%------------------------------------------------------------------------------ % File : iProver-SAT---3.9.4 % Problem : LCL948_10 : TPTP v9.3.1. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT % Computer : n016.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 02:10:45 PM UTC 2026 % Result : CounterSatisfiable 71.42s 11.23s % Output : Model 71.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL948_10 : TPTP v9.3.1. Released v8.2.0. % 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT % 0.09/0.35 % Computer : n016.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Thu Sep 24 00:47:41 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT % 0.14/0.39 Running model finding % 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fnt_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p % 0.14/0.40 % 0.14/0.40 % ======== iProver multi-core TPTP/SMT ========= % 0.14/0.40 % 0.14/0.40 % Detected problem language: tptp % 0.14/0.41 % Proving... % 71.42/11.23 % SZS status Started for theBenchmark.p % 71.42/11.23 % SZS status Satisfiable for theBenchmark.p % 71.42/11.23 % 71.42/11.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------% % 71.42/11.23 % 71.42/11.23 ------ iProver source info % 71.42/11.23 % 71.42/11.23 git: date: 2026-07-19 20:42:38 +0200 % 71.42/11.23 git: sha1: 804e7d636a263075307957e923b7a22a4035de61 % 71.42/11.23 git: non_committed_changes: false % 71.42/11.23 % 71.42/11.23 ------ Parsing... % 71.42/11.23 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim % 71.42/11.23 % 71.42/11.23 ------ Proving... % 71.42/11.23 ------ Problem Properties % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 clauses 144 % 71.42/11.23 conjectures 4 % 71.42/11.23 EPR 10 % 71.42/11.23 Horn 60 % 71.42/11.23 unary 6 % 71.42/11.23 binary 0 % 71.42/11.23 lits 1237 % 71.42/11.23 lits eq 0 % 71.42/11.23 fd_pure 0 % 71.42/11.23 fd_pseudo 0 % 71.42/11.23 fd_cond 0 % 71.42/11.23 fd_pseudo_cond 0 % 71.42/11.23 AC symbols 0 % 71.42/11.23 % 71.42/11.23 ------ Schedule Sat is on % 71.42/11.23 % 71.42/11.23 ------ no equalities: superposition off % 71.42/11.23 % 71.42/11.23 ------ Input Options sat_mode off Time Limit: 30. % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 ------ % 71.42/11.23 Current options: % 71.42/11.23 ------ % 71.42/11.23 % 71.42/11.23 ------ Input Options % 71.42/11.23 % 71.42/11.23 --out_options all % 71.42/11.23 --tptp_safe_out true % 71.42/11.23 --problem_path "" % 71.42/11.23 --include_path "" % 71.42/11.23 --clausifier res/vclausify_rel % 71.42/11.23 --clausifier_options --mode tclausify --show_fool true -t 101.66 -updr off % 71.42/11.23 --stdin false % 71.42/11.23 --proof_out true % 71.42/11.23 --proof_dot_file "" % 71.42/11.23 --proof_reduce_dot [] % 71.42/11.23 --suppress_sat_res false % 71.42/11.23 --suppress_unsat_res true % 71.42/11.23 --stats_out none % 71.42/11.23 --stats_mem false % 71.42/11.23 --theory_stats_out false % 71.42/11.23 % 71.42/11.23 ------ General Options % 71.42/11.23 % 71.42/11.23 --fof false % 71.42/11.23 --time_out_real 304.99 % 71.42/11.23 --time_out_virtual -1. % 71.42/11.23 --rnd_seed 13 % 71.42/11.23 --symbol_type_check false % 71.42/11.23 --clausify_out false % 71.42/11.23 --sig_cnt_out false % 71.42/11.23 --trig_cnt_out false % 71.42/11.23 --trig_cnt_out_tolerance 1. % 71.42/11.23 --trig_cnt_out_sk_spl false % 71.42/11.23 --abstr_cl_out false % 71.42/11.23 % 71.42/11.23 ------ Interactive Mode % 71.42/11.23 % 71.42/11.23 --interactive_mode false % 71.42/11.23 --external_ip_address "" % 71.42/11.23 --external_port 0 % 71.42/11.23 % 71.42/11.23 ------ Global Options % 71.42/11.23 % 71.42/11.23 --schedule sat % 71.42/11.23 --add_important_lit false % 71.42/11.23 --prop_solver_per_cl 500 % 71.42/11.23 --subs_bck_mult 8 % 71.42/11.23 --min_unsat_core false % 71.42/11.23 --soft_assumptions false % 71.42/11.23 --soft_lemma_size 3 % 71.42/11.23 --prop_impl_unit_size 0 % 71.42/11.23 --prop_impl_unit [] % 71.42/11.23 --share_sel_clauses true % 71.42/11.23 --reset_solvers false % 71.42/11.23 --bc_imp_inh [conj_cone] % 71.42/11.23 --conj_cone_tolerance 3. % 71.42/11.23 --extra_neg_conj none % 71.42/11.23 --large_theory_mode true % 71.42/11.23 --prolific_symb_bound 200 % 71.42/11.23 --lt_threshold 2000 % 71.42/11.23 --clause_weak_htbl true % 71.42/11.23 --gc_record_bc_elim false % 71.42/11.23 % 71.42/11.23 ------ Preprocessing Options % 71.42/11.23 % 71.42/11.23 --preprocessing_flag false % 71.42/11.23 --time_out_prep_mult 0.1 % 71.42/11.23 --splitting_mode input % 71.42/11.23 --splitting_grd true % 71.42/11.23 --splitting_cvd false % 71.42/11.23 --splitting_cvd_svl false % 71.42/11.23 --splitting_nvd 32 % 71.42/11.23 --sub_typing false % 71.42/11.23 --prep_eq_flat_conj false % 71.42/11.23 --prep_ineq_split false % 71.42/11.23 --prep_eq_flat_all_gr false % 71.42/11.23 --prep_gs_sim true % 71.42/11.23 --prep_unflatten true % 71.42/11.23 --prep_res_sim true % 71.42/11.23 --prep_sup_sim_all true % 71.42/11.23 --prep_sup_sim_sup false % 71.42/11.23 --prep_upred true % 71.42/11.23 --prep_well_definedness true % 71.42/11.23 --prep_sem_filter exhaustive % 71.42/11.23 --prep_sem_filter_out false % 71.42/11.23 --pred_elim true % 71.42/11.23 --res_sim_input true % 71.42/11.23 --eq_ax_congr_red true % 71.42/11.23 --pure_diseq_elim true % 71.42/11.23 --brand_transform false % 71.42/11.23 --non_eq_to_eq false % 71.42/11.23 --prep_eq_proxy false % 71.42/11.23 --prep_def_merge true % 71.42/11.23 --prep_def_merge_prop_impl false % 71.42/11.23 --prep_def_merge_mbd true % 71.42/11.23 --prep_def_merge_tr_red false % 71.42/11.23 --prep_def_merge_tr_cl false % 71.42/11.23 --smt_preprocessing false % 71.42/11.23 --smt_ac_axioms fast % 71.42/11.23 --preprocessed_out false % 71.42/11.23 --preprocessed_stats false % 71.42/11.23 % 71.42/11.23 ------ Abstraction refinement Options % 71.42/11.23 % 71.42/11.23 --abstr_ref [] % 71.42/11.23 --abstr_ref_prep false % 71.42/11.23 --abstr_ref_until_sat false % 71.42/11.23 --abstr_ref_sig_restrict funpre % 71.42/11.23 --abstr_ref_af_restrict_to_split_sk false % 71.42/11.23 --abstr_ref_under [] % 71.42/11.23 % 71.42/11.23 ------ SAT Options % 71.42/11.23 % 71.42/11.23 --sat_mode false % 71.42/11.23 --sat_fm_restart_options "" % 71.42/11.23 --sat_gr_def false % 71.42/11.23 --sat_epr_types true % 71.42/11.23 --sat_non_cyclic_types false % 71.42/11.23 --sat_finite_models false % 71.42/11.23 --sat_fm_lemmas false % 71.42/11.23 --sat_fm_prep false % 71.42/11.23 --sat_fm_uc_incr true % 71.42/11.23 --sat_out_model small % 71.42/11.23 --sat_out_clauses false % 71.42/11.23 % 71.42/11.23 ------ QBF Options % 71.42/11.23 % 71.42/11.23 --qbf_mode false % 71.42/11.23 --qbf_elim_univ false % 71.42/11.23 --qbf_dom_inst none % 71.42/11.23 --qbf_dom_pre_inst false % 71.42/11.23 --qbf_sk_in false % 71.42/11.23 --qbf_pred_elim true % 71.42/11.23 --qbf_split 512 % 71.42/11.23 % 71.42/11.23 ------ BMC1 Options % 71.42/11.23 % 71.42/11.23 --bmc1_incremental false % 71.42/11.23 --bmc1_axioms reachable_all % 71.42/11.23 --bmc1_min_bound 0 % 71.42/11.23 --bmc1_max_bound -1 % 71.42/11.23 --bmc1_max_bound_default -1 % 71.42/11.23 --bmc1_symbol_reachability true % 71.42/11.23 --bmc1_property_lemmas false % 71.42/11.23 --bmc1_k_induction false % 71.42/11.23 --bmc1_non_equiv_states false % 71.42/11.23 --bmc1_deadlock false % 71.42/11.23 --bmc1_ucm false % 71.42/11.23 --bmc1_add_unsat_core none % 71.42/11.23 --bmc1_unsat_core_children false % 71.42/11.23 --bmc1_unsat_core_extrapolate_axioms false % 71.42/11.23 --bmc1_out_stat full % 71.42/11.23 --bmc1_ground_init false % 71.42/11.23 --bmc1_pre_inst_next_state false % 71.42/11.23 --bmc1_pre_inst_state false % 71.42/11.23 --bmc1_pre_inst_reach_state false % 71.42/11.23 --bmc1_out_unsat_core false % 71.42/11.23 --bmc1_aig_witness_out false % 71.42/11.23 --bmc1_verbose false % 71.42/11.23 --bmc1_dump_clauses_tptp false % 71.42/11.23 --bmc1_dump_unsat_core_tptp false % 71.42/11.23 --bmc1_dump_file - % 71.42/11.23 --bmc1_ucm_expand_uc_limit 128 % 71.42/11.23 --bmc1_ucm_n_expand_iterations 6 % 71.42/11.23 --bmc1_ucm_extend_mode 1 % 71.42/11.23 --bmc1_ucm_init_mode 2 % 71.42/11.23 --bmc1_ucm_cone_mode none % 71.42/11.23 --bmc1_ucm_reduced_relation_type 0 % 71.42/11.23 --bmc1_ucm_relax_model 4 % 71.42/11.23 --bmc1_ucm_full_tr_after_sat true % 71.42/11.23 --bmc1_ucm_expand_neg_assumptions false % 71.42/11.23 --bmc1_ucm_layered_model none % 71.42/11.23 --bmc1_ucm_max_lemma_size 10 % 71.42/11.23 % 71.42/11.23 ------ AIG Options % 71.42/11.23 % 71.42/11.23 --aig_mode false % 71.42/11.23 % 71.42/11.23 ------ Instantiation Options % 71.42/11.23 % 71.42/11.23 --instantiation_flag true % 71.42/11.23 --inst_sos_flag false % 71.42/11.23 --inst_sos_phase true % 71.42/11.23 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb] % 71.42/11.23 --inst_lit_sel [-sign;+ground;-num_var;-num_symb] % 71.42/11.23 --inst_lit_sel_side num_symb % 71.42/11.23 --inst_solver_per_active 1400 % 71.42/11.23 --inst_solver_calls_frac 1. % 71.42/11.23 --inst_to_smt_solver true % 71.42/11.23 --inst_passive_queue_type priority_queues % 71.42/11.23 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]] % 71.42/11.23 --inst_passive_queues_freq [25;2] % 71.42/11.23 --inst_dismatching true % 71.42/11.23 --inst_eager_unprocessed_to_passive true % 71.42/11.23 --inst_unprocessed_bound 1000 % 71.42/11.23 --inst_prop_sim_given true % 71.42/11.23 --inst_prop_sim_new false % 71.42/11.23 --inst_subs_new false % 71.42/11.23 --inst_eq_res_simp false % 71.42/11.23 --inst_subs_given false % 71.42/11.23 --inst_orphan_elimination true % 71.42/11.23 --inst_learning_loop_flag true % 71.42/11.23 --inst_learning_start 3000 % 71.42/11.23 --inst_learning_factor 2 % 71.42/11.23 --inst_start_prop_sim_after_learn 3 % 71.42/11.23 --inst_sel_renew solver % 71.42/11.23 --inst_lit_activity_flag true % 71.42/11.23 --inst_restr_to_given false % 71.42/11.23 --inst_activity_threshold 500 % 71.42/11.23 % 71.42/11.23 ------ Resolution Options % 71.42/11.23 % 71.42/11.23 --resolution_flag true % 71.42/11.23 --res_lit_sel neg_min % 71.42/11.23 --res_lit_sel_side none % 71.42/11.23 --res_ordering kbo % 71.42/11.23 --res_to_prop_solver active % 71.42/11.23 --res_prop_simpl_new false % 71.42/11.23 --res_prop_simpl_given true % 71.42/11.23 --res_to_smt_solver true % 71.42/11.23 --res_passive_queue_type priority_queues % 71.42/11.23 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]] % 71.42/11.23 --res_passive_queues_freq [15;5] % 71.42/11.23 --res_forward_subs full % 71.42/11.23 --res_backward_subs full % 71.42/11.23 --res_forward_subs_resolution true % 71.42/11.23 --res_backward_subs_resolution true % 71.42/11.23 --res_orphan_elimination true % 71.42/11.23 --res_time_limit 300. % 71.42/11.23 % 71.42/11.23 ------ Superposition Options % 71.42/11.23 % 71.42/11.23 --superposition_flag true % 71.42/11.23 --sup_passive_queue_type priority_queues % 71.42/11.23 --sup_passive_queues [[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]] % 71.42/11.23 --sup_passive_queues_freq [1;1;1] % 71.42/11.23 --twee_lhs_weight 4 % 71.42/11.23 --sup_set_join false % 71.42/11.23 --sup_set_join_goals true % 71.42/11.23 --sup_set_join_limit 1000 % 71.42/11.23 --demod_completeness_check fast % 71.42/11.23 --demod_use_ground true % 71.42/11.23 --sup_unprocessed_bound 0 % 71.42/11.23 --sup_to_prop_solver passive % 71.42/11.23 --sup_prop_simpl_new true % 71.42/11.23 --sup_prop_simpl_given true % 71.42/11.23 --sup_fun_splitting false % 71.42/11.23 --sup_iter_deepening 2 % 71.42/11.23 --sup_restarts_mult 12 % 71.42/11.23 --sup_score sim_d_gen % 71.42/11.23 --sup_share_score_frac 0.2 % 71.42/11.23 --sup_share_max_num_cl 500 % 71.42/11.23 --sup_ordering lpo % 71.42/11.23 --sup_symb_ordering invfreq % 71.42/11.23 --sup_term_weight default % 71.42/11.23 % 71.42/11.23 ------ Superposition Simplification Setup % 71.42/11.23 % 71.42/11.23 --sup_indices_passive [LightNormIndex;FwDemodIndex] % 71.42/11.23 --sup_full_triv [SMTSimplify;PropSubs] % 71.42/11.23 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] % 71.42/11.23 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 71.42/11.23 --sup_immed_triv [] % 71.42/11.23 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes] % 71.42/11.23 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes] % 71.42/11.23 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod] % 71.42/11.23 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 71.42/11.23 --sup_input_triv [Unflattening;SMTSimplify] % 71.42/11.23 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] % 71.42/11.23 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] % 71.42/11.23 --sup_full_fixpoint true % 71.42/11.23 --sup_main_fixpoint true % 71.42/11.23 --sup_immed_fixpoint false % 71.42/11.23 --sup_input_fixpoint true % 71.42/11.23 --sup_cache_sim none % 71.42/11.23 --sup_smt_interval 500 % 71.42/11.23 --sup_bw_gjoin_interval 0 % 71.42/11.23 % 71.42/11.23 ------ Combination Options % 71.42/11.23 % 71.42/11.23 --comb_mode clause_based % 71.42/11.23 --comb_inst_mult 5 % 71.42/11.23 --comb_res_mult 1 % 71.42/11.23 --comb_sup_mult 1 % 71.42/11.23 --comb_sup_deep_mult 1 % 71.42/11.23 % 71.42/11.23 ------ Debug Options % 71.42/11.23 % 71.42/11.23 --dbg_backtrace false % 71.42/11.23 --dbg_dump_prop_clauses false % 71.42/11.23 --dbg_dump_prop_clauses_file - % 71.42/11.23 --dbg_out_stat false % 71.42/11.23 --dbg_just_parse false % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 ------ Proving... % 71.42/11.23 % 71.42/11.23 % 71.42/11.23 % SZS status Satisfiable for theBenchmark.p % 71.42/11.23 % 71.42/11.23 ------ Building Model...Done % 71.42/11.23 % 71.42/11.23 %------ The model is defined over ground terms (initial term algebra). % 71.42/11.23 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) % 71.42/11.23 %------ where \phi is a formula over the term algebra. % 71.42/11.23 %------ If we have equality in the problem then it is also defined as a predicate above, % 71.42/11.23 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type % 71.42/11.23 %------ See help for --sat_out_model for different model outputs. % 71.42/11.23 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" % 71.42/11.23 %------ where the first argument stands for the sort ($i in the unsorted case) % 71.42/11.23 % SZS output start Model for theBenchmark.p % 71.42/11.23 % 71.42/11.23 %------ Positive definition of '$ki_accessible' % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X1_'ki_world'] : % 71.42/11.23 ( '$ki_accessible'(X0_'ki_world',X1_'ki_world') <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'!=X0_'ki_world' | X1_'ki_world'!=sK43(sK59(intersection(X0,X1),X2,X0_'ki_world'),X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=X0_'ki_world' | X1_'ki_world'!=sK60(X0,sK59(sum(X0),X1,X0_'ki_world'),X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK53(sK33(X0,X1,X0_'ki_world'),X0,X2_'ki_world') | X1_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK34(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK35(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK32(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK41(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK60(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK31(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X1,X0] : ( X1_'ki_world'!=sK39(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1_'ki_world'!=sK40(X0,X1,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X1_'ki_world'!=sK43(X0,X1,X2,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'='$ki_local_world' & X1_'ki_world'=sK69 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,X1,X2_'ki_world') & X1_'ki_world'=sK39(X0,X1,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK59(power_set(X0),X1,X2_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X1!=difference(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=intersection(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=union(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=unordered_pair(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=sK4(sK35(X1,X2,X2_'ki_world')) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK40(X0,X1,X2_'ki_world') & X1_'ki_world'=sK40(X0,X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK69 & X1_'ki_world'=sK71 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK31(X0,X1,X2_'ki_world') & X1_'ki_world'=sK31(X0,X1,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK4(sK35(X0,X1,X2_'ki_world')) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK60(X0,X1,X2_'ki_world') & X1_'ki_world'=sK60(X0,X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(X0,X1,X2_'ki_world') & X1_'ki_world'=sK35(X0,X1,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0!=difference(X0,X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=intersection(X0,X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=singleton(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sum(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=union(X0,X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=unordered_pair(X0,X1) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK41(X0,X1,X2_'ki_world') & X1_'ki_world'=sK41(X0,X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK43(X0,X1,X2,X2_'ki_world') & X1_'ki_world'=sK43(X0,X1,X2,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(sum(X0),X1,X2_'ki_world') & X1_'ki_world'=sK35(sum(X0),X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK34(X0,X1,X2_'ki_world') & X1_'ki_world'=sK35(X0,X1,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X0!=difference(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=intersection(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=intersection(X0,X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=singleton(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sum(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=union(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=unordered_pair(X0,X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK34(X0,X1,X2_'ki_world') & X1_'ki_world'=sK34(X0,X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(power_set(X0),X1,X2_'ki_world') & X1_'ki_world'=sK35(power_set(X0),X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(singleton(X0),X1,X2_'ki_world') & X1_'ki_world'=sK35(singleton(X0),X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,intersection(X1,X2),X2_'ki_world') & X1_'ki_world'=sK39(X0,intersection(X1,X2),X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,union(X1,X2),X2_'ki_world') & X1_'ki_world'=sK39(X0,union(X1,X2),X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,difference(X1,X2),X2_'ki_world') & X1_'ki_world'=sK39(X0,difference(X1,X2),X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,unordered_pair(X1,X2),X2_'ki_world') & X1_'ki_world'=sK39(X0,unordered_pair(X1,X2),X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world',X3_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(sK59(power_set(X0),X1,X2_'ki_world'),X0,X3_'ki_world') & X1_'ki_world'=sK39(sK59(power_set(X0),X1,X2_'ki_world'),X0,X3_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(union(X0,X1),X2,X2_'ki_world') & X1_'ki_world'=sK35(union(X0,X1),X2,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(unordered_pair(X0,X1),X2,X2_'ki_world') & X1_'ki_world'=sK35(unordered_pair(X0,X1),X2,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(intersection(X0,X1),X2,X2_'ki_world') & X1_'ki_world'=sK35(intersection(X0,X1),X2,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(difference(X0,X1),X2,X2_'ki_world') & X1_'ki_world'=sK35(difference(X0,X1),X2,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK32(X0,X1,X2_'ki_world') & X1_'ki_world'=sK32(X0,X1,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2,X2_'ki_world',X3_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,sK4(sK35(X1,X2,X2_'ki_world')),X3_'ki_world') & X1_'ki_world'=sK39(X0,sK4(sK35(X1,X2,X2_'ki_world')),X3_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2_'ki_world',X2,X3_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK31(sK4(sK35(X0,X1,X2_'ki_world')),X2,X3_'ki_world') & X1_'ki_world'=sK31(sK4(sK35(X0,X1,X2_'ki_world')),X2,X3_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=X0_'ki_world' ) % 71.42/11.23 & % 71.42/11.23 ! [X1,X0] : ( X0_'ki_world'!=sK31(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK39(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK40(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK41(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X0_'ki_world'!=sK43(X0,X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK60(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK32(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(singleton(X0),X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(difference(X0,X1),X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(power_set(X0),X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK20(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X2,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X2,X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK21(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK23(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK25(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK26(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X2,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X2,X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK28(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK29(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X2,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X2,X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK38(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK42(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X0,X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK49(X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X1] : ( X0_'ki_world'!=sK34(X0,X1,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1,X2] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK51(X0,X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X4,X3] : ( X0_'ki_world'!=sK34(X3,X4,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X3,X4,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK50(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X4,X3] : ( X0_'ki_world'!=sK34(X3,X4,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X3,X4,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X0,X1] : % 71.42/11.23 ( % 71.42/11.23 ( X1_'ki_world'=sK53(X0,X1,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK34(X1,X3,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X3,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of qmltpeq % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X0,X1] : % 71.42/11.23 ( qmltpeq(X0_'ki_world',X0,X1) <=> % 71.42/11.23 $true % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of equal_set % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X0,X1] : % 71.42/11.23 ( equal_set(X0_'ki_world',X0,X1) <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK21(X0,X1,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK38(X0,X1,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK23(X1,X0,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK23(X1,X0,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK21(X1,X0,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK38(X1,X0,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=union(sK70,sK70) | X0_'ki_world'!=sK71 | X1!=sK70 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK38(X0,X1,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK21(X0,X1,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK23(X1,X0,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of member % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X0,X1] : % 71.42/11.23 ( member(X0_'ki_world',X0,X1) <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK41(X0,X1,X0_'ki_world') | X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK43(X0,X1,X2,X4_'ki_world') | X1!=intersection(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK49(X0,X0_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X1,X0,X0_'ki_world') | X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X2,X0_'ki_world') | X1!=difference(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK49(X0,X2_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK41(X0,X1,X2_'ki_world') | X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK41(X0,X1,X5_'ki_world') | X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK49(X0,X5_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X1,X0,X2_'ki_world') | X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X2,X0,X3_'ki_world') | X1!=sum(X2) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0!=X0 | X0_'ki_world'!=sK43(X0,X1,X3,X2_'ki_world') | X1!=intersection(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X3,X2_'ki_world') | X1!=difference(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK49(X0,X4_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X1,X0,X4_'ki_world') | X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK41(X0,X1,X4_'ki_world') | X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0!=X0 | X0_'ki_world'!=sK43(X0,X1,X3,X4_'ki_world') | X1!=intersection(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X3,X4_'ki_world') | X1!=difference(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X2,X4_'ki_world') | X1!=difference(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X2,X0,X1,X3_'ki_world') | X1!=difference(X2,X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X1,X0,X5_'ki_world') | X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0!=X0 | X0_'ki_world'!=sK43(X0,X1,X3,X5_'ki_world') | X1!=intersection(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X3,X5_'ki_world') | X1!=difference(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0!=X0 | X0_'ki_world'!=sK43(X0,X1,X3,X0_'ki_world') | X1!=intersection(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X1,X0,X3,X0_'ki_world') | X1!=difference(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK41(X1,X0,X0_'ki_world') | X1!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK43(X1,X0,X2,X0_'ki_world') | X1!=intersection(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK49(X1,X2_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK43(X1,X2,X0,X3_'ki_world') | X1!=intersection(X2,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK41(X1,X2,X3_'ki_world') | X1!=power_set(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK49(X1,X3_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK60(X2,X1,X3_'ki_world') | X1!=sum(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK51(X2,X1,X0,X3_'ki_world') | X1!=difference(X2,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK49(X1,X0_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK51(X1,X2,X0,X3_'ki_world') | X1!=difference(X1,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK60(X1,X2,X3_'ki_world') | X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK49(X2,X3_'ki_world') | X1!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK41(X2,X1,X3_'ki_world') | X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK43(X2,X1,X0,X3_'ki_world') | X1!=intersection(X1,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK41(X2,X0,X3_'ki_world') | X1!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK43(X2,X0,X1,X3_'ki_world') | X1!=intersection(X0,X1) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0!=X3 | X0_'ki_world'!=sK51(X1,X3,X0,X2_'ki_world') | X1!=difference(X1,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X3 | X0_'ki_world'!=sK43(X3,X1,X0,X2_'ki_world') | X1!=intersection(X1,X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X0,X1,X1_'ki_world') | X0_'ki_world'!=sK35(X0,X1,X1_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X1,X0,X0_'ki_world') | X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X0,X1,X2_'ki_world') | X0_'ki_world'!=sK35(X0,X1,X2_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X1,X0,X2_'ki_world') | X0_'ki_world'!=sK35(X1,X0,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X1,X2,X3_'ki_world') | X0_'ki_world'!=sK35(X1,X2,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X2,X1,X3_'ki_world') | X0_'ki_world'!=sK35(X2,X1,X3_'ki_world') | X1!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X0,X2,X1_'ki_world') | X0_'ki_world'!=sK35(X0,X2,X1_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(X2,X0,X3_'ki_world') | X0_'ki_world'!=sK35(X2,X0,X3_'ki_world') | X1!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0=sK59(X1,X2,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X0_'ki_world'!=sK51(X1,sK59(difference(X1,X2),X3,X1_'ki_world'),X2,X0_'ki_world') | X1!=difference(X1,X2) | X1_'ki_world'!=X1_'ki_world' | X2!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK43(sK59(intersection(X1,X2),X3,X1_'ki_world'),X1,X2,X0_'ki_world') | X1!=intersection(X1,X2) | X1_'ki_world'!=X1_'ki_world' | X2!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK41(sK59(power_set(X1),X2,X1_'ki_world'),X1,X0_'ki_world') | X1!=power_set(X1) | X1_'ki_world'!=X1_'ki_world' | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK60(X1,sK59(sum(X1),X2,X1_'ki_world'),X0_'ki_world') | X1!=sum(X1) | X1_'ki_world'!=X1_'ki_world' | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK49(sK59(empty_set,X1,X1_'ki_world'),X0_'ki_world') | X1!=empty_set | X1_'ki_world'!=X1_'ki_world' | X2!=X1 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK34(X2,X1,X1_'ki_world') & X0=sK33(X2,X1,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2] : % 71.42/11.23 ( % 71.42/11.23 ( X1=sum(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK60(X2,X0,X2_'ki_world') | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X3 | X0_'ki_world'!=sK60(X2,X3,X0_'ki_world') | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(sum(X2),X0,X2_'ki_world') | X0_'ki_world'!=sK35(sum(X2),X0,X2_'ki_world') | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(sum(X0),X3,X1_'ki_world') | X0_'ki_world'!=sK35(sum(X0),X3,X1_'ki_world') | X2!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(sum(X2),X3,X0_'ki_world') | X0_'ki_world'!=sK35(sum(X2),X3,X0_'ki_world') | X2!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2] : % 71.42/11.23 ( % 71.42/11.23 ( X1=product(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(product(X2),X0,X1_'ki_world') | X0_'ki_world'!=sK35(product(X2),X0,X1_'ki_world') | X2!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2] : % 71.42/11.23 ( % 71.42/11.23 ( X1=power_set(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK41(X0,X2,X2_'ki_world') | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK41(X2,X0,X0_'ki_world') | X2!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(power_set(X0),X2,X1_'ki_world') | X0_'ki_world'!=sK35(power_set(X0),X2,X1_'ki_world') | X2!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(power_set(X2),X0,X0_'ki_world') | X0_'ki_world'!=sK35(power_set(X2),X0,X0_'ki_world') | X2!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2] : % 71.42/11.23 ( % 71.42/11.23 ( X1=singleton(X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(singleton(X0),X2,X1_'ki_world') | X0_'ki_world'!=sK35(singleton(X0),X2,X1_'ki_world') | X2!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(singleton(X2),X0,X0_'ki_world') | X0_'ki_world'!=sK35(singleton(X2),X0,X0_'ki_world') | X2!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3] : % 71.42/11.23 ( % 71.42/11.23 ( X1=unordered_pair(X2,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(unordered_pair(X0,X2),X3,X1_'ki_world') | X0_'ki_world'!=sK35(unordered_pair(X0,X2),X3,X1_'ki_world') | X2!=X0 | X3!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(unordered_pair(X2,X3),X0,X0_'ki_world') | X0_'ki_world'!=sK35(unordered_pair(X2,X3),X0,X0_'ki_world') | X2!=X2 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(unordered_pair(X0,X3),X2,X1_'ki_world') | X0_'ki_world'!=sK35(unordered_pair(X0,X3),X2,X1_'ki_world') | X2!=X0 | X3!=X3 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X1=sK59(X2,X0,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3] : % 71.42/11.23 ( % 71.42/11.23 ( X1=union(X2,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(union(X0,X2),X3,X1_'ki_world') | X0_'ki_world'!=sK35(union(X0,X2),X3,X1_'ki_world') | X2!=X0 | X3!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(union(X2,X3),X0,X0_'ki_world') | X0_'ki_world'!=sK35(union(X2,X3),X0,X0_'ki_world') | X2!=X2 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(union(X0,X3),X2,X1_'ki_world') | X0_'ki_world'!=sK35(union(X0,X3),X2,X1_'ki_world') | X2!=X0 | X3!=X3 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3] : % 71.42/11.23 ( % 71.42/11.23 ( X1=intersection(X2,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK43(X0,X2,X3,X2_'ki_world') | X2!=X2 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK43(X2,X3,X0,X0_'ki_world') | X2!=X3 | X3!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(intersection(X0,X2),X3,X1_'ki_world') | X0_'ki_world'!=sK35(intersection(X0,X2),X3,X1_'ki_world') | X2!=X0 | X3!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(intersection(X0,X3),X2,X1_'ki_world') | X0_'ki_world'!=sK35(intersection(X0,X3),X2,X1_'ki_world') | X2!=X0 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(intersection(X2,X3),X0,X0_'ki_world') | X0_'ki_world'!=sK35(intersection(X2,X3),X0,X0_'ki_world') | X2!=X2 | X3!=X3 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3] : % 71.42/11.23 ( % 71.42/11.23 ( X1=difference(X2,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK51(X2,X0,X3,X3_'ki_world') | X2!=X2 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X2 | X0_'ki_world'!=sK51(X3,X2,X0,X0_'ki_world') | X2!=X3 | X3!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(difference(X0,X2),X3,X1_'ki_world') | X0_'ki_world'!=sK35(difference(X0,X2),X3,X1_'ki_world') | X2!=X0 | X3!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(difference(X0,X3),X2,X1_'ki_world') | X0_'ki_world'!=sK35(difference(X0,X3),X2,X1_'ki_world') | X2!=X0 | X3!=X3 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(difference(X3,X2),X0,X0_'ki_world') | X0_'ki_world'!=sK35(difference(X3,X2),X0,X0_'ki_world') | X2!=X3 | X3!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X1=sK4(sK35(X2,X3,X1_'ki_world')) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(sK4(sK35(X0,X2,X1_'ki_world')),X3,X0_'ki_world') | X0_'ki_world'!=sK35(sK4(sK35(X0,X2,X1_'ki_world')),X3,X0_'ki_world') | X1_'ki_world'!=X1_'ki_world' | X2!=X0 | X3!=X2 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3,X4,X5,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X1=sK59(X2,X3,sK35(X4,X5,X1_'ki_world')) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK33(sK59(X2,X3,sK35(X4,X5,X1_'ki_world')),X0,X0_'ki_world') | X0_'ki_world'!=sK35(sK59(X2,X3,sK35(X4,X5,X1_'ki_world')),X0,X0_'ki_world') | X1_'ki_world'!=X1_'ki_world' | X2!=X2 | X3!=X3 | X4!=X4 | X5!=X5 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of subset % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X0,X1] : % 71.42/11.23 ( subset(X0_'ki_world',X0,X1) <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK29(X0,X1,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK39(X0,X1,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK39(X0,X1,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK42(X0,X1,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK40(X1,X0,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK29(X0,X1,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK42(X0,X1,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK31(X1,X0,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK40(X1,X0,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK31(X1,X0,X2_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK40(X1,X0,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK31(X1,X0,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK39(X0,X1,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK29(X0,X1,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK42(X0,X1,X3_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK31(X0,X1,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK40(X0,X1,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK42(X1,X0,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK39(X1,X0,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK29(X1,X0,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK31(X0,X1,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK39(X1,X0,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK40(X0,X1,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK42(X1,X0,X3_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK29(X1,X0,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK40(X1,X0,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK42(X0,X1,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK29(X0,X1,X1_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK39(X0,power_set(X2),X1_'ki_world') & X1=power_set(X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK29(X0,power_set(X2),X1_'ki_world') & X1=power_set(X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK29(X0,singleton(X2),X1_'ki_world') & X1=singleton(X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK29(X0,sum(X2),X1_'ki_world') & X1=sum(X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK40(sum(X2),X0,X1_'ki_world') & X1=sum(X2) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK40(intersection(X2,X3),X0,X1_'ki_world') & X1=intersection(X2,X3) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X2,X3,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK29(X0,difference(X2,X3),X1_'ki_world') & X1=difference(X2,X3) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of '$ki_exists_in_world % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0_'ki_world',X0] : % 71.42/11.23 ( '$ki_exists_in_world(X0_'ki_world',X0) <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0=sK4(X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK32(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X2,X1] : ( X0_'ki_world'!=sK35(X1,X2,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1,X2] : % 71.42/11.23 ( % 71.42/11.23 ( X0=sK59(X1,X2,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X4,X3] : ( X0_'ki_world'!=sK34(X3,X4,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK32(X3,X4,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X3,X4,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1!=difference(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=intersection(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=empty_set ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK69 & X0=sK70 ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1,X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK35(X1,X2,X1_'ki_world') & X0=sK4(sK35(X1,X2,X1_'ki_world')) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1,X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK32(X1,X2,X1_'ki_world') & X0=sK33(X1,X2,X1_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X1!=difference(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=intersection(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=power_set(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=product(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=singleton(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=sum(X1) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=union(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=unordered_pair(X1,X2) ) % 71.42/11.23 & % 71.42/11.23 ! [X3] : ( X1!=difference(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=intersection(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=union(X1,X3) ) % 71.42/11.23 & % 71.42/11.23 ( X1!=unordered_pair(X1,X3) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1,X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK32(X1,X2,X1_'ki_world') & X0=sK4(sK32(X1,X2,X1_'ki_world')) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 | % 71.42/11.23 ? [X1,X2,X1_'ki_world'] : % 71.42/11.23 ( % 71.42/11.23 ( X0_'ki_world'=sK34(X1,X2,X1_'ki_world') & X0=sK4(sK34(X1,X2,X1_'ki_world')) ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of sP0 % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0,X1,X0_'ki_world'] : % 71.42/11.23 ( sP0(X0,X1,X0_'ki_world') <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ( X0!=X0 | X0_'ki_world'!=sK39(X1,X0,X0_'ki_world') | X1!=X1 ) % 71.42/11.23 & % 71.42/11.23 ( X0!=X1 | X0_'ki_world'!=sK31(X1,X0,X0_'ki_world') | X1!=X0 ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X0!=difference(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=intersection(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=product(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=singleton(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sum(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=union(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=unordered_pair(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ! [X2_'ki_world'] : ( X0!=sK4(sK35(X0,X2,X2_'ki_world')) ) % 71.42/11.23 & % 71.42/11.23 ! [X4,X3] : ( X0!=sK59(X0,X2,sK35(X3,X4,X2_'ki_world')) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK4(sK35(X1,X0,X0_'ki_world')) | X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of sP1 % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0,X1,X2,X0_'ki_world'] : % 71.42/11.23 ( sP1(X0,X1,X2,X0_'ki_world') <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ! [X3_'ki_world'] : ( X0!=X0 | X1!=sK59(difference(X0,X2),X1,X3_'ki_world') | X2!=X2 ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X2,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X2,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK32(X2,X0,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of sP2 % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0,X1,X0_'ki_world'] : % 71.42/11.23 ( sP2(X0,X1,X0_'ki_world') <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ! [X2_'ki_world'] : ( X0!=X1 | X1!=sK59(sum(X1),X0,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ! [X2] : ( X0!=difference(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=intersection(X0,X2) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=power_set(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sum(X0) ) % 71.42/11.23 & % 71.42/11.23 ( X0!=empty_set ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK4(sK35(X1,X0,X0_'ki_world')) | X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0!=sK4(sK35(X1,X0,X0_'ki_world')) | X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') | X1!=sK59(sum(sK4(sK35(X1,X0,X0_'ki_world'))),X2,X2_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK32(X1,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK34(X1,X0,X0_'ki_world') ) % 71.42/11.23 & % 71.42/11.23 ( X0_'ki_world'!=sK35(X1,X0,X0_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % 71.42/11.23 %------ Positive definition of sP3 % 71.42/11.23 fof(lit_def,axiom, % 71.42/11.23 (! [X0,X1,X0_'ki_world'] : % 71.42/11.23 ( sP3(X0,X1,X0_'ki_world') <=> % 71.42/11.23 ( % 71.42/11.23 ( % 71.42/11.23 ! [X2_'ki_world'] : ( X0!=X1 | X1!=sK33(product(X1),X0,X2_'ki_world') ) % 71.42/11.23 ) % 71.42/11.23 % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ) % 71.42/11.23 ). % 71.42/11.23 % SZS output end Model for theBenchmark.p % 71.42/11.23 %------------------------------------------------------------------------------