0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n032.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % DateTime : Thu Jul 2 08:57:04 EDT 2020 0.10/0.31 % CPUTime : 1.41/1.73 ============================== Prover9 =============================== 1.41/1.73 Prover9 (32) version 2009-11A, November 2009. 1.41/1.73 Process 26550 was started by sandbox2 on n032.cluster.edu, 1.41/1.73 Thu Jul 2 08:57:05 2020 1.41/1.73 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_26390_n032.cluster.edu". 1.41/1.73 ============================== end of head =========================== 1.41/1.73 1.41/1.73 ============================== INPUT ================================= 1.41/1.73 1.41/1.73 % Reading from file /tmp/Prover9_26390_n032.cluster.edu 1.41/1.73 1.41/1.73 set(prolog_style_variables). 1.41/1.73 set(auto2). 1.41/1.73 % set(auto2) -> set(auto). 1.41/1.73 % set(auto) -> set(auto_inference). 1.41/1.73 % set(auto) -> set(auto_setup). 1.41/1.73 % set(auto_setup) -> set(predicate_elim). 1.41/1.73 % set(auto_setup) -> assign(eq_defs, unfold). 1.41/1.73 % set(auto) -> set(auto_limits). 1.41/1.73 % set(auto_limits) -> assign(max_weight, "100.000"). 1.41/1.73 % set(auto_limits) -> assign(sos_limit, 20000). 1.41/1.73 % set(auto) -> set(auto_denials). 1.41/1.73 % set(auto) -> set(auto_process). 1.41/1.73 % set(auto2) -> assign(new_constants, 1). 1.41/1.73 % set(auto2) -> assign(fold_denial_max, 3). 1.41/1.73 % set(auto2) -> assign(max_weight, "200.000"). 1.41/1.73 % set(auto2) -> assign(max_hours, 1). 1.41/1.73 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.41/1.73 % set(auto2) -> assign(max_seconds, 0). 1.41/1.73 % set(auto2) -> assign(max_minutes, 5). 1.41/1.73 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.41/1.73 % set(auto2) -> set(sort_initial_sos). 1.41/1.73 % set(auto2) -> assign(sos_limit, -1). 1.41/1.73 % set(auto2) -> assign(lrs_ticks, 3000). 1.41/1.73 % set(auto2) -> assign(max_megs, 400). 1.41/1.73 % set(auto2) -> assign(stats, some). 1.41/1.73 % set(auto2) -> clear(echo_input). 1.41/1.73 % set(auto2) -> set(quiet). 1.41/1.73 % set(auto2) -> clear(print_initial_clauses). 1.41/1.73 % set(auto2) -> clear(print_given). 1.41/1.73 assign(lrs_ticks,-1). 1.41/1.73 assign(sos_limit,10000). 1.41/1.73 assign(order,kbo). 1.41/1.73 set(lex_order_vars). 1.41/1.73 clear(print_given). 1.41/1.73 1.41/1.73 % formulas(sos). % not echoed (527 formulas) 1.41/1.73 1.41/1.73 ============================== end of input ========================== 1.41/1.73 1.41/1.73 % From the command line: assign(max_seconds, 960). 1.41/1.73 1.41/1.73 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.41/1.73 1.41/1.73 % Formulas that are not ordinary clauses: 1.41/1.73 1 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 2 (all V_r_2 all T_b all V_a_2 all T_a (c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)) -> -(all B_y -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,B_y),V_r_2)))) # label(fact_DomainE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 3 (all V_A_2 all V_B_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_B_2) -> 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),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2))) # label(fact_insert__Diff1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 4 (all V_r_2 all T_a c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ORange(T_a,T_a,V_r_2)) # label(fact_trancl__range) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 5 (all V_B_2 all T_a 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) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 6 (all T_a c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a))) # label(fact_refl__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 7 (all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_r__into__trancl_H) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 8 (all V_b_2 all V_a_2 all V_r_2 all T_a (c_Relation_Orefl__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_Relation_Oantisym(T_a,V_r_2) -> (c_member(T_a,V_a_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_b_2,c_Relation_OField(T_a,V_r_2)) -> (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_a_2 = V_b_2)))))) # label(fact_Refl__antisym__eq__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 9 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 10 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 11 (all V_b_H_2 all V_a_H_2 all V_b_2 all V_a_2 all T_b all T_a (c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2) = c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2) <-> V_b_2 = V_b_H_2 & V_a_2 = V_a_H_2)) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 12 (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) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> c_member(T_a,V_x_2,V_A_2)))) # label(fact_refl__onD1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 13 (all V_S_2 all V_R_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 14 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> (c_Relation_Oantisym(T_a,V_r_2) -> c_Relation_Otrans(T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))))) # label(fact_trans__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 15 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 16 (all T_a c_Order__Relation_Opartial__order__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_partial__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 17 (all V_r_2 all T_b all T_a (V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) <-> c_Relation_ODomain(T_a,T_b,V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Domain__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 18 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) = hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2))) # label(fact_inf__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 19 (all V_Q_2 all V_P_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_P_2,V_Q_2))) -> ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_x),c_Transitive__Closure_Ortrancl(T_a,V_P_2)) -> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_Q_2) -> B_y = B_x)))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_P_2))))) # label(fact_rtrancl__Un__separatorE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 20 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 21 (all V_c_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)) -> -(-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 22 (all V_r_2 all V_z_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),V_r_2) -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))))) # label(fact_converse__tranclE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 23 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 24 (all V_R_2 all T_a c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Domain__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 25 (all V_b_2 all V_a_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,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 26 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 27 (all T_a c_Relation_Oantisym(T_a,c_Relation_OId(T_a))) # label(fact_antisym__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 28 (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,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 29 (all V_y_2 all V_x_2 (V_y_2 = V_x_2 | -hBOOL(hAPP(c_fequal(V_x_2),V_y_2)))) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 30 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b))))) # label(fact_le__infE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 31 (all V_r_2 all T_b all V_b_2 all T_a (c_member(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2)) -> -(all B_x -c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_b_2),V_r_2)))) # label(fact_RangeE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 32 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_A_2))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 33 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))) # label(fact_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 34 (all V_A_2 all V_r_2 all T_b all V_b_2 all T_a (c_member(T_a,V_b_2,c_Relation_OImage(T_b,T_a,V_r_2,V_A_2)) <-> (exists B_x (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_b_2),V_r_2) & c_member(T_b,B_x,V_A_2))))) # label(fact_Image__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 35 (all V_B_2 all V_a_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_a_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,V_B_2),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_Diff__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 36 (all V_b_2 all V_a_2 all V_r_2 all T_a (c_Order__Relation_Opreorder__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_member(T_a,V_a_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_b_2,c_Relation_OField(T_a,V_r_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),V_r_2)))))) # label(fact_subset__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 37 (all V_x_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc__wfD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 38 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d)))))) # label(fact_sup__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 39 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))))) # label(fact_distrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 40 (all V_r_2 all V_b_2 all V_a_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2) -> c_member(T_b,V_b_2,c_Relation_ORange(T_a,T_b,V_r_2)))) # label(fact_RangeI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 41 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__top__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 42 (all V_b_2 all V_a_2 all T_a (c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) -> V_a_2 = V_b_2)) # label(fact_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 43 (all V_b_2 all V_a_2 all V_c_2 all T_a all T_c all T_b hAPP(hAPP(V_c_2,V_a_2),V_b_2) = c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_c_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))) # label(fact_internal__split__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 44 (all V_B_2 all V_A_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))))) # label(fact_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 45 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 46 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__into__trancl1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 47 (all V_z_2 all V_r_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_rtrancl__trancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 48 (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 = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2)))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 49 (all T_a c_Order__Relation_Opreorder__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_preorder__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 50 (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,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = 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]. 1.41/1.73 51 (all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> -(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)))) # label(fact_equalityE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 52 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a,V_r_2),c_Relation_OField(T_a,V_s_2)))) # label(fact_mono__Field) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 53 (all V_b_2 all V_a_2 all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),V_r_2) -> V_b_2 = V_a_2)))) # label(fact_antisymD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 54 (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(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1I2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 55 (all B_x (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)))) # label(conj_1) # label(hypothesis) # label(non_clause). [assumption]. 1.41/1.73 56 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z))) # label(fact_sup__assoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 57 (all V_S_2 all V_R_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) | c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_S_2)) -> c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))))) # label(fact_in__rtrancl__UnI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 58 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Int__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 59 (all V_a_2 all V_b_2 all T_a (V_b_2 = V_a_2 <-> c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 60 (all V_a_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_member(T_a,V_a_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2)))) # label(fact_refl__onD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 61 (all V_R_2 all T_a all T_b c_Relation_OImage(T_b,T_a,V_R_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Image__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 62 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)) # label(fact_Int__Diff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 63 (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_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = V_x))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 64 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 65 (all V_r_2 all V_x_2 all T_a ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2) -> c_member(T_a,B_y,c_Wellfounded_Oacc(T_a,V_r_2)))) -> c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc_OaccI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 66 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 67 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_IntI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 68 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 69 (all V_r_2 all T_a c_Relation_Otrans(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))) # label(fact_trans__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 70 (all V_B_2 all V_a_2 all T_a c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))) # label(fact_insertI1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 71 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x))))) # label(fact_le__supE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 72 (all V_R_2 all V_y_2 all V_x_2 all T_a (V_x_2 = V_y_2 | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) & V_y_2 != V_x_2 <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))) # label(fact_rtrancl__eq__or__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 73 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__assoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 74 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2)) <-> V_x_2 != V_z_2 & (V_y_2 = V_z_2 -> V_y_2 != V_x_2) & (V_z_2 != V_y_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)))) # label(fact_in__mktop) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 75 (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 (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,B_z,hAPP(V_g_2,B_z)))) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_Fa_2,V_x_2,hAPP(hAPP(V_Fa_2,V_g_2),V_x_2)))) # label(fact_wfrec__rel_Ointros) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 76 (all V_B_2 all V_A_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,V_A_2) -> (-c_member(T_a,V_x_2,V_B_2) -> (V_B_2 = V_A_2 <-> c_Set_Oinsert(T_a,V_x_2,V_B_2) = c_Set_Oinsert(T_a,V_x_2,V_A_2))))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 77 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) | c_member(T_a,V_c_2,V_B_2) <-> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 78 (all V_b_2 all V_a_2 all V_L_2 (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) -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_2,V_b_2),V_L_2) -> -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_b_2,V_a_2),V_L_2)))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 79 (all V_s_2 all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> (c_Relation_Otrans(T_a,V_s_2) -> c_Relation_Otrans(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_trans__Int) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 80 (all V_x_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> (c_member(T_a,V_x_2,V_A_2) <-> c_member(T_a,V_x_2,V_B_2)))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 81 (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]. 1.41/1.73 82 (all V_A_2 all V_b_2 all V_a_2 all V_r_2 all T_a (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_b_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2))))) # label(fact_eq__equiv__class) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 83 (all T_a c_Order__Relation_Owell__order__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_well__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 84 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z))) # label(fact_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 85 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> V_x = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a)))) # label(fact_sup__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 86 (all V_A_2 all V_y_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 87 (all V_a5_2 all V_a1_2 all V_a2_2 all V_a4_2 all V_a3_2 all T_b all T_a (c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) <-> (exists B_x exists B_y (hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,B_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) & c_member(T_a,B_x,V_a2_2))) | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) & V_a4_2 = hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))) # label(fact_fold__graph_H_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 88 (all V_P_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_P_2,V_b_2)) -> ((all B_y all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_P_2,B_z)) -> hBOOL(hAPP(V_P_2,B_y)))))) -> hBOOL(hAPP(V_P_2,V_a_2)))))) # label(fact_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 89 (all V_x_2 all T_b all T_a (class_Orderings_Otop(T_a) -> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_top__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 90 (all V_A_2 all V_b_2 all V_a_2 all T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2)) -> (V_a_2 != V_b_2 -> c_member(T_a,V_a_2,V_A_2)))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.73 91 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> 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]. 1.41/1.73 92 (all V_B_2 all V_A_2 all V_C_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))))) # label(fact_Int__greatest) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 93 (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) <-> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),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]. 1.41/1.74 94 (all V_r_2 all T_a c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2)) # label(fact_total__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 95 (all V_a2_2 all V_a1_2 all T_b all T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2)) # label(fact_fold__graph_H_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 96 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Opartial__order__on(T_a,V_A_2,V_r_2) & c_Relation_Ototal__on(T_a,V_A_2,V_r_2))) # label(fact_linear__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 97 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 98 (all V_R_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) -> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),V_R_2) & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))))) # label(fact_tranclD2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 99 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 100 (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) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> c_member(T_a,V_y_2,V_A_2)))) # label(fact_refl__onD2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 101 (all V_r_2 all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2) -> B_x = B_y))) <-> c_Relation_Oantisym(T_a,V_r_2))) # label(fact_antisym__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 102 (all V_A_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,V_A_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2)) # label(fact_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 103 (all V_B_2 all V_A_2 all V_C_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 104 (all V_A_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Groups_Ominus__class_Ominus(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__Diff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 105 (all V_B_2 all V_a_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_a_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_a_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]. 1.41/1.74 106 (all V_f_2 all T_b all V_r_2 all V_a_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2) -> hAPP(c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2),V_x_2) = hAPP(V_f_2,V_x_2))) # label(fact_cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 107 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))) # label(fact_sup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 108 (all T_2 all T_1 (class_Orderings_Obot(T_1) -> class_Orderings_Obot(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Obot) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 109 (all V_c_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 110 (all V_B_2 all V_x_2 all V_A_2 all T_a (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,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2) -> (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,c_Set_Oinsert(T_a,V_x_2,V_B_2))))) # label(fact_diff__single__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 111 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 112 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 113 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Un__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 114 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 115 (all V_B_2 all V_C_2 all V_a_2 all T_a (-c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2))) # label(fact_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 116 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 117 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 118 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 119 (all V_A_2 all V_B_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnI2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 120 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_r_2) -> c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_acyclic__impl__antisym__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 121 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 122 (all V_R2_2 all V_R1_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)))) # label(fact_acc__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 123 (all V_a_2 all T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Relation_OId(T_a))) # label(fact_IdI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 124 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 125 (all V_x_2 all V_a_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2)))) # label(fact_wf__not__sym) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 126 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)) # label(fact_Int__lower2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 127 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_rtrancl__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 128 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 129 (all B_P ((all B_x (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(B_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(B_P,B_x)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(B_P,B_x)))) -> (all B_a all B_b (B_b != B_a -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(B_P,v_i)) -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(B_P))))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption]. 1.41/1.74 130 (all V_r_2 all V_z_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (V_z_2 != V_x_2 -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))))) # label(fact_converse__rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 131 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 132 (all V_b_2 all V_a_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)))) # label(fact_equiv__class__nondisjoint) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 133 (all T_2 all T_1 (class_Lattices_Odistrib__lattice(T_1) -> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 134 (all T_b all T_a all B_M all B_R (c_Wellfounded_Owf(T_a,B_R) -> (all B_x hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x) = hAPP(hAPP(B_M,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_R,B_x)),B_x)))) # label(fact_tfl__wfrec) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 135 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 136 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d)))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 137 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2) -> c_Order__Relation_Ostrict__linear__order__on(T_a,V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))))) # label(fact_strict__linear__order__on__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 138 (all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> 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))))) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 139 (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]. 1.41/1.74 140 (all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) <-> c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))))) # label(fact_antisym__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 141 (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) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_r_2) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_z_2),V_r_2) -> V_z_2 = V_y_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 142 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Otop__class_Otop(T_a),V_x) = V_x)) # label(fact_inf__top__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 143 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 144 (all V_b_2 all V_B_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_B_2) -> c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)))) # label(fact_insertI2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 145 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) # label(fact_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 146 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 147 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2)))) # label(fact_Domain__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 148 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_B_2) & c_member(T_a,V_c_2,V_A_2) <-> c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 149 (all V_r_2 all V_A_2 all T_a (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2))) # label(fact_quotient__is__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 150 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x))))) # label(fact_sup__least) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 151 (all V_x_2 all V_L_2 (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) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_x_2),c_Arrow__Order__Mirabelle_OLin))) # label(fact_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 152 (all V_r_2 all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2))))) -> c_Relation_Otrans(T_a,V_r_2))) # label(fact_transI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 153 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 154 (all V_A_2 all V_b_2 all V_a_2 all T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2)) <-> c_member(T_a,V_a_2,V_A_2) | V_b_2 = V_a_2)) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 155 (all T_b all V_a_2 all V_x_2 all T_a all B_f all B_R (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),B_R) -> hAPP(B_f,V_x_2) = hAPP(c_Recdef_Ocut(T_a,T_b,B_f,B_R,V_a_2),V_x_2))) # label(fact_tfl__cut__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 156 (all V_R_2 all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) -> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),V_R_2) & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))))) # label(fact_tranclD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 157 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 158 (all V_f_2 all T_a c_Wellfounded_Owf(T_a,c_Wellfounded_Omeasure(T_a,V_f_2))) # label(fact_wf__measure) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 159 (all T_a c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_UNIV__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 160 (all V_b_2 all V_a_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))) # label(fact_equiv__class__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 161 (all V_B_2 all V_A_2 all V_R_2 all T_a all T_b c_Relation_OImage(T_b,T_a,V_R_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_R_2,V_B_2))) # label(fact_Image__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 162 (all V_r_2 all V_x_2 all V_y_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_r_2) & -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) <-> c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2)))) # label(fact_acyclic__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 163 (all V_A_2 all T_a all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> (c_member(T_a,V_a_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2))))) # label(fact_Id__on__eqI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 164 (all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> (all B_x -c_member(T_a,B_x,V_A_2)))) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 165 (all V_x all V_y all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 166 (all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Relation_OId(T_a)) -> -(all B_x c_Product__Type_OPair(T_a,T_a,B_x,B_x) != V_p_2))) # label(fact_IdE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 167 (all V_r_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = c_Equiv__Relations_Oquotient(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2)) # label(fact_quotient__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 168 (all V_a_2 all V_b_2 all T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) -> V_b_2 = V_a_2)) # label(fact_singletonE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 169 (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]. 1.41/1.74 170 (all V_y_2 all V_z_2 all V_f_2 all T_b all V_A_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_A_2) -> (c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) -> c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2))))) # label(fact_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 171 (all V_y_2 all V_x_2 all V_L_2 all V_b_2 all V_a_2 (V_b_2 != V_a_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (V_y_2 != V_x_2 & (V_x_2 = V_b_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_2,V_y_2),V_L_2)) & (V_x_2 != V_b_2 -> (V_y_2 = V_b_2 -> V_a_2 = V_x_2 | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_a_2),V_L_2)) & (V_b_2 != V_y_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2))) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_a_2,V_b_2)))))) # label(fact_in__above) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 172 (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(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1CI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 173 (all V_r_2 all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2) -> B_x = B_y))) -> c_Relation_Oantisym(T_a,V_r_2))) # label(fact_antisymI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 174 (all V_s_2 all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_s_2))))) # label(fact_trancl__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 175 (all V_P_2 all V_B_2 all V_A_2 all T_a ((all B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> hBOOL(hAPP(V_P_2,B_x)))) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> hBOOL(hAPP(V_P_2,B_x)))) & (all B_x (c_member(T_a,B_x,V_B_2) -> hBOOL(hAPP(V_P_2,B_x)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 176 (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) -> (c_member(T_a,V_x_2,V_A_2) -> c_member(T_a,V_x_2,V_B_2)))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 177 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Un__UNIV__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 178 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 179 (all V_r_2 all V_x_2 all V_y_2 all T_a (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) & c_Wellfounded_Owf(T_a,V_r_2) <-> c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2)))) # label(fact_wf__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 180 (all V_r_2 all T_a c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_refl__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 181 (all V_Q_2 all T_a all V_x_2 all V_P_2 (hBOOL(hAPP(V_P_2,V_x_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 182 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 183 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_inf1D1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 184 (all V_A_2 all T_a all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> (c_member(T_a,V_b_2,V_A_2) -> c_member(T_a,V_a_2,V_A_2)))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 185 (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]. 1.41/1.74 186 (all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (class_Groups_Ominus(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) = hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 187 (all V_y_2 all V_x_2 all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> (V_y_2 = c_Orderings_Obot__class_Obot(T_a) & V_x_2 = c_Orderings_Obot__class_Obot(T_a) <-> c_Orderings_Obot__class_Obot(T_a) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 188 (all V_B_2 all V_A_2 all V_x_2 all T_a (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_member(T_a,V_x_2,V_B_2)))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 189 (all V_r_2 all V_a_2 all T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 190 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> V_x = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 191 (all V_R_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_rtrancl__reflcl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 192 (all V_B_2 all V_A_2 all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Lattices_Osemilattice__inf__class_Oinf(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__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 193 (all V_x all T_a (class_Orderings_Otop(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)))) # label(fact_top__greatest) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 194 (all V_r_2 all V_a_2 all V_b_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downwards__aux) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 195 (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,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),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__Int) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 196 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Transitive__Closure_Ortrancl(T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))) # label(fact_rtrancl__r__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 197 (all V_r_2 all T_a ((all B_x c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))) <-> c_Wellfounded_Owf(T_a,V_r_2))) # label(fact_wf__acc__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 198 (all V_A_2 all V_B_2 all V_x_2 all T_a ((c_member(T_a,V_x_2,V_B_2) -> c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & (-c_member(T_a,V_x_2,V_B_2) -> c_Set_Oinsert(T_a,V_x_2,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),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)))) # label(fact_insert__Diff__if) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 199 (all V_C_2 all V_B_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 200 (all V_r_2 all T_b all V_a_2 all T_a ((exists B_y c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,B_y),V_r_2)) <-> c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)))) # label(fact_Domain__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 201 (all V_r_2 all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 <-> c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2))) # label(fact_quotient__is__empty2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 202 (all V_r_2 all T_a c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))) # label(fact_refl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 203 (all V_x_2 all V_Fa_2 all V_R_2 all T_a all T_b hAPP(hAPP(V_Fa_2,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) = c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_Fa_2,V_x_2)) # label(fact_Nitpick_Owf__wfrec_H__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 204 (all V_r_2 all T_a all T_b (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ORange(T_b,T_a,V_r_2) <-> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) = V_r_2)) # label(fact_Range__empty__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 205 (all V_x_2 all T_a c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 206 (all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_trancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 207 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> -(c_member(T_a,V_c_2,V_A_2) -> -c_member(T_a,V_c_2,V_B_2)))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 208 (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),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)))) # label(fact_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 209 (all V_r_2 all V_a_2 all T_a ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2) -> c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))) <-> c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2)))) # label(fact_acc_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 210 (all V_r_H_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_H_2,V_r_2)))) # label(fact_wf__Int2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 211 (all V_R_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) -> V_a_2 = V_b_2 | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)) & V_b_2 != V_a_2)) # label(fact_rtranclD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 212 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2)))) # label(fact_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 213 (all V_r_2 all T_b all V_a_2 all T_a (c_member(T_a,V_a_2,c_Relation_ORange(T_b,T_a,V_r_2)) <-> (exists B_y c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_y,V_a_2),V_r_2)))) # label(fact_Range__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 214 (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 (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_A_2) -> (B_x != B_xa -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2) | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)))))))) # label(fact_total__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 215 (all V_A_2 all V_a_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Set_Oinsert(T_a,V_a_2,V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 216 (all V_b_H all V_a_H all V_b all V_a all T_b all T_a (c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H) = c_Product__Type_OPair(T_a,T_b,V_a,V_b) -> -(V_a_H = V_a -> V_b != V_b_H))) # label(fact_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 217 (all V_r_2 all V_b_2 all T_b all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2) -> c_member(T_b,V_b_2,c_Relation_OImage(T_a,T_b,V_r_2,V_A_2))))) # label(fact_rev__ImageI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 218 (all V_A_2 all T_a 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))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Int__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 219 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,V_A_2) -> (c_member(T_a,V_y_2,V_A_2) -> (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)))))) # label(fact_eq__equiv__class__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 220 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) <-> (all B_x all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_z),V_r_2))))))) # label(fact_trans__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 221 (all V_A_2 all V_R_2 all T_a (c_Wellfounded_Owf(T_a,V_R_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Relation_OImage(T_a,T_a,V_R_2,V_A_2)) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_wfE__pf) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 222 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 223 (all V_y_2 all V_x_2 all T_a (V_x_2 = V_y_2 <-> c_member(T_a,V_x_2,c_fequal(V_y_2)))) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 224 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 225 (all T_a all V_B_2 all V_A_2 (V_B_2 = V_A_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 226 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Relation_OId(T_a))) # label(fact_reflcl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 227 (all V_A_2 all V_C_2 all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),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]. 1.41/1.74 228 (all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 229 (all V_r_2 all V_A_2 all T_a (c_Relation_Ototal__on(T_a,V_A_2,V_r_2) <-> c_Relation_Ototal__on(T_a,V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))))) # label(fact_total__on__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 230 (all V_a_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_a_2,V_A_2) -> c_member(T_a,V_a_2,c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))) # label(fact_equiv__class__self) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 231 (all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> -(all B_c (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_c),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_c,V_b_2),V_r_2)))))) # label(fact_tranclE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.74 232 (all V_P_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 (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) -> ((all B_a all B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (all B_aa all B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2) -> (hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) -> hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))))))) -> hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)))))) # label(fact_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 233 (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) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_z_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) | c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 234 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2)) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 235 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 236 (all T_a c_Relation_ORange(T_a,T_a,c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Range__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 237 (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 (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_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]. 1.41/1.75 238 (all V_A_2 all V_B_2 all V_c_2 all T_a ((-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,V_A_2)) -> c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_UnCI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 239 (all V_L_2 all V_y_2 all V_x_2 (V_y_2 != V_x_2 -> (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) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_above__Lin) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 240 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> hBOOL(hAPP(V_B_2,V_x_2)))) # label(fact_inf1D2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 241 (all V_A_2 all T_a c_Relation_Otrans(T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_trans__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 242 (all V_s_2 all V_r_2 all V_b_H_2 all V_a_H_2 all V_b_2 all V_a_2 all T_b all T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2)),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_H_2),V_r_2) | V_a_2 = V_a_H_2 & c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_b_2,V_b_H_2),V_s_2))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 243 (all V_A_2 all V_y_2 all V_x_2 all T_a (c_member(T_a,V_x_2,V_A_2) & V_x_2 = V_y_2 <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2)))) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 244 (all V_A_2 all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_single__valued__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 245 (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),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2) <-> c_member(T_a,V_x_2,V_B_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 246 (all T_a c_Relation_ODomain(T_a,T_a,c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Domain__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 247 (all V_A_2 all T_a c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a),V_A_2) = V_A_2) # label(fact_Image__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 248 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)) <-> c_Relation_Oirrefl(T_a,V_r_2))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 249 (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 = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 250 (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),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)))) # label(fact_Un__least) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 251 (all T_a c_Relation_Oantisym(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_antisym__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 252 (all V_r_2 all T_a (c_Nitpick_Orefl_H(T_a,V_r_2) <-> (all B_x c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)))) # label(fact_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 253 (all V_a_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2))) # label(fact_wf__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 254 (all V_r_2 all V_b_2 all V_a_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2) -> c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)))) # label(fact_DomainI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 255 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Transitive__Closure_Otrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))) # label(fact_trancl__reflcl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 256 (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]. 1.41/1.75 257 (all V_r_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_a,V_r_2),c_Relation_ORange(T_a,T_a,V_r_2)) = c_Relation_OField(T_a,V_r_2)) # label(fact_Field__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 258 (all V_y_2 all V_x_2 all V_L_2 (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 -> (-c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_y_2,V_x_2),V_L_2))))) # label(fact_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 259 (all V_y_2 all V_x_2 all T_a (class_Lattices_Obounded__lattice__top(T_a) -> (c_Orderings_Otop__class_Otop(T_a) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x_2,V_y_2) <-> V_y_2 = c_Orderings_Otop__class_Otop(T_a) & V_x_2 = c_Orderings_Otop__class_Otop(T_a)))) # label(fact_inf__eq__top__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 260 (all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId(T_a)) <-> V_a_2 = V_b_2)) # label(fact_pair__in__Id__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 261 (all V_C_2 all V_B_2 all V_A_2 all T_a 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)) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)) # label(fact_Un__Diff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 262 (all V_a_2 all T_a -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_emptyE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 263 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 264 (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,V_a2_2),V_a1_2) = hAPP(hAPP(V_Fa_2,B_g),V_a1_2) & (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2) -> c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_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,hAPP(hAPP(V_Fa_2,V_a2_2),V_a1_2)))) # label(fact_wfrec__rel_Oequations) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 265 (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,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_refl__on__Int) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 266 (all V_B_2 all V_A_2 all V_a_2 all T_a (-c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 267 (all V_r_2 all T_b all T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2) <-> (all B_x all B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2) -> B_z = B_y)))))) # label(fact_single__valued__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 268 (all V_rb_2 all T_b all V_ra_2 all T_a (c_Wellfounded_Owf(T_a,V_ra_2) -> (c_Wellfounded_Owf(T_b,V_rb_2) -> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2))))) # label(fact_wf__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 269 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 270 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 271 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Int__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 272 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 273 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 274 (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) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = V_y))) # label(fact_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 275 (all V_b_2 all V_r_2 all V_a_2 all T_a (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downwards) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 276 (all V_B_2 all V_A_2 all T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> (all B_x (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_B_2) -> B_x != B_xa)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 277 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Int__lower1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 278 (all V_b_2 all V_B_2 all V_a_2 all T_a ((-c_member(T_a,V_a_2,V_B_2) -> V_b_2 = V_a_2) -> c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)))) # label(fact_insertCI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 279 (all T_a c_Order__Relation_Olinear__order__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_lnear__order__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 280 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,V_A_2) -> (-c_member(T_a,V_c_2,V_B_2) -> c_member(T_a,V_c_2,c_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]. 1.41/1.75 281 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 282 (all V_a_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_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2)))) # label(fact_insert__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 283 (all V_x_2 all V_L_2 (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) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_x_2),c_Arrow__Order__Mirabelle_OLin))) # label(fact_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 284 (all V_A_2 all T_a V_A_2 = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Int__UNIV__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 285 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> (-hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(V_B_2,V_x_2))))) # label(fact_sup1E) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 286 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> c_Lattices_Osemilattice__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)) = V_B_2)) # label(fact_Diff__partition) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 287 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Relation_Otrans(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))))) # label(fact_trans__reflclI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 288 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 289 (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 (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2) != c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2) -> -(all B_a all B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),V_r_2) -> -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))))))) # label(fact_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 290 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2))))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 291 (all V_P_2 all V_B_2 all V_A_2 all T_a ((exists B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & hBOOL(hAPP(V_P_2,B_x)))) <-> (exists B_x (hBOOL(hAPP(V_P_2,B_x)) & c_member(T_a,B_x,V_A_2))) | (exists B_x (hBOOL(hAPP(V_P_2,B_x)) & c_member(T_a,B_x,V_B_2))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 292 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 293 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Olinear__order__on(T_a,V_A_2,V_r_2) & c_Wellfounded_Owf(T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))) <-> c_Order__Relation_Owell__order__on(T_a,V_A_2,V_r_2))) # label(fact_well__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 294 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Un__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 295 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))) # label(fact_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 296 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 297 (all V_x_2 all V_a_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2)))) # label(fact_wf__asym) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 298 (all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a) = V_a)) # label(fact_sup_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 299 (all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_trancl_Or__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 300 (all V_B_2 all V_D_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_D_2,V_B_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),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2))))) # label(fact_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 301 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 302 (all T_b all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) # label(fact_Domain__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 303 (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,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Un__upper2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 304 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 305 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 306 (all V_y_2 all V_x_2 all V_R_2 all T_b all T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2) <-> c_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]. 1.41/1.75 307 (all V_R2_2 all T_b all V_R1_2 all T_a (c_Relation_Otrans(T_a,V_R1_2) -> (c_Relation_Otrans(T_b,V_R2_2) -> c_Relation_Otrans(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_R1_2,V_R2_2))))) # label(fact_trans__lex__prod) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 308 (all V_A_2 all V_B_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 309 (all V_R_2 all T_a c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Range__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 310 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 311 (all V_A_2 all T_a c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_antisym__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 312 (all V_A_2 all T_a c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2))) # label(fact_refl__on__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 313 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_fequal(V_x_2),V_y_2)) | V_x_2 != V_y_2)) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 314 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 315 (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 = 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]. 1.41/1.75 316 (all V_a_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2))) # label(fact_wf__not__refl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 317 (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]. 1.41/1.75 318 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))) # label(fact_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 319 (all V_B_2 all V_A_2 all V_c_2 all T_a (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)) <-> -c_member(T_a,V_c_2,V_B_2) & c_member(T_a,V_c_2,V_A_2))) # label(fact_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 320 (all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> V_x = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x))) # label(fact_sup__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 321 (all V_a_2 all V_H_2 all V_r_2 all T_b all T_a all V_f_2 (V_f_2 = c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2) -> (c_Wellfounded_Owf(T_a,V_r_2) -> hAPP(V_f_2,V_a_2) = hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2)),V_a_2)))) # label(fact_def__wfrec) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 322 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 323 (all V_r_2 all T_a c_Relation_Otrans(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))) # label(fact_trans__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 324 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Set_Oinsert(T_a,V_a_2,V_A_2)) # label(fact_insert__Diff__single) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 325 (all V_a_2 all V_b_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) -> (c_member(T_a,V_b_2,V_A_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2))))) # label(fact_subset__equiv__class) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 326 (all V_y_2 all V_x_2 all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> V_x_2 != V_y_2))) # label(fact_irrefl__trancl__rD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 327 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 328 (all V_B_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),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) # label(fact_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 329 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_z,V_x)))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 330 (all V_A_2 all T_a (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> (exists B_x c_member(T_a,B_x,V_A_2)))) # label(fact_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 331 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> V_x = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 332 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 333 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 334 (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_Groups_Ominus__class_Ominus(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,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Range__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 335 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> c_member(T_a,V_c_2,V_B_2))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 336 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x))) # label(fact_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 337 (all V_g_2 all V_x_2 all V_r_2 all V_f_2 all T_b all T_a (c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2) = c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2) <-> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2) -> hAPP(V_f_2,B_y) = hAPP(V_g_2,B_y))))) # label(fact_cuts__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 338 (all V_B_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = V_B_2) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 339 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 340 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 341 (all V_A_2 all T_a 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_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Diff__UNIV) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 342 (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)))) -> V_A_2 = c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) | c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2)) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 343 (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) -> V_A_2 = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))))) # label(fact_double__diff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 344 (all T_b all T_a all V_P_2 ((all B_x1 hBOOL(hAPP(V_P_2,B_x1))) <-> (all B_a all B_b hBOOL(hAPP(V_P_2,c_Product__Type_OPair(T_a,T_b,B_a,B_b)))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 345 (all B_x (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)) & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))) -> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) # label(conj_3) # label(hypothesis) # label(non_clause). [assumption]. 1.41/1.75 346 (all V_p_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2) -> c_Wellfounded_Owf(T_a,V_p_2)))) # label(fact_wf__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 347 (all V_a_2 all V_r_2 all T_b all V_b_2 all T_a (c_member(T_a,V_b_2,c_Relation_OImage(T_b,T_a,V_r_2,c_Set_Oinsert(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) <-> c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_a_2,V_b_2),V_r_2))) # label(fact_Image__singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 348 (exists B_L c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),B_L,c_Arrow__Order__Mirabelle_OLin)) # label(fact_linear__alt) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 349 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Transitive__Closure_Otrancl(T_a,V_r_2) = V_r_2)) # label(fact_trancl__id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 350 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2))) # label(fact_sup__apply) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 351 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 352 (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) -> (c_member(T_a,V_x_2,V_A_2) -> c_member(T_a,V_x_2,V_B_2)))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 353 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) <-> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 354 (all V_A_2 all V_a_2 all T_a c_Set_Oinsert(T_a,V_a_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 355 (all V_c_2 all T_a -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]. 1.41/1.75 356 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_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]. 1.41/1.75 357 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> V_x = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x))) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 358 (all V_a_2 all V_H_2 all T_b all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_a_2) = hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_r_2,V_a_2)),V_a_2))) # label(fact_wfrec) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 359 (all T_a c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_wf__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 360 (all V_s_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))) # label(fact_rtrancl__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 361 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 362 (all V_A_2 all V_c_2 all T_a (c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2)) -> -(all B_x (c_member(T_a,B_x,V_A_2) -> V_c_2 != c_Product__Type_OPair(T_a,T_a,B_x,B_x))))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.75 363 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 364 (all V_B_2 all V_A_2 all T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_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,V_B_2) = V_A_2)) # label(fact_Diff__triv) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 365 (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 = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 366 (all V_B_2 all V_A_2 all T_a 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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = V_A_2) # label(fact_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 367 (all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a))) # label(fact_single__valued__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 368 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))) # label(fact_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 369 (all V_B_2 all V_A_2 all V_r_2 all T_a (c_Order__Relation_Opreorder__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Relation_OField(T_a,V_r_2)) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Relation_OField(T_a,V_r_2)) -> ((all B_x (c_member(T_a,B_x,V_A_2) -> (exists B_xa (c_member(T_a,B_xa,V_B_2) & c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2))))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,V_A_2),c_Relation_OImage(T_a,T_a,V_r_2,V_B_2))))))) # label(fact_subset__Image__Image__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 370 (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,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]. 1.41/1.76 371 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 372 (all T_a c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a)) # label(fact_rtrancl__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 373 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_b_2 = V_c_2 & V_d_2 = V_a_2 | V_d_2 = V_b_2 & V_a_2 = V_c_2)) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 374 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclicI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 375 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) -> V_B_2 = V_A_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 376 (all V_f_2 all T_b all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_b,c_Relation_Oinv__image(T_a,T_b,V_r_2,V_f_2)))) # label(fact_wf__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 377 (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_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_subset__UNIV) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 378 (all V_B_2 all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 379 (all V_r_2 all V_s_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_s_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2) -> c_Wellfounded_Oacyclic(T_a,V_r_2)))) # label(fact_acyclic__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 380 (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(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))) # label(fact_sup1I1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 381 (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,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))))) # label(fact_refl__on__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 382 (all V_A_2 all V_B_2 all T_a 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) = 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]. 1.41/1.76 383 (all V_c_2 all V_R_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_R_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_R_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))))) # label(fact_r__r__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 384 (all V_r_2 all V_p_2 all T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2) -> c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 385 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 386 (all V_B_2 all V_A_2 all V_a_2 all T_a ((-c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) & (c_member(T_a,V_a_2,V_A_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__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]. 1.41/1.76 387 (all V_c_2 all V_b_2 all V_a_2 all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),V_r_2))))) # label(fact_transD) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 388 (all V_B_2 all V_C_2 all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),V_B_2) = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))) # label(fact_Diff__Int2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 389 (all V_r_2 all V_b_2 all V_a_2 all T_a all T_b c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_a_2,V_b_2),V_r_2)) = c_Set_Oinsert(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2))) # label(fact_Range__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 390 (all V_r_2 all V_A_2 all T_a (c_Relation_Otrans(T_a,V_r_2) & c_Relation_Orefl__on(T_a,V_A_2,V_r_2) <-> c_Order__Relation_Opreorder__on(T_a,V_A_2,V_r_2))) # label(fact_preorder__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 391 (all V_A_2 all T_a 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]. 1.41/1.76 392 (all V_y_2 all V_x_2 all V_L_2 all V_b_2 all V_a_2 (V_a_2 != V_b_2 -> (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_L_2,c_Arrow__Order__Mirabelle_OLin) -> (V_y_2 != V_x_2 & (V_a_2 != V_y_2 -> (V_a_2 != V_x_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)) & (V_a_2 = V_x_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_b_2,V_y_2),V_L_2) | V_b_2 = V_y_2)) & (V_y_2 = V_a_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_b_2),V_L_2)) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_a_2,V_b_2)))))) # label(fact_in__below) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 393 (all V_b_2 all V_a_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) # label(fact_equiv__class__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 394 (all V_A_2 all T_a all V_y_2 all V_x_2 (V_x_2 = V_y_2 -> (c_member(T_a,V_x_2,V_A_2) <-> c_member(T_a,V_y_2,V_A_2)))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 395 (all T_a c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_OField(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_Field__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 396 (all V_r_2 all V_b_2 all V_a_2 all T_b all T_a c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)) = c_Set_Oinsert(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))) # label(fact_Domain__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 397 (all V_B_2 all V_A_2 all T_b all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)) = c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2))) # label(fact_Domain__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 398 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2)) # label(fact_trancl__rtrancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 399 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))) # label(fact_wf__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 400 (all V_r_2 all V_b_2 all V_a_2 all T_a c_Relation_OField(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Relation_OField(T_a,V_r_2))) # label(fact_Field__insert) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 401 (all V_x_2 all T_a c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 402 (all V_A_2 all T_a c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) = V_A_2) # label(fact_Range__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 403 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 404 (all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2) # label(fact_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 405 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)) = V_x)) # label(fact_inf__top__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 406 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(T_a,V_x_2,V_A_2) -> (c_member(T_a,V_y_2,V_A_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) <-> c_Equiv__Relations_Oquotient(T_a,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Equiv__Relations_Oquotient(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2)))))) # label(fact_eq__equiv__class__iff2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 407 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Ostrict__linear__order__on(T_a,V_A_2,V_r_2) <-> c_Relation_Otrans(T_a,V_r_2) & c_Relation_Oirrefl(T_a,V_r_2) & c_Relation_Ototal__on(T_a,V_A_2,V_r_2))) # label(fact_strict__linear__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 408 (all V_f_2 all T_b all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Relation_Otrans(T_b,c_Relation_Oinv__image(T_a,T_b,V_r_2,V_f_2)))) # label(fact_trans__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 409 (all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_wf__acyclic) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 410 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 411 (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,c_Set_Oinsert(T_a,V_a_2,V_B_2))) # label(fact_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 412 (all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> V_A_2 = c_Set_Oinsert(T_a,V_a_2,V_A_2))) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 413 (all V_A_2 all V_x_2 all T_a 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_x_2,V_A_2))) # label(fact_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 414 (all V_B_2 all V_C_2 all V_a_2 all T_a ((-c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)) & (c_member(T_a,V_a_2,V_C_2) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2) = c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__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]. 1.41/1.76 415 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x) = V_x)) # label(fact_sup__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 416 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 417 (all V_S_2 all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)) = c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))) # label(fact_rtrancl__Un__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 418 (all V_B_2 all V_a_2 all V_A_2 all T_a c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))) # label(fact_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 419 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 420 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)) -> -(hBOOL(hAPP(V_A_2,V_x_2)) -> -hBOOL(hAPP(V_B_2,V_x_2))))) # label(fact_inf1E) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 421 (all V_A_2 all V_A_H_2 all V_r_2 all V_r_H_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_H_2,V_r_2) -> (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(T_b,tc_HOL_Obool),c_Relation_OImage(T_a,T_b,V_r_H_2,V_A_H_2),c_Relation_OImage(T_a,T_b,V_r_2,V_A_2))))) # label(fact_Image__mono) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 422 (all T_2 all T_1 (class_Orderings_Otop(T_1) -> class_Orderings_Otop(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Otop) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 423 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 424 (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_P_2 (hBOOL(hAPP(V_P_2,V_x_2)) -> (c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_y_H_2,V_y_2),hAPP(V_R_2,V_x_2)) -> c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_H_2),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2)),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 425 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))))) # label(fact_distrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 426 (all V_B_2 all T_a c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) # label(fact_Un__UNIV__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 427 (all V_r_2 all T_b all T_a ((all B_x all B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2) -> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2) -> B_y = B_z)))) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2))) # label(fact_single__valuedI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 428 (all V_b_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_b_2,V_B_2)))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 429 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) -> (V_a_2 = V_b_2 <-> V_d_2 = V_c_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 430 (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]. 1.41/1.76 431 (all V_a_2 all V_r_2 all V_b_2 all T_a (c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))))) # label(fact_acc__downward) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 432 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 433 (all V_r_2 all T_a c_Relation_Oirrefl(T_a,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))) # label(fact_irrefl__diff__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 434 (all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (V_b_2 != V_a_2 -> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_b_2),V_r_2)))))) # label(fact_rtranclE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 435 (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),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)))) # label(fact_rtrancl__Un__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 436 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> c_Orderings_Otop__class_Otop(T_a) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Otop__class_Otop(T_a),V_x))) # label(fact_sup__top__left) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 437 (all V_P_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (hBOOL(hAPP(V_P_2,V_a_2)) -> ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2) -> (hBOOL(hAPP(V_P_2,B_y)) -> hBOOL(hAPP(V_P_2,B_z))))))) -> hBOOL(hAPP(V_P_2,V_b_2)))))) # label(fact_rtrancl__induct) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 438 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__rtrancl__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 439 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_Transitive__Closure_Otrancl__into__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 440 (all V_A_2 all V_S_2 all V_R_2 all T_a all T_b c_Relation_OImage(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_R_2,V_S_2),V_A_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_S_2,V_A_2))) # label(fact_Un__Image) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 441 (all V_R_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_R_2) = c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2))) # label(fact_rtrancl__trancl__absorb) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 442 (all V_R_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_R_2)) -> -(all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2) -> c_member(T_a,B_z,c_Wellfounded_Oacc(T_a,V_R_2)))))) # label(fact_not__acc__down) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 443 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)))) # label(fact_Domain__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 444 (all V_X_2 all V_r_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_a,T_a,V_r_2,V_X_2),V_X_2) -> c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_X_2) = V_X_2)) # label(fact_Image__closed__trancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 445 (all V_x all T_a (class_Orderings_Obot(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a),V_x))) # label(fact_bot__least) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 446 (all V_C_2 all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 447 (all V_A_2 all T_a 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]. 1.41/1.76 448 (all V_B_2 all V_A_2 all V_c_2 all T_a (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)) -> -c_member(T_a,V_c_2,V_B_2))) # label(fact_DiffD2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 449 (all V_B_2 all V_A_2 all V_c_2 all T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)) -> (-c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_UnE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 450 (all V_r_2 all T_a c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) = c_Relation_ODomain(T_a,T_a,V_r_2)) # label(fact_trancl__domain) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 451 (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]. 1.41/1.76 452 (all V_x_2 all T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2))) # label(fact_top1I) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 453 (all V_B_2 all V_A_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2)))) # label(fact_Range__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 454 (all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) <-> c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = V_B_2)) # label(fact_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 455 (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 = 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]. 1.41/1.76 456 (all V_f_2 all V_r_2 all T_b all V_y_2 all V_x_2 all T_a (c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)),V_r_2) <-> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oinv__image(T_b,T_a,V_r_2,V_f_2)))) # label(fact_in__inv__image) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 457 (all V_r_2 all V_A_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,V_A_2,V_r_2) <-> c_Relation_Oantisym(T_a,V_r_2) & c_Order__Relation_Opreorder__on(T_a,V_A_2,V_r_2))) # label(fact_partial__order__on__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 458 (all V_r_H_2 all V_r_2 all T_a (c_Wellfounded_Owf(T_a,V_r_2) -> c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_r_H_2)))) # label(fact_wf__Int1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 459 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)))) # label(fact_sup__ge2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 460 (all V_Q_2 all V_P_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_P_2,V_Q_2))) -> ((all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_P_2)) -> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_Q_2) -> B_x = B_y)))) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_P_2))))) # label(fact_rtrancl__Un__separator__converseE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 461 (all V_B_2 all V_A_2 all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2)) # label(fact_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 462 (all T_a c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) # label(fact_refl__on__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 463 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) <-> c_member(T_a,V_y_2,V_A_2) & c_member(T_a,V_x_2,V_A_2) & c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_y_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) # label(fact_equiv__class__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 464 (all V_A_2 all T_a V_A_2 = c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))) # label(fact_Domain__Id__on) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 465 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y) = c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x))) # label(fact_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 466 (all V_L_2 all V_y_2 all V_x_2 (V_x_2 != V_y_2 -> (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) -> c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_below__Lin) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 467 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 468 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))))) # label(fact_le__supI1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 469 (all T_2 all T_1 (class_Lattices_Olattice(T_1) -> class_Lattices_Olattice(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Olattice) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 470 (all V_B_2 all V_A_2 all T_a all T_b 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,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]. 1.41/1.76 471 (all V_B_2 all V_A_2 all V_R_2 all T_b all T_a c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Relation_OImage(T_b,T_a,V_R_2,V_A_2),c_Relation_OImage(T_b,T_a,V_R_2,V_B_2)))) # label(fact_Image__Int__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 472 (all V_P_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 (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) -> ((all B_a all B_b all B_aa all B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2) -> (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)) -> (hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) -> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)))))) -> hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)))))) # label(fact_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 473 (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_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)),c_Relation_ODomain(T_a,T_b,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2)))) # label(fact_Domain__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 474 (all V_A_2 all T_a V_A_2 = c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_Diff__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 475 (all V_s_2 all V_r_2 all T_b all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2) -> (c_Relation_Osingle__valued(T_a,T_b,V_s_2) -> c_Relation_Osingle__valued(T_a,T_b,V_r_2)))) # label(fact_single__valued__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 476 (all V_B_2 all V_A_2 all T_a c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 477 (all V_Y_2 all V_X_2 all V_r_2 all V_A_2 all T_a (c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> (c_member(tc_fun(T_a,tc_HOL_Obool),V_Y_2,c_Equiv__Relations_Oquotient(T_a,V_A_2,V_r_2)) -> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) | V_X_2 = V_Y_2)))) # label(fact_quotient__disj) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 478 (all T_a c_Relation_Otrans(T_a,c_Relation_OId(T_a))) # label(fact_trans__Id) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 479 (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]. 1.41/1.76 480 (all V_B_2 all V_C_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_C_2) -> c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 481 (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_Relation_Oantisym(T_a,V_s_2) -> c_Relation_Oantisym(T_a,V_r_2)))) # label(fact_antisym__subset) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 482 (all V_a_2 all T_a all V_A_2 (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = V_A_2 -> -c_member(T_a,V_a_2,V_A_2))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 483 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 484 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 485 (all V_s_2 all V_r_2 all T_a c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a,V_r_2),c_Relation_OField(T_a,V_s_2)) = c_Relation_OField(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2))) # label(fact_Field__Un) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 486 (all T_a all T_b c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Relation_ORange(T_b,T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)))) # label(fact_Range__empty) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 487 (all T_a all V_B_2 all V_x_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_x_2)) -> (hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))))) # label(fact_inf1I) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 488 (all V_x all V_y all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_y = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 489 (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,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x))))) # label(fact_le__supI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 490 (all V_x_2 all V_A_2 all V_y_2 all T_a (hBOOL(hAPP(V_A_2,V_x_2)) | V_x_2 = V_y_2 <-> hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 491 (all V_B_2 all V_A_2 all V_c_2 all T_a (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)) -> -(c_member(T_a,V_c_2,V_A_2) -> c_member(T_a,V_c_2,V_B_2)))) # label(fact_DiffE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 492 (all V_c_2 all V_r_2 all V_b_2 all V_a_2 all T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)) -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))))) # label(fact_trancl__into__trancl2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.76 493 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 494 (all T_a all V_R_2 all T_b all V_P_2 ((all B_x (hBOOL(hAPP(V_P_2,B_x)) -> c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)))) -> c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)))) # label(fact_wf__same__fst) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 495 (all V_A_2 all V_a_2 all T_a (c_member(T_a,V_a_2,V_A_2) -> c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2)) # label(fact_insert__Diff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 496 (all V_B_2 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,V_B_2)) <-> (c_member(T_a,V_x_2,V_A_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,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)) & (-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)))) # label(fact_subset__insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 497 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 498 (all V_B_2 all V_A_2 all V_c_2 all T_a (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)) -> c_member(T_a,V_c_2,V_A_2))) # label(fact_DiffD1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 499 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 500 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x)))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 501 (all V_z_2 all V_f_2 all T_b all T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2)) # label(fact_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 502 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_z,V_x)) = c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z),V_x))) # label(fact_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 503 (all V_b_2 all V_a_2 all V_r_2 all T_a (c_Order__Relation_Opartial__order__on(T_a,c_Relation_OField(T_a,V_r_2),V_r_2) -> (c_member(T_a,V_a_2,c_Relation_OField(T_a,V_r_2)) -> (c_member(T_a,V_b_2,c_Relation_OField(T_a,V_r_2)) -> (c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Relation_OImage(T_a,T_a,V_r_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) <-> V_b_2 = V_a_2))))) # label(fact_Partial__order__eq__Image1__Image1__iff) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 504 (all V_A_2 all T_a c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) # label(fact_Diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 505 (all V_x_2 all V_Q_2 all V_P_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2) -> (hBOOL(hAPP(V_P_2,V_x_2)) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 506 (all V_y_2 all V_R_2 all V_x_2 all T_a (-c_member(T_a,V_x_2,c_Relation_ODomain(T_a,T_a,V_R_2)) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) <-> V_y_2 = V_x_2))) # label(fact_Not__Domain__rtrancl) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 507 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (V_y_2 != V_z_2 & (V_x_2 != V_z_2 -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_L_2)) & (V_z_2 = V_x_2 -> V_y_2 != V_x_2) <-> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2)))) # label(fact_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 508 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)) = c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 509 (all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(V_A_2,V_x_2)) <-> c_member(T_a,V_x_2,V_A_2))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 510 (all V_C_2 all V_B_2 all V_A_2 all T_a (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2) -> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 511 (all V_A_2 all V_r_2 all T_b all V_b_2 all T_a (c_member(T_a,V_b_2,c_Relation_OImage(T_b,T_a,V_r_2,V_A_2)) -> -(all B_x (c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_b_2),V_r_2) -> -c_member(T_b,B_x,V_A_2))))) # label(fact_ImageE) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 512 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) <-> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclic__def) # label(axiom) # label(non_clause). [assumption]. 1.41/1.77 1.41/1.77 ============================== end of process non-clausal formulas === 1.41/1.77 1.41/1.77 ============================== PROCESS INITIAL CLAUSES =============== 1.41/1.77 1.41/1.77 ============================== PREDICATE ELIMINATION ================= 1.41/1.77 513 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__inf(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__inf) # label(axiom). [clausify(23)]. 1.41/1.77 514 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf_Ocommute) # label(axiom). [clausify(9)]. 1.41/1.77 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),D,C). [resolve(513,b,514,a)]. 1.41/1.77 515 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__infE) # label(axiom). [clausify(30)]. 1.41/1.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -class_Lattices_Olattice(B). [resolve(515,a,513,b)]. 1.41/1.77 516 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_le__infE) # label(axiom). [clausify(30)]. 1.41/1.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,E)) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,E) | -class_Lattices_Olattice(B). [resolve(516,a,513,b)]. 1.41/1.77 517 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_le__iff__inf) # label(axiom). [clausify(48)]. 1.41/1.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D) = C | -class_Lattices_Olattice(B). [resolve(517,a,513,b)]. 1.41/1.77 518 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) != B # label(fact_le__iff__inf) # label(axiom). [clausify(48)]. 1.41/1.77 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D) != C | -class_Lattices_Olattice(B). [resolve(518,a,513,b)]. 1.41/1.77 519 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = B # label(fact_inf__absorb1) # label(axiom). [clausify(63)]. 1.41/1.77 520 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C) # label(fact_le__infI2) # label(axiom). [clausify(64)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),E,C),D) | -class_Lattices_Olattice(B). [resolve(520,a,513,b)]. 1.41/1.78 521 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf_Oidem) # label(axiom). [clausify(68)]. 1.41/1.78 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,C) = C | -class_Lattices_Olattice(B). [resolve(521,a,513,b)]. 1.41/1.78 522 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B) # label(fact_inf__le1) # label(axiom). [clausify(99)]. 1.41/1.78 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D),C) | -class_Lattices_Olattice(B). [resolve(522,a,513,b)]. 1.41/1.78 523 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf_Oleft__idem) # label(axiom). [clausify(112)]. 1.41/1.78 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D) | -class_Lattices_Olattice(B). [resolve(523,a,513,b)]. 1.41/1.78 524 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) # label(fact_inf__commute) # label(axiom). [clausify(124)]. 1.41/1.78 525 class_Lattices_Osemilattice__inf(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.41/1.78 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A). [resolve(525,a,514,a)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B). [resolve(525,a,515,a)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(525,a,516,a)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) = A. [resolve(525,a,517,a)]. 1.41/1.78 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) != A. [resolve(525,a,518,a)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B). [resolve(525,a,520,a)]. 1.41/1.78 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,A) = A. [resolve(525,a,521,a)]. 1.41/1.78 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),A). [resolve(525,a,522,a)]. 1.41/1.78 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B). [resolve(525,a,523,a)]. 1.41/1.78 526 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),c_Lattices_Osemilattice__inf__class_Oinf(A,C,E)) # label(fact_inf__mono) # label(axiom). [clausify(136)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,E),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,F)) | -class_Lattices_Olattice(B). [resolve(526,a,513,b)]. 1.41/1.78 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,D)). [resolve(526,a,525,a)]. 1.41/1.80 527 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__greatest) # label(axiom). [clausify(305)]. 1.41/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,E) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,E)) | -class_Lattices_Olattice(B). [resolve(527,a,513,b)]. 1.41/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(527,a,525,a)]. 1.41/1.80 528 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf__assoc) # label(axiom). [clausify(340)]. 1.41/1.80 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D),E) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,E)) | -class_Lattices_Olattice(B). [resolve(528,a,513,b)]. 1.41/1.80 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)). [resolve(528,a,525,a)]. 1.41/1.80 529 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,B) = B # label(fact_inf__idem) # label(axiom). [clausify(357)]. 1.41/1.80 530 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C) # label(fact_inf__le2) # label(axiom). [clausify(361)]. 1.41/1.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,D),D) | -class_Lattices_Olattice(B). [resolve(530,a,513,b)]. 1.41/1.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),B). [resolve(530,a,525,a)]. 1.41/1.80 531 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__inf__iff) # label(axiom). [clausify(370)]. 1.41/1.80 532 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__inf__iff) # label(axiom). [clausify(370)]. 1.41/1.80 533 -class_Lattices_Osemilattice__inf(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,D,C)) # label(fact_le__inf__iff) # label(axiom). [clausify(370)]. 1.41/1.80 534 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) # label(fact_inf__left__idem) # label(axiom). [clausify(403)]. 1.41/1.80 535 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf_Oleft__commute) # label(axiom). [clausify(483)]. 1.41/1.80 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,E)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,E)) | -class_Lattices_Olattice(B). [resolve(535,a,513,b)]. 1.41/1.81 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C)). [resolve(535,a,525,a)]. 1.41/1.81 536 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_inf_Oassoc) # label(axiom). [clausify(484)]. 1.41/1.81 537 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__inf__class_Oinf(A,C,B) = B # label(fact_inf__absorb2) # label(axiom). [clausify(488)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),D,C) = C | -class_Lattices_Olattice(B). [resolve(537,a,513,b)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,B,A) = A. [resolve(537,a,525,a)]. 1.41/1.81 538 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) # label(fact_le__infI) # label(axiom). [clausify(493)]. 1.41/1.81 539 -class_Lattices_Osemilattice__inf(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C) # label(fact_le__infI1) # label(axiom). [clausify(500)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,E),D) | -class_Lattices_Olattice(B). [resolve(539,a,513,b)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C),B). [resolve(539,a,525,a)]. 1.41/1.81 540 -class_Lattices_Osemilattice__inf(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)) = c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)) # label(fact_inf__left__commute) # label(axiom). [clausify(508)]. 1.41/1.81 541 class_Lattices_Osemilattice__sup(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.41/1.81 542 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup_Oleft__idem) # label(axiom). [clausify(33)]. 1.41/1.81 543 -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,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),c_Lattices_Osemilattice__sup__class_Osup(A,C,E)) # label(fact_sup__mono) # label(axiom). [clausify(38)]. 1.41/1.81 544 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup__assoc) # label(axiom). [clausify(56)]. 1.41/1.81 545 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)) # label(fact_le__supI2) # label(axiom). [clausify(66)]. 1.41/1.81 546 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,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(71)]. 1.41/1.81 547 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,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(71)]. 1.41/1.81 548 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup_Ocommute) # label(axiom). [clausify(107)]. 1.41/1.81 549 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D) = c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_sup_Oassoc) # label(axiom). [clausify(117)]. 1.41/1.81 550 -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,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_sup__least) # label(axiom). [clausify(150)]. 1.41/1.81 551 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup_Oleft__commute) # label(axiom). [clausify(178)]. 1.41/1.81 552 -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,c_Lattices_Osemilattice__sup__class_Osup(A,D,B),C) # label(fact_le__sup__iff) # label(axiom). [clausify(212)]. 1.41/1.81 553 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,D,B),C) # label(fact_le__sup__iff) # label(axiom). [clausify(212)]. 1.41/1.81 554 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_le__sup__iff) # label(axiom). [clausify(212)]. 1.41/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B). [resolve(541,a,542,a)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,C,D) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,D)). [resolve(541,a,543,a)]. 1.41/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(541,a,544,a)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,C,B)). [resolve(541,a,545,a)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,C). [resolve(541,a,546,a)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,B,C). [resolve(541,a,547,a)]. 1.41/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A). [resolve(541,a,548,a)]. 1.41/1.81 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,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C),B). [resolve(541,a,550,a)]. 1.41/1.81 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,C)). [resolve(541,a,551,a)]. 1.41/1.81 555 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) = C # label(fact_sup__absorb1) # label(axiom). [clausify(249)]. 1.41/1.81 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) = B. [resolve(555,a,541,a)]. 1.41/1.83 556 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = c_Lattices_Osemilattice__sup__class_Osup(A,C,B) # label(fact_sup__commute) # label(axiom). [clausify(269)]. 1.41/1.83 557 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C # label(fact_sup__absorb2) # label(axiom). [clausify(274)]. 1.41/1.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) = B. [resolve(557,a,541,a)]. 1.41/1.83 558 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup_Oidem) # label(axiom). [clausify(298)]. 1.41/1.83 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,A) = A. [resolve(558,a,541,a)]. 1.41/1.83 559 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) = c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)) # label(fact_sup__left__commute) # label(axiom). [clausify(314)]. 1.41/1.83 560 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,B) = B # label(fact_sup__idem) # label(axiom). [clausify(320)]. 1.41/1.83 561 -class_Lattices_Osemilattice__sup(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) = c_Lattices_Osemilattice__sup__class_Osup(A,B,C) # label(fact_sup__left__idem) # label(axiom). [clausify(332)]. 1.41/1.83 562 -class_Lattices_Olattice(A) | class_Lattices_Osemilattice__sup(tc_fun(B,A)) # label(arity_fun__Lattices_Osemilattice__sup) # label(axiom). [clausify(410)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D). [resolve(562,b,542,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,F)). [resolve(562,b,543,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)). [resolve(562,b,544,a)]. 1.41/1.83 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,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),E,D)). [resolve(562,b,545,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,E). [resolve(562,b,546,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E) | c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),D,E). [resolve(562,b,547,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C). [resolve(562,b,548,a)]. 1.41/1.83 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),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E),D). [resolve(562,b,550,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,E)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,E)). [resolve(562,b,551,a)]. 1.41/1.83 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C) = D. [resolve(562,b,555,a)]. 1.41/1.85 Derived: -class_Lattices_Olattice(A) | -c_Orderings_Oord__class_Oless__eq(tc_fun(B,A),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) = D. [resolve(562,b,557,a)]. 1.41/1.85 Derived: -class_Lattices_Olattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,C) = C. [resolve(562,b,558,a)]. 1.41/1.85 563 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)) # label(fact_sup__ge1) # label(axiom). [clausify(432)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B)). [resolve(563,a,541,a)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D)) | -class_Lattices_Olattice(B). [resolve(563,a,562,b)]. 1.41/1.85 564 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) = C # label(fact_le__iff__sup) # label(axiom). [clausify(455)]. 1.41/1.85 565 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) != C # label(fact_le__iff__sup) # label(axiom). [clausify(455)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) != B. [resolve(565,a,541,a)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),C,D) != D | -class_Lattices_Olattice(B). [resolve(565,a,562,b)]. 1.41/1.85 566 -class_Lattices_Osemilattice__sup(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)) # label(fact_sup__ge2) # label(axiom). [clausify(459)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A)). [resolve(566,a,541,a)]. 1.41/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,C)) | -class_Lattices_Olattice(B). [resolve(566,a,562,b)]. 1.41/1.85 567 -class_Lattices_Osemilattice__sup(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)) # label(fact_le__supI1) # label(axiom). [clausify(468)]. 1.41/1.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,C)). [resolve(567,a,541,a)]. 1.41/1.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,D) | c_Orderings_Oord__class_Oless__eq(tc_fun(A,B),C,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),D,E)) | -class_Lattices_Olattice(B). [resolve(567,a,562,b)]. 1.41/1.85 568 -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,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C) # label(fact_le__supI) # label(axiom). [clausify(489)]. 1.41/1.85 569 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__top(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom). [clausify(288)]. 1.41/1.85 570 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Otop__class_Otop(A)) = c_Orderings_Otop__class_Otop(A) # label(fact_sup__top__right) # label(axiom). [clausify(41)]. 1.41/1.85 571 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Otop__class_Otop(A),B) = B # label(fact_inf__top__left) # label(axiom). [clausify(142)]. 1.41/1.85 572 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) != c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) | c_Orderings_Otop__class_Otop(A) = C # label(fact_inf__eq__top__iff) # label(axiom). [clausify(259)]. 1.41/1.85 573 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) != c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) | c_Orderings_Otop__class_Otop(A) = B # label(fact_inf__eq__top__iff) # label(axiom). [clausify(259)]. 1.41/1.88 574 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) = c_Lattices_Osemilattice__inf__class_Oinf(A,B,C) | c_Orderings_Otop__class_Otop(A) != C | c_Orderings_Otop__class_Otop(A) != B # label(fact_inf__eq__top__iff) # label(axiom). [clausify(259)]. 1.41/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Orderings_Otop__class_Otop(tc_fun(B,A))) = c_Orderings_Otop__class_Otop(tc_fun(B,A)). [resolve(569,b,570,a)]. 1.41/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Orderings_Otop__class_Otop(tc_fun(B,A)),C) = C. [resolve(569,b,571,a)]. 1.41/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = D. [resolve(569,b,572,a)]. 1.41/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = C. [resolve(569,b,573,a)]. 1.41/1.88 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != D | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != C. [resolve(569,b,574,a)]. 1.41/1.88 575 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__top) # label(axiom). [assumption]. 1.41/1.88 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Orderings_Otop__class_Otop(tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_HOL_Obool). [resolve(575,a,570,a)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Orderings_Otop__class_Otop(tc_HOL_Obool),A) = A. [resolve(575,a,571,a)]. 1.41/1.88 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) != c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = B. [resolve(575,a,572,a)]. 1.41/1.88 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) != c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = A. [resolve(575,a,573,a)]. 1.41/1.88 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) = c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != B | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != A. [resolve(575,a,574,a)]. 1.41/1.88 576 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Otop__class_Otop(A)) = B # label(fact_inf__top__right) # label(axiom). [clausify(405)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,B),C,c_Orderings_Otop__class_Otop(tc_fun(A,B))) = C | -class_Lattices_Obounded__lattice(B). [resolve(576,a,569,b)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Orderings_Otop__class_Otop(tc_HOL_Obool)) = A. [resolve(576,a,575,a)]. 1.41/1.88 577 -class_Lattices_Obounded__lattice__top(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Otop__class_Otop(A),B) = c_Orderings_Otop__class_Otop(A) # label(fact_sup__top__left) # label(axiom). [clausify(436)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,B),c_Orderings_Otop__class_Otop(tc_fun(A,B)),C) = c_Orderings_Otop__class_Otop(tc_fun(A,B)) | -class_Lattices_Obounded__lattice(B). [resolve(577,a,569,b)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Otop__class_Otop(tc_HOL_Obool),A) = c_Orderings_Otop__class_Otop(tc_HOL_Obool). [resolve(577,a,575,a)]. 1.41/1.88 578 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption]. 1.41/1.88 579 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Obot__class_Obot(A)) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__right) # label(axiom). [clausify(45)]. 1.41/1.88 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(578,a,579,a)]. 1.41/1.89 580 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Obot__class_Obot(A)) = B # label(fact_sup__bot__right) # label(axiom). [clausify(85)]. 1.41/1.89 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(580,a,578,a)]. 1.41/1.89 581 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Obot__class_Obot(A),B) = c_Orderings_Obot__class_Obot(A) # label(fact_inf__bot__left) # label(axiom). [clausify(91)]. 1.41/1.89 Derived: c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(581,a,578,a)]. 1.41/1.89 582 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != B | c_Orderings_Obot__class_Obot(A) != C | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) = c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(187)]. 1.41/1.89 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != A | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != B | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) = c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(582,a,578,a)]. 1.41/1.89 583 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = B | c_Lattices_Osemilattice__sup__class_Osup(A,C,B) != c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(187)]. 1.41/1.89 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,B,A) != c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(583,a,578,a)]. 1.41/1.89 584 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = B | c_Lattices_Osemilattice__sup__class_Osup(A,B,C) != c_Orderings_Obot__class_Obot(A) # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(187)]. 1.41/1.89 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A | c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,A,B) != c_Orderings_Obot__class_Obot(tc_HOL_Obool). [resolve(584,a,578,a)]. 1.41/1.89 585 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(296)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(585,b,579,a)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,c_Orderings_Obot__class_Obot(tc_fun(B,A))) = C. [resolve(585,b,580,a)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),c_Orderings_Obot__class_Obot(tc_fun(B,A)),C) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(585,b,581,a)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != C | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != D | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C) = c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(585,b,582,a)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),D,C) != c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(585,b,583,a)]. 1.41/1.89 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C | c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D) != c_Orderings_Obot__class_Obot(tc_fun(B,A)). [resolve(585,b,584,a)]. 1.41/1.89 586 -class_Lattices_Obounded__lattice__bot(A) | c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Obot__class_Obot(A),B) = B # label(fact_sup__bot__left) # label(axiom). [clausify(415)]. 1.41/1.89 Derived: c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool,c_Orderings_Obot__class_Obot(tc_HOL_Obool),A) = A. [resolve(586,a,578,a)]. 1.41/1.89 Derived: 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(586,a,585,b)]. 1.41/2.08 587 c_Order__Relation_Olinear__order__on(A,B,C) | -c_Order__Relation_Owell__order__on(A,B,C) # label(fact_well__order__on__def) # label(axiom). [clausify(293)]. 1.41/2.08 588 c_Order__Relation_Owell__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))) # label(fact_well__order__on__empty) # label(axiom). [clausify(83)]. 1.41/2.08 589 -c_Order__Relation_Olinear__order__on(A,B,C) | -c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))) | c_Order__Relation_Owell__order__on(A,B,C) # label(fact_well__order__on__def) # label(axiom). [clausify(293)]. 1.41/2.08 Derived: c_Order__Relation_Olinear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))). [resolve(587,b,588,a)]. 1.41/2.08 590 c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,c_Relation_OId(A))) | -c_Order__Relation_Owell__order__on(A,C,B) # label(fact_well__order__on__def) # label(axiom). [clausify(293)]. 1.41/2.08 Derived: c_Wellfounded_Owf(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(590,b,588,a)]. 1.41/2.08 591 c_Order__Relation_Olinear__order__on(A,B,C) | -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) # label(fact_linear__order__on__def) # label(axiom). [clausify(96)]. 1.41/2.08 592 -c_Order__Relation_Olinear__order__on(A,B,C) | c_Order__Relation_Opartial__order__on(A,B,C) # label(fact_linear__order__on__def) # label(axiom). [clausify(96)]. 1.41/2.08 593 -c_Order__Relation_Olinear__order__on(A,B,C) | c_Relation_Ototal__on(A,B,C) # label(fact_linear__order__on__def) # label(axiom). [clausify(96)]. 1.41/2.08 594 -c_Order__Relation_Olinear__order__on(A,B,C) | c_Order__Relation_Ostrict__linear__order__on(A,B,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))) # label(fact_strict__linear__order__on__diff__Id) # label(axiom). [clausify(137)]. 1.41/2.08 Derived: c_Order__Relation_Ostrict__linear__order__on(A,B,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))) | -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C). [resolve(594,a,591,a)]. 1.41/2.08 595 c_Order__Relation_Olinear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))) # label(fact_lnear__order__on__empty) # label(axiom). [clausify(279)]. 1.41/2.08 Derived: c_Order__Relation_Opartial__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))). [resolve(595,a,592,a)]. 1.41/2.08 Derived: c_Relation_Ototal__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))). [resolve(595,a,593,a)]. 1.41/2.08 Derived: c_Order__Relation_Ostrict__linear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(595,a,594,a)]. 1.41/2.08 596 c_Order__Relation_Olinear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))). [resolve(587,b,588,a)]. 1.41/2.08 597 c_Nitpick_Orefl_H(A,B) | -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f47(B,A),f47(B,A)),B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(252)]. 1.41/2.08 598 -c_Nitpick_Orefl_H(A,B) | c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(252)]. 1.41/2.08 Derived: -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f47(B,A),f47(B,A)),B) | c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B). [resolve(597,a,598,a)]. 1.41/2.08 599 c_member(tc_prod(A,B),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(306)]. 2.02/2.30 600 -c_member(tc_prod(A,B),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(306)]. 2.02/2.30 601 c_Order__Relation_Ostrict__linear__order__on(A,B,C) | -c_Relation_Otrans(A,C) | -c_Relation_Oirrefl(A,C) | -c_Relation_Ototal__on(A,B,C) # label(fact_strict__linear__order__on__def) # label(axiom). [clausify(407)]. 2.02/2.30 602 -c_Order__Relation_Ostrict__linear__order__on(A,B,C) | c_Relation_Otrans(A,C) # label(fact_strict__linear__order__on__def) # label(axiom). [clausify(407)]. 2.02/2.30 603 -c_Order__Relation_Ostrict__linear__order__on(A,B,C) | c_Relation_Oirrefl(A,C) # label(fact_strict__linear__order__on__def) # label(axiom). [clausify(407)]. 2.02/2.30 604 -c_Order__Relation_Ostrict__linear__order__on(A,B,C) | c_Relation_Ototal__on(A,B,C) # label(fact_strict__linear__order__on__def) # label(axiom). [clausify(407)]. 2.02/2.30 605 c_Order__Relation_Ostrict__linear__order__on(A,B,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))) | -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C). [resolve(594,a,591,a)]. 2.02/2.30 Derived: -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | c_Relation_Otrans(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))). [resolve(605,a,602,a)]. 2.02/2.30 Derived: -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | c_Relation_Oirrefl(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))). [resolve(605,a,603,a)]. 2.02/2.30 Derived: -c_Order__Relation_Opartial__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | c_Relation_Ototal__on(A,B,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_OId(A))). [resolve(605,a,604,a)]. 2.02/2.30 606 c_Order__Relation_Ostrict__linear__order__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(595,a,594,a)]. 2.02/2.30 Derived: c_Relation_Otrans(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(606,a,602,a)]. 2.02/2.30 Derived: c_Relation_Oirrefl(A,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(606,a,603,a)]. 2.02/2.30 Derived: c_Relation_Ototal__on(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool)),c_Relation_OId(A))). [resolve(606,a,604,a)]. 2.02/2.30 2.02/2.30 ============================== end predicate elimination ============= 2.02/2.30 2.02/2.30 Auto_denials: (non-Horn, no changes). 2.02/2.30 2.02/2.30 Term ordering decisions: 2.02/2.30 Function symbol KB weights: tc_HOL_Obool=1. tc_Arrow__Order__Mirabelle_Oalt=1. c_Arrow__Order__Mirabelle_OLin=1. v_P=1. v_a=1. v_b=1. v_i=1. c1=1. c2=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Relation_OField=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Set_Othe__elem=1. c_Wellfounded_Omeasure=1. f14=1. f15=1. f18=1. f19=1. f20=1. f22=1. f23=1. f24=1. f25=1. f26=1. f30=1. f36=1. f37=1. f38=1. f46=1. f47=1. f62=1. f70=1. f86=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_Relation_OId=1. v_F=1. c_fequal=1. f16=1. c_Lattices_Osemilattice__sup__class_Osup=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_Set_Oinsert=1. c_Groups_Ominus__class_Ominus=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Equiv__Relations_Oquotient=1. f7=1. f32=1. f34=1. f35=1. f50=1. f51=1. f52=1. f53=1. f54=1. f64=1. f65=1. f66=1. f67=1. f71=1. f72=1. f73=1. f77=1. c_Product__Type_OPair=1. c_Relation_OImage=1. c_Wellfounded_Olex__prod=1. c_Recdef_Owfrec=1. c_Relation_Oinv__image=1. c_Recdef_Osame__fst=1. c_Nitpick_Owf__wfrec=1. f1=1. f4=1. f5=1. f13=1. f17=1. f21=1. f27=1. f28=1. f29=1. f31=1. f33=1. f39=1. f57=1. f58=1. f59=1. f60=1. f61=1. f68=1. f74=1. f84=1. c_Recdef_Ocut=1. c_Nitpick_Owf__wfrec_H=1. c_Product__Type_Ointernal__split=1. c_Product__Type_Oprod_Oprod__rec=1. f2=1. f3=1. f6=1. f11=1. f12=1. f69=1. f75=1. f76=1. f78=1. f79=1. f85=1. f8=1. f45=1. f49=1. f63=1. f9=1. f10=1. f44=1. f48=1. f55=1. f56=1. f40=1. f41=1. f42=1. f43=1. f80=1. f81=1. f82=1. f83=1. 48.85/49.17 48.85/49.17 ============================== end of process initial clauses ======== 48.85/49.17 48.85/49.17 ============================== CLAUSES FOR SEARCH ==================== 48.85/49.17 48.85/49.17 ============================== end of clauses for search ============= 48.85/49.17 48.85/49.17 ============================== SEARCH ================================ 48.85/49.17 48.85/49.17 % Starting search at 0.62 seconds. 48.85/49.17 48.85/49.17 Low Water (keep): wt=95.000, iters=3586 48.85/49.17 48.85/49.17 Low Water (keep): wt=93.000, iters=3586 48.85/49.17 48.85/49.17 Low Water (keep): wt=88.000, iters=3567 48.85/49.17 48.85/49.17 Low Water (keep): wt=71.000, iters=3475 48.85/49.17 48.85/49.17 Low Water (keep): wt=68.000, iters=3452 48.85/49.17 48.85/49.17 Low Water (keep): wt=64.000, iters=3378 48.85/49.17 48.85/49.17 Low Water (keep): wt=61.000, iters=3346 48.85/49.17 48.85/49.17 Low Water (keep): wt=58.000, iters=3345 48.85/49.17 48.85/49.17 Low Water (keep): wt=56.000, iters=3437 48.85/49.17 48.85/49.17 Low Water (keep): wt=55.000, iters=3568 48.85/49.17 48.85/49.17 Low Water (keep): wt=51.000, iters=3339 48.85/49.17 48.85/49.17 Low Water (keep): wt=50.000, iters=3350 48.85/49.17 48.85/49.17 Low Water (keep): wt=49.000, iters=3351 48.85/49.17 48.85/49.17 Low Water (keep): wt=47.000, iters=3407 48.85/49.17 48.85/49.17 Low Water (keep): wt=46.000, iters=3424 48.85/49.17 48.85/49.17 Low Water (keep): wt=45.000, iters=3404 48.85/49.17 48.85/49.17 Low Water (keep): wt=44.000, iters=3334 48.85/49.17 48.85/49.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 53 (0.00 of 2.08 sec). 48.85/49.17 48.85/49.17 Low Water (keep): wt=43.000, iters=3376 48.85/49.17 48.85/49.17 Low Water (keep): wt=42.000, iters=3403 48.85/49.17 48.85/49.17 Low Water (keep): wt=41.000, iters=3343 48.85/49.17 48.85/49.17 Low Water (keep): wt=40.000, iters=3393 48.85/49.17 48.85/49.17 Low Water (keep): wt=39.000, iters=3400 48.85/49.17 48.85/49.17 Low Water (keep): wt=38.000, iters=3514 48.85/49.17 48.85/49.17 Low Water (keep): wt=37.000, iters=3340 48.85/49.17 48.85/49.17 Low Water (keep): wt=36.000, iters=3408 48.85/49.17 48.85/49.17 Low Water (keep): wt=35.000, iters=3381 48.85/49.17 48.85/49.17 Low Water (keep): wt=33.000, iters=3344 48.85/49.17 48.85/49.17 Low Water (keep): wt=32.000, iters=3358 48.85/49.17 48.85/49.17 Low Water (keep): wt=31.000, iters=3385 48.85/49.17 48.85/49.17 Low Water (keep): wt=30.000, iters=3336 48.85/49.17 48.85/49.17 Low Water (keep): wt=29.000, iters=3344 48.85/49.17 48.85/49.17 Low Water (keep): wt=28.000, iters=3494 48.85/49.17 48.85/49.17 Low Water (keep): wt=27.000, iters=3402 48.85/49.17 48.85/49.17 Low Water (keep): wt=26.000, iters=3454 48.85/49.17 48.85/49.17 Low Water (keep): wt=25.000, iters=3449 48.85/49.17 48.85/49.17 Low Water (keep): wt=24.000, iters=3337 48.85/49.17 48.85/49.17 Low Water (keep): wt=23.000, iters=3353 48.85/49.17 48.85/49.17 Low Water (keep): wt=22.000, iters=3386 48.85/49.17 48.85/49.17 Low Water (keep): wt=21.000, iters=3367 48.85/49.17 48.85/49.17 Low Water (keep): wt=20.000, iters=3361 48.85/49.17 48.85/49.17 Low Water (keep): wt=19.000, iters=3344 48.85/49.17 48.85/49.17 Low Water (keep): wt=18.000, iters=3341 48.85/49.17 48.85/49.17 Low Water (displace): id=3217, wt=170.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3590, wt=160.000 48.85/49.17 48.85/49.17 Low Water (displace): id=2720, wt=156.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3213, wt=153.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3593, wt=146.000 48.85/49.17 48.85/49.17 Low Water (displace): id=2707, wt=143.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3208, wt=141.000 48.85/49.17 48.85/49.17 Low Water (displace): id=2719, wt=140.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3907, wt=138.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3600, wt=137.000 48.85/49.17 48.85/49.17 Low Water (displace): id=2715, wt=136.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3901, wt=134.000 48.85/49.17 48.85/49.17 Low Water (displace): id=2722, wt=129.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3606, wt=128.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3618, wt=127.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3589, wt=125.000 48.85/49.17 48.85/49.17 Low Water (displace): id=3905, wt=123.000 48.85/49.17 48.85/49.17 Low Water (displace): id=13092, wt=16.000 48.85/49.17 48.85/49.17 Low Water (displace): id=13141, wt=14.000 48.85/49.17 48.85/49.17 Low Water (keep): wt=17.000, iters=3334 48.85/49.17 48.85/49.17 Low Water (displace): id=15452, wt=13.000 48.85/49.17 48.85/49.17 Low Water (keep): wt=16.000, iters=3348 48.85/49.17 48.85/49.17 Low Water (keep): wt=15.000, iters=3336 48.85/49.17 48.85/49.17 ============================== PROOF ================================= 48.85/49.17 % SZS status Theorem 48.85/49.17 % SZS output start Refutation 48.85/49.17 48.85/49.17 % Proof 1 at 46.79 (+ 0.70) seconds. 48.85/49.17 % Length of proof is 53. 48.85/49.17 % Level of proof is 9. 48.85/49.17 % Maximum clause weight is 48.000. 48.85/49.17 % Given clauses 11431. 48.85/49.17 48.85/49.17 53 (all V_b_2 all V_a_2 all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),V_r_2) -> V_b_2 = V_a_2)))) # label(fact_antisymD) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 55 (all B_x (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)))) # label(conj_1) # label(hypothesis) # label(non_clause). [assumption]. 48.85/49.17 120 (all V_r_2 all T_a (c_Wellfounded_Oacyclic(T_a,V_r_2) -> c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) # label(fact_acyclic__impl__antisym__rtrancl) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 129 (all B_P ((all B_x (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(B_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(B_P,B_x)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(B_P,B_x)))) -> (all B_a all B_b (B_b != B_a -> (c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),hAPP(B_P,v_i)) -> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B_a,B_b),v_F(B_P))))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption]. 48.85/49.17 140 (all V_r_2 all T_a (c_Relation_Oantisym(T_a,V_r_2) <-> c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a))))) # label(fact_antisym__reflcl) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 205 (all V_x_2 all T_a c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 214 (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 (c_member(T_a,B_x,V_A_2) -> (all B_xa (c_member(T_a,B_xa,V_A_2) -> (B_x != B_xa -> c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2) | c_member(tc_prod(T_a,T_a),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]. 48.85/49.17 226 (all V_r_2 all T_a c_Transitive__Closure_Ortrancl(T_a,V_r_2) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Relation_OId(T_a))) # label(fact_reflcl__trancl) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 248 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)) <-> c_Relation_Oirrefl(T_a,V_r_2))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 326 (all V_y_2 all V_x_2 all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2) -> V_x_2 != V_y_2))) # label(fact_irrefl__trancl__rD) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 345 (all B_x (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,B_x)) & c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,B_x)))) -> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) & c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) & c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) # label(conj_3) # label(hypothesis) # label(non_clause). [assumption]. 48.85/49.17 349 (all V_r_2 all T_a (c_Relation_Otrans(T_a,V_r_2) -> c_Transitive__Closure_Otrancl(T_a,V_r_2) = V_r_2)) # label(fact_trancl__id) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 374 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) -> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclicI) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 512 (all V_r_2 all T_a ((all B_x -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))) <-> c_Wellfounded_Oacyclic(T_a,V_r_2))) # label(fact_acyclic__def) # label(axiom) # label(non_clause). [assumption]. 48.85/49.17 669 -c_Relation_Oantisym(A,B) | -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),B) | -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,C),B) | C = D # label(fact_antisymD) # label(axiom). [clausify(53)]. 48.85/49.17 671 c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,A)) # label(conj_1) # label(hypothesis). [clausify(55)]. 48.85/49.17 672 c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,A)) # label(conj_1) # label(hypothesis). [clausify(55)]. 48.85/49.17 673 c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,A)) # label(conj_1) # label(hypothesis). [clausify(55)]. 48.85/49.17 757 -c_Wellfounded_Oacyclic(A,B) | c_Relation_Oantisym(A,c_Transitive__Closure_Ortrancl(A,B)) # label(fact_acyclic__impl__antisym__rtrancl) # label(axiom). [clausify(120)]. 48.85/49.17 761 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)) # label(conj_2) # label(hypothesis). [assumption]. 48.85/49.17 766 -c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(A,f16(A))) | -c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(A,f16(A))) | -c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(A,f16(A))) | B = C | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,B),hAPP(A,v_i)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,B),v_F(A)) # label(conj_0) # label(hypothesis). [clausify(129)]. 48.85/49.17 777 c_Relation_Oantisym(A,B) | -c_Relation_Oantisym(A,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,c_Relation_OId(A))) # label(fact_antisym__reflcl) # label(axiom). [clausify(140)]. 48.85/49.17 872 c_member(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))) # label(fact_UNIV__I) # label(axiom). [clausify(205)]. 48.85/49.17 882 -c_Relation_Ototal__on(A,B,C) | -c_member(A,D,B) | -c_member(A,E,B) | E = D | c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,E,D),C) | c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,E),C) # label(fact_total__on__def) # label(axiom). [clausify(214)]. 48.85/49.17 898 c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Transitive__Closure_Otrancl(A,B),c_Relation_OId(A)) = c_Transitive__Closure_Ortrancl(A,B) # label(fact_reflcl__trancl) # label(axiom). [clausify(226)]. 48.85/49.17 937 -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),C) | -c_Relation_Oirrefl(A,C) # label(fact_irrefl__def) # label(axiom). [clausify(248)]. 48.85/49.17 1015 c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f61(B,C,D,A),f61(B,C,D,A)),c_Transitive__Closure_Otrancl(A,D)) | -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),D) | B != C # label(fact_irrefl__trancl__rD) # label(axiom). [clausify(326)]. 48.85/49.17 1036 -c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,c1)) | -c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,c1)) | -c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,c1)) | c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) # label(conj_3) # label(hypothesis). [clausify(345)]. 48.85/49.17 1037 c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)). [copy(1036),unit_del(a,672),unit_del(b,673),unit_del(c,671)]. 48.85/49.17 1038 -c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,c1)) | -c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,c1)) | -c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,c1)) | c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) # label(conj_3) # label(hypothesis). [clausify(345)]. 48.85/49.17 1039 c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)). [copy(1038),unit_del(a,672),unit_del(b,673),unit_del(c,671)]. 48.85/49.17 1046 -c_Relation_Otrans(A,B) | c_Transitive__Closure_Otrancl(A,B) = B # label(fact_trancl__id) # label(axiom). [clausify(349)]. 48.85/49.17 1084 c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,f70(B,A),f70(B,A)),c_Transitive__Closure_Otrancl(A,B)) | c_Wellfounded_Oacyclic(A,B) # label(fact_acyclicI) # label(axiom). [clausify(374)]. 48.85/49.17 1246 -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,B),c_Transitive__Closure_Otrancl(A,C)) | -c_Wellfounded_Oacyclic(A,C) # label(fact_acyclic__def) # label(axiom). [clausify(512)]. 48.85/49.17 1247 -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)) # label(conj_4) # label(negated_conjecture). [assumption]. 48.85/49.17 1722 -c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)) | v_b = v_a. [resolve(761,a,669,c)]. 48.85/49.17 1758 A = B | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,A),hAPP(v_P,v_i)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,A),v_F(v_P)). [resolve(766,b,673,a),unit_del(a,671),unit_del(b,672)]. 48.85/49.17 2926 A = B | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,A,B),hAPP(v_P,C)) | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,A),hAPP(v_P,C)). [resolve(882,a,673,a),unit_del(a,872),unit_del(b,872)]. 48.85/49.17 3141 c_Relation_Oantisym(A,c_Transitive__Closure_Otrancl(A,B)) | -c_Relation_Oantisym(A,c_Transitive__Closure_Ortrancl(A,B)). [para(898(a,1),777(b,2))]. 48.85/49.17 4344 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f61(v_b,v_a,v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),f61(v_b,v_a,v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)),c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))) | v_b != v_a. [resolve(1015,b,761,a)]. 48.85/49.17 4749 c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P). [resolve(1046,a,1037,a)]. 48.85/49.17 4753 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,f61(v_b,v_a,v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),f61(v_b,v_a,v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P)) | v_b != v_a. [back_rewrite(4344),rewrite([4749(22)])]. 48.85/49.17 4977 c_Wellfounded_Oacyclic(A,B) | -c_Relation_Oirrefl(A,c_Transitive__Closure_Otrancl(A,B)). [resolve(1084,a,937,a)]. 48.85/49.17 7020 -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,A,A),v_F(v_P)) | -c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)). [para(4749(a,1),1246(a,3))]. 48.85/49.17 7364 c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)). [para(4749(a,1),4977(b,2)),unit_del(b,1039)]. 48.85/49.17 7367 -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,A,A),v_F(v_P)). [back_unit_del(7020),unit_del(b,7364)]. 48.85/49.18 7368 v_b != v_a. [back_unit_del(4753),unit_del(a,7367)]. 48.85/49.18 7380 -c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) | -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)). [back_unit_del(1722),unit_del(c,7368)]. 48.85/49.18 7383 c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))). [resolve(7364,a,757,a)]. 48.85/49.18 8768 c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)). [resolve(3141,b,7383,a),rewrite([4749(5)])]. 48.85/49.18 8771 -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)). [back_unit_del(7380),unit_del(a,8768)]. 48.85/49.18 39535 c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)). [resolve(2926,b,1247,a),flip(a),unit_del(a,7368)]. 48.85/49.18 39555 $F. [resolve(39535,a,1758,b),flip(a),unit_del(a,7368),unit_del(b,8771)]. 48.85/49.18 48.85/49.18 % SZS output end Refutation 48.85/49.18 ============================== end of proof ========================== 48.85/49.18 48.85/49.18 ============================== STATISTICS ============================ 48.85/49.18 48.85/49.18 Given=11431. Generated=694285. Kept=38868. proofs=1. 48.85/49.18 Usable=10556. Sos=9988. Demods=871. Limbo=16, Disabled=19190. Hints=0. 48.85/49.18 Megabytes=63.79. 48.85/49.18 User_CPU=46.79, System_CPU=0.70, Wall_clock=48. 48.85/49.18 48.85/49.18 ============================== end of statistics ===================== 48.85/49.18 48.85/49.18 ============================== end of search ========================= 48.85/49.18 48.85/49.18 THEOREM PROVED 48.85/49.18 % SZS status Theorem 48.85/49.18 48.85/49.18 Exiting with 1 proof. 48.85/49.18 48.85/49.18 Process 26550 exit (max_proofs) Thu Jul 2 08:57:53 2020 48.85/49.18 Prover9 interrupted 48.85/49.18 EOF