0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n004.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:47:57 CDT 2018 0.03/0.23 % CPUTime : 0.91/1.11 ============================== Prover9 =============================== 0.91/1.11 Prover9 (32) version 2009-11A, November 2009. 0.91/1.11 Process 10796 was started by sandbox on n004.star.cs.uiowa.edu, 0.91/1.11 Sat Jul 14 05:47:57 2018 0.91/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10750_n004.star.cs.uiowa.edu". 0.91/1.11 ============================== end of head =========================== 0.91/1.11 0.91/1.11 ============================== INPUT ================================= 0.91/1.11 0.91/1.11 % Reading from file /tmp/Prover9_10750_n004.star.cs.uiowa.edu 0.91/1.11 0.91/1.11 set(prolog_style_variables). 0.91/1.11 set(auto2). 0.91/1.11 % set(auto2) -> set(auto). 0.91/1.11 % set(auto) -> set(auto_inference). 0.91/1.11 % set(auto) -> set(auto_setup). 0.91/1.11 % set(auto_setup) -> set(predicate_elim). 0.91/1.11 % set(auto_setup) -> assign(eq_defs, unfold). 0.91/1.11 % set(auto) -> set(auto_limits). 0.91/1.11 % set(auto_limits) -> assign(max_weight, "100.000"). 0.91/1.11 % set(auto_limits) -> assign(sos_limit, 20000). 0.91/1.11 % set(auto) -> set(auto_denials). 0.91/1.11 % set(auto) -> set(auto_process). 0.91/1.11 % set(auto2) -> assign(new_constants, 1). 0.91/1.11 % set(auto2) -> assign(fold_denial_max, 3). 0.91/1.11 % set(auto2) -> assign(max_weight, "200.000"). 0.91/1.11 % set(auto2) -> assign(max_hours, 1). 0.91/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.91/1.11 % set(auto2) -> assign(max_seconds, 0). 0.91/1.11 % set(auto2) -> assign(max_minutes, 5). 0.91/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.91/1.11 % set(auto2) -> set(sort_initial_sos). 0.91/1.11 % set(auto2) -> assign(sos_limit, -1). 0.91/1.11 % set(auto2) -> assign(lrs_ticks, 3000). 0.91/1.11 % set(auto2) -> assign(max_megs, 400). 0.91/1.11 % set(auto2) -> assign(stats, some). 0.91/1.11 % set(auto2) -> clear(echo_input). 0.91/1.11 % set(auto2) -> set(quiet). 0.91/1.11 % set(auto2) -> clear(print_initial_clauses). 0.91/1.11 % set(auto2) -> clear(print_given). 0.91/1.11 assign(lrs_ticks,-1). 0.91/1.11 assign(sos_limit,10000). 0.91/1.11 assign(order,kbo). 0.91/1.11 set(lex_order_vars). 0.91/1.11 clear(print_given). 0.91/1.11 0.91/1.11 % formulas(sos). % not echoed (533 formulas) 0.91/1.11 0.91/1.11 ============================== end of input ========================== 0.91/1.11 0.91/1.11 % From the command line: assign(max_seconds, 300). 0.91/1.11 0.91/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.91/1.11 0.91/1.11 % Formulas that are not ordinary clauses: 0.91/1.11 1 (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]. 0.91/1.11 2 (all V_aa_2 all T_a all V_A_2 (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 -> -hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 3 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 4 (all V_R_2 all V_f_2 all T_a c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a,c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a,c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a)))) # label(fact_mlex__prod__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 5 (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_C_2,V_A_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)) = 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))) # label(fact_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 6 (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]. 0.91/1.11 7 (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__valued__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 8 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> V_B_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_Diff__partition) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 9 (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]. 0.91/1.11 10 (all V_r_2 all V_x_2 all T_a ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc_OaccI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 11 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2)) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 12 (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]. 0.91/1.11 13 (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]. 0.91/1.11 14 (all V_s_2 all V_r_2 all T_a 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)) = 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))) # label(fact_Field__Un) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 15 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_Transitive__Closure_Otrancl__into__trancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 16 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))))) # label(fact_DiffE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 17 (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]. 0.91/1.11 18 (all V_R_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) -> -(all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))))))) # label(fact_not__acc__down) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 19 (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]. 0.91/1.11 20 (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]. 0.91/1.11 21 (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_Obelow(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_below__Lin) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 22 (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]. 0.91/1.11 23 (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_F,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_F,B_xa)))))))))) # label(fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_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_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 24 (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]. 0.91/1.11 25 (all V_r_2 all T_a c_Transitive__Closure_Ortranclp(T_a,V_r_2) = c_Transitive__Closure_Ortranclp(T_a,c_Transitive__Closure_Ortranclp(T_a,V_r_2))) # label(fact_rtranclp__idemp) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 26 (all V_r_2 all T_b all T_a (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) = V_r_2 <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ODomain(T_a,T_b,V_r_2))) # label(fact_Domain__empty__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 27 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) -> (V_aa_2 != V_ba_2 -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 28 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (V_aa_2 = V_ba_2 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))))) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 29 (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]. 0.91/1.11 30 (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]. 0.91/1.11 31 (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__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)) = 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))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 32 (all V_A_2 all V_aa_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_Set_Oinsert(T_a,V_aa_2,V_A_2)) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 33 (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 | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 34 (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]. 0.91/1.11 35 (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]. 0.91/1.11 36 (all V_R_2 all V_y_2 all V_x_2 all T_a (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))) | 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_Ortrancl(T_a,V_R_2))))) # label(fact_rtrancl__eq__or__trancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 37 (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]. 0.91/1.11 38 (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]. 0.91/1.11 39 (all V_x_2 all V_Qa_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_Qa_2) -> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(V_Qa_2,V_x_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 40 (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]. 0.91/1.11 41 (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]. 0.91/1.11 42 (all V_aa_2 all V_ba_2 all V_r_2 all T_a (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_ba_2)) -> (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2))))) # label(fact_accp__downward) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 43 (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]. 0.91/1.11 44 (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_A_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)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 45 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) -> ((all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) -> (all B_aa all B_ba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)))))) # label(fact_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 46 (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) = 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)))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 47 (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]. 0.91/1.11 48 (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__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) = hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2))) # label(fact_inf__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 49 (all V_B_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 50 (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]. 0.91/1.11 51 (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]. 0.91/1.11 52 (all V_c_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_c_2)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_c_2))))) # label(fact_rtranclp_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 53 (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]. 0.91/1.11 54 (all V_r_2 all T_a c_Relation_ORange(T_a,T_a,V_r_2) = c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))) # label(fact_trancl__range) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 55 (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]. 0.91/1.11 56 (all V_R_2 all V_Qa_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 57 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 58 (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]. 0.91/1.11 59 (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]. 0.91/1.11 60 (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_ba_2 = V_aa_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]. 0.91/1.11 61 (all V_B_2 all T_b all V_g_2 all V_f_2 all V_A_2 all T_a ((all B_w (hBOOL(hAPP(hAPP(c_member(T_a),B_w),V_A_2)) -> hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_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_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))))) # label(fact_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 62 (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]. 0.91/1.11 63 (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]. 0.91/1.11 64 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_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]. 0.91/1.11 65 (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]. 0.91/1.11 66 (all V_T_2 all T_b all T_a 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))) = c_FuncSet_Oextensional__funcset(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_T_2)) # label(fact_extensional__funcset__empty__domain) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 67 (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]. 0.91/1.11 68 (all V_aa_2 all V_r_2 all T_a (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) <-> (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)))))) # label(fact_accp_Oequations) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 69 (all V_B_2 all V_aa_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2))) # label(fact_Diff__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 70 (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]. 0.91/1.11 71 (all V_B_2 all V_A_2 all V_g_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_g_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_g_2 = c_FuncSet_Ocompose(T_a,T_a,T_b,V_A_2,V_g_2,c_FuncSet_Orestrict(T_a,T_a,c_COMBI(T_a),V_A_2))))) # label(fact_compose__Id) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 72 (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]. 0.91/1.11 73 (all V_R_2 all T_a all V_y_2 all V_x_2 all V_f_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))))) # label(fact_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 74 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_rtrancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 75 (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]. 0.91/1.11 76 (all V_B_2 all V_A_2 all T_b all T_a 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)) = 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))) # label(fact_Domain__Un__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 77 (all V_Pa_2 all V_r_2 all V_by_2 all V_bx_2 all V_ay_2 all V_ax_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) -> ((all B_a all B_b all B_aa all B_ba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba))),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))) -> (hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)))))) # label(fact_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 78 (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]. 0.91/1.11 79 (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)) -> 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) = 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))))) # label(fact_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 80 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))))) # label(fact_DomainI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 81 (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]. 0.91/1.11 82 (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]. 0.91/1.11 83 (all V_A_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> V_A_2 = c_Set_Oinsert(T_a,V_aa_2,V_A_2))) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 84 (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]. 0.91/1.11 85 (all V_R_2 all T_a c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__trancl__absorb) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 86 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_A_2)))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 87 (all V_C_2 all V_g_2 all T_c all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_c)),V_g_2),c_FuncSet_OPi(T_b,T_c,V_B_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b,V_C_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_c)),c_FuncSet_Ocompose(T_a,T_b,T_c,V_A_2,V_g_2,V_f_2)),c_FuncSet_OPi(T_a,T_c,V_A_2,c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a,V_C_2))))))) # label(fact_funcset__compose) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 88 (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]. 0.91/1.11 89 (all V_B_2 all V_A_2 all V_I_2 all T_b all T_a 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)) = 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))) # label(fact_Sigma__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 90 (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]. 0.91/1.11 91 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 92 (all T_b all T_a c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Domain__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 93 (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]. 0.91/1.11 94 (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____),v_b_H____)),hAPP(v_P_H____,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,B_i))))) # label(fact__C1_C) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 95 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))))) # label(fact_r__r__into__trancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 96 (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]. 0.91/1.11 97 (all V_x_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 98 (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]. 0.91/1.11 99 (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]. 0.91/1.11 100 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 101 (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]. 0.91/1.11 102 (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]. 0.91/1.11 103 (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]. 0.91/1.11 104 (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]. 0.91/1.11 105 (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]. 0.91/1.11 106 (all V_Qa_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_Qa_2) -> hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))))) # label(fact_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 107 (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)) -> 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))) & (-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)) = 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) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 108 (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]. 0.91/1.11 109 (all V_aa_2 all V_r_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downward) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 110 (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]. 0.91/1.11 111 (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]. 0.91/1.11 112 (all V_i_2 hAPP(v_Q____,V_i_2) = c_HOL_OLet(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_a____),v_a_H____)),hAPP(v_P____,V_i_2)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,V_i_2),v_a_H____,v_a____)),hAPP(hAPP(c_COMBS(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_b____),v_b_H____))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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))),c_Arrow__Order__Mirabelle_Oabove),v_b____)),v_b_H____)))) # label(fact_Q__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 113 (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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 0.91/1.11 114 (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]. 0.91/1.12 115 (all V_B_2 all V_A_2 all V_aa_2 all T_a 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)) = 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_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 116 (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]. 0.91/1.12 117 (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]. 0.91/1.12 118 (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_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_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 119 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_ba_2 = V_aa_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 120 (all V_b_H all V_a_H all V_b all V_a all T_b all T_a (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) -> -(V_a_H = V_a -> V_b_H != V_b))) # label(fact_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 121 (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]. 0.91/1.12 122 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_y = V_x)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 123 (all V_y_2 all V_x_2 all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> (c_Orderings_Obot__class_Obot(T_a) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) <-> V_y_2 = c_Orderings_Obot__class_Obot(T_a) & c_Orderings_Obot__class_Obot(T_a) = V_x_2))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 124 (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]. 0.91/1.12 125 (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]. 0.91/1.12 126 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))))) # label(fact_DiffI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 127 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Olattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Olattice) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 128 (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]. 0.91/1.12 129 (all V_y_2 all V_x_2 all V_S_2 all V_R_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_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))) <-> 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)))) # label(fact_sup__Un__eq2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 130 (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]. 0.91/1.12 131 (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_b),V_a))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 132 (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]. 0.91/1.12 133 (all V_x_2 all V_A_2 all V_y_2 all T_a (hBOOL(hAPP(V_A_2,V_x_2)) | V_y_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]. 0.91/1.12 134 (all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 all T_b all T_a (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_Ha_2),V_b_Ha_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2) <-> V_aa_2 = V_a_Ha_2 & V_ba_2 = V_b_Ha_2)) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 135 (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]. 0.91/1.12 136 (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]. 0.91/1.12 137 (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]. 0.91/1.12 138 (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_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,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]. 0.91/1.12 139 (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]. 0.91/1.12 140 (all V_A_2 all T_a c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2) # label(fact_Domain__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 141 (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]. 0.91/1.12 142 (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]. 0.91/1.12 143 (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]. 0.91/1.12 144 (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]. 0.91/1.12 145 (all V_A_2 all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_single__valued__Id__on) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 146 (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]. 0.91/1.12 147 (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]. 0.91/1.12 148 (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) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 149 (all V_C_2 all V_B_2 all V_aa_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_B_2),V_C_2)) = 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)) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 150 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 151 (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]. 0.91/1.12 152 (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(B_f,V_x_2) = hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(T_a,T_b),B_f),B_R),V_aa_2),V_x_2))) # label(fact_tfl__cut__apply) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 153 (all V_Pa_2 (--hBOOL(V_Pa_2) | hBOOL(hAPP(c_fNot,V_Pa_2)))) # label(help_c__fNot__2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 154 (all T_b all T_a all V_S_2 (V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) -> 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]. 0.91/1.12 155 (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]. 0.91/1.12 156 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 157 (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]. 0.91/1.12 158 (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]. 0.91/1.12 159 (all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,V_L_2)),c_Arrow__Order__Mirabelle_OProf)))) # label(fact_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 160 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_c_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]. 0.91/1.12 161 (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_x),V_y)) = 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]. 0.91/1.12 162 (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]. 0.91/1.12 163 (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]. 0.91/1.12 164 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(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)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__Diff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 165 (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]. 0.91/1.12 166 (all V_B_2 all T_b all V_A_2 all V_A_H_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2,V_A_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2)))) # label(fact_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 167 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2))) <-> V_y_2 != V_x_2 & (V_aa_2 = V_y_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2))) & (V_y_2 != V_aa_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_ba_2),V_y_2)),V_L_2)) | V_ba_2 = V_y_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_y_2)),V_L_2)))))))) # label(fact_in__below) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 168 (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]. 0.91/1.12 169 (all V_d_2 all V_ba_2 all V_m_2 all T_b all T_a all V_c_2 all V_aa_2 (V_c_2 != V_aa_2 -> c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_c_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_c_2,V_d_2))) # label(fact_fun__upd__twist) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 170 (all V_z_2 all V_L_2 all V_y_2 all V_x_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_z_2 = V_y_2 -> V_y_2 != V_x_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)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2))))) # label(fact_in__mktop) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 171 (all V_B_2 all T_b all T_a c_Product__Type_OSigma(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) # label(fact_Sigma__empty1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 172 (all V_A_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a,V_A_2))))) # label(fact_funcset__id) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 173 (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]. 0.91/1.12 174 (all V_A_2 all V_C_2 all V_B_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_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)) = 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)) # label(fact_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 175 (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) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 176 (all T_b all T_a all V_Pa_2 ((all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (all B_a all B_b hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 177 (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]. 0.91/1.12 178 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> V_B_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 179 (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),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__assoc) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 180 (all V_S_2 all V_R_2 all T_a (V_S_2 = 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) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2))) # label(fact_pred__equals__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 181 (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_B_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 182 (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 -> hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2) & (V_x_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) = hAPP(V_f_2,V_z_2)))) # label(fact_fun__upd__apply) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 183 (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),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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 184 (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]. 0.91/1.12 185 (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]. 0.91/1.12 186 (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]. 0.91/1.12 187 (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]. 0.91/1.12 188 (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]. 0.91/1.12 189 (all V_f_2 all V_g_2 all T_b all T_c all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(V_g_2,hAPP(V_f_2,V_x_2)) = hAPP(c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_g_2,V_f_2),V_x_2))) # label(fact_compose__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 190 (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]. 0.91/1.12 191 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 192 (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]. 0.91/1.12 193 (all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) != V_c_2)))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 194 (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]. 0.91/1.12 195 (all V_y_2 all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (V_y_2 != V_x_2 -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_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]. 0.91/1.12 196 (all V_y_2 all V_x_2 all T_a (V_x_2 = V_y_2 <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))))) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 197 (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]. 0.91/1.12 198 (all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(V_A_2,V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 199 (all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),B_x)) & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x),c_Arrow__Order__Mirabelle_OLin)))))) # label(fact_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 200 (all V_B_2 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),V_B_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_B_2)) -> B_x != B_xa)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 201 (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]. 0.91/1.12 202 (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]. 0.91/1.12 203 (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]. 0.91/1.12 204 (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]. 0.91/1.12 205 (all V_R_2 all V_Qa_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_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 206 (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]. 0.91/1.12 207 (all V_r_2 all T_b all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Relation_ORange(T_b,T_a,V_r_2))) -> -(all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_ba_2)),V_r_2))))) # label(fact_RangeE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 208 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a 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)) = c_Set_Oinsert(T_a,V_aa_2,c_Relation_ODomain(T_a,T_b,V_r_2))) # label(fact_Domain__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 209 (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_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)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 210 (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]. 0.91/1.12 211 (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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_above__Lin) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 212 (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]. 0.91/1.12 213 (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]. 0.91/1.12 214 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 215 (all V_g_2 all V_f_2 ((all B_x hAPP(V_g_2,B_x) = hAPP(V_f_2,B_x)) -> V_g_2 = V_f_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 216 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 217 (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]. 0.91/1.12 218 (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]. 0.91/1.12 219 (all V_x_2 all T_b all T_a (class_Orderings_Obot(T_a) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 220 (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]. 0.91/1.12 221 (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(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(V_f_2,V_x_2) = hAPP(c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2),V_x_2)))) # label(fact_restrict__apply) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 222 (all V_a3_2 all V_a1_2 all V_r_2 all T_a ((exists B_b (hBOOL(hAPP(hAPP(V_r_2,B_b),V_a3_2)) & hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),B_b)))) | V_a3_2 = V_a1_2 <-> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_a1_2),V_a3_2)))) # label(fact_rtranclp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 223 (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]. 0.91/1.12 224 (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]. 0.91/1.12 225 (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]. 0.91/1.12 226 (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]. 0.91/1.12 227 (all V_r_2 all T_b all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ODomain(T_a,T_b,V_r_2))) -> -(all B_y -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),B_y)),V_r_2))))) # label(fact_DomainE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 228 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 229 (all V_B_2 all T_a all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) -> c_Orderings_Oord__class_Oless__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]. 0.91/1.12 230 (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]. 0.91/1.12 231 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> V_x = 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)))) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 232 (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]. 0.91/1.12 233 (all V_Q all V_P all T_b all T_a hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 234 (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),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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 235 (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]. 0.91/1.12 236 (all V_r_2 all V_x_2 all V_y_2 all T_a (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)) <-> -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))) # label(fact_acyclic__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 237 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x)) # label(fact_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 238 (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]. 0.91/1.12 239 (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]. 0.91/1.12 240 (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]. 0.91/1.12 241 (all V_B_2 all V_A_2 all T_b all T_a ((exists B_x (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(V_B_2,B_x) & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)))) <-> 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]. 0.91/1.12 242 (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]. 0.91/1.12 243 (all V_B_2 all V_A_2 all V_x_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_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]. 0.91/1.12 244 (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_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 245 (all V_i_2 all V_Fa_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b (B_b != B_a -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))))))) -> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)))) # label(fact_dictatorI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 246 (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,hAPP(V_f_2,V_x_2))) # label(fact_fun__upd__triv) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 247 (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_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_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 248 (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]. 0.91/1.12 249 (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]. 0.91/1.12 250 (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_b____)),hAPP(v_Q____,B_i))))) # 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_062Q_Ai_092_060_094esub_062_Ab_J_096) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 251 (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]. 0.91/1.12 252 (all V_ba_2 all V_aa_2 all T_a (c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_ba_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]. 0.91/1.12 253 (all V_y_2 all V_x_2 all V_R_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_x_2),V_y_2)),V_R_2)) <-> c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2))) # label(fact_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 254 (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,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2))) # label(fact_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 255 (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]. 0.91/1.12 256 (all V_r_2 all T_b all V_aa_2 all T_a ((exists B_y hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_aa_2)),V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Relation_ORange(T_b,T_a,V_r_2))))) # label(fact_Range__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 257 (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]. 0.91/1.12 258 (all V_ba_2 all V_f_2 all T_b all T_a all V_aa_2 all V_x_2 ((V_x_2 = V_aa_2 -> V_ba_2 = hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_aa_2,V_ba_2),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) = hAPP(V_f_2,V_x_2)))) # label(fact_fun__upd__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 259 (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]. 0.91/1.12 260 (all V_T_2 all V_S_2 all T_b all T_a c_FuncSet_Oextensional__funcset(T_a,T_b,V_S_2,V_T_2) = 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))) # label(fact_extensional__funcset__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 261 (all V_ba_2 all V_r_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downwards) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 262 (all V_aa_2 all V_r_2 all T_a (hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_aa_2)) <-> (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)))))) # label(fact_accp_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 263 (all V_g_2 all V_f_2 all V_A_2 all T_c all T_b all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Ocompose(T_a,T_c,T_b,V_A_2,V_f_2,V_g_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))) # label(fact_compose__extensional) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 264 (all V_y_2 all V_x_2 (V_y_2 = V_x_2 | -hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 265 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2)) -> V_y_2 = V_z_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 266 (all V_Qa_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_Qa_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_Qa_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__separator__converseE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 267 (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) = 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_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)))) # label(fact_cut__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 268 (all V_y_2 all V_R_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Relation_ODomain(T_a,T_a,V_R_2))) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))))) # label(fact_Not__Domain__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 269 (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]. 0.91/1.12 270 (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))) & hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)))) # label(fact_mem__Sigma__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.12 271 (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]. 0.91/1.12 272 (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]. 0.91/1.12 273 (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]. 0.91/1.13 274 (all V_ba_2 all V_aa_2 all V_c_2 all T_a all T_c all T_b hAPP(hAPP(V_c_2,V_aa_2),V_ba_2) = c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2))) # label(fact_internal__split__conv) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 275 (all V_A_2 all V_y_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 276 (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]. 0.91/1.13 277 (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_A_2 = V_B_2 <-> c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2))))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 278 (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]. 0.91/1.13 279 (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]. 0.91/1.13 280 (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]. 0.91/1.13 281 (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]. 0.91/1.13 282 (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_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)) = 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))))) # label(fact_compose__assoc) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 283 (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]. 0.91/1.13 284 (all V_A_2 all T_a ((all B_x -hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 285 (all T_a all T_b all V_y_2 all V_x_2 all V_f_2 (hAPP(V_f_2,V_x_2) = V_y_2 -> c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2) = V_f_2)) # label(fact_fun__upd__idem) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 286 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 287 (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]. 0.91/1.13 288 (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]. 0.91/1.13 289 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 290 (all V_x_2 all T_b all T_a (class_Orderings_Obot(T_a) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_bot__apply) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 291 (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]. 0.91/1.13 292 (all V_B_2 all V_A_2 all T_b all T_a (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)) <-> 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)))) # label(fact_Times__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 293 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 294 (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_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 295 (all T_b all T_a all V_ba_2 all V_aa_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> c_Predicate_ORangeP(T_a,T_b,V_r_2,V_ba_2))) # label(fact_RangeP_Ointros) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 296 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> (c_Relation_Osingle__valued(T_a,T_b,V_s_2) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2)))) # label(fact_single__valued__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 297 (all V_y_2 all V_x_2 all V_c_2 all T_a all T_c all T_b c_Product__Type_Ocurry(T_b,T_c,T_a,V_c_2,V_x_2,V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))) # label(fact_curry__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 298 (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]. 0.91/1.13 299 (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__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__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))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 300 (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]. 0.91/1.13 301 (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_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 302 (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]. 0.91/1.13 303 (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_A_2) = V_A_2) # label(fact_Int__absorb) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 304 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a ((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)))) & hAPP(hAPP(V_Fa_2,B_g),V_a1_2) = hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2))) <-> 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)))) # label(fact_wfrec__rel_Oequations) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 305 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_restrictI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 306 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))))) # label(fact_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 307 (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]. 0.91/1.13 308 (all V_r_2 all T_a c_Transitive__Closure_Ortranclp(T_a,V_r_2) = 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)))) # label(fact_rtranclp__r__diff__Id) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 309 (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(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))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Times__subset__cancel2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 310 (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_x_2 != V_y_2 & (V_x_2 != V_ba_2 -> (V_ba_2 != V_y_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))) & (V_y_2 = V_ba_2 -> V_x_2 = V_aa_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2)))) & (V_ba_2 = V_x_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_aa_2),V_ba_2))))))) # label(fact_in__above) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 311 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> V_x = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x))) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 312 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_ba_2 = V_aa_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_ba_2)),c_Relation_OId__on(T_a,V_A_2)))))) # label(fact_Id__on__eqI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 313 (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]. 0.91/1.13 314 (all V_C_2 all V_B_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x),hAPP(V_C_2,B_x)))) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2)))) # label(fact_Pi__mono) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 315 (all V_c_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_c_2)) -> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(T_a,V_r_2),V_aa_2),V_c_2))))) # label(fact_converse__rtranclp__into__rtranclp) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 316 (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_A_2) = V_A_2) # label(fact_Un__absorb) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 317 (all V_B_2 all V_A_2 all V_c_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))) -> -(all B_x (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_c_2)))))) # label(fact_SigmaE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 318 (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]. 0.91/1.13 319 (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]. 0.91/1.13 320 (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]. 0.91/1.13 321 (all V_A_2 all V_f_2 all T_b all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_Oextensional(T_a,T_b,V_A_2)))) # label(fact_restrict__extensional) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 322 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(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__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Diff__Un) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 323 (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]. 0.91/1.13 324 (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]. 0.91/1.13 325 (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]. 0.91/1.13 326 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))))) # label(fact_UnE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 327 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_a (c_Relation_Osingle__valued(T_a,T_a,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 328 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 329 (all V_A_2 all V_aa_2 all T_a c_Set_Oinsert(T_a,V_aa_2,V_A_2) = c_Set_Oinsert(T_a,V_aa_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_insert__Diff__single) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 330 (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]. 0.91/1.13 331 (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]. 0.91/1.13 332 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 333 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__rtrancl__trancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 334 (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]. 0.91/1.13 335 (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]. 0.91/1.13 336 (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)) -> 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__if1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 337 (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]. 0.91/1.13 338 (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) = hAPP(V_f_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]. 0.91/1.13 339 (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]. 0.91/1.13 340 (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),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 341 (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]. 0.91/1.13 342 (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]. 0.91/1.13 343 (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__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))) # label(fact_sup__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 344 (all T_a all V_R_2 all V_y_2 all V_y_H_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 345 (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]. 0.91/1.13 346 (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]. 0.91/1.13 347 (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]. 0.91/1.13 348 (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]. 0.91/1.13 349 (all V_d_2 all V_c_2 all V_ba_2 all V_aa_2 all T_a (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_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_aa_2 = V_c_2 & V_ba_2 = V_d_2 | V_aa_2 = V_d_2 & V_c_2 = V_ba_2)) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 350 (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]. 0.91/1.13 351 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 352 (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]. 0.91/1.13 353 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 354 (all V_r_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Relation_ORange(T_a,T_b,V_r_2))))) # label(fact_RangeI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 355 (all V_r_2 all V_ba_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,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)) = 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))) # label(fact_Field__insert) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 356 (all V_a2_2 all V_a1_2 all V_Fa_2 all V_R_2 all T_b all T_a ((exists B_g (hAPP(hAPP(V_Fa_2,B_g),V_a1_2) = V_a2_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)))))) <-> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_a1_2,V_a2_2))) # label(fact_wfrec__rel_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 357 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 358 (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]. 0.91/1.13 359 (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]. 0.91/1.13 360 (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]. 0.91/1.13 361 (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]. 0.91/1.13 362 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oaccp(T_a,V_R2_2),c_Wellfounded_Oaccp(T_a,V_R1_2)))) # label(fact_accp__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 363 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 364 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 365 (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__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_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__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 366 (all V_B_2 all V_A_2 all T_a all T_b 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)) = 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))) # label(fact_Range__Un__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 367 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2))))) # label(fact_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 368 (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]. 0.91/1.13 369 (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]. 0.91/1.13 370 (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]. 0.91/1.13 371 (all V_A_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_Relation_OId__on(T_a,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) & V_y_2 = V_x_2)) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 372 (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]. 0.91/1.13 373 (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_y_2 != V_z_2 & (V_z_2 = V_x_2 -> V_y_2 != V_x_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))))) # label(fact_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 374 (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]. 0.91/1.13 375 (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]. 0.91/1.13 376 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 377 (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]. 0.91/1.13 378 (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]. 0.91/1.13 379 (all V_S_2 all V_R_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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)) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2,V_S_2))) # label(fact_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 380 (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]. 0.91/1.13 381 (all T_b all T_a all V_ba_2 all V_aa_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_aa_2),V_ba_2)) -> c_Predicate_ODomainP(T_a,T_b,V_r_2,V_aa_2))) # label(fact_DomainP_Ointros) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 382 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_B_2)))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 383 (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(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2))) # label(fact_fun__upd__other) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 384 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> ((all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 385 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 386 (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]. 0.91/1.13 387 (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]. 0.91/1.13 388 (all V_B_2 all T_a V_B_2 = 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)) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 389 (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]. 0.91/1.13 390 (all V_A_2 all V_B_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_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]. 0.91/1.13 391 (all V_c_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_c_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))) -> -(-hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 392 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_f_2 = c_FuncSet_Ocompose(T_a,T_b,T_b,V_A_2,c_FuncSet_Orestrict(T_b,T_b,c_COMBI(T_b),V_B_2),V_f_2)))) # label(fact_Id__compose) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 393 (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]. 0.91/1.13 394 (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_y_2) <-> V_y_2 = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)))) # label(fact_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 395 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 396 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2)))) # label(fact_Domain__mono) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 397 (all T_a c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) # label(fact_trancl__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 398 (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]. 0.91/1.13 399 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_y = V_x -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 400 (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_x != B_xa -> 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]. 0.91/1.13 401 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__mono) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 402 (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) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 403 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 404 (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]. 0.91/1.13 405 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_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_c_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 406 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_PiE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 407 (all V_ba_2 all V_aa_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2))))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 408 (all V_r_2 all V_p_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 409 (all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)))) # label(fact_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 410 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_rtrancl__into__trancl1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 411 (all V_B_2 all V_A_2 all V_c_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),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_IntI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 412 (all T_a c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) # label(fact_Id__on__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 413 (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]. 0.91/1.13 414 (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]. 0.91/1.13 415 (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__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__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 416 (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]. 0.91/1.13 417 (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]. 0.91/1.13 418 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 419 (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]. 0.91/1.13 420 (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]. 0.91/1.13 421 (all V_r_2 all T_a all T_b (V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) <-> c_Relation_ORange(T_b,T_a,V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Range__empty__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 422 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_B_2)))))) # label(fact_extensional__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 423 (all V_x_2 all T_a V_x_2 = 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))))) # label(fact_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 424 (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]. 0.91/1.13 425 (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]. 0.91/1.13 426 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 427 (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]. 0.91/1.13 428 (all V_B_2 all V_A_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_A_2)),c_Product__Type_OSigma(T_a,T_b,V_I_2,V_B_2)) = 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))) # label(fact_Sigma__Un__distrib2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 429 (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]. 0.91/1.13 430 (all V_ba_2 all V_aa_2 all V_f1_2 all T_a all T_c all T_b c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_aa_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_aa_2),V_ba_2)) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 431 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 432 (all V_i_2 all V_Fa_2 ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2))) <-> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2))) # label(fact_dictator__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 433 (all V_Qa_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_Qa_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_Qa_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__separatorE) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 434 (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))) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.13 435 (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_y),V_x))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 436 (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]. 0.91/1.14 437 (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]. 0.91/1.14 438 (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]. 0.91/1.14 439 (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)) -> (V_B_2 = V_A_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))))) # label(fact_Times__eq__cancel2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 440 (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_g_2,B_y) = hAPP(V_f_2,B_y))))) # label(fact_cuts__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 441 (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]. 0.91/1.14 442 (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]. 0.91/1.14 443 (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]. 0.91/1.14 444 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))))) # label(fact_restrict__in__funcset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 445 (all V_A_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,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) = c_Set_Oinsert(T_a,V_aa_2,V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 446 (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]. 0.91/1.14 447 (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]. 0.91/1.14 448 (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]. 0.91/1.14 449 (all V_c_2 all T_a -hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_empty__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 450 (all V_r_2 all V_aa_2 all V_ba_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_ba_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Wellfounded_Oacc(T_a,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Wellfounded_Oacc(T_a,V_r_2)))))) # label(fact_acc__downwards__aux) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 451 (all V_B_2 all V_aa_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,V_B_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_aa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)) # label(fact_Diff__insert2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 452 (all V_Qa_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_Qa_2) -> hBOOL(hAPP(V_Qa_2,V_x_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 453 (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]. 0.91/1.14 454 (all V_y_2 all V_x_2 all V_f_2 all T_a all T_b hAPP(c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2) # label(fact_fun__upd__same) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 455 (all V_y_2 all V_x_2 all V_Qa_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_Qa_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))))) # label(fact_predicate2D) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 456 (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]. 0.91/1.14 457 (all V_Fa_2 all V_R_2 all T_b all T_a ((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_f,B_z) = hAPP(B_g,B_z))) -> hAPP(hAPP(V_Fa_2,B_f),B_x) = hAPP(hAPP(V_Fa_2,B_g),B_x))) <-> c_Recdef_Oadm__wf(T_a,T_b,V_R_2,V_Fa_2))) # label(fact_adm__wf__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 458 (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__sup__class_Osup(T_a),V_x),V_y)) = 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]. 0.91/1.14 459 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 460 (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]. 0.91/1.14 461 (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)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Groups_Ominus__class_Ominus(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_Diff__Int) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 462 (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]. 0.91/1.14 463 (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]. 0.91/1.14 464 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 465 (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),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 466 (all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_Oextensional(T_a,T_b,V_A_2))) -> V_f_2 = c_FuncSet_Orestrict(T_a,T_b,V_f_2,V_A_2))) # label(fact_extensional__restrict) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 467 (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]. 0.91/1.14 468 (all V_C_2 all V_B_2 all V_A_2 all T_b all T_a 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))) = 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))) # label(fact_Times__Int__distrib1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 469 (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]. 0.91/1.14 470 (all T_b all T_a 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))) = c_FuncSet_Oextensional(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_extensional__empty) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 471 (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]. 0.91/1.14 472 (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_x_2 != V_z_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]. 0.91/1.14 473 (all V_s_2 all V_r_2 all V_b_Ha_2 all V_a_Ha_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_Ha_2),V_b_Ha_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) <-> V_a_Ha_2 = V_aa_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_Ha_2)),V_s_2)) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_Ha_2)),V_r_2)))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 474 (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]. 0.91/1.14 475 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 476 (all V_R_2 all V_Qa_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) = hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_Pa_2),V_Qa_2),V_R_2)) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 477 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2))))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 478 (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]. 0.91/1.14 479 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a,V_B_2)))))) # label(fact_funcsetI) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 480 (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_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__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 481 (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]. 0.91/1.14 482 (all V_r_2 all V_aa_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_aa_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 483 (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) -> 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__absorb2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 484 (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]. 0.91/1.14 485 (all V_Fa_2 ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_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(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))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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)))))))))) <-> c_Arrow__Order__Mirabelle_OIIA(V_Fa_2))) # label(fact_IIA__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 486 (all V_B_2 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)),c_Groups_Ominus__class_Ominus(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_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 487 (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,V_y_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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 488 (all V_A_2 all V_B_2 all V_c_2 all T_a ((-hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_member(T_a),V_c_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]. 0.91/1.14 489 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)))) # label(fact_acc__subset) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 490 (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]. 0.91/1.14 491 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x)) # label(fact_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 492 (all V_r_2 all T_a ((all B_x hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))) <-> c_Nitpick_Orefl_H(T_a,V_r_2))) # label(fact_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 493 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 494 (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]. 0.91/1.14 495 (all V_c_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_c_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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))) # label(fact_trancl__trans) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 496 (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]. 0.91/1.14 497 (all V_x_2 all V_r_2 all T_b all T_a (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) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Relation_ORange(T_a,T_b,V_r_2))))) # label(fact_RangeP__Range__eq) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 498 (all V_A_2 all V_B_2 all T_a hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)),V_A_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__Diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 0.91/1.14 499 (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]. 0.91/1.14 500 (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 | V_ba_2 != V_aa_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_rtranclD) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 501 (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) <-> hAPP(V_f_2,V_x_2) = V_y_2)) # label(fact_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption]. 0.97/1.15 0.97/1.15 ============================== end of process non-clausal formulas === 0.97/1.15 0.97/1.15 ============================== PROCESS INITIAL CLAUSES =============== 0.97/1.15 0.97/1.15 ============================== PREDICATE ELIMINATION ================= 0.97/1.15 502 class_Lattices_Osemilattice__sup(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 0.97/1.15 503 -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(29)]. 0.97/1.15 504 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),B) = B # label(fact_sup_Oidem) # label(axiom). [clausify(59)]. 0.97/1.15 505 -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(82)]. 0.97/1.15 506 -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),D),B),C) # label(fact_le__sup__iff) # label(axiom). [clausify(138)]. 0.97/1.15 507 -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(138)]. 0.97/1.15 508 -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(138)]. 0.97/1.15 509 -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(155)]. 0.97/1.15 510 -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(161)]. 0.97/1.15 511 -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(192)]. 0.97/1.15 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(502,a,503,a)]. 0.97/1.15 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),A) = A. [resolve(502,a,504,a)]. 0.97/1.15 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(502,a,505,a)]. 0.97/1.15 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),C),A),B). [resolve(502,a,506,a)]. 0.97/1.15 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(502,a,507,a)]. 0.97/1.15 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(502,a,508,a)]. 0.97/1.15 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(502,a,509,a)]. 0.97/1.15 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(502,a,510,a)]. 0.97/1.15 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(502,a,511,a)]. 0.97/1.15 512 -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(203)]. 0.97/1.15 513 -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(203)]. 0.97/1.15 514 -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(212)]. 0.97/1.15 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(514,a,502,a)]. 0.97/1.15 515 -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(220)]. 0.97/1.15 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(515,a,502,a)]. 0.97/1.15 516 -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(234)]. 0.97/1.15 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(516,a,502,a)]. 0.97/1.15 517 -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(247)]. 0.97/1.15 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(517,a,502,a)]. 0.97/1.15 518 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__sup(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom). [clausify(280)]. 0.97/1.15 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(518,b,503,a)]. 0.97/1.15 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(518,b,504,a)]. 0.97/1.15 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),D),C) = D. [resolve(518,b,505,a)]. 0.97/1.15 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)),E),C),D). [resolve(518,b,506,a)]. 0.97/1.16 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(518,b,507,a)]. 0.97/1.16 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(518,b,508,a)]. 0.97/1.16 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(518,b,509,a)]. 0.97/1.16 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(518,b,510,a)]. 0.97/1.16 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(518,b,511,a)]. 0.97/1.16 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(518,b,514,a)]. 0.97/1.16 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(518,b,515,a)]. 0.97/1.16 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(518,b,516,a)]. 0.97/1.16 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(518,b,517,a)]. 0.97/1.16 519 -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(294)]. 0.97/1.16 520 -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(320)]. 0.97/1.16 521 -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(330)]. 0.97/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) = B. [resolve(521,a,502,a)]. 0.97/1.16 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)),C),D) = D | -class_Lattices_Olattice(B). [resolve(521,a,518,b)]. 0.97/1.16 522 -class_Lattices_Osemilattice__sup(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),B) = B # label(fact_sup__idem) # label(axiom). [clausify(360)]. 0.97/1.16 523 -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_le__iff__sup) # label(axiom). [clausify(394)]. 0.98/1.16 524 -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_le__iff__sup) # label(axiom). [clausify(394)]. 0.98/1.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) != B. [resolve(524,a,502,a)]. 0.98/1.16 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)),C),D) != D | -class_Lattices_Olattice(B). [resolve(524,a,518,b)]. 0.98/1.16 525 -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(414)]. 0.98/1.16 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(525,a,502,a)]. 0.98/1.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B)),E),D)) | -class_Lattices_Olattice(B). [resolve(525,a,518,b)]. 0.98/1.16 526 -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(435)]. 0.98/1.16 527 -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(446)]. 0.98/1.16 528 class_Lattices_Osemilattice__sup(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 0.98/1.16 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(528,a,503,a)]. 0.98/1.16 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),A) = A. [resolve(528,a,504,a)]. 0.98/1.16 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(528,a,505,a)]. 0.98/1.16 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),C),A),B). [resolve(528,a,506,a)]. 0.98/1.16 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(528,a,507,a)]. 0.98/1.16 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(528,a,508,a)]. 0.98/1.16 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(528,a,509,a)]. 0.98/1.16 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(528,a,510,a)]. 0.98/1.16 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(528,a,511,a)]. 0.98/1.16 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(528,a,514,a)]. 0.98/1.16 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(528,a,515,a)]. 0.98/1.18 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(528,a,516,a)]. 0.98/1.18 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(528,a,517,a)]. 0.98/1.18 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B) = B. [resolve(528,a,521,a)]. 0.98/1.18 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),A),B) != B. [resolve(528,a,524,a)]. 0.98/1.18 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(528,a,525,a)]. 0.98/1.18 529 -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(471)]. 0.98/1.18 530 -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(481)]. 0.98/1.18 531 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 0.98/1.18 532 -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(40)]. 0.98/1.18 533 -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(63)]. 0.98/1.18 534 -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(67)]. 0.98/1.18 535 -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(131)]. 0.98/1.18 536 -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(148)]. 0.98/1.18 537 -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(168)]. 0.98/1.18 538 -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(179)]. 0.98/1.18 539 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(201)]. 0.98/1.18 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(531,a,532,a)]. 0.98/1.19 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(531,a,533,a)]. 0.98/1.19 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(531,a,534,a)]. 0.98/1.19 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(531,a,536,a)]. 0.98/1.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),B),C)). [resolve(531,a,537,a)]. 0.98/1.19 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(531,a,538,a)]. 0.98/1.19 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),A) = A. [resolve(531,a,539,a)]. 0.98/1.19 540 -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(235)]. 0.98/1.19 541 -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(239)]. 0.98/1.19 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(541,a,531,a)]. 0.98/1.19 542 -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(269)]. 0.98/1.19 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(542,a,531,a)]. 0.98/1.19 543 -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(298)]. 0.98/1.19 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(543,a,531,a)]. 0.98/1.19 544 -class_Lattices_Osemilattice__inf(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),B) = B # label(fact_inf__idem) # label(axiom). [clausify(311)]. 0.98/1.19 545 -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(313)]. 0.98/1.19 546 -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(325)]. 0.98/1.19 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(546,a,531,a)]. 0.98/1.19 547 -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(325)]. 0.98/1.19 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(547,a,531,a)]. 0.98/1.19 548 -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(345)]. 0.98/1.19 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(548,a,531,a)]. 0.98/1.19 549 -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(345)]. 0.98/1.19 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(549,a,531,a)]. 0.98/1.19 550 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(353)]. 0.98/1.19 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__inf__class_Oinf(tc_fun(B,A)),C),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),D),F)). [resolve(550,b,532,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | 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)),D),C). [resolve(550,b,533,a)]. 0.98/1.19 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(550,b,534,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),D),C) = C. [resolve(550,b,536,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),D),E)). [resolve(550,b,537,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D)),E) = 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)),D),E)). [resolve(550,b,538,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(550,b,539,a)]. 0.98/1.19 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__inf__class_Oinf(tc_fun(B,A)),E),C),D). [resolve(550,b,541,a)]. 0.98/1.19 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__inf__class_Oinf(tc_fun(B,A)),C),E),D). [resolve(550,b,542,a)]. 0.98/1.19 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(550,b,543,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D) = C. [resolve(550,b,546,a)]. 0.98/1.19 Derived: -class_Lattices_Olattice(A) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D) != C. [resolve(550,b,547,a)]. 0.98/1.19 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(550,b,548,a)]. 0.98/1.19 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(550,b,549,a)]. 0.98/1.19 551 -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(370)]. 0.98/1.19 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(551,a,531,a)]. 0.98/1.19 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(551,a,550,b)]. 0.98/1.19 552 class_Lattices_Osemilattice__inf(tc_Nat_Onat) # label(arity_Nat__Onat__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 0.98/1.19 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(552,a,532,a)]. 0.98/1.19 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(552,a,533,a)]. 0.98/1.19 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(552,a,534,a)]. 0.98/1.19 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(552,a,536,a)]. 0.98/1.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),B),C)). [resolve(552,a,537,a)]. 0.98/1.19 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(552,a,538,a)]. 0.98/1.19 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),A),A) = A. [resolve(552,a,539,a)]. 0.98/1.19 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(552,a,541,a)]. 0.98/1.19 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(552,a,542,a)]. 0.98/1.19 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(552,a,543,a)]. 0.98/1.19 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(552,a,546,a)]. 0.98/1.19 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(552,a,547,a)]. 0.98/1.19 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(552,a,548,a)]. 0.98/1.19 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(552,a,549,a)]. 1.03/1.23 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(552,a,551,a)]. 1.03/1.23 553 -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(429)]. 1.03/1.23 554 -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(447)]. 1.03/1.23 555 -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(465)]. 1.03/1.23 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(555,a,531,a)]. 1.03/1.23 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(555,a,550,b)]. 1.03/1.23 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(555,a,552,a)]. 1.03/1.23 556 -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__inf__iff) # label(axiom). [clausify(487)]. 1.03/1.23 557 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),C),D)) # label(fact_le__inf__iff) # label(axiom). [clausify(487)]. 1.03/1.23 558 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),D),C)) # label(fact_le__inf__iff) # label(axiom). [clausify(487)]. 1.03/1.23 559 -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(499)]. 1.03/1.23 560 -hBOOL(hAPP(hAPP(c_member(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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 561 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(fact_assms_I3_J) # label(axiom). [assumption]. 1.03/1.23 562 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f94(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 563 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f95(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 564 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(A)),f97(A))),hAPP(f95(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),f96(A)),f97(A))),hAPP(f94(A),B))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 565 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(A)),f97(A))),hAPP(f95(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),f96(A)),f97(A))),hAPP(f94(A),B))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 566 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(A)),f97(A))),hAPP(A,f94(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),f96(A)),f97(A))),hAPP(A,f95(A)))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 567 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(A)),f97(A))),hAPP(A,f94(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),f96(A)),f97(A))),hAPP(A,f95(A)))) | c_Arrow__Order__Mirabelle_OIIA(A) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 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(B,f98(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(A,f98(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(560,g,561,a)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f94(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(560,g,562,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f95(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(560,g,563,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(560,g,564,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(560,g,565,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(560,g,566,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(560,g,567,c)]. 1.03/1.23 568 -hBOOL(hAPP(hAPP(c_member(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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 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(B,f98(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(A,f98(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(568,g,561,a)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f94(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(568,g,562,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f95(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(568,g,563,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(568,g,564,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(568,g,565,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(568,g,566,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(568,g,567,c)]. 1.03/1.23 569 -hBOOL(hAPP(hAPP(c_member(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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 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(B,f98(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(A,f98(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(569,g,561,a)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f94(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(569,g,562,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f95(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(569,g,563,b)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(569,g,564,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(569,g,565,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(569,g,566,c)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(569,g,567,c)]. 1.03/1.23 570 -hBOOL(hAPP(hAPP(c_member(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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -c_Arrow__Order__Mirabelle_OIIA(E) # label(fact_IIA__def) # label(axiom). [clausify(485)]. 1.03/1.23 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(B,f98(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(A,f98(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(570,g,561,a)]. 1.03/1.23 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f94(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(570,g,562,b)]. 1.03/1.24 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,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))),f95(E)),c_Arrow__Order__Mirabelle_OProf)). [resolve(570,g,563,b)]. 1.03/1.24 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(570,g,564,c)]. 1.03/1.24 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(f95(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),f96(E)),f97(E))),hAPP(f94(E),F))). [resolve(570,g,565,c)]. 1.03/1.24 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(570,g,566,c)]. 1.03/1.24 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(B,f98(E,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f98(E,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(E,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(E,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f96(E)),f97(E))),hAPP(E,f94(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),f96(E)),f97(E))),hAPP(E,f95(E)))). [resolve(570,g,567,c)]. 1.07/1.27 571 hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f91(B,C,D,A,E,F,V6)),V6)),C)) | hAPP(hAPP(B,F),V6) = hAPP(hAPP(B,E),V6) | -c_Recdef_Oadm__wf(A,D,C,B) # label(fact_adm__wf__def) # label(axiom). [clausify(457)]. 1.07/1.27 572 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(116)]. 1.07/1.27 573 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),f90(C,D,E,A))),D)) | hAPP(f89(C,D,E,A),B) = hAPP(f88(C,D,E,A),B) | c_Recdef_Oadm__wf(A,E,D,C) # label(fact_adm__wf__def) # label(axiom). [clausify(457)]. 1.07/1.27 574 hAPP(hAPP(A,f89(A,B,C,D)),f90(A,B,C,D)) != hAPP(hAPP(A,f88(A,B,C,D)),f90(A,B,C,D)) | c_Recdef_Oadm__wf(D,C,B,A) # label(fact_adm__wf__def) # label(axiom). [clausify(457)]. 1.07/1.27 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f91(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(571,c,572,a)]. 1.07/1.27 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f91(B,C,D,A,E,F,V6)),V6)),C)) | hAPP(hAPP(B,F),V6) = hAPP(hAPP(B,E),V6) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),V7),f90(B,C,D,A))),C)) | hAPP(f89(B,C,D,A),V7) = hAPP(f88(B,C,D,A),V7). [resolve(571,c,573,c)]. 1.07/1.27 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f91(B,C,D,A,E,F,V6)),V6)),C)) | hAPP(hAPP(B,F),V6) = hAPP(hAPP(B,E),V6) | hAPP(hAPP(B,f89(B,C,D,A)),f90(B,C,D,A)) != hAPP(hAPP(B,f88(B,C,D,A)),f90(B,C,D,A)). [resolve(571,c,574,b)]. 1.07/1.27 575 hAPP(A,f91(B,C,D,E,F,A,V6)) != hAPP(F,f91(B,C,D,E,F,A,V6)) | hAPP(hAPP(B,A),V6) = hAPP(hAPP(B,F),V6) | -c_Recdef_Oadm__wf(E,D,C,B) # label(fact_adm__wf__def) # label(axiom). [clausify(457)]. 1.07/1.27 Derived: hAPP(A,f91(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,f91(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(575,c,572,a)]. 1.07/1.29 Derived: hAPP(A,f91(B,C,D,E,F,A,V6)) != hAPP(F,f91(B,C,D,E,F,A,V6)) | hAPP(hAPP(B,A),V6) = hAPP(hAPP(B,F),V6) | -hBOOL(hAPP(hAPP(c_member(tc_prod(E,E)),hAPP(hAPP(c_Product__Type_OPair(E,E),V7),f90(B,C,D,E))),C)) | hAPP(f89(B,C,D,E),V7) = hAPP(f88(B,C,D,E),V7). [resolve(575,c,573,c)]. 1.07/1.29 Derived: hAPP(A,f91(B,C,D,E,F,A,V6)) != hAPP(F,f91(B,C,D,E,F,A,V6)) | hAPP(hAPP(B,A),V6) = hAPP(hAPP(B,F),V6) | hAPP(hAPP(B,f89(B,C,D,E)),f90(B,C,D,E)) != hAPP(hAPP(B,f88(B,C,D,E)),f90(B,C,D,E)). [resolve(575,c,574,b)]. 1.07/1.29 576 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(438)]. 1.07/1.29 577 -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(123)]. 1.07/1.29 578 -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(123)]. 1.07/1.29 579 -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(123)]. 1.07/1.29 580 -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(237)]. 1.07/1.29 581 -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(307)]. 1.07/1.29 582 -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(363)]. 1.07/1.29 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(576,b,577,a)]. 1.07/1.29 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(576,b,578,a)]. 1.07/1.31 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(576,b,579,a)]. 1.07/1.31 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),c_Orderings_Obot__class_Obot(tc_fun(B,A))) = C. [resolve(576,b,580,a)]. 1.07/1.31 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(576,b,581,a)]. 1.07/1.31 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(576,b,582,a)]. 1.07/1.31 583 -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(491)]. 1.07/1.31 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B)),c_Orderings_Obot__class_Obot(tc_fun(A,B))),C) = C | -class_Lattices_Obounded__lattice(B). [resolve(583,a,576,b)]. 1.07/1.31 584 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption]. 1.07/1.31 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,577,a)]. 1.07/1.31 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(584,a,578,a)]. 1.07/1.31 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(584,a,579,a)]. 1.07/1.31 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(584,a,580,a)]. 1.07/1.31 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(584,a,581,a)]. 1.07/1.31 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(584,a,582,a)]. 1.07/1.31 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),A) = A. [resolve(584,a,583,a)]. 1.07/1.31 585 -hBOOL(hAPP(hAPP(c_member(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,f30(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(143)]. 1.07/1.31 586 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(fact_u) # label(axiom). [assumption]. 1.07/1.31 587 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f27(A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(143)]. 1.07/1.31 588 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f28(A)),f29(A))),hAPP(f27(A),B))) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(143)]. 1.16/1.36 589 -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f28(A)),f29(A))),hAPP(A,f27(A)))) | c_Arrow__Order__Mirabelle_Ounanimity(A) # label(fact_unanimity__def) # label(axiom). [clausify(143)]. 1.16/1.36 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,f30(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(585,d,586,a)]. 1.16/1.36 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,f30(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))),f27(D)),c_Arrow__Order__Mirabelle_OProf)). [resolve(585,d,587,b)]. 1.16/1.36 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,f30(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),f28(D)),f29(D))),hAPP(f27(D),E))). [resolve(585,d,588,b)]. 1.16/1.36 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,f30(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),f28(D)),f29(D))),hAPP(D,f27(D)))). [resolve(585,d,589,b)]. 1.16/1.36 590 -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(418)]. 1.21/1.42 591 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 1.21/1.42 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(590,a,591,a)]. 1.21/1.42 592 -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(496)]. 1.21/1.42 593 c_Relation_Oirrefl(A,B) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f53(B,A)),f53(B,A))),B)) # label(fact_irrefl__def) # label(axiom). [clausify(223)]. 1.21/1.42 594 -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(223)]. 1.21/1.42 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f53(B,A)),f53(B,A))),B)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)). [resolve(593,a,594,a)]. 1.21/1.42 595 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | -c_Arrow__Order__Mirabelle_Odictator(B,C) # label(fact_dictator__def) # label(axiom). [clausify(432)]. 1.21/1.42 596 -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)))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f56(B,A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(245)]. 1.21/1.42 597 -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)))) | f58(B,A) != f57(B,A) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(245)]. 1.21/1.42 598 -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),f57(B,A)),f58(B,A))),hAPP(f56(B,A),B))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(245)]. 1.21/1.42 599 -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),f57(B,A)),f58(B,A))),hAPP(A,f56(B,A)))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom). [clausify(245)]. 1.21/1.42 600 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f83(A,B)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(B,A) # label(fact_dictator__def) # label(axiom). [clausify(432)]. 1.21/1.42 601 hAPP(A,f83(B,A)) != hAPP(f83(B,A),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictator__def) # label(axiom). [clausify(432)]. 1.21/1.42 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))),f56(C,B)),c_Arrow__Order__Mirabelle_OProf)). [resolve(595,c,596,c)]. 1.21/1.42 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)))) | f58(C,B) != f57(C,B). [resolve(595,c,597,c)]. 1.21/1.42 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),f57(C,B)),f58(C,B))),hAPP(f56(C,B),C))). [resolve(595,c,598,c)]. 1.21/1.42 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),f57(C,B)),f58(C,B))),hAPP(B,f56(C,B)))). [resolve(595,c,599,c)]. 1.21/1.42 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f83(C,B)),c_Arrow__Order__Mirabelle_OProf)). [resolve(595,c,600,b)]. 1.21/1.42 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,A) = hAPP(A,C) | hAPP(B,f83(C,B)) != hAPP(f83(C,B),C). [resolve(595,c,601,b)]. 1.28/1.51 602 hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),C),D)),E)) | -c_FunDef_Oin__rel(A,B,E,C,D) # label(fact_in__rel__def) # label(axiom). [clausify(253)]. 1.28/1.51 603 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),C),D)),E)) | c_FunDef_Oin__rel(A,B,E,C,D) # label(fact_in__rel__def) # label(axiom). [clausify(253)]. 1.28/1.51 604 -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(400)]. 1.28/1.51 605 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(377)]. 1.28/1.51 606 c_Relation_Ototal__on(A,B,C) | hBOOL(hAPP(hAPP(c_member(A),f78(C,B,A)),B)) # label(fact_total__on__def) # label(axiom). [clausify(400)]. 1.28/1.51 Derived: hBOOL(hAPP(hAPP(c_member(A),f78(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(606,a,604,a)]. 1.28/1.51 607 c_Relation_Ototal__on(A,B,C) | hBOOL(hAPP(hAPP(c_member(A),f79(C,B,A)),B)) # label(fact_total__on__def) # label(axiom). [clausify(400)]. 1.28/1.51 Derived: hBOOL(hAPP(hAPP(c_member(A),f79(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(607,a,604,a)]. 1.28/1.51 608 c_Relation_Ototal__on(A,B,C) | f79(C,B,A) != f78(C,B,A) # label(fact_total__on__def) # label(axiom). [clausify(400)]. 1.28/1.51 Derived: f79(A,B,C) != f78(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(608,a,604,a)]. 1.28/1.51 609 c_Relation_Ototal__on(A,B,C) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f79(C,B,A)),f78(C,B,A))),C)) # label(fact_total__on__def) # label(axiom). [clausify(400)]. 1.28/1.51 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f79(B,C,A)),f78(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(609,a,604,a)]. 1.28/1.51 610 c_Relation_Ototal__on(A,B,C) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f78(C,B,A)),f79(C,B,A))),C)) # label(fact_total__on__def) # label(axiom). [clausify(400)]. 1.28/1.51 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f78(B,C,A)),f79(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(610,a,604,a)]. 1.28/1.51 611 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(492)]. 1.28/1.51 612 -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f99(B,A)),f99(B,A))),B)) | c_Nitpick_Orefl_H(A,B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(492)]. 1.28/1.51 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),C)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f99(C,A)),f99(C,A))),C)). [resolve(611,b,612,b)]. 4.01/4.18 4.01/4.18 ============================== end predicate elimination ============= 4.01/4.18 4.01/4.18 Auto_denials: (non-Horn, no changes). 4.01/4.18 4.01/4.18 Term ordering decisions: 4.01/4.18 Function symbol KB weights: tc_Arrow__Order__Mirabelle_Oalt=1. tc_HOL_Obool=1. tc_Arrow__Order__Mirabelle_Oindi=1. tc_Nat_Onat=1. c_Arrow__Order__Mirabelle_OProf=1. c_Arrow__Order__Mirabelle_OLin=1. v_F=1. c_Arrow__Order__Mirabelle_Oabove=1. v_a____=1. v_b____=1. c_fequal=1. v_P____=1. v_Q____=1. v_a_H____=1. v_b_H____=1. v_P_H____=1. c_fNot=1. c_Wellfounded_Oless__than=1. hAPP=1. tc_fun=1. tc_prod=1. c_Product__Type_OPair=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Ortranclp=1. c_Transitive__Closure_Otrancl=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_If=1. c_Set_Othe__elem=1. f9=1. f23=1. f46=1. f51=1. f53=1. f56=1. f57=1. f58=1. f65=1. f75=1. f83=1. f99=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_HOL_Oundefined=1. f27=1. f28=1. f29=1. f94=1. f95=1. f96=1. f97=1. c_Set_Oinsert=1. c_COMBC=1. c_COMBK=1. c_Groups_Ominus__class_Ominus=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Obelow=1. c_FuncSet_Oextensional=1. c_COMBS=1. c_Wellfounded_Omlex__prod=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f8=1. f18=1. f33=1. f34=1. f35=1. f42=1. f43=1. f44=1. f45=1. f47=1. f48=1. f60=1. f63=1. f78=1. f79=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_HOL_OLet=1. c_Nitpick_Owf__wfrec=1. c_Recdef_Osame__fst=1. f7=1. f10=1. f11=1. f12=1. f30=1. f31=1. f38=1. f39=1. f40=1. f41=1. f49=1. f50=1. f52=1. f54=1. f55=1. f59=1. f64=1. f77=1. f82=1. f88=1. f89=1. f90=1. f92=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. f24=1. f25=1. f26=1. f36=1. f37=1. f61=1. f62=1. f66=1. f69=1. f70=1. f71=1. f72=1. f84=1. f85=1. f87=1. f93=1. f98=1. f100=1. c_FuncSet_Ocompose=1. c_Product__Type_Ocurry=1. f17=1. f32=1. f68=1. f74=1. f76=1. f86=1. f67=1. f73=1. f80=1. f81=1. f91=1. f13=1. f14=1. f15=1. f16=1. f19=1. f20=1. f21=1. f22=1. 4.01/4.18 4.01/4.18 ============================== end of process initial clauses ======== 4.01/4.18 4.01/4.18 ============================== CLAUSES FOR SEARCH ==================== 4.01/4.18 4.01/4.18 ============================== end of clauses for search ============= 4.01/4.18 4.01/4.18 ============================== SEARCH ================================ 4.01/4.18 4.01/4.18 % Starting search at 0.67 seconds. 4.01/4.18 4.01/4.18 Low Water (keep): wt=196.000, iters=3863 4.01/4.18 4.01/4.18 Low Water (keep): wt=113.000, iters=3393 4.01/4.18 4.01/4.18 Low Water (keep): wt=109.000, iters=3366 4.01/4.18 4.01/4.18 Low Water (keep): wt=101.000, iters=3359 4.01/4.18 4.01/4.18 Low Water (keep): wt=96.000, iters=3333 4.01/4.18 4.01/4.18 Low Water (keep): wt=95.000, iters=3461 4.01/4.18 4.01/4.18 Low Water (keep): wt=94.000, iters=3446 4.01/4.18 4.01/4.18 Low Water (keep): wt=91.000, iters=3407 4.01/4.18 4.01/4.18 Low Water (keep): wt=81.000, iters=3353 4.01/4.18 4.01/4.18 Low Water (keep): wt=77.000, iters=3423 4.01/4.18 4.01/4.18 Low Water (keep): wt=72.000, iters=3378 4.01/4.18 4.01/4.18 Low Water (keep): wt=70.000, iters=3364 4.01/4.18 4.01/4.18 Low Water (keep): wt=68.000, iters=3431 4.01/4.18 4.01/4.18 Low Water (keep): wt=67.000, iters=3384 4.01/4.18 4.01/4.18 Low Water (keep): wt=65.000, iters=3353 4.01/4.18 4.01/4.18 Low Water (keep): wt=64.000, iters=3531 4.01/4.18 4.01/4.18 Low Water (keep): wt=62.000, iters=3580 4.01/4.18 4.01/4.18 Low Water (keep): wt=59.000, iters=3514 4.01/4.18 4.01/4.18 Low Water (keep): wt=56.000, iters=3432 4.01/4.18 4.01/4.18 Low Water (keep): wt=55.000, iters=3371 4.01/4.18 4.01/4.18 Low Water (keep): wt=54.000, iters=3450 4.01/4.18 4.01/4.18 Low Water (keep): wt=53.000, iters=3424 4.01/4.18 4.01/4.18 Low Water (keep): wt=52.000, iters=3341 4.01/4.18 4.01/4.18 Low Water (keep): wt=51.000, iters=3412 4.01/4.18 4.01/4.18 Low Water (keep): wt=50.000, iters=3347 4.01/4.18 4.01/4.18 Low Water (keep): wt=49.000, iters=3382 4.01/4.18 4.01/4.18 Low Water (keep): wt=48.000, iters=3374 4.01/4.18 4.01/4.18 Low Water (keep): wt=47.000, iters=3371 4.01/4.18 4.01/4.18 Low Water (keep): wt=46.000, iters=3383 4.01/4.18 4.01/4.18 Low Water (keep): wt=45.000, iters=3355 4.01/4.18 4.01/4.18 Low Water (keep): wt=44.000, iters=3374 4.01/4.18 4.01/4.18 Low Water (keep): wt=43.000, iters=3422 4.01/4.18 4.01/4.18 Low Water (keep): wt=42.000, iters=3349 4.01/4.18 4.01/4.18 Low Water (keep): wt=41.000, iters=3350 4.01/4.18 300.04/300.22 Cputime limit exceeded (core dumped) 300.04/300.23 EOF