_c____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____))),v_b____)),v_a____))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 1.25/1.64 1.25/1.64 ============================== end of process non-clausal formulas === 1.25/1.64 1.25/1.64 ============================== PROCESS INITIAL CLAUSES =============== 1.25/1.64 1.25/1.64 ============================== PREDICATE ELIMINATION ================= 1.25/1.64 505 class_Lattices_Osemilattice__sup(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.25/1.64 506 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),D)) # label(fact_sup__assoc) # label(axiom). [clausify(8)]. 1.25/1.64 507 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D)) # label(fact_sup_Oleft__commute) # label(axiom). [clausify(21)]. 1.25/1.64 508 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D)) # label(fact_sup__left__commute) # label(axiom). [clausify(26)]. 1.25/1.64 509 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),D),C)) # label(fact_le__supI2) # label(axiom). [clausify(85)]. 1.25/1.64 510 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),B)) # label(fact_sup__ge2) # label(axiom). [clausify(96)]. 1.25/1.64 511 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) != C | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__sup) # label(axiom). [clausify(166)]. 1.25/1.64 512 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) = C | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__sup) # label(axiom). [clausify(166)]. 1.25/1.64 513 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C)) # label(fact_sup__ge1) # label(axiom). [clausify(179)]. 1.25/1.64 514 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) # label(fact_sup__left__idem) # label(axiom). [clausify(207)]. 1.25/1.64 515 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) = C # label(fact_sup__absorb2) # label(axiom). [clausify(211)]. 1.25/1.64 516 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),B) = B # label(fact_sup_Oidem) # label(axiom). [clausify(215)]. 1.25/1.64 517 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D),C) # label(fact_le__supI) # label(axiom). [clausify(228)]. 1.25/1.64 518 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D),C) # label(fact_le__sup__iff) # label(axiom). [clausify(246)]. 1.25/1.64 519 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D),C) # label(fact_le__sup__iff) # label(axiom). [clausify(246)]. 1.25/1.64 520 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),D),B),C) # label(fact_le__sup__iff) # label(axiom). [clausify(246)]. 1.25/1.64 521 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),D)) # label(fact_le__supI1) # label(axiom). [clausify(248)]. 1.25/1.64 522 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D),C) # label(fact_sup__least) # label(axiom). [clausify(249)]. 1.25/1.64 523 -class_Lattices_Osemilattice__sup(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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),E)) # label(fact_sup__mono) # label(axiom). [clausify(252)]. 1.25/1.64 524 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),B) # label(fact_sup_Ocommute) # label(axiom). [clausify(270)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),C)). [resolve(505,a,506,a)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),C)). [resolve(505,a,507,a)]. 1.25/1.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),C),B)). [resolve(505,a,509,a)]. 1.25/1.64 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),A)). [resolve(505,a,510,a)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B) != B | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(505,a,511,a)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B) = B | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(505,a,512,a)]. 1.25/1.64 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B)). [resolve(505,a,513,a)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B). [resolve(505,a,514,a)]. 1.25/1.64 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),A) = A. [resolve(505,a,516,a)]. 1.25/1.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),C),B). [resolve(505,a,517,a)]. 1.40/1.65 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),C),B). [resolve(505,a,519,a)]. 1.40/1.65 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),C),A),B). [resolve(505,a,520,a)]. 1.40/1.65 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),C)). [resolve(505,a,521,a)]. 1.40/1.65 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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),D)). [resolve(505,a,523,a)]. 1.40/1.65 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),A). [resolve(505,a,524,a)]. 1.40/1.65 525 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__supE) # label(axiom). [clausify(284)]. 1.40/1.65 526 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C),D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_le__supE) # label(axiom). [clausify(284)]. 1.40/1.65 527 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__sup(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom). [clausify(295)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),E)). [resolve(527,b,506,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),E)). [resolve(527,b,507,a)]. 1.40/1.65 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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),E),D)). [resolve(527,b,509,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),C)). [resolve(527,b,510,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) != D | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(527,b,511,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) = D | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(527,b,512,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D)). [resolve(527,b,513,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D). [resolve(527,b,514,a)]. 1.40/1.65 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(527,b,516,a)]. 1.40/1.65 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,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),E),D). [resolve(527,b,517,a)]. 1.40/1.66 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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),E),D). [resolve(527,b,519,a)]. 1.40/1.66 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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),E),C),D). [resolve(527,b,520,a)]. 1.40/1.66 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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),E)). [resolve(527,b,521,a)]. 1.40/1.66 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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),F)). [resolve(527,b,523,a)]. 1.40/1.66 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),C). [resolve(527,b,524,a)]. 1.40/1.66 528 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),B) = B # label(fact_sup__idem) # label(axiom). [clausify(367)]. 1.40/1.66 529 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) # label(fact_sup_Oleft__idem) # label(axiom). [clausify(408)]. 1.40/1.66 530 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),B) = C # label(fact_sup__absorb1) # label(axiom). [clausify(481)]. 1.40/1.66 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),B),A) = B. [resolve(530,a,505,a)]. 1.40/1.66 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B)),D),C) = D | -class_Lattices_Olattice(B). [resolve(530,a,527,b)]. 1.40/1.66 531 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),D)) # label(fact_sup_Oassoc) # label(axiom). [clausify(483)]. 1.40/1.66 532 class_Lattices_Osemilattice__sup(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.40/1.66 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B)),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),C)). [resolve(532,a,506,a)]. 1.40/1.66 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),C)). [resolve(532,a,507,a)]. 1.40/1.66 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),C),B)). [resolve(532,a,509,a)]. 1.40/1.66 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),A)). [resolve(532,a,510,a)]. 1.40/1.66 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) != B | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(532,a,511,a)]. 1.43/1.70 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) = B | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(532,a,512,a)]. 1.43/1.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B)). [resolve(532,a,513,a)]. 1.43/1.70 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B). [resolve(532,a,514,a)]. 1.43/1.70 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),A) = A. [resolve(532,a,516,a)]. 1.43/1.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),C),B). [resolve(532,a,517,a)]. 1.43/1.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),C),B). [resolve(532,a,519,a)]. 1.43/1.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),C),A),B). [resolve(532,a,520,a)]. 1.43/1.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),C)). [resolve(532,a,521,a)]. 1.43/1.70 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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),C),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),D)). [resolve(532,a,523,a)]. 1.43/1.70 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),A). [resolve(532,a,524,a)]. 1.43/1.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),B),A) = B. [resolve(532,a,530,a)]. 1.43/1.70 533 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),C),B) # label(fact_sup__commute) # label(axiom). [clausify(492)]. 1.43/1.70 534 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(13)]. 1.43/1.70 535 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f7(B,A)),f7(B,A))),B)) | c_Nitpick_Orefl_H(A,B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(13)]. 1.43/1.70 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),f7(C,A)),f7(C,A))),C)). [resolve(534,b,535,b)]. 1.43/1.70 536 c_Relation_Ototal__on(A,B,C) | hBOOL(hAPP(hAPP(c_member(A),f8(C,B,A)),B)) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.43/1.70 537 -c_Relation_Ototal__on(A,B,C) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | -hBOOL(hAPP(hAPP(c_member(A),E),B)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),D)),C)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),D),E)),C)) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.43/1.70 Derived: hBOOL(hAPP(hAPP(c_member(A),f8(B,C,A)),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),C)) | -hBOOL(hAPP(hAPP(c_member(A),E),C)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),D)),B)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),D),E)),B)). [resolve(536,a,537,a)]. 1.43/1.70 538 c_Relation_Ototal__on(A,B,C) | hBOOL(hAPP(hAPP(c_member(A),f9(C,B,A)),B)) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.52/1.78 Derived: hBOOL(hAPP(hAPP(c_member(A),f9(B,C,A)),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),C)) | -hBOOL(hAPP(hAPP(c_member(A),E),C)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),D)),B)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),D),E)),B)). [resolve(538,a,537,a)]. 1.52/1.78 539 c_Relation_Ototal__on(A,B,C) | f9(C,B,A) != f8(C,B,A) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.52/1.78 Derived: f9(A,B,C) != f8(A,B,C) | -hBOOL(hAPP(hAPP(c_member(C),D),B)) | -hBOOL(hAPP(hAPP(c_member(C),E),B)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(C,C)),hAPP(hAPP(c_Product__Type_OPair(C,C),E),D)),A)) | hBOOL(hAPP(hAPP(c_member(tc_prod(C,C)),hAPP(hAPP(c_Product__Type_OPair(C,C),D),E)),A)). [resolve(539,a,537,a)]. 1.52/1.78 540 c_Relation_Ototal__on(A,B,C) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f9(C,B,A)),f8(C,B,A))),C)) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.52/1.78 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f9(B,C,A)),f8(B,C,A))),B)) | -hBOOL(hAPP(hAPP(c_member(A),D),C)) | -hBOOL(hAPP(hAPP(c_member(A),E),C)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),D)),B)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),D),E)),B)). [resolve(540,a,537,a)]. 1.52/1.78 541 c_Relation_Ototal__on(A,B,C) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f8(C,B,A)),f9(C,B,A))),C)) # label(fact_total__on__def) # label(axiom). [clausify(16)]. 1.52/1.78 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f8(B,C,A)),f9(B,C,A))),B)) | -hBOOL(hAPP(hAPP(c_member(A),D),C)) | -hBOOL(hAPP(hAPP(c_member(A),E),C)) | E = D | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),D)),B)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),D),E)),B)). [resolve(541,a,537,a)]. 1.52/1.78 542 c_Relation_Ototal__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),B) # label(fact_total__on__empty) # label(axiom). [clausify(383)]. 1.52/1.78 543 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 1.52/1.78 544 -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(37)]. 1.52/1.78 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(543,a,544,a)]. 1.52/1.78 545 -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(374)]. 1.52/1.78 546 -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,f81(D,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(D,A))) | -c_Arrow__Order__Mirabelle_Ounanimity(D) # label(fact_unanimity__def) # label(axiom). [clausify(357)]. 1.52/1.78 547 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(fact_u) # label(axiom). [assumption]. 1.52/1.78 548 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))),f78(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(357)]. 1.52/1.78 549 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f79(A)),f80(A))),hAPP(f78(A),B))) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(357)]. 1.52/1.80 550 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f79(A)),f80(A))),hAPP(A,f78(A)))) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(357)]. 1.52/1.80 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,f81(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(546,d,547,a)]. 1.52/1.80 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,f81(D,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(D,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))),f78(D)),c_Arrow__Order__Mirabelle_OProf)). [resolve(546,d,548,b)]. 1.52/1.80 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,f81(D,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(D,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),f79(D)),f80(D))),hAPP(f78(D),E))). [resolve(546,d,549,b)]. 1.52/1.80 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,f81(D,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(D,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),f79(D)),f80(D))),hAPP(D,f78(D)))). [resolve(546,d,550,b)]. 1.52/1.80 551 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(105)]. 1.52/1.81 552 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C),B) # label(fact_inf__le1) # label(axiom). [clausify(40)]. 1.52/1.81 553 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) # label(fact_inf__left__idem) # label(axiom). [clausify(64)]. 1.52/1.81 554 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(100)]. 1.52/1.81 555 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(100)]. 1.52/1.81 556 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__inf__iff) # label(axiom). [clausify(100)]. 1.52/1.81 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D),C). [resolve(551,b,552,a)]. 1.52/1.81 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D). [resolve(551,b,553,a)]. 1.52/1.81 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(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(551,b,554,a)]. 1.52/1.81 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(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(551,b,555,a)]. 1.52/1.81 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),D),E)) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D). [resolve(551,b,556,a)]. 1.52/1.81 557 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),D)) # label(fact_inf_Oleft__commute) # label(axiom). [clausify(119)]. 1.52/1.81 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),E)) | -class_Lattices_Olattice(B). [resolve(557,a,551,b)]. 1.52/1.81 558 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),B) # label(fact_inf_Ocommute) # label(axiom). [clausify(218)]. 1.52/1.81 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),D) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),C) | -class_Lattices_Olattice(B). [resolve(558,a,551,b)]. 1.52/1.81 559 -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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) # label(fact_le__infI) # label(axiom). [clausify(233)]. 1.52/1.81 560 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) # label(fact_inf_Oassoc) # label(axiom). [clausify(277)]. 1.57/1.81 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),D)),E) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),E)) | -class_Lattices_Olattice(B). [resolve(560,a,551,b)]. 1.57/1.81 561 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(283)]. 1.57/1.81 562 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(283)]. 1.57/1.81 563 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),D),C) # label(fact_le__infI1) # label(axiom). [clausify(285)]. 1.57/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),E),D) | -class_Lattices_Olattice(B). [resolve(563,a,551,b)]. 1.57/1.81 564 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) = B # label(fact_le__iff__inf) # label(axiom). [clausify(306)]. 1.57/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),D) = C | -class_Lattices_Olattice(B). [resolve(564,a,551,b)]. 1.57/1.81 565 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) != B # label(fact_le__iff__inf) # label(axiom). [clausify(306)]. 1.57/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),D) != C | -class_Lattices_Olattice(B). [resolve(565,a,551,b)]. 1.57/1.81 566 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C),C) # label(fact_inf__le2) # label(axiom). [clausify(309)]. 1.57/1.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),D),D) | -class_Lattices_Olattice(B). [resolve(566,a,551,b)]. 1.57/1.81 567 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),D)) # label(fact_inf__left__commute) # label(axiom). [clausify(323)]. 1.57/1.81 568 -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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),E)) # label(fact_inf__mono) # label(axiom). [clausify(347)]. 1.57/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),F)) | -class_Lattices_Olattice(B). [resolve(568,a,551,b)]. 1.57/1.81 569 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),B) = B # label(fact_inf__absorb2) # label(axiom). [clausify(348)]. 1.57/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),D),C) = C | -class_Lattices_Olattice(B). [resolve(569,a,551,b)]. 1.57/1.82 570 -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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) # label(fact_inf__greatest) # label(axiom). [clausify(362)]. 1.57/1.82 571 class_Lattices_Osemilattice__inf(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.57/1.82 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B),A). [resolve(571,a,552,a)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B). [resolve(571,a,553,a)]. 1.57/1.82 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(571,a,554,a)]. 1.57/1.82 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(571,a,555,a)]. 1.57/1.82 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(571,a,556,a)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),C)). [resolve(571,a,557,a)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),A). [resolve(571,a,558,a)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)). [resolve(571,a,560,a)]. 1.57/1.82 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),C),B). [resolve(571,a,563,a)]. 1.57/1.82 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B) = A. [resolve(571,a,564,a)]. 1.57/1.82 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B) != A. [resolve(571,a,565,a)]. 1.57/1.82 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),B),B). [resolve(571,a,566,a)]. 1.57/1.82 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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),D)). [resolve(571,a,568,a)]. 1.57/1.82 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),A) = A. [resolve(571,a,569,a)]. 1.57/1.82 572 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),B) = B # label(fact_inf__idem) # label(axiom). [clausify(410)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),C),C) = C | -class_Lattices_Olattice(B). [resolve(572,a,551,b)]. 1.57/1.82 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),A) = A. [resolve(572,a,571,a)]. 1.57/1.82 573 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),B) # label(fact_inf__commute) # label(axiom). [clausify(421)]. 1.57/1.83 574 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(435)]. 1.57/1.83 575 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) = B # label(fact_inf__absorb1) # label(axiom). [clausify(436)]. 1.57/1.83 576 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) # label(fact_inf_Oleft__idem) # label(axiom). [clausify(454)]. 1.57/1.83 577 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) # label(fact_inf__assoc) # label(axiom). [clausify(461)]. 1.57/1.83 578 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),D),B),C) # label(fact_le__infI2) # label(axiom). [clausify(474)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B)),E),C),D) | -class_Lattices_Olattice(B). [resolve(578,a,551,b)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),C),A),B). [resolve(578,a,571,a)]. 1.57/1.83 579 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.57/1.83 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B),A). [resolve(579,a,552,a)]. 1.57/1.83 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B). [resolve(579,a,553,a)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(579,a,554,a)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(579,a,555,a)]. 1.57/1.83 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(579,a,556,a)]. 1.57/1.83 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),C)). [resolve(579,a,557,a)]. 1.57/1.83 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),A). [resolve(579,a,558,a)]. 1.57/1.83 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B)),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)). [resolve(579,a,560,a)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),C),B). [resolve(579,a,563,a)]. 1.57/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) = A. [resolve(579,a,564,a)]. 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) != A. [resolve(579,a,565,a)]. 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B),B). [resolve(579,a,566,a)]. 1.60/1.85 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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),D)). [resolve(579,a,568,a)]. 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),A) = A. [resolve(579,a,569,a)]. 1.60/1.85 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),A) = A. [resolve(579,a,572,a)]. 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),C),A),B). [resolve(579,a,578,a)]. 1.60/1.85 580 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption]. 1.60/1.85 581 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),c_Orderings_Obot__class_Obot(A)),B) # label(fact_inf__bot__left) # label(axiom). [clausify(99)]. 1.60/1.85 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),A). [resolve(580,a,581,a)]. 1.60/1.85 582 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),c_Orderings_Obot__class_Obot(A)) # label(fact_inf__bot__right) # label(axiom). [clausify(116)]. 1.60/1.85 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_HOL_Obool)). [resolve(582,a,580,a)]. 1.60/1.85 583 -class_Lattices_Obounded__lattice__bot(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),c_Orderings_Obot__class_Obot(A)),B) = B # label(fact_sup__bot__left) # label(axiom). [clausify(201)]. 1.60/1.85 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),A) = A. [resolve(583,a,580,a)]. 1.60/1.85 584 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) = C # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(312)]. 1.60/1.85 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = B. [resolve(584,a,580,a)]. 1.60/1.85 585 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) = B # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(312)]. 1.60/1.85 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A. [resolve(585,a,580,a)]. 1.60/1.85 586 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) != C | c_Orderings_Obot__class_Obot(A) != B # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(312)]. 1.60/1.85 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != B | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != A. [resolve(586,a,580,a)]. 1.60/1.85 587 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(361)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),c_Orderings_Obot__class_Obot(tc_fun(B,A))),C). [resolve(587,b,581,a)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),c_Orderings_Obot__class_Obot(tc_fun(B,A))). [resolve(587,b,582,a)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),c_Orderings_Obot__class_Obot(tc_fun(B,A))),C) = C. [resolve(587,b,583,a)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = D. [resolve(587,b,584,a)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C. [resolve(587,b,585,a)]. 1.60/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != D | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != C. [resolve(587,b,586,a)]. 1.60/1.88 588 -class_Lattices_Obounded__lattice__bot(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),c_Orderings_Obot__class_Obot(A)) = B # label(fact_sup__bot__right) # label(axiom). [clausify(434)]. 1.60/1.88 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(588,a,580,a)]. 1.60/1.88 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B)),C),c_Orderings_Obot__class_Obot(tc_fun(A,B))) = C | -class_Lattices_Obounded__lattice(B). [resolve(588,a,587,b)]. 1.60/1.88 589 c_Recdef_Oadm__wf(A,B,C,D) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),E),f30(D,C,B,A))),C)) | hAPP(f29(D,C,B,A),E) = hAPP(f28(D,C,B,A),E) # label(fact_adm__wf__def) # label(axiom). [clausify(127)]. 1.60/1.88 590 -c_Recdef_Oadm__wf(A,B,C,D) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f27(D,C,B,A,E,F,V6)),V6)),C)) | hAPP(hAPP(D,F),V6) = hAPP(hAPP(D,E),V6) # label(fact_adm__wf__def) # label(axiom). [clausify(127)]. 1.60/1.88 591 -c_Recdef_Oadm__wf(A,B,C,D) | hAPP(E,f27(D,C,B,A,F,E,V6)) != hAPP(F,f27(D,C,B,A,F,E,V6)) | hAPP(hAPP(D,E),V6) = hAPP(hAPP(D,F),V6) # label(fact_adm__wf__def) # label(axiom). [clausify(127)]. 1.60/1.88 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),f30(C,D,E,A))),D)) | hAPP(f29(C,D,E,A),B) = hAPP(f28(C,D,E,A),B) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f27(C,D,E,A,F,V6,V7)),V7)),D)) | hAPP(hAPP(C,V6),V7) = hAPP(hAPP(C,F),V7). [resolve(589,a,590,a)]. 1.60/1.88 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),f30(C,D,E,A))),D)) | hAPP(f29(C,D,E,A),B) = hAPP(f28(C,D,E,A),B) | hAPP(F,f27(C,D,E,A,V6,F,V7)) != hAPP(V6,f27(C,D,E,A,V6,F,V7)) | hAPP(hAPP(C,F),V7) = hAPP(hAPP(C,V6),V7). [resolve(589,a,591,a)]. 1.60/1.88 592 c_Recdef_Oadm__wf(A,B,C,D) | hAPP(hAPP(D,f29(D,C,B,A)),f30(D,C,B,A)) != hAPP(hAPP(D,f28(D,C,B,A)),f30(D,C,B,A)) # label(fact_adm__wf__def) # label(axiom). [clausify(127)]. 1.60/1.88 Derived: hAPP(hAPP(A,f29(A,B,C,D)),f30(A,B,C,D)) != hAPP(hAPP(A,f28(A,B,C,D)),f30(A,B,C,D)) | hBOOL(hAPP(hAPP(c_member(tc_prod(D,D)),hAPP(hAPP(c_Product__Type_OPair(D,D),f27(A,B,C,D,E,F,V6)),V6)),B)) | hAPP(hAPP(A,F),V6) = hAPP(hAPP(A,E),V6). [resolve(592,a,590,a)]. 1.60/1.88 Derived: hAPP(hAPP(A,f29(A,B,C,D)),f30(A,B,C,D)) != hAPP(hAPP(A,f28(A,B,C,D)),f30(A,B,C,D)) | hAPP(E,f27(A,B,C,D,F,E,V6)) != hAPP(F,f27(A,B,C,D,F,E,V6)) | hAPP(hAPP(A,E),V6) = hAPP(hAPP(A,F),V6). [resolve(592,a,591,a)]. 1.60/1.88 593 c_Recdef_Oadm__wf(A,B,C,hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(A,A),tc_fun(A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(tc_fun(A,A),tc_fun(A,B)),tc_fun(A,B),c_COMBS(A,A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(A,tc_fun(A,B)),tc_fun(A,B),c_COMBB(tc_fun(A,B),tc_fun(A,B),A,D)),hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(tc_prod(A,A),tc_HOL_Obool),tc_fun(A,tc_fun(A,B))),c_Recdef_Ocut(A,B)),C)))),c_COMBI(A))) # label(fact_adm__lemma) # label(axiom). [clausify(314)]. 1.60/1.91 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f27(hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(A,A),tc_fun(A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(tc_fun(A,A),tc_fun(A,B)),tc_fun(A,B),c_COMBS(A,A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(A,tc_fun(A,B)),tc_fun(A,B),c_COMBB(tc_fun(A,B),tc_fun(A,B),A,C)),hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(tc_prod(A,A),tc_HOL_Obool),tc_fun(A,tc_fun(A,B))),c_Recdef_Ocut(A,B)),D)))),c_COMBI(A)),D,B,A,E,F,V6)),V6)),D)) | hAPP(hAPP(hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(A,A),tc_fun(A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(tc_fun(A,A),tc_fun(A,B)),tc_fun(A,B),c_COMBS(A,A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(A,tc_fun(A,B)),tc_fun(A,B),c_COMBB(tc_fun(A,B),tc_fun(A,B),A,C)),hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(tc_prod(A,A),tc_HOL_Obool),tc_fun(A,tc_fun(A,B))),c_Recdef_Ocut(A,B)),D)))),c_COMBI(A)),F),V6) = hAPP(hAPP(hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(A,A),tc_fun(A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(tc_fun(A,A),tc_fun(A,B)),tc_fun(A,B),c_COMBS(A,A,B)),hAPP(c_COMBB(tc_fun(A,tc_fun(A,B)),tc_fun(A,tc_fun(A,B)),tc_fun(A,B),c_COMBB(tc_fun(A,B),tc_fun(A,B),A,C)),hAPP(hAPP(c_COMBC(tc_fun(A,B),tc_fun(tc_prod(A,A),tc_HOL_Obool),tc_fun(A,tc_fun(A,B))),c_Recdef_Ocut(A,B)),D)))),c_COMBI(A)),E),V6). [resolve(593,a,590,a)]. 1.60/1.91 Derived: hAPP(A,f27(hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(B,B),tc_fun(B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(tc_fun(B,B),tc_fun(B,C)),tc_fun(B,C),c_COMBS(B,B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(B,tc_fun(B,C)),tc_fun(B,C),c_COMBB(tc_fun(B,C),tc_fun(B,C),B,D)),hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(tc_prod(B,B),tc_HOL_Obool),tc_fun(B,tc_fun(B,C))),c_Recdef_Ocut(B,C)),E)))),c_COMBI(B)),E,C,B,F,A,V6)) != hAPP(F,f27(hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(B,B),tc_fun(B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(tc_fun(B,B),tc_fun(B,C)),tc_fun(B,C),c_COMBS(B,B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(B,tc_fun(B,C)),tc_fun(B,C),c_COMBB(tc_fun(B,C),tc_fun(B,C),B,D)),hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(tc_prod(B,B),tc_HOL_Obool),tc_fun(B,tc_fun(B,C))),c_Recdef_Ocut(B,C)),E)))),c_COMBI(B)),E,C,B,F,A,V6)) | hAPP(hAPP(hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(B,B),tc_fun(B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(tc_fun(B,B),tc_fun(B,C)),tc_fun(B,C),c_COMBS(B,B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(B,tc_fun(B,C)),tc_fun(B,C),c_COMBB(tc_fun(B,C),tc_fun(B,C),B,D)),hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(tc_prod(B,B),tc_HOL_Obool),tc_fun(B,tc_fun(B,C))),c_Recdef_Ocut(B,C)),E)))),c_COMBI(B)),A),V6) = hAPP(hAPP(hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(B,B),tc_fun(B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(tc_fun(B,B),tc_fun(B,C)),tc_fun(B,C),c_COMBS(B,B,C)),hAPP(c_COMBB(tc_fun(B,tc_fun(B,C)),tc_fun(B,tc_fun(B,C)),tc_fun(B,C),c_COMBB(tc_fun(B,C),tc_fun(B,C),B,D)),hAPP(hAPP(c_COMBC(tc_fun(B,C),tc_fun(tc_prod(B,B),tc_HOL_Obool),tc_fun(B,tc_fun(B,C))),c_Recdef_Ocut(B,C)),E)))),c_COMBI(B)),F),V6). [resolve(593,a,591,a)]. 1.60/1.91 594 -c_Arrow__Order__Mirabelle_Odictator(A,B) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B) # label(fact_dictator__def) # label(axiom). [clausify(304)]. 1.60/1.91 595 -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))),f31(B,A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(132)]. 1.60/1.91 596 -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)))) | f33(B,A) != f32(B,A) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(132)]. 1.60/1.91 597 -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),f32(B,A)),f33(B,A))),hAPP(f31(B,A),B))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(132)]. 1.60/1.91 598 -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),f32(B,A)),f33(B,A))),hAPP(A,f31(B,A)))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(132)]. 1.60/1.91 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_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))),B),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))),f31(C,B)),c_Arrow__Order__Mirabelle_OProf)). [resolve(594,a,595,c)]. 1.60/1.91 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_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))),B),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)))) | f33(C,B) != f32(C,B). [resolve(594,a,596,c)]. 1.60/1.91 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_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))),B),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),f32(C,B)),f33(C,B))),hAPP(f31(C,B),C))). [resolve(594,a,597,c)]. 1.60/1.91 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_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))),B),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),f32(C,B)),f33(C,B))),hAPP(B,f31(C,B)))). [resolve(594,a,598,c)]. 1.68/1.94 599 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f72(B,A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_dictator__def) # label(axiom). [clausify(304)]. 1.68/1.94 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))),f72(A,B)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,C) = hAPP(C,A). [resolve(599,a,594,a)]. 1.68/1.94 600 c_Arrow__Order__Mirabelle_Odictator(A,B) | hAPP(A,f72(B,A)) != hAPP(f72(B,A),B) # label(fact_dictator__def) # label(axiom). [clausify(304)]. 1.68/1.94 Derived: hAPP(A,f72(B,A)) != hAPP(f72(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(600,a,594,a)]. 1.68/1.94 601 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f51(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.94 602 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.94 603 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.94 604 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.94 605 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.94 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))),f51(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(601,a,602,a)]. 1.68/1.95 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))),f51(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(601,a,603,a)]. 1.68/1.95 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))),f51(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(601,a,604,a)]. 1.68/1.95 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))),f51(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(601,a,605,a)]. 1.68/1.95 606 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f52(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.95 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))),f52(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(606,a,602,a)]. 1.68/1.95 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))),f52(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(606,a,603,a)]. 1.68/1.95 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))),f52(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(606,a,604,a)]. 1.68/1.95 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))),f52(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(606,a,605,a)]. 1.68/1.95 607 c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(607,a,602,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(607,a,603,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(607,a,604,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(607,a,605,a)]. 1.68/1.95 608 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(608,a,602,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(608,a,603,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(608,a,604,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(f51(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),f53(A)),f54(A))),hAPP(f52(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f50(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f50(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))). [resolve(608,a,605,a)]. 1.68/1.95 609 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(609,a,602,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(609,a,603,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(609,a,604,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(609,a,605,a)]. 1.68/1.95 610 c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) # label(fact_IIA__def) # label(axiom). [clausify(241)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(610,a,602,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(610,a,603,a)]. 1.68/1.95 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(610,a,604,a)]. 1.68/1.96 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),f53(A)),f54(A))),hAPP(A,f51(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),f53(A)),f54(A))),hAPP(A,f52(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f50(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f50(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))). [resolve(610,a,605,a)]. 1.68/1.96 611 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(fact_assms_I3_J) # label(axiom). [assumption]. 1.68/1.96 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,f50(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,f50(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))). [resolve(611,a,602,a)]. 1.68/1.96 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,f50(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,f50(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))). [resolve(611,a,603,a)]. 1.73/1.99 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,f50(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,f50(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))). [resolve(611,a,604,a)]. 1.73/1.99 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,f50(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,f50(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))). [resolve(611,a,605,a)]. 1.73/1.99 612 c_Relation_Oirrefl(A,B) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f89(B,A)),f89(B,A))),B)) # label(fact_irrefl__def) # label(axiom). [clausify(392)]. 1.73/1.99 613 -c_Relation_Oirrefl(A,B) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)) # label(fact_irrefl__def) # label(axiom). [clausify(392)]. 3.40/3.69 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f89(B,A)),f89(B,A))),B)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)). [resolve(612,a,613,a)]. 3.40/3.69 614 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(424)]. 3.40/3.69 615 -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(424)]. 3.40/3.69 3.40/3.69 ============================== end predicate elimination ============= 3.40/3.69 3.40/3.69 Auto_denials: (non-Horn, no changes). 3.40/3.69 3.40/3.69 Term ordering decisions: 3.40/3.69 Function symbol KB weights: tc_Arrow__Order__Mirabelle_Oalt=1. tc_HOL_Obool=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. tc_Nat_Onat=1. c_Arrow__Order__Mirabelle_Obelow=1. v_b____=1. c_Arrow__Order__Mirabelle_OLin=1. v_F=1. v_c____=1. v_a____=1. v_P____=1. c_fequal=1. v_P_H____=1. c_fNot=1. hAPP=1. tc_fun=1. tc_prod=1. c_Product__Type_OPair=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Transitive__Closure_Ortranclp=1. c_Wellfounded_Oacc=1. c_Wellfounded_Oaccp=1. c_Recdef_Ocut=1. c_Relation_OId__on=1. c_Relation_OField=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Set_Othe__elem=1. f2=1. f7=1. f13=1. f24=1. f31=1. f32=1. f33=1. f36=1. f44=1. f72=1. f89=1. f95=1. c_member=1. c_Lattices_Osemilattice__sup__class_Osup=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_Orderings_Obot__class_Obot=1. c_COMBI=1. c_Relation_OId=1. c_HOL_Oundefined=1. f51=1. f52=1. f53=1. f54=1. f78=1. f79=1. f80=1. c_COMBC=1. c_Set_Oinsert=1. c_COMBK=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_FuncSet_Oextensional=1. c_COMBS=1. c_Groups_Ominus__class_Ominus=1. c_Wellfounded_Omlex__prod=1. f8=1. f9=1. f10=1. f11=1. f23=1. f55=1. f56=1. f57=1. f62=1. f63=1. f67=1. f68=1. f69=1. f70=1. f75=1. f83=1. f84=1. f85=1. f87=1. f91=1. f101=1. c_COMBB=1. c_Product__Type_OSigma=1. c_FuncSet_OPi=1. c_FuncSet_Orestrict=1. c_FuncSet_Oextensional__funcset=1. c_Wellfounded_Olex__prod=1. c_Relation_Oinv__image=1. c_Nitpick_Owf__wfrec=1. c_Recdef_Osame__fst=1. f1=1. f14=1. f15=1. f16=1. f19=1. f26=1. f28=1. f29=1. f30=1. f41=1. f45=1. f47=1. f49=1. f64=1. f65=1. f66=1. f71=1. f81=1. f82=1. f92=1. f94=1. f100=1. c_Fun_Ofun__upd=1. c_Nitpick_Owf__wfrec_H=1. c_Product__Type_Ointernal__split=1. c_Product__Type_Oprod_Oprod__rec=1. f21=1. f22=1. f34=1. f35=1. f37=1. f38=1. f42=1. f43=1. f50=1. f58=1. f59=1. f73=1. f74=1. f76=1. f77=1. f86=1. f90=1. f93=1. c_FuncSet_Ocompose=1. c_Product__Type_Ocurry=1. f12=1. f20=1. f25=1. f39=1. f46=1. f48=1. f60=1. f88=1. f17=1. f18=1. f27=1. f40=1. f61=1. f3=1. f4=1. f5=1. f6=1. f96=1. f97=1. f98=1. f99=1. 3.40/3.69 3.40/3.69 ============================== end of process initial clauses ======== 3.40/3.69 3.40/3.69 ============================== CLAUSES FOR SEARCH ==================== 3.40/3.69 3.40/3.69 ============================== end of clauses for search ============= 3.40/3.69 3.40/3.69 ============================== SEARCH ================================ 3.40/3.69 3.40/3.69 % Starting search at 0.70 seconds. 3.40/3.69 3.40/3.69 Low Water (keep): wt=149.000, iters=3351 3.40/3.69 3.40/3.69 Low Water (keep): wt=146.000, iters=3382 3.40/3.69 3.40/3.69 Low Water (keep): wt=142.000, iters=3417 3.40/3.69 3.40/3.69 Low Water (keep): wt=141.000, iters=3434 3.40/3.69 3.40/3.69 Low Water (keep): wt=131.000, iters=3376 3.40/3.69 3.40/3.69 Low Water (keep): wt=123.000, iters=3429 3.40/3.69 3.40/3.69 Low Water (keep): wt=118.000, iters=3392 3.40/3.69 3.40/3.69 Low Water (keep): wt=115.000, iters=3390 3.40/3.69 3.40/3.69 Low Water (keep): wt=106.000, iters=3393 3.40/3.69 3.40/3.69 Low Water (keep): wt=101.000, iters=3351 3.40/3.69 3.40/3.69 Low Water (keep): wt=93.000, iters=3370 3.40/3.69 3.40/3.69 Low Water (keep): wt=92.000, iters=3404 3.40/3.69 3.40/3.69 Low Water (keep): wt=85.000, iters=3333 3.40/3.69 3.40/3.69 Low Water (keep): wt=82.000, iters=3403 3.40/3.69 3.40/3.69 Low Water (keep): wt=76.000, iters=3380 3.40/3.69 3.40/3.69 Low Water (keep): wt=73.000, iters=3368 3.40/3.69 3.40/3.69 Low Water (keep): wt=71.000, iters=3413 3.40/3.69 3.40/3.69 Low Water (keep): wt=70.000, iters=3410 3.40/3.69 3.40/3.69 Low Water (keep): wt=69.000, itersCputime limit exceeded (core dumped) 180.03/180.28 EOF