%------------------------------------------------------------------------------ % File : iProver-SAT---3.9.4 % Problem : TOP007-1 : TPTP v9.3.1. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Sep 25 03:55:31 PM UTC 2026 % Result : Satisfiable 3.42s 1.31s % Output : Model 3.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : TOP007-1 : TPTP v9.3.1. Released v1.0.0. % 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT % 0.09/0.36 % Computer : n015.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Fri Sep 25 04:11:12 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT % 0.09/0.39 Running model finding % 0.09/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fnt_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.14/0.41 % 0.14/0.41 % ======== iProver multi-core TPTP/SMT ========= % 0.14/0.41 % 0.14/0.41 % Detected problem language: tptp % 0.14/0.43 % Proving... % 3.42/1.31 % SZS status Started for theBenchmark.p % 3.42/1.31 % SZS status Satisfiable for theBenchmark.p % 3.42/1.31 % 3.42/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------% % 3.42/1.31 % 3.42/1.31 ------ iProver source info % 3.42/1.31 % 3.42/1.31 git: date: 2026-07-19 20:42:38 +0200 % 3.42/1.31 git: sha1: 804e7d636a263075307957e923b7a22a4035de61 % 3.42/1.31 git: non_committed_changes: false % 3.42/1.31 % 3.42/1.31 ------ Parsing...successful % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 ------ Clausification by vclausify_rel & Parsing by iProver... % 3.42/1.31 ------ Proving... % 3.42/1.31 ------ Problem Properties % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 clauses 114 % 3.42/1.31 conjectures 5 % 3.42/1.31 EPR 35 % 3.42/1.31 Horn 91 % 3.42/1.31 unary 3 % 3.42/1.31 binary 57 % 3.42/1.31 lits 343 % 3.42/1.31 lits eq 0 % 3.42/1.31 fd_pure 0 % 3.42/1.31 fd_pseudo 0 % 3.42/1.31 fd_cond 0 % 3.42/1.31 fd_pseudo_cond 0 % 3.42/1.31 AC symbols 0 % 3.42/1.31 % 3.42/1.31 ------ Schedule Sat is on % 3.42/1.31 % 3.42/1.31 ------ no equalities: superposition off % 3.42/1.31 % 3.42/1.31 ------ Input Options sat_mode off Time Limit: 30. % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 ------ % 3.42/1.31 Current options: % 3.42/1.31 ------ % 3.42/1.31 % 3.42/1.31 ------ Input Options % 3.42/1.31 % 3.42/1.31 --out_options all % 3.42/1.31 --tptp_safe_out true % 3.42/1.31 --problem_path "" % 3.42/1.31 --include_path "" % 3.42/1.31 --clausifier res/vclausify_rel % 3.42/1.31 --clausifier_options --mode clausify -t 101.66 -updr off % 3.42/1.31 --stdin false % 3.42/1.31 --proof_out true % 3.42/1.31 --proof_dot_file "" % 3.42/1.31 --proof_reduce_dot [] % 3.42/1.31 --suppress_sat_res false % 3.42/1.31 --suppress_unsat_res true % 3.42/1.31 --stats_out none % 3.42/1.31 --stats_mem false % 3.42/1.31 --theory_stats_out false % 3.42/1.31 % 3.42/1.31 ------ General Options % 3.42/1.31 % 3.42/1.31 --fof false % 3.42/1.31 --time_out_real 304.99 % 3.42/1.31 --time_out_virtual -1. % 3.42/1.31 --rnd_seed 13 % 3.42/1.31 --symbol_type_check false % 3.42/1.31 --clausify_out false % 3.42/1.31 --sig_cnt_out false % 3.42/1.31 --trig_cnt_out false % 3.42/1.31 --trig_cnt_out_tolerance 1. % 3.42/1.31 --trig_cnt_out_sk_spl false % 3.42/1.31 --abstr_cl_out false % 3.42/1.31 % 3.42/1.31 ------ Interactive Mode % 3.42/1.31 % 3.42/1.31 --interactive_mode false % 3.42/1.31 --external_ip_address "" % 3.42/1.31 --external_port 0 % 3.42/1.31 % 3.42/1.31 ------ Global Options % 3.42/1.31 % 3.42/1.31 --schedule sat % 3.42/1.31 --add_important_lit false % 3.42/1.31 --prop_solver_per_cl 500 % 3.42/1.31 --subs_bck_mult 8 % 3.42/1.31 --min_unsat_core false % 3.42/1.31 --soft_assumptions false % 3.42/1.31 --soft_lemma_size 3 % 3.42/1.31 --prop_impl_unit_size 0 % 3.42/1.31 --prop_impl_unit [] % 3.42/1.31 --share_sel_clauses true % 3.42/1.31 --reset_solvers false % 3.42/1.31 --bc_imp_inh [conj_cone] % 3.42/1.31 --conj_cone_tolerance 3. % 3.42/1.31 --extra_neg_conj none % 3.42/1.31 --large_theory_mode true % 3.42/1.31 --prolific_symb_bound 200 % 3.42/1.31 --lt_threshold 2000 % 3.42/1.31 --clause_weak_htbl true % 3.42/1.31 --gc_record_bc_elim false % 3.42/1.31 % 3.42/1.31 ------ Preprocessing Options % 3.42/1.31 % 3.42/1.31 --preprocessing_flag false % 3.42/1.31 --time_out_prep_mult 0.1 % 3.42/1.31 --splitting_mode input % 3.42/1.31 --splitting_grd true % 3.42/1.31 --splitting_cvd false % 3.42/1.31 --splitting_cvd_svl false % 3.42/1.31 --splitting_nvd 32 % 3.42/1.31 --sub_typing false % 3.42/1.31 --prep_eq_flat_conj false % 3.42/1.31 --prep_ineq_split false % 3.42/1.31 --prep_eq_flat_all_gr false % 3.42/1.31 --prep_gs_sim true % 3.42/1.31 --prep_unflatten true % 3.42/1.31 --prep_res_sim true % 3.42/1.31 --prep_sup_sim_all true % 3.42/1.31 --prep_sup_sim_sup false % 3.42/1.31 --prep_upred true % 3.42/1.31 --prep_well_definedness true % 3.42/1.31 --prep_sem_filter exhaustive % 3.42/1.31 --prep_sem_filter_out false % 3.42/1.31 --pred_elim true % 3.42/1.31 --res_sim_input true % 3.42/1.31 --eq_ax_congr_red true % 3.42/1.31 --pure_diseq_elim true % 3.42/1.31 --brand_transform false % 3.42/1.31 --non_eq_to_eq false % 3.42/1.31 --prep_eq_proxy false % 3.42/1.31 --prep_def_merge true % 3.42/1.31 --prep_def_merge_prop_impl false % 3.42/1.31 --prep_def_merge_mbd true % 3.42/1.31 --prep_def_merge_tr_red false % 3.42/1.31 --prep_def_merge_tr_cl false % 3.42/1.31 --smt_preprocessing false % 3.42/1.31 --smt_ac_axioms fast % 3.42/1.31 --preprocessed_out false % 3.42/1.31 --preprocessed_stats false % 3.42/1.31 % 3.42/1.31 ------ Abstraction refinement Options % 3.42/1.31 % 3.42/1.31 --abstr_ref [] % 3.42/1.31 --abstr_ref_prep false % 3.42/1.31 --abstr_ref_until_sat false % 3.42/1.31 --abstr_ref_sig_restrict funpre % 3.42/1.31 --abstr_ref_af_restrict_to_split_sk false % 3.42/1.31 --abstr_ref_under [] % 3.42/1.31 % 3.42/1.31 ------ SAT Options % 3.42/1.31 % 3.42/1.31 --sat_mode false % 3.42/1.31 --sat_fm_restart_options "" % 3.42/1.31 --sat_gr_def false % 3.42/1.31 --sat_epr_types true % 3.42/1.31 --sat_non_cyclic_types false % 3.42/1.31 --sat_finite_models false % 3.42/1.31 --sat_fm_lemmas false % 3.42/1.31 --sat_fm_prep false % 3.42/1.31 --sat_fm_uc_incr true % 3.42/1.31 --sat_out_model small % 3.42/1.31 --sat_out_clauses false % 3.42/1.31 % 3.42/1.31 ------ QBF Options % 3.42/1.31 % 3.42/1.31 --qbf_mode false % 3.42/1.31 --qbf_elim_univ false % 3.42/1.31 --qbf_dom_inst none % 3.42/1.31 --qbf_dom_pre_inst false % 3.42/1.31 --qbf_sk_in false % 3.42/1.31 --qbf_pred_elim true % 3.42/1.31 --qbf_split 512 % 3.42/1.31 % 3.42/1.31 ------ BMC1 Options % 3.42/1.31 % 3.42/1.31 --bmc1_incremental false % 3.42/1.31 --bmc1_axioms reachable_all % 3.42/1.31 --bmc1_min_bound 0 % 3.42/1.31 --bmc1_max_bound -1 % 3.42/1.31 --bmc1_max_bound_default -1 % 3.42/1.31 --bmc1_symbol_reachability true % 3.42/1.31 --bmc1_property_lemmas false % 3.42/1.31 --bmc1_k_induction false % 3.42/1.31 --bmc1_non_equiv_states false % 3.42/1.31 --bmc1_deadlock false % 3.42/1.31 --bmc1_ucm false % 3.42/1.31 --bmc1_add_unsat_core none % 3.42/1.31 --bmc1_unsat_core_children false % 3.42/1.31 --bmc1_unsat_core_extrapolate_axioms false % 3.42/1.31 --bmc1_out_stat full % 3.42/1.31 --bmc1_ground_init false % 3.42/1.31 --bmc1_pre_inst_next_state false % 3.42/1.31 --bmc1_pre_inst_state false % 3.42/1.31 --bmc1_pre_inst_reach_state false % 3.42/1.31 --bmc1_out_unsat_core false % 3.42/1.31 --bmc1_aig_witness_out false % 3.42/1.31 --bmc1_verbose false % 3.42/1.31 --bmc1_dump_clauses_tptp false % 3.42/1.31 --bmc1_dump_unsat_core_tptp false % 3.42/1.31 --bmc1_dump_file - % 3.42/1.31 --bmc1_ucm_expand_uc_limit 128 % 3.42/1.31 --bmc1_ucm_n_expand_iterations 6 % 3.42/1.31 --bmc1_ucm_extend_mode 1 % 3.42/1.31 --bmc1_ucm_init_mode 2 % 3.42/1.31 --bmc1_ucm_cone_mode none % 3.42/1.31 --bmc1_ucm_reduced_relation_type 0 % 3.42/1.31 --bmc1_ucm_relax_model 4 % 3.42/1.31 --bmc1_ucm_full_tr_after_sat true % 3.42/1.31 --bmc1_ucm_expand_neg_assumptions false % 3.42/1.31 --bmc1_ucm_layered_model none % 3.42/1.31 --bmc1_ucm_max_lemma_size 10 % 3.42/1.31 % 3.42/1.31 ------ AIG Options % 3.42/1.31 % 3.42/1.31 --aig_mode false % 3.42/1.31 % 3.42/1.31 ------ Instantiation Options % 3.42/1.31 % 3.42/1.31 --instantiation_flag true % 3.42/1.31 --inst_sos_flag false % 3.42/1.31 --inst_sos_phase true % 3.42/1.31 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb] % 3.42/1.31 --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb] % 3.42/1.31 --inst_lit_sel_side num_symb % 3.42/1.31 --inst_solver_per_active 1400 % 3.42/1.31 --inst_solver_calls_frac 1. % 3.42/1.31 --inst_to_smt_solver true % 3.42/1.31 --inst_passive_queue_type priority_queues % 3.42/1.31 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]] % 3.42/1.31 --inst_passive_queues_freq [25;2] % 3.42/1.31 --inst_dismatching true % 3.42/1.31 --inst_eager_unprocessed_to_passive true % 3.42/1.31 --inst_unprocessed_bound 1000 % 3.42/1.31 --inst_prop_sim_given true % 3.42/1.31 --inst_prop_sim_new false % 3.42/1.31 --inst_subs_new false % 3.42/1.31 --inst_eq_res_simp false % 3.42/1.31 --inst_subs_given false % 3.42/1.31 --inst_orphan_elimination true % 3.42/1.31 --inst_learning_loop_flag true % 3.42/1.31 --inst_learning_start 3000 % 3.42/1.31 --inst_learning_factor 2 % 3.42/1.31 --inst_start_prop_sim_after_learn 3 % 3.42/1.31 --inst_sel_renew solver % 3.42/1.31 --inst_lit_activity_flag true % 3.42/1.31 --inst_restr_to_given false % 3.42/1.31 --inst_activity_threshold 500 % 3.42/1.31 % 3.42/1.31 ------ Resolution Options % 3.42/1.31 % 3.42/1.31 --resolution_flag true % 3.42/1.31 --res_lit_sel adaptive % 3.42/1.31 --res_lit_sel_side none % 3.42/1.31 --res_ordering kbo % 3.42/1.31 --res_to_prop_solver active % 3.42/1.31 --res_prop_simpl_new false % 3.42/1.31 --res_prop_simpl_given true % 3.42/1.31 --res_to_smt_solver true % 3.42/1.31 --res_passive_queue_type priority_queues % 3.42/1.31 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]] % 3.42/1.31 --res_passive_queues_freq [15;5] % 3.42/1.31 --res_forward_subs full % 3.42/1.31 --res_backward_subs full % 3.42/1.31 --res_forward_subs_resolution true % 3.42/1.31 --res_backward_subs_resolution true % 3.42/1.31 --res_orphan_elimination true % 3.42/1.31 --res_time_limit 300. % 3.42/1.31 % 3.42/1.31 ------ Superposition Options % 3.42/1.31 % 3.42/1.31 --superposition_flag true % 3.42/1.31 --sup_passive_queue_type priority_queues % 3.42/1.31 --sup_passive_queues [[-conj_dist;-num_symb];[+score;+min_def_symb;-max_atom_input_occur;+conj_non_prolific_symb];[+age;-num_symb];[+score;-num_symb]] % 3.42/1.31 --sup_passive_queues_freq [8;1;4;4] % 3.42/1.31 --twee_lhs_weight 4 % 3.42/1.31 --sup_set_join false % 3.42/1.31 --sup_set_join_goals true % 3.42/1.31 --sup_set_join_limit 1000 % 3.42/1.31 --demod_completeness_check fast % 3.42/1.31 --demod_use_ground true % 3.42/1.31 --sup_unprocessed_bound 0 % 3.42/1.31 --sup_to_prop_solver passive % 3.42/1.31 --sup_prop_simpl_new true % 3.42/1.31 --sup_prop_simpl_given true % 3.42/1.31 --sup_fun_splitting false % 3.42/1.31 --sup_iter_deepening 2 % 3.42/1.31 --sup_restarts_mult 12 % 3.42/1.31 --sup_score sim_d_gen % 3.42/1.31 --sup_share_score_frac 0.2 % 3.42/1.31 --sup_share_max_num_cl 500 % 3.42/1.31 --sup_ordering kbo % 3.42/1.31 --sup_symb_ordering invfreq % 3.42/1.31 --sup_term_weight default % 3.42/1.31 % 3.42/1.31 ------ Superposition Simplification Setup % 3.42/1.31 % 3.42/1.31 --sup_indices_passive [LightNormIndex;FwDemodIndex] % 3.42/1.31 --sup_full_triv [SMTSimplify;PropSubs] % 3.42/1.31 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] % 3.42/1.31 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 3.42/1.31 --sup_immed_triv [] % 3.42/1.31 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes] % 3.42/1.31 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes] % 3.42/1.31 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod] % 3.42/1.31 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 3.42/1.31 --sup_input_triv [Unflattening;SMTSimplify] % 3.42/1.31 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] % 3.42/1.31 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 3.42/1.31 --sup_full_fixpoint true % 3.42/1.31 --sup_main_fixpoint true % 3.42/1.31 --sup_immed_fixpoint false % 3.42/1.31 --sup_input_fixpoint true % 3.42/1.31 --sup_cache_sim none % 3.42/1.31 --sup_smt_interval 500 % 3.42/1.31 --sup_bw_gjoin_interval 0 % 3.42/1.31 % 3.42/1.31 ------ Combination Options % 3.42/1.31 % 3.42/1.31 --comb_mode clause_based % 3.42/1.31 --comb_inst_mult 5 % 3.42/1.31 --comb_res_mult 1 % 3.42/1.31 --comb_sup_mult 1 % 3.42/1.31 --comb_sup_deep_mult 1 % 3.42/1.31 % 3.42/1.31 ------ Debug Options % 3.42/1.31 % 3.42/1.31 --dbg_backtrace false % 3.42/1.31 --dbg_dump_prop_clauses false % 3.42/1.31 --dbg_dump_prop_clauses_file - % 3.42/1.31 --dbg_out_stat false % 3.42/1.31 --dbg_just_parse false % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 ------ Proving... % 3.42/1.31 % 3.42/1.31 % 3.42/1.31 % SZS status Satisfiable for theBenchmark.p % 3.42/1.31 % 3.42/1.31 ------ Building Model...Done % 3.42/1.31 % 3.42/1.31 %------ The model is defined over ground terms (initial term algebra). % 3.42/1.31 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) % 3.42/1.31 %------ where \phi is a formula over the term algebra. % 3.42/1.31 %------ If we have equality in the problem then it is also defined as a predicate above, % 3.42/1.31 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type % 3.42/1.31 %------ See help for --sat_out_model for different model outputs. % 3.42/1.31 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" % 3.42/1.31 %------ where the first argument stands for the sort ($i in the unsorted case) % 3.42/1.31 % SZS output start Model for theBenchmark.p % 3.42/1.31 % 3.42/1.31 %------ Positive definition of topological_space % 3.42/1.31 fof(lit_def,axiom, % 3.42/1.31 (! [X0,X1] : % 3.42/1.31 ( topological_space(X0,X1) <=> % 3.42/1.31 ( % 3.42/1.31 ( % 3.42/1.31 ( X0=cx & X1=ct ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 ) % 3.42/1.31 ) % 3.42/1.31 ) % 3.42/1.31 ). % 3.42/1.31 % 3.42/1.31 %------ Positive definition of subset_sets % 3.42/1.31 fof(lit_def,axiom, % 3.42/1.31 (! [X0,X1] : % 3.42/1.31 ( subset_sets(X0,X1) <=> % 3.42/1.31 ( % 3.42/1.31 ( % 3.42/1.31 ( X0=a & X1=cx ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 | % 3.42/1.31 ? [X2] : % 3.42/1.31 ( % 3.42/1.31 ( X0=a & X1=f14(a,cx,ct,X2) ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 | % 3.42/1.31 ? [X2] : % 3.42/1.31 ( % 3.42/1.31 ( X0=f30(X2) & X1=a ) % 3.42/1.31 & % 3.42/1.31 ( X2!=f11(X2,a) ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 | % 3.42/1.31 ? [X2,X3,X4] : % 3.42/1.31 ( % 3.42/1.31 ( X0=f10(X2,f1(ct,X3),X4) & X1=f1(ct,X3) ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 | % 3.42/1.31 ? [X2,X3] : % 3.42/1.31 ( % 3.42/1.31 ( X0=f10(X2,f1(ct,X3),X3) & X1=f1(ct,X3) ) % 3.42/1.31 ) % 3.42/1.31 % 3.42/1.31 ) % 3.42/1.31 ) % 3.42/1.31 ) % 3.42/1.31 ). % 3.42/1.31 % 3.42/1.31 %------ Positive definition of element_of_set % 3.42/1.31 fof(lit_def,axiom, % 3.42/1.31 (! [X0,X1] : % 3.42/1.31 ( element_of_set(X0,X1) <=> % 3.42/1.31 ( % 3.42/1.31 ( % 3.42/1.31 ( X0!=X0 | X1!=f1(X1,X0) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=X0 | X1!=f2(X1,X0) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=X0 | X1!=f14(a,cx,ct,X0) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=X1 | X1!=f14(a,cx,ct,X1) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f20(X0,X1) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f20(X0,X1) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,a) | X1!=f30(X1) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f19(cx,ct) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f19(cx,ct) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f20(cx,ct) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f20(cx,ct) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=a ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=union_of_members(X1) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=intersection_of_sets(X1,X2) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=interior(X1,X2,X3) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=closure(X1,X2,X3) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=boundary(X1,X2,X3) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(X1,X2) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=intersection_of_members(top_of_basis(X1)) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f16(X1,a,cx,ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=intersection_of_sets(f16(X1,a,cx,ct),a) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(ct,X1) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(ct,f19(cx,ct)) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(ct,f20(cx,ct)) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f1(ct,X1) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f1(X1,f11(X0,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f2(X1,f11(X0,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f14(a,cx,ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_members(ct)) | X1!=f1(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X1,union_of_members(top_of_basis(X0))) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(top_of_basis(X1))) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(top_of_basis(X1))) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=intersection_of_sets(X1,X2) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ! [X4] : ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=intersection_of_sets(X3,X4) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,intersection_of_sets(X1,X2)) | X1!=f1(ct,X3) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f15(X0,a,cx,ct,X1) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f15(X0,a,cx,ct,X1) | X1!=intersection_of_members(ct) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f15(X1,a,cx,ct,X0) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X1,intersection_of_members(ct)) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X1,intersection_of_members(ct)) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X1,intersection_of_members(ct)) | X1!=f1(ct,f11(X1,intersection_of_members(ct))) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(ct)) | X1!=cx ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(ct)) | X1!=empty_set ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(ct)) | X1!=intersection_of_sets(X1,X2) ) % 3.42/1.31 & % 3.42/1.31 ( X0!=f11(X0,union_of_members(ct)) | X1!=intersection_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,union_of_members(ct)) | X1!=intersection_of_sets(f16(X1,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f16(X1,a,cx,ct)) | X1!=f16(X1,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X0!=f11(X2,intersection_of_sets(X3,X4)) | X1!=intersection_of_sets(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f1(ct,X1)) | X1!=intersection_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f1(ct,X1)) | X1!=f1(ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X1,union_of_members(ct)) | X1!=cx ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X1,union_of_members(ct)) | X1!=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f1(ct,f11(X1,intersection_of_members(ct)))) | X1!=f1(ct,f11(X1,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_sets(X2,X3)) | X1!=f16(X1,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_sets(X2,X3)) | X1!=f1(ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f20(X1,X0) | X1!=cx ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=f11(X1,intersection_of_sets(X0,X2)) | X1!=cx ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X1,intersection_of_sets(X0,X2)) | X1!=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X1,intersection_of_sets(X0,X2)) | X1!=f16(f11(X1,intersection_of_sets(X0,X2)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X2,intersection_of_sets(X1,X0)) | X1!=intersection_of_sets(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=a ) % 3.42/1.32 & % 3.42/1.32 ( X1!=union_of_members(X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X1!=intersection_of_sets(X1,X2) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X1!=interior(X1,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=closure(X1,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_sets(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=boundary(X1,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(X1,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_members(top_of_basis(X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_sets(f16(X1,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f30(X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(X1,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(ct,f11(X1,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=interior(X1,X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=closure(X1,X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=boundary(X1,X0,X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=cx ) % 3.42/1.32 & % 3.42/1.32 ( X1!=a ) % 3.42/1.32 & % 3.42/1.32 ( X1!=union_of_members(X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_members(X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=union_of_members(top_of_basis(X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_members(top_of_basis(X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f30(f11(X1,a)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f16(X1,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_sets(f16(X1,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f30(X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(ct,f11(X1,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(ct,f11(X1,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X1!=intersection_of_sets(X1,X3) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X1!=interior(X1,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=closure(X1,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=boundary(X1,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(X1,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(top_of_basis(X1),X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(X1,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f2(X1,f11(X3,intersection_of_members(X1))) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f1(top_of_basis(X2),X1) | X2!=X2 ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f19(cx,ct) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f20(cx,ct) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f7(cx,ct) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(ct)) & X1=closure(a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(ct)) & X1=intersection_of_members(X3) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(ct)) & X1=intersection_of_members(subspace_topology(X3,X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(ct)) & X1=f16(f11(X2,intersection_of_members(ct)),a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,closure(a,cx,ct)) & X1=closure(a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_sets(X3,X4)) & X1=closure(a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_sets(X3,X4)) & X1=f1(ct,f11(X2,intersection_of_sets(X3,X4))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_sets(X3,X4)) & X1=intersection_of_members(X5) ) % 3.42/1.32 & % 3.42/1.32 ( X5!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X5!=top_of_basis(X5) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5,X6,X7] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_sets(X3,X4)) & X1=intersection_of_members(subspace_topology(X5,X6,X7)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(ct)) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(ct)) & X1=empty_set ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(ct)) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(ct)) & X1=f1(ct,f11(X2,union_of_members(ct))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(top_of_basis(X3))) & X1=empty_set ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,union_of_members(top_of_basis(X3))) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f2(X3,X4)) & X1=f2(X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=ct | X4!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=X3 | X4!=f11(X4,intersection_of_members(X3)) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(X3)) & X1=intersection_of_members(X3) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=top_of_basis(X3) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X3!=subspace_topology(X3,X2,X4) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,empty_set) & X1=empty_set ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,empty_set) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,cx) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,cx) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f30(f11(X3,a))) & X1=f30(f11(X3,a)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_members(subspace_topology(X3,X4,X5))) & X1=intersection_of_members(subspace_topology(X3,X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f2(ct,X3)) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f30(X3)) & X1=f30(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f1(ct,X3)) & X1=union_of_members(ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f1(ct,X3)) & X1=f1(ct,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f16(X3,a,cx,ct)) & X1=f16(X3,a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,f1(ct,f11(X3,intersection_of_members(ct)))) & X1=f1(ct,f11(X3,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X2!=subspace_topology(X2,X3,X4) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(top_of_basis(X2),f1(ct,f11(X3,intersection_of_members(ct)))) & X1=f1(ct,f11(X3,intersection_of_members(ct))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(subspace_topology(X2,X3,X4),f1(ct,f11(X5,intersection_of_members(ct)))) & X1=f1(ct,f11(X5,intersection_of_members(ct))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=cx ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f19(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f20(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=f20(X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f15(X0,a,cx,ct,X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X1=intersection_of_members(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f19(cx,ct) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f20(cx,ct) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) | X2!=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X2,intersection_of_members(ct)) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f15(X2,a,cx,ct,X0) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X2,union_of_members(ct)) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X2,union_of_members(top_of_basis(X0))) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f20(X2,X0) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f11(X2,intersection_of_sets(X0,X3)) | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(X2)) | X2!=X2 ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X0!=f11(X0,intersection_of_sets(X3,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_sets(X3,X4)) | X2!=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(top_of_basis(X2))) | X2!=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=subspace_topology(X2,X0,X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=f11(X0,union_of_members(top_of_basis(X2))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=union_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,cx) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,empty_set) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=f11(X0,union_of_members(top_of_basis(X2))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,closure(a,cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3,X2] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=f16(X0,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3,X2] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=f1(ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X3,X2] : ( X0!=f11(X0,intersection_of_sets(X2,X3)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X1=intersection_of_members(subspace_topology(X2,X3,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(subspace_topology(X2,X3,X4))) | X2!=X2 | X3!=X3 | X4!=X4 ) % 3.42/1.32 & % 3.42/1.32 ! [X6,X5] : ( X0!=f11(X0,intersection_of_sets(X5,X6)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X1=f1(ct,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X2,intersection_of_members(ct)) | X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X4,X3] : ( X0!=f11(X0,intersection_of_sets(X3,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f1(ct,X2)) | X2!=X2 ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,f1(ct,f11(X2,intersection_of_members(ct)))) | X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X1=f10(X2,f1(ct,X0),X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X1=f10(X2,f1(ct,X3),X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5,X4] : ( X0!=f11(X0,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of neighborhood % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2,X3] : % 3.42/1.32 ( neighborhood(X0,X1,X2,X3) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=f19(cx,ct) & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=f20(cx,ct) & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=empty_set & X1=f11(X4,union_of_members(ct)) & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=empty_set & X1=f11(X4,union_of_members(top_of_basis(X5))) & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f16(X1,a,cx,ct) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5,X4] : ( X1!=f11(X1,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,X1) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5,X4] : ( X1!=f11(X1,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,X4) & X1=f11(X5,f1(ct,X4)) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X7,X6] : ( X4!=f11(X4,intersection_of_sets(X6,X7)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,X4) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X4,intersection_of_members(ct)) | X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X6,X5] : ( X1!=f11(X1,intersection_of_sets(X5,X6)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X4,intersection_of_sets(X1,X5)) | X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,f1(ct,X4)) | X4!=X4 ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,f1(ct,f11(X4,intersection_of_members(ct)))) | X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X6,f1(ct,f11(X4,intersection_of_sets(X1,X5)))) | X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f16(X4,a,cx,ct) & X1=f11(X5,f16(X4,a,cx,ct)) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X7,X6] : ( X4!=f11(X4,intersection_of_sets(X6,X7)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f16(X4,a,cx,ct) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X4,intersection_of_members(ct)) | X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X6,X5] : ( X1!=f11(X1,intersection_of_sets(X5,X6)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,f16(X4,a,cx,ct)) | X4!=X4 ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,f16(f11(X4,intersection_of_members(ct)),a,cx,ct)) | X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X4,intersection_of_sets(X1,X5)) | X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X6,f16(f11(X4,intersection_of_sets(X1,X5)),a,cx,ct)) | X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X4!=f11(X4,intersection_of_sets(X1,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4] : % 3.42/1.32 ( % 3.42/1.32 ( X1=f11(X4,X0) & X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=a ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ! [X6] : ( X0!=interior(X0,X5,X6) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(X0,X5,X6) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=boundary(X0,X5,X6) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f8(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=relative_complement_sets(X0,cx) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f16(X0,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_members(ct)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ! [X5] : ( X0!=intersection_of_sets(X0,X5) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(X0,X5) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X5) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_sets(X5,X6))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X5),X6) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(ct,f1(ct,X0),X5) ) % 3.42/1.32 & % 3.42/1.32 ! [X8,X7] : ( X0!=f10(X0,f1(ct,X5),f11(X6,intersection_of_sets(X7,X8))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X5),f11(X6,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_sets(X5,X6)),a,cx,ct) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X2=cx & X3=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx | X1!=f20(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx | X1!=f19(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx | X1!=f20(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx | X1!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx | X1!=f15(X0,a,cx,ct,X1) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X0!=cx | X1!=f11(X0,intersection_of_sets(X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=a ) % 3.42/1.32 & % 3.42/1.32 ( X0!=X0 | X1!=f11(X1,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) | X1!=X0 ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) | X1!=f11(X1,a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_members(X0) | X1!=f11(X1,intersection_of_members(X0)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=empty_set | X1!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=empty_set | X1!=f11(X0,union_of_members(top_of_basis(X1))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=empty_set | X1!=f11(X0,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=empty_set | X1!=f11(X0,intersection_of_sets(X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(X0) | X1!=f11(X1,union_of_members(X0)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(ct) | X1!=f11(X0,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,X1) | X1!=f11(X4,intersection_of_sets(X0,X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f8(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f8(cx,ct) | X1!=f11(X0,f8(cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(top_of_basis(X0)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=relative_complement_sets(X0,cx) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=relative_complement_sets(X0,cx) | X1!=f11(X1,relative_complement_sets(X0,cx)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) | X1!=X0 ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) | X1!=f11(X1,f14(a,cx,ct,X0)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(a,cx,ct) | X1!=f11(X0,closure(a,cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(top_of_basis(X0),X1) | X1!=f11(X4,intersection_of_members(top_of_basis(X0))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) | X1!=X0 ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) | X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) | X1!=f11(X1,f16(X0,a,cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) | X1!=f11(X1,intersection_of_sets(X4,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X1) | X1!=X1 ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X1) | X1!=f11(X4,f1(X0,X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,X0) | X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,X0) | X1!=f11(X1,intersection_of_sets(X4,X5)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f16(X0,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) | X1!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) | X1!=f11(X1,f1(ct,f11(X0,intersection_of_members(ct)))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_members(ct)),a,cx,ct) | X1!=f11(X0,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_members(ct)),a,cx,ct) | X1!=f11(X1,f16(f11(X0,intersection_of_members(ct)),a,cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(ct,f1(ct,X0),X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(ct,f1(ct,X0),X1) | X1!=f11(X4,f10(ct,f1(ct,X0),X1)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X1),X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X1),X4) | X1!=f11(X5,f10(X0,f1(ct,X1),X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=interior(X0,X1,X4) ) % 3.42/1.32 & % 3.42/1.32 ! [X6] : ( X0!=interior(X0,X1,X4) | X1!=f11(X5,intersection_of_members(top_of_basis(X6))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=interior(X0,X1,X4) | X1!=f11(X5,interior(X0,X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(X0,X1,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(X0,X1,X4) | X1!=f11(X5,closure(X0,X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=boundary(X0,X1,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=boundary(X0,X1,X4) | X1!=f11(X5,boundary(X0,X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_sets(X1,X4))) | X1!=f11(X0,intersection_of_sets(X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_sets(X1,X4))) | X1!=f11(X5,f1(ct,f11(X0,intersection_of_sets(X1,X4)))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_sets(X1,X4)),a,cx,ct) | X1!=f11(X0,intersection_of_sets(X1,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_sets(X1,X4)),a,cx,ct) | X1!=f11(X5,f16(f11(X0,intersection_of_sets(X1,X4)),a,cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X1),f11(X4,intersection_of_sets(X5,X6))) ) % 3.42/1.32 & % 3.42/1.32 ! [X7] : ( X0!=f10(X0,f1(ct,X1),f11(X4,intersection_of_sets(X5,X6))) | X1!=f11(X7,f10(X0,f1(ct,X1),f11(X4,intersection_of_sets(X5,X6)))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X1),f11(X4,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X1),f11(X4,intersection_of_members(ct))) | X1!=f11(X5,f10(X0,f1(ct,X1),f11(X4,intersection_of_members(ct)))) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=f11(X1,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5] : ( X1!=f11(X1,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of open % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( open(X0,X1,X2) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=cx & X2=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(X3,X4) & X1=cx & X2=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f8(cx,ct) | X4!=f9(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f16(X3,a,cx,ct) | X4!=a ) % 3.42/1.32 & % 3.42/1.32 ( X4!=a ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f19(cx,ct)) & X1=cx & X2=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f20(cx,ct)) & X1=cx & X2=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,X3) & X1=cx & X2=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5,X4] : ( X3!=f11(X3,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f16(X3,a,cx,ct) & X1=cx & X2=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X5,X4] : ( X3!=f11(X3,intersection_of_sets(X4,X5)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,X3) & X1=cx & X2=ct ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f19(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f20(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X3,intersection_of_members(ct))) & X1=cx & X2=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=cx & X2=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=cx ) % 3.42/1.32 & % 3.42/1.32 ( X0!=a ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(f11(X0,a)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f8(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f8(cx,ct),f9(cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=relative_complement_sets(X0,cx) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f16(X0,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_members(ct)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X0!=interior(X0,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(X0,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=boundary(X0,X3,X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,X3) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=f2(X0,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(top_of_basis(X0),X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_sets(X3,X4))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X3),X4) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_sets(X3,X4)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ! [X6,X5] : ( X0!=f10(X0,f1(ct,X3),f11(X4,intersection_of_sets(X5,X6))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X3),f11(X4,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(ct,f1(ct,X0),X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of element_of_collection % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( element_of_collection(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=a & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=union_of_members(X2) & X1=top_of_basis(X3) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=empty_set & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(X2,X3) & X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f8(cx,ct) | X3!=f9(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f16(X2,a,cx,ct) | X3!=a ) % 3.42/1.32 & % 3.42/1.32 ( X3!=a ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(X2,X3) & X1=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f8(cx,ct) | X3!=f9(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f16(X2,a,cx,ct) | X3!=a ) % 3.42/1.32 & % 3.42/1.32 ( X3!=a ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_members(ct) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f9(cx,ct) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(f8(cx,ct),f9(cx,ct)) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=union_of_members(top_of_basis(X2)) & X1=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=interior(X2,X3,X4) & X1=top_of_basis(X5) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=closure(X2,X3,X4) & X1=top_of_basis(X5) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=a | X3!=cx | X4!=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=boundary(X2,X3,X4) & X1=top_of_basis(X5) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_members(top_of_basis(X2)) & X1=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(top_of_basis(X2),X3) & X1=top_of_basis(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=X2 | X3!=f11(X3,intersection_of_members(top_of_basis(X2))) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(top_of_basis(X2),X3) & X1=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=X4 | X3!=f11(X2,intersection_of_members(top_of_basis(X4))) | X4!=X4 ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(X2,X3) & X1=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct | X3!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct | X3!=f11(X2,intersection_of_members(ct)) | X4!=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ! [X5] : ( X2!=ct | X3!=f11(X5,intersection_of_members(ct)) | X4!=subspace_topology(X4,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X4) | X4!=X4 ) % 3.42/1.32 & % 3.42/1.32 ( X3!=f11(X3,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f19(cx,ct)) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f20(cx,ct)) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,X2) & X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f19(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f20(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X4] : ( X2!=f11(X2,intersection_of_sets(X3,X4)) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,union_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,union_of_members(top_of_basis(X3))) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f15(X2,a,cx,ct,X3) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X2!=f20(X2,X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,X2) & X1=top_of_basis(X3) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(X2,f11(X3,intersection_of_members(X2))) & X1=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X4) | X4!=X4 ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,X2) & X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X4,X3] : ( X2!=f11(X2,intersection_of_sets(X3,X4)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X2,intersection_of_members(ct))) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X2,intersection_of_members(ct))) & X1=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(X2,f11(X3,intersection_of_members(ct))) & X1=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct | X4!=top_of_basis(X4) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct | X4!=subspace_topology(X4,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=top_of_basis(X4) | X4!=X4 ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f16(X2,a,cx,ct) & X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=f11(X2,intersection_of_members(ct)) ) % 3.42/1.32 & % 3.42/1.32 ! [X4,X3] : ( X2!=f11(X2,intersection_of_sets(X3,X4)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(f16(X2,a,cx,ct),a) & X1=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=intersection_of_sets(X2,a) & X1=top_of_basis(X3) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(top_of_basis(X2),X3) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(top_of_basis(X2),f11(X3,intersection_of_members(top_of_basis(X2)))) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(ct,f11(X2,union_of_members(ct))) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X2,intersection_of_sets(X3,X4))) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X2,union_of_members(ct))) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f11(X2,union_of_members(top_of_basis(X3)))) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f15(X2,a,cx,ct,X3)) & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(ct,f20(X2,X3)) & X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X2!=cx | X3!=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4,X5] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(top_of_basis(X2),f11(X3,intersection_of_sets(X4,X5))) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f1(top_of_basis(X2),f11(X3,intersection_of_members(ct))) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f2(top_of_basis(X2),f11(X3,intersection_of_members(ct))) & X1=top_of_basis(X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X1=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=a ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=union_of_members(X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f30(f11(X0,a)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f8(cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f8(cx,ct),f9(cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=relative_complement_sets(X0,cx) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f14(a,cx,ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(X0,a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,X0) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(f16(X0,a,cx,ct),a) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(ct,f19(cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(ct,f20(cx,ct)) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_members(ct)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f2(top_of_basis(X0),X2) ) % 3.42/1.32 & % 3.42/1.32 ! [X3] : ( X0!=interior(X0,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=closure(X0,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=boundary(X0,X2,X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=f2(X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f1(ct,f11(X0,intersection_of_sets(X2,X3))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X2),X3) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f16(f11(X0,intersection_of_sets(X2,X3)),a,cx,ct) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(X0,f1(ct,X2),f11(X3,intersection_of_members(ct))) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f10(ct,f1(ct,X0),X2) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of equal_sets % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( equal_sets(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=union_of_members(X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=cx | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X1!=empty_set | X2!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X1!=intersection_of_sets(X1,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2] : % 3.42/1.32 ( % 3.42/1.32 ( X0=union_of_members(X2) & X1=empty_set ) % 3.42/1.32 & % 3.42/1.32 ( X2!=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=union_of_members(ct) & X1=cx ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of subset_collections % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( subset_collections(X0,X1) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of closed % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( closed(X0,X1,X2) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of finer % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( finer(X0,X1,X2) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of basis % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( basis(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0!=cx | X1!=ct ) % 3.42/1.32 & % 3.42/1.32 ( X0!=intersection_of_sets(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ! [X2] : ( X0!=intersection_of_sets(X0,X2) ) % 3.42/1.32 & % 3.42/1.32 ( X1!=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of limit_point % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2,X3] : % 3.42/1.32 ( limit_point(X0,X1,X2,X3) <=> % 3.42/1.32 ( % 3.42/1.32 ? [X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X4,intersection_of_members(ct)) & X1=a & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X4,X5,X6] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X4,intersection_of_sets(X5,X6)) & X1=a & X2=cx & X3=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of eq_p % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( eq_p(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0!=f19(X0,X1) | X1!=f20(X0,X1) ) % 3.42/1.32 & % 3.42/1.32 ( X0!=f15(X0,a,cx,ct,X1) | X1!=X0 ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 | % 3.42/1.32 ? [X2,X3,X4] : % 3.42/1.32 ( % 3.42/1.32 ( X0=f11(X2,intersection_of_sets(X3,X4)) ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of hausdorff % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( hausdorff(X0,X1) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of disjoint_s % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( disjoint_s(X0,X1) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of separation % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2,X3] : % 3.42/1.32 ( separation(X0,X1,X2,X3) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of connected_space % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( connected_space(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of connected_set % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( connected_set(X0,X1,X2) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of open_covering % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( open_covering(X0,X1,X2) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of compact_space % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1] : % 3.42/1.32 ( compact_space(X0,X1) <=> % 3.42/1.32 ( % 3.42/1.32 ( % 3.42/1.32 ( X0=cx & X1=ct ) % 3.42/1.32 ) % 3.42/1.32 % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of finite % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0] : % 3.42/1.32 ( finite(X0) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % 3.42/1.32 %------ Positive definition of compact_set % 3.42/1.32 fof(lit_def,axiom, % 3.42/1.32 (! [X0,X1,X2] : % 3.42/1.32 ( compact_set(X0,X1,X2) <=> % 3.42/1.32 $false % 3.42/1.32 ) % 3.42/1.32 ) % 3.42/1.32 ). % 3.42/1.32 % SZS output end Model for theBenchmark.p % 3.42/1.32 %------------------------------------------------------------------------------