%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP343_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:49:28 PM UTC 2026
% Result : Theorem 18.49s 13.54s
% Output : CNFRefutation 18.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP343_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.55 % Computer : n006.cluster.edu
% 0.12/10.55 % Model : x86_64 x86_64
% 0.12/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.55 % Memory : 8046.5625MB
% 0.12/10.55 % OS : Linux 6.8.0-71-generic
% 0.12/10.55 % CPULimit : 300
% 0.12/10.55 % WCLimit : 300
% 0.12/10.55 % DateTime : Wed Sep 23 18:26:09 UTC 2026
% 0.12/10.55 % CPUTime :
% 0.12/10.55 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.59 Running TFA theorem proving
% 0.12/10.59 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.60
% 0.16/10.60 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.60
% 0.16/10.60 % Detected problem language: tptp
% 0.16/10.61 % Proving...
% 18.49/13.54 % SZS status Started for theBenchmark.p
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_65520:11.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_mode time_based --comb_res_mult 6 --comb_sup_deep_mult 0 --comb_sup_mult 6 --conj_cone_tolerance 1.8969679945890683 --demod_completeness_check fullold --demod_use_ground false --extra_neg_conj all_neg --instantiation_flag false --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 1024 --proof_out true --prop_solver_per_cl 512 --res_to_smt_solver false --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 16 --sup_bw_gjoin_interval 100 --sup_cache_sim none --sup_full_bw "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_full_fixpoint false --sup_full_fw "[]" --sup_fun_splitting false --sup_immed_bw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[Subsumption;SubsumptionRes;FullSubsAndRes;Demod;LightNorm;ACDemod]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;FullSubsAndRes;Demod;LightNorm;ACNormalisation;GroundJoinability;Connectedness]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint false --sup_main_fixpoint true --sup_ordering lpo --sup_passive_queue_type priority_queues --sup_passive_queues "[[+has_eq;-has_eq];[-num_var;-num_var];[+conj_dist;+ground;-max_atom_input_occur]]" --sup_passive_queues_freq "[1;4;4]" --sup_prop_simpl_given false --sup_prop_simpl_new false --sup_score sim_d_gen --sup_share_max_num_cl 10 --sup_share_score_frac 0.2 --sup_smt_interval 32 --sup_symb_ordering invfreq_arity --sup_term_weight default --sup_to_prop_solver passive --sup_unprocessed_bound 10 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 3.67 --show_fool true" --time_out_real 11.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/2ido5bse 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/2ido5bse_error
% 18.49/13.54 ERROR - "ProverProcess:heur/schedule_none:304.9999694824219" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --schedule none --sub_typing false --suppress_sat_res true --tptp_safe_out true --stats_out none --out_options none --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 101.67 --show_fool true" --time_out_real 305.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/m6ccwbpg 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/m6ccwbpg_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_65097:3.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 3 --comb_sup_deep_mult 0 --comb_sup_mult 0 --conj_cone_tolerance 4.0357851670394345 --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 2048 --inst_lit_activity_flag true --inst_lit_sel "[+split;-sign;-depth]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[+age;+num_lits;-age];[-age;-min_def_symb;+bc_imp_inh]]" --inst_passive_queues_freq "[2;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 1.0 --inst_solver_per_active 1024 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+split;-ground;-depth]" --inst_start_prop_sim_after_learn 3 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --prep_sup_sim_all true --prep_sup_sim_sup false --preprocessed_out false --preprocessing_flag true --prolific_symb_bound 256 --proof_out true --prop_solver_per_cl 16384 --resolution_flag true --schedule none --share_sel_clauses false --stats_out none --subs_bck_mult 8 --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 1.00 --show_fool true" --time_out_real 3.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/9p46zvnj 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/9p46zvnj_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_65080:40.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_mode time_based --comb_res_mult 6 --comb_sup_deep_mult 4 --comb_sup_mult 6 --conj_cone_tolerance 1.895766803319499 --demod_completeness_check fullold --demod_use_ground false --extra_neg_conj all_pos_neg --instantiation_flag false --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 1024 --proof_out true --prop_solver_per_cl 128 --res_to_smt_solver false --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 16 --sup_bw_gjoin_interval 100 --sup_cache_sim none --sup_full_bw "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_full_fixpoint false --sup_full_fw "[]" --sup_fun_splitting false --sup_immed_bw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[Subsumption;SubsumptionRes;FullSubsAndRes;Demod;LightNorm;ACDemod]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;FullSubsAndRes;Demod;LightNorm;ACNormalisation;GroundJoinability;Connectedness]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint false --sup_iter_deepening 2 --sup_main_fixpoint true --sup_ordering lpo --sup_passive_queue_type priority_queues --sup_passive_queues "[[+has_eq;-has_eq];[-num_var;-num_var];[+conj_dist;+ground;-max_atom_input_occur]]" --sup_passive_queues_freq "[1;4;4]" --sup_prop_simpl_given false --sup_prop_simpl_new false --sup_restarts_mult 4 --sup_score sim_d_gen --sup_share_max_num_cl 10 --sup_share_score_frac 0.2 --sup_smt_interval 32 --sup_symb_ordering invfreq_arity --sup_term_weight default --sup_to_prop_solver passive --sup_unprocessed_bound 10 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 13.33 --show_fool true" --time_out_real 40.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/i97zffac 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/i97zffac_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_66020:200.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 16 --comb_mode time_based --comb_res_mult 3 --comb_sup_deep_mult 1 --comb_sup_mult 0 --conj_cone_tolerance 2.250068292082666 --demod_completeness_check fastold --demod_use_ground true --extra_neg_conj none --inst_activity_threshold 16 --inst_dismatching false --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 3 --inst_learning_loop_flag true --inst_learning_start 32 --inst_lit_activity_flag false --inst_lit_sel "[+ground;+num_var]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[-num_lits;-has_eq]]" --inst_passive_queues_freq "[512]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 0.13028534399813618 --inst_solver_per_active 4096 --inst_sos_flag true --inst_sos_phase true --inst_sos_sth_lit_sel "[+non_prol_conj_symb;-depth;-non_prol_conj_symb;+non_prol_conj_symb;+eq]" --inst_start_prop_sim_after_learn 7 --inst_subs_given false --inst_subs_new true --inst_to_smt_solver false --instantiation_flag true --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 128 --proof_out true --prop_solver_per_cl 512 --res_to_smt_solver true --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 8 --sup_bw_gjoin_interval 10000 --sup_cache_sim none --sup_full_bw "[]" --sup_full_fixpoint true --sup_full_fw "[Subsumption;SubsumptionRes;FullSubsAndRes;ACJoinability;Connectedness]" --sup_fun_splitting false --sup_immed_bw_immed "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;Demod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[SubsumptionRes;UnitSubsAndRes;Demod;ACDemod;GroundJoinability;Connectedness]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint true --sup_iter_deepening 2 --sup_main_fixpoint true --sup_ordering kbo --sup_passive_queue_type queue --sup_passive_queues "[[-min_def_symb;+reachable_state;-age];[-epr];[+horn;-reachable_state;-num_var]]" --sup_passive_queues_freq "[2;5;15]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 12 --sup_score sim --sup_share_max_num_cl 80 --sup_share_score_frac 0.1 --sup_smt_interval 16384 --sup_symb_ordering random --sup_term_weight default --sup_to_prop_solver none --sup_unprocessed_bound 1000 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 66.67 --show_fool true" --time_out_real 200.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/0iqkhitv 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/0iqkhitv_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_65511:44.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 2 --comb_mode clause_based --comb_sup_deep_mult 3 --comb_sup_mult 0 --conj_cone_tolerance 3.378762210374529 --demod_completeness_check full --demod_use_ground false --extra_neg_conj all_pos --inst_activity_threshold 4 --inst_dismatching false --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 6 --inst_learning_loop_flag true --inst_learning_start 8192 --inst_lit_activity_flag true --inst_lit_sel "[-conj_symb;-conj_symb;+conj_symb;+num_var;-non_prol_conj_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[-has_eq;-conj_dist];[+ground;-min_def_symb]]" --inst_passive_queues_freq "[5;3]" --inst_prop_sim_given true --inst_prop_sim_new true --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.60162165485836 --inst_solver_per_active 1024 --inst_sos_flag true --inst_sos_phase true --inst_sos_sth_lit_sel "[-conj_symb;-num_symb;+num_var;-eq;+num_var]" --inst_start_prop_sim_after_learn 9 --inst_subs_given false --inst_subs_new true --inst_to_smt_solver false --instantiation_flag true --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 16384 --proof_out true --prop_solver_per_cl 128 --resolution_flag false --schedule none --share_sel_clauses false --stats_out none --subs_bck_mult 4 --sup_bw_gjoin_interval 1000 --sup_cache_sim none --sup_full_bw "[]" --sup_full_fixpoint false --sup_full_fw "[]" --sup_fun_splitting true --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fixpoint false --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;Demod;ACJoinability;Connectedness]" --sup_immed_fw_main "[]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[UnitSubsumption;NonunitSubsumption;Subsumption;FwDemod;BwDemod;LightNorm;FwACDemod;BwACDemod;SMTIncr;SMTSet;BwGjoin]" --sup_input_fixpoint true --sup_iter_deepening 8 --sup_main_fixpoint true --sup_ordering lpo --sup_passive_queue_type queue --sup_passive_queues "[[+next_state;-horn;-epr];[+max_atom_input_occur];[-num_lits;-num_lits]]" --sup_passive_queues_freq "[2;1;5]" --sup_prop_simpl_given true --sup_prop_simpl_new false --sup_restarts_mult 16 --sup_smt_interval 8192 --sup_symb_ordering invfreq_arity --sup_term_weight default --sup_to_prop_solver none --sup_unprocessed_bound 10000 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 14.67 --show_fool true" --time_out_real 44.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/a6rjrg7i 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/a6rjrg7i_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_64741:92.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 3 --comb_sup_deep_mult 2 --comb_sup_mult 8 --conj_cone_tolerance 3 --demod_completeness_check fast --demod_use_ground true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 2048 --inst_lit_activity_flag true --inst_lit_sel "[+split;-sign;-depth]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[+age;+num_lits;-age];[-age;-min_def_symb;+bc_imp_inh]]" --inst_passive_queues_freq "[2;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 1 --inst_solver_per_active 1024 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+split;-ground;-depth]" --inst_start_prop_sim_after_learn 3 --inst_subs_given true --inst_subs_new false --inst_to_smt_solver false --instantiation_flag true --out_options none --prep_sup_sim_all true --prep_sup_sim_sup false --preprocessed_out false --preprocessing_flag true --prolific_symb_bound 256 --proof_out true --prop_solver_per_cl 512 --res_to_smt_solver false --resolution_flag false --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 8 --sup_bw_gjoin_interval 0 --sup_cache_sim none --sup_full_bw "[Subsumption;SubsumptionRes;FullSubsAndRes;Demod]" --sup_full_fixpoint true --sup_full_fw "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;LightNorm;ACNormalisation;GroundJoinability]" --sup_fun_splitting false --sup_immed_bw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_immed_bw_main "[SubsumptionRes;Demod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[UnitSubsAndRes;ACNormalisation]" --sup_immed_fw_main "[UnitSubsAndRes;LightNorm;ACNormalisation]" --sup_immed_triv "[]" --sup_indices_passive "[FwDemod;LightNorm]" --sup_input_bw "[Subsumption;SubsumptionRes;UnitSubsAndRes;Demod;ACDemod]" --sup_input_fixpoint true --sup_input_fw "[Subsumption;UnitSubsAndRes;FullSubsAndRes;Demod;LightNorm;ACNormalisation;ACDemod;GroundJoinability]" --sup_input_triv "[Unflattening;SMTSimplify]" --sup_iter_deepening 2 --sup_main_fixpoint true --sup_ordering kbo --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[1;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 12 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 512 --sup_symb_ordering invfreq --sup_term_weight default --sup_to_prop_solver passive --sup_unprocessed_bound 0 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 30.67 --show_fool true" --time_out_real 92.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/1yp57nbl 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/1yp57nbl_error
% 18.49/13.54 ERROR - "ProverProcess:heur/vip_65089:37.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 18.49/13.54 Fatal error: exception Failure("undefined enum value")
% 18.49/13.54 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 16 --comb_mode time_based --comb_res_mult 3 --comb_sup_deep_mult 0 --comb_sup_mult 1 --conj_cone_tolerance 2.250068292082666 --demod_completeness_check fastold --demod_use_ground true --extra_neg_conj none --inst_activity_threshold 16 --inst_dismatching false --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 3 --inst_learning_loop_flag true --inst_learning_start 32 --inst_lit_activity_flag false --inst_lit_sel "[+ground;+num_var]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[-num_lits;-has_eq]]" --inst_passive_queues_freq "[512]" --inst_prop_sim_given false --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 0.13028534399813618 --inst_solver_per_active 4096 --inst_sos_flag true --inst_sos_phase true --inst_sos_sth_lit_sel "[+non_prol_conj_symb;-depth;-non_prol_conj_symb;+non_prol_conj_symb;+eq]" --inst_start_prop_sim_after_learn 7 --inst_subs_given false --inst_subs_new true --inst_to_smt_solver false --instantiation_flag true --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 128 --proof_out true --prop_solver_per_cl 32768 --res_to_smt_solver true --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 8 --sup_bw_gjoin_interval 10000 --sup_cache_sim none --sup_full_bw "[]" --sup_full_fixpoint true --sup_full_fw "[Subsumption;SubsumptionRes;FullSubsAndRes;ACJoinability;Connectedness]" --sup_fun_splitting false --sup_immed_bw_immed "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;Demod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[SubsumptionRes;UnitSubsAndRes;Demod;ACDemod;GroundJoinability;Connectedness]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint true --sup_main_fixpoint true --sup_ordering kbo --sup_passive_queue_type queue --sup_passive_queues "[[-min_def_symb;+reachable_state;-age];[-epr];[+horn;-reachable_state;-num_var]]" --sup_passive_queues_freq "[2;5;15]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_score sim --sup_share_max_num_cl 80 --sup_share_score_frac 0.1 --sup_smt_interval 16384 --sup_symb_ordering random --sup_term_weight default --sup_to_prop_solver none --sup_unprocessed_bound 1000 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 12.33 --show_fool true" --time_out_real 37.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/rir3ln6c 2>> /export/starexec/sandbox/tmp/iprover_out_grpjpwiy/rir3ln6c_error
% 18.49/13.54 % SZS status Theorem for theBenchmark.p
% 18.49/13.54
% 18.49/13.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.49/13.54
% 18.49/13.54 % ------ iProver source info
% 18.49/13.54
% 18.49/13.54 % git: date: 2026-07-19 20:42:38 +0200
% 18.49/13.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.49/13.54 % git: non_committed_changes: false
% 18.49/13.54
% 18.49/13.54 % ------ Parsing...
% 18.49/13.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.49/13.54
% 18.49/13.54 % ------ Preprocessing...%
% 18.49/13.54
% 18.49/13.54 % SZS status Theorem for theBenchmark.p
% 18.49/13.54
% 18.49/13.54 % SZS output start CNFRefutation for theBenchmark.p
% 18.49/13.54
% 18.49/13.54 tff(func_def_0, type, 'snd$': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$').
% 18.49/13.54 tff(pred_def_1, type, 'fun_app$s': ('A_n_vec_n_vec_option_bool_fun$' * 'A_n_vec_n_vec_option$') > $o).
% 18.49/13.54 tff(pred_def_2, type, 'fun_app$o': ('A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$') > $o).
% 18.49/13.54 tff(pred_def_3, type, 'member$q': ('Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$' * 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_4, type, 'member$p': ('A_iarray_iarray_list_a_iarray_iarray_list_prod$' * 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_5, type, 'fun_app$f': ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$') > $o).
% 18.49/13.54 tff(pred_def_6, type, 'csquare$': ('A_n_vec_n_vec_a_n_vec_n_vec_prod_set$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$') > $o).
% 18.49/13.54 tff(pred_def_7, type, 'fun_app$c': ('Nat_bool_fun$' * 'Nat$') > $o).
% 18.49/13.54 tff(pred_def_8, type, 'fun_app$ae': ('Int_int_prod_bool_fun$' * 'Int_int_prod$') > $o).
% 18.49/13.54 tff(pred_def_9, type, 'member$r': ('Nat_a_iarray_prod_nat_a_iarray_prod_prod$' * 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_10, type, 'member$c': ('Nat$' * 'Nat_set$') > $o).
% 18.49/13.54 tff(pred_def_11, type, 'member$a': ('A_iarray$' * 'A_iarray_set$') > $o).
% 18.49/13.54 tff(pred_def_12, type, 'member$l': ('A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_13, type, 'member$e': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_14, type, 'fun_app$d': ('Int_bool_fun$' * $int) > $o).
% 18.49/13.54 tff(pred_def_15, type, 'member$m': ('A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$' * 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_16, type, 'csquare$b': ('Int_int_prod_set$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_int_prod_fun$' * 'Int_int_prod_int_int_prod_fun$') > $o).
% 18.49/13.54 tff(pred_def_17, type, 'fun_app$a': ('A_iarray_list_a_iarray_list_prod_bool_fun$' * 'A_iarray_list_a_iarray_list_prod$') > $o).
% 18.49/13.54 tff(pred_def_18, type, 'member$d': ($int * 'Int_set$') > $o).
% 18.49/13.54 tff(pred_def_19, type, 'fun_app$': ('A_iarray_bool_fun$' * 'A_iarray$') > $o).
% 18.49/13.54 tff(pred_def_20, type, 'fun_app$n': ('Bool_bool_fun$' * tlbool) > $o).
% 18.49/13.54 tff(pred_def_21, type, 'member$b': ('A_iarray_list$' * 'A_iarray_list_set$') > $o).
% 18.49/13.54 tff(pred_def_22, type, 'fun_app$af': ('A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > $o).
% 18.49/13.54 tff(pred_def_23, type, 'member$n': ('A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$' * 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_24, type, 'member$k': ('Int_int_prod_int_int_prod_prod$' * 'Int_int_prod_int_int_prod_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_25, type, 'fun_app$b': ('A_iarray_list_bool_fun$' * 'A_iarray_list$') > $o).
% 18.49/13.54 tff(pred_def_26, type, 'member$s': ('A_iarray_list_list_a_iarray_list_list_prod$' * 'A_iarray_list_list_a_iarray_list_list_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_27, type, 'member$i': ('Int_set$' * 'Int_set_set$') > $o).
% 18.49/13.54 tff(pred_def_28, type, 'member$j': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$') > $o).
% 18.49/13.54 tff(pred_def_29, type, 'fun_app$e': ('Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$') > $o).
% 18.49/13.54 tff(pred_def_30, type, 'member$g': ('Int_int_prod$' * 'Int_int_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_31, type, 'member$o': ('Int_list_int_list_prod$' * 'Int_list_int_list_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_32, type, 'fun_app$t': ('A_iarray_iarray_option_bool_fun$' * 'A_iarray_iarray_option$') > $o).
% 18.49/13.54 tff(pred_def_33, type, 'csquare$a': ('A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$') > $o).
% 18.49/13.54 tff(pred_def_34, type, 'member$f': ('A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_35, type, 'member$': ('A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod_set$') > $o).
% 18.49/13.54 tff(pred_def_36, type, 'fun_app$ag': ('A_iarray_a_iarray_prod_bool_fun$' * 'A_iarray_a_iarray_prod$') > $o).
% 18.49/13.54 tff(pred_def_37, type, 'member$h': ('A_iarray_iarray$' * 'A_iarray_iarray_set$') > $o).
% 18.49/13.54 tff(pred_def_38, type, 'is_zero_iarray$a': 'A_n_vec_iarray$' > $o).
% 18.49/13.54 tff(func_def_39, type, def_4: (tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$') > tlbool).
% 18.49/13.54 tff(func_def_40, type, 'lexord$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$').
% 18.49/13.54 tff(func_def_41, type, 'fst$c': 'Int_int_set_prod$' > $int).
% 18.49/13.54 tff(pred_def_42, type, sP1: ('A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$') > $o).
% 18.49/13.54 tff(pred_def_43, type, sP2: ('A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$') > $o).
% 18.49/13.54 tff(pred_def_44, type, sP3: ('A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$') > $o).
% 18.49/13.54 tff(pred_def_45, type, sP4: ('A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$') > $o).
% 18.49/13.54 tff(func_def_46, type, 'sndOp$a': ('Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$') > 'Int_int_prod_int_int_prod_fun$').
% 18.49/13.54 tff(func_def_47, type, 'lex$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_48, type, 'lexord$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$').
% 18.49/13.54 tff(func_def_49, type, 'plus$o': ('Int_int_set_prod$' * 'Int_int_set_prod$') > 'Int_int_set_prod$').
% 18.49/13.54 tff(func_def_50, type, 'snd$k': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_51, type, 'product_lists$': 'A_iarray_list_list$' > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_52, type, 'plus$n': ('Int_int_prod_set$' * 'Int_int_prod_set$') > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_53, type, 'same_fst$a': ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$') > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$').
% 18.49/13.54 tff(func_def_54, type, 'lexn$': ('Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' * 'Nat$') > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$').
% 18.49/13.54 tff(func_def_55, type, 'fun_app$ad': ('A_iarray_a_iarray_fun$' * 'A_iarray$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_56, type, 'splice$b': ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_57, type, 'plus$s': ('Int_int_int_prod_prod$' * 'Int_int_int_prod_prod$') > 'Int_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_58, type, 'listrel1$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$').
% 18.49/13.54 tff(func_def_59, type, 'relcompp$': ('A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$') > 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$').
% 18.49/13.54 tff(func_def_60, type, 'swap$b': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_61, type, 'image2$': ('Nat_set$' * 'Nat_int_fun$' * 'Nat_int_fun$') > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_62, type, 'nat$': 'Int_nat_fun$').
% 18.49/13.54 tff(func_def_63, type, 'pair$e': ('Int_set$' * $int) > 'Int_set_int_prod$').
% 18.49/13.54 tff(func_def_64, type, 'snd$h': 'A_iarray_iarray_int_prod$' > $int).
% 18.49/13.54 tff(func_def_65, type, 'fst$d': 'Int_set_int_prod$' > 'Int_set$').
% 18.49/13.54 tff(func_def_66, type, 'size$': 'A_iarray_list_nat_fun$').
% 18.49/13.54 tff(func_def_67, type, 'listrel1$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$').
% 18.49/13.54 tff(func_def_68, type, 'snd$c': 'Int_int_set_prod$' > 'Int_set$').
% 18.49/13.54 tff(func_def_69, type, 'size$b': 'A_iarray_list_list_nat_fun$').
% 18.49/13.54 tff(func_def_70, type, 'plus$w': ('A_iarray_iarray_int_set_prod$' * 'A_iarray_iarray_int_set_prod$') > 'A_iarray_iarray_int_set_prod$').
% 18.49/13.54 tff(func_def_71, type, 'plus$x': ('A_n_vec_iarray$' * 'A_n_vec_iarray$') > 'A_n_vec_iarray$').
% 18.49/13.54 tff(func_def_72, type, 'collect$': 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_73, type, 'plus$q': ('A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$') > 'A_iarray_a_iarray_prod$').
% 18.49/13.54 tff(func_def_74, type, 'pair$j': ('Int_int_prod$' * $int) > 'Int_int_prod_int_prod$').
% 18.49/13.54 tff(func_def_75, type, 'pair$b': ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray_list_a_iarray_list_prod$').
% 18.49/13.54 tff(func_def_76, type, 'cons$a': ('Nat_a_iarray_prod$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_77, type, 'collect$c': 'Nat_bool_fun$' > 'Nat_set$').
% 18.49/13.54 tff(func_def_78, type, 'set$a': 'A_iarray_list_list$' > 'A_iarray_list_set$').
% 18.49/13.54 tff(func_def_79, type, 'cons$': ('A_iarray$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_80, type, 'zero$': 'Int_set$').
% 18.49/13.54 tff(func_def_81, type, 'n_lists$': ('Nat$' * 'A_iarray_list$') > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_82, type, 'pick_middlep$': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_83, type, 'fun_app$ax': ('A_n_vec_n_vec_option_nat_fun$' * 'A_n_vec_n_vec_option$') > 'Nat$').
% 18.49/13.54 tff(func_def_84, type, 'gauss_Jordan_in_ij_PA$': ('A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'N$' * 'N$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_85, type, 'image2$e': ('Int_set$' * 'Int_a_iarray_fun$' * 'Int_a_iarray_fun$') > 'A_iarray_a_iarray_prod_set$').
% 18.49/13.54 tff(func_def_86, type, 'of_nat$': 'Nat_int_fun$').
% 18.49/13.54 tff(func_def_87, type, 'sndOp$b': ('A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$').
% 18.49/13.54 tff(func_def_88, type, 'pair$x': ('Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$').
% 18.49/13.54 tff(func_def_89, type, 'uuh$': 'A_n_vec_n_vec_bool_fun$').
% 18.49/13.54 tff(func_def_90, type, 'snd$d': 'Int_set_int_prod$' > $int).
% 18.49/13.54 tff(func_def_91, type, 'matrix_inv$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_92, type, 'fun_app$bf': ('A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' * 'A_iarray_list$') > 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$').
% 18.49/13.54 tff(func_def_93, type, 'plus$e': 'A_iarray$' > 'A_iarray_a_iarray_fun$').
% 18.49/13.54 tff(func_def_94, type, 'fst$g': 'Int_int_int_prod_prod$' > $int).
% 18.49/13.54 tff(func_def_95, type, 'fst$a': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$').
% 18.49/13.54 tff(func_def_96, type, 'nil$': 'A_iarray_list$').
% 18.49/13.54 tff(func_def_97, type, 'fun_app$g': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$') > 'A_iarray_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_98, type, 'uuk$': 'A_iarray_list_set$' > 'A_iarray_list_bool_fun$').
% 18.49/13.54 tff(func_def_99, type, 'filter$': 'A_iarray_bool_fun$' > 'A_iarray_list_a_iarray_list_fun$').
% 18.49/13.54 tff(func_def_100, type, 'uu$': 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_101, type, 'equivalent_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$').
% 18.49/13.54 tff(func_def_102, type, 'fun_app$k': ('Int_nat_fun$' * $int) > 'Nat$').
% 18.49/13.54 tff(func_def_103, type, 'fun_app$bc': ('A_iarray_nat_fun$' * 'A_iarray$') > 'Nat$').
% 18.49/13.54 tff(func_def_104, type, 'image2$i': ('Nat_set$' * 'Nat_a_iarray_list_fun$' * 'Nat_a_iarray_list_fun$') > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_105, type, 'collect$a': 'A_iarray_list_bool_fun$' > 'A_iarray_list_set$').
% 18.49/13.54 tff(func_def_106, type, 'fun_app$as': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 18.49/13.54 tff(func_def_107, type, 'set$': 'A_iarray_list$' > 'A_iarray_set$').
% 18.49/13.54 tff(func_def_108, type, 'pair$h': ('A_iarray_iarray$' * $int) > 'A_iarray_iarray_int_prod$').
% 18.49/13.54 tff(func_def_109, type, 'pair$q': ('A_n_vec_n_vec$' * 'Int_int_prod$') > 'A_n_vec_n_vec_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_110, type, 'lexord$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_111, type, 'fun_app$w': ('A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$') > 'A_n_vec_n_vec_option_bool_fun$').
% 18.49/13.54 tff(func_def_112, type, tltrue: tlbool).
% 18.49/13.54 tff(func_def_113, type, 'uuo$': 'Int_int_prod_set$' > 'Int_int_bool_fun_fun$').
% 18.49/13.54 tff(func_def_114, type, 'cons$b': ('A_iarray_list$' * 'A_iarray_list_list$') > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_115, type, 'zero$a': 'Int_int_prod$').
% 18.49/13.54 tff(func_def_116, type, 'swap$a': 'A_iarray_a_iarray_prod$' > 'A_iarray_a_iarray_prod$').
% 18.49/13.54 tff(func_def_117, type, 'image2$f': ('A_iarray_set$' * 'A_iarray_a_iarray_fun$' * 'A_iarray_a_iarray_fun$') > 'A_iarray_a_iarray_prod_set$').
% 18.49/13.54 tff(func_def_118, type, 'plus$h': ('Nat_set$' * 'Nat_set$') > 'Nat_set$').
% 18.49/13.54 tff(func_def_119, type, 'pair$t': ('A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$') > 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$').
% 18.49/13.54 tff(func_def_120, type, 'rank$': 'A_n_vec_n_vec_nat_fun$').
% 18.49/13.54 tff(func_def_121, type, 'gauss_Jordan_upt_k$': ('A_n_vec_n_vec$' * 'Nat$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_122, type, 'fun_app$bb': ('A_iarray_a_iarray_a_iarray_prod_set_fun$' * 'A_iarray$') > 'A_iarray_a_iarray_prod_set$').
% 18.49/13.54 tff(func_def_123, type, 'gauss_Jordan_in_ij$': ('A_n_vec_n_vec$' * 'N$' * 'N$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_124, type, 'size_prod$': ('A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$') > 'Nat$').
% 18.49/13.54 tff(func_def_125, type, 'fun_app$aj': ('Int_int_prod_int_int_prod_fun$' * 'Int_int_prod$') > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_126, type, 'fun_app$v': ('A_iarray_list_list_nat_fun$' * 'A_iarray_list_list$') > 'Nat$').
% 18.49/13.54 tff(func_def_127, type, 'plus$i': ('A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray_a_iarray_iarray_prod_set$').
% 18.49/13.54 tff(func_def_128, type, 'pair$y': ('Nat_a_iarray_prod$' * 'Nat_a_iarray_prod$') > 'Nat_a_iarray_prod_nat_a_iarray_prod_prod$').
% 18.49/13.54 tff(func_def_129, type, 'filter$a': ('Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_130, type, 'uuj$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_prod_bool_fun$').
% 18.49/13.54 tff(func_def_131, type, 'fun_app$h': ('A_iarray_a_iarray_bool_fun_fun$' * 'A_iarray$') > 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_132, type, 'filter$b': ('A_iarray_list_bool_fun$' * 'A_iarray_list_list$') > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_133, type, 'fun_app$ar': ('Nat_a_iarray_list_fun$' * 'Nat$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_134, type, 'relcompp$a': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$') > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$').
% 18.49/13.54 tff(func_def_135, type, 'list_of$': 'A_iarray_iarray$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_136, type, 'fun_app$ba': ('A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$' * 'A_iarray_list$') > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_137, type, 'snd$e': 'A_iarray_a_iarray_prod$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_138, type, 'a$': 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_139, type, 'fun_app$ao': ('Int_a_iarray_fun$' * $int) > 'A_iarray$').
% 18.49/13.54 tff(func_def_140, type, 'uuq$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_bool_fun_fun$').
% 18.49/13.54 tff(func_def_141, type, 'lex$d': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_142, type, 'pair$': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_143, type, 'sndOp$': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$') > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$').
% 18.49/13.54 tff(func_def_144, type, 'rank_iarray$': 'A_iarray_iarray_nat_fun$').
% 18.49/13.54 tff(func_def_145, type, 'fun_app$ah': ('A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec_bool_fun$').
% 18.49/13.54 tff(func_def_146, type, 'listrel1$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_147, type, 'p_Gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_148, type, 'gauss_Jordan_iarrays_PA$': 'A_iarray_iarray$' > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_149, type, 'some$a': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$').
% 18.49/13.54 tff(func_def_150, type, 'matrix_to_iarray$': 'A_n_vec_n_vec$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_151, type, 'uuu$': ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_152, type, 'reduced_row_echelon_form$': 'A_n_vec_n_vec_bool_fun$').
% 18.49/13.54 tff(func_def_153, type, 'lexn$a': ('A_iarray_list_a_iarray_list_prod_set$' * 'Nat$') > 'A_iarray_list_list_a_iarray_list_list_prod_set$').
% 18.49/13.54 tff(func_def_154, type, 'swap$d': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_155, type, 'fun_app$at': ('A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun_a_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$').
% 18.49/13.54 tff(func_def_156, type, 'append$b': ('A_iarray_iarray_list$' * 'A_iarray_iarray_list$') > 'A_iarray_iarray_list$').
% 18.49/13.54 tff(func_def_157, type, 'plus$l': ('Int_set_set$' * 'Int_set_set$') > 'Int_set_set$').
% 18.49/13.54 tff(func_def_158, type, 'uua$': ('A_iarray_bool_fun$' * 'A_iarray_bool_fun$') > 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_159, type, 'uur$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_a_iarray_bool_fun_fun$').
% 18.49/13.54 tff(func_def_160, type, 'pair$n': ('Int_int_prod$' * 'Int_int_prod$') > 'Int_int_prod_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_161, type, 'gen_length$a': 'Nat$' > 'A_iarray_list_list_nat_fun$').
% 18.49/13.54 tff(func_def_162, type, 'size$e': 'Int_list$' > 'Nat$').
% 18.49/13.54 tff(func_def_163, type, 'pair$p': ('A_n_vec_n_vec$' * $int) > 'A_n_vec_n_vec_int_prod$').
% 18.49/13.54 tff(func_def_164, type, 'pick_middlep$a': ('Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' * $int) > 'Int_int_fun$').
% 18.49/13.54 tff(func_def_165, type, 'pair$d': ($int * 'Int_set$') > 'Int_int_set_prod$').
% 18.49/13.54 tff(func_def_166, type, 'snd$f': 'Int_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_167, type, 'append$d': 'A_iarray_list$' > 'A_iarray_list_a_iarray_list_fun$').
% 18.49/13.54 tff(func_def_168, type, 'uus$': ('A_iarray_list_set$' * 'A_iarray$') > 'A_iarray_list_bool_fun$').
% 18.49/13.54 tff(func_def_169, type, 'gauss_Jordan_PA$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_170, type, 'fun_app$au': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun_a_iarray_iarray_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$') > 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$').
% 18.49/13.54 tff(func_def_171, type, def_2: (tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$') > tlbool).
% 18.49/13.54 tff(func_def_172, type, 'plus$t': ('A_iarray_iarray_int_prod$' * 'A_iarray_iarray_int_prod$') > 'A_iarray_iarray_int_prod$').
% 18.49/13.54 tff(func_def_173, type, 'cons$d': ('A_iarray_iarray$' * 'A_iarray_iarray_list$') > 'A_iarray_iarray_list$').
% 18.49/13.54 tff(func_def_174, type, 'image2$b': ('A_iarray_set$' * 'A_iarray_int_fun$' * 'A_iarray_int_fun$') > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_175, type, 'none$a': 'A_n_vec_n_vec_option$').
% 18.49/13.54 tff(func_def_176, type, 'uut$': ('A_iarray_list$' * 'Nat_set$') > 'Nat_bool_fun$').
% 18.49/13.54 tff(func_def_177, type, 'lex$c': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$').
% 18.49/13.54 tff(func_def_178, type, 'uue$': ('Bool_bool_fun$' * 'A_iarray_iarray_bool_fun$') > 'A_iarray_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_179, type, 'plus$m': ('A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > 'A_n_vec_n_vec_set$').
% 18.49/13.54 tff(func_def_180, type, 'fun_app$ay': ('Int_int_int_prod_set_fun$' * $int) > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_181, type, 'pair$k': ('A_iarray_iarray$' * 'Int_set$') > 'A_iarray_iarray_int_set_prod$').
% 18.49/13.54 tff(func_def_182, type, 'same_fst$b': ('A_iarray_list_bool_fun$' * 'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$') > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$').
% 18.49/13.54 tff(func_def_183, type, 'plus$a': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_184, type, 'fun_app$bd': ('Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_185, type, 'pair$g': ($int * 'Int_int_prod$') > 'Int_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_186, type, 'collect$b': 'Int_bool_fun$' > 'Int_set$').
% 18.49/13.54 tff(func_def_187, type, 'plus$p': ('Int_set_int_prod$' * 'Int_set_int_prod$') > 'Int_set_int_prod$').
% 18.49/13.54 tff(func_def_188, type, 'cons$c': ($int * 'Int_list$') > 'Int_list$').
% 18.49/13.54 tff(func_def_189, type, 'fun_app$m': ('A_iarray_list_nat_fun$' * 'A_iarray_list$') > 'Nat$').
% 18.49/13.54 tff(func_def_190, type, 'matrix_matrix_mult$': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_191, type, 'plus$r': ('Int_a_iarray_iarray_prod$' * 'Int_a_iarray_iarray_prod$') > 'Int_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_192, type, 'snd$i': 'Int_set_int_set_prod$' > 'Int_set$').
% 18.49/13.54 tff(func_def_193, type, 'matrix_to_iarray_option$': 'A_n_vec_n_vec_option$' > 'A_iarray_iarray_option$').
% 18.49/13.54 tff(func_def_194, type, 'plus$j': ('A_iarray_iarray_set$' * 'A_iarray_iarray_set$') > 'A_iarray_iarray_set$').
% 18.49/13.54 tff(func_def_195, type, 'fun_app$ab': ('A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_196, type, 'lenlex$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$').
% 18.49/13.54 tff(func_def_197, type, 'zero$i': 'A_n_vec_n_vec_int_prod$').
% 18.49/13.54 tff(func_def_198, type, 'uul$': 'Int_set$' > 'Int_bool_fun$').
% 18.49/13.54 tff(func_def_199, type, 'size$g': 'Nat_nat_a_iarray_prod_prod_list$' > 'Nat$').
% 18.49/13.54 tff(func_def_200, type, 'fun_app$an': ('Nat_a_iarray_fun$' * 'Nat$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_201, type, 'fun_app$al': ('A_iarray_int_fun$' * 'A_iarray$') > $int).
% 18.49/13.54 tff(func_def_202, type, 'snd$a': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$').
% 18.49/13.54 tff(func_def_203, type, 'fst$f': 'Int_a_iarray_iarray_prod$' > $int).
% 18.49/13.54 tff(func_def_204, type, 'uuf$': 'A_n_vec_n_vec_bool_fun$').
% 18.49/13.54 tff(func_def_205, type, 'size$h': 'Nat_a_iarray_list_prod_list$' > 'Nat$').
% 18.49/13.54 tff(func_def_206, type, 'fstOp$': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$') > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$').
% 18.49/13.54 tff(func_def_207, type, 'uui$': 'A_iarray_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_208, type, 'plus$b': ('Int_int_prod$' * 'Int_int_prod$') > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_209, type, 'zero$j': 'A_n_vec_n_vec_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_210, type, 'plus$u': ('Int_set_int_set_prod$' * 'Int_set_int_set_prod$') > 'Int_set_int_set_prod$').
% 18.49/13.54 tff(func_def_211, type, 'shift$': ('A_iarray_list_set$' * 'A_iarray$') > 'A_iarray_list_set$').
% 18.49/13.54 tff(func_def_212, type, def_7: ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$') > tlbool).
% 18.49/13.54 tff(func_def_213, type, 'uuc$': 'A_iarray_list_bool_fun$' > 'A_iarray_list_bool_fun$').
% 18.49/13.54 tff(func_def_214, type, 'zero$h': 'Int_int_prod_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_215, type, 'pair$a': ('A_iarray$' * 'A_iarray$') > 'A_iarray_a_iarray_prod$').
% 18.49/13.54 tff(func_def_216, type, 'snd$j': 'Int_int_prod_int_prod$' > $int).
% 18.49/13.54 tff(func_def_217, type, 'gauss_Jordan_iarrays$': 'A_iarray_iarray$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_218, type, 'divides_aux$': 'Int_int_prod_bool_fun$').
% 18.49/13.54 tff(func_def_219, type, 'same_fst$': ('Int_bool_fun$' * 'Int_int_int_prod_set_fun$') > 'Int_int_prod_int_int_prod_prod_set$').
% 18.49/13.54 tff(func_def_220, type, 'fun_app$l': ('Nat_int_fun$' * 'Nat$') > $int).
% 18.49/13.54 tff(func_def_221, type, 'fst$b': 'Int_int_prod_int_fun$').
% 18.49/13.54 tff(func_def_222, type, 'plus$k': ('Int_set$' * 'Int_set$') > 'Int_set$').
% 18.49/13.54 tff(func_def_223, type, 'fun_app$j': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 18.49/13.54 tff(func_def_224, type, 'size_prod$b': ('A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'Nat$').
% 18.49/13.54 tff(func_def_225, type, 'image2$c': ('A_iarray_list_set$' * 'A_iarray_list_int_fun$' * 'A_iarray_list_int_fun$') > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_226, type, 'uum$': 'Nat_set$' > 'Nat_bool_fun$').
% 18.49/13.54 tff(func_def_227, type, 'zero$b': 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_228, type, def_6: (tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$') > tlbool).
% 18.49/13.54 tff(func_def_229, type, 'plus$d': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_230, type, 'relcompp$b': ('Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$') > 'Int_int_bool_fun_fun$').
% 18.49/13.54 tff(func_def_231, type, 'invertible_iarray$': 'A_iarray_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_232, type, 'uud$': 'A_iarray_bool_fun$' > 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_233, type, 'pair$c': ($int * $int) > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_234, type, tlfalse: tlbool).
% 18.49/13.54 tff(func_def_235, type, 'fun_app$x': ('A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$') > 'A_iarray_iarray_option_bool_fun$').
% 18.49/13.54 tff(func_def_236, type, 'gen_length$': 'Nat$' > 'Nat_a_iarray_prod_list_nat_fun$').
% 18.49/13.54 tff(func_def_237, type, 'plus$': ('A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_238, type, 'lex$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$').
% 18.49/13.54 tff(func_def_239, type, 'fst$h': 'A_iarray_iarray_int_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_240, type, 'swap$': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list_a_iarray_list_prod$').
% 18.49/13.54 tff(func_def_241, type, 'pair$z': ('A_iarray_list_list$' * 'A_iarray_list_list$') > 'A_iarray_list_list_a_iarray_list_list_prod$').
% 18.49/13.54 tff(func_def_242, type, 'id_upt_k$': 'A_n_vec_n_vec$' > 'Nat_bool_fun$').
% 18.49/13.54 tff(func_def_243, type, 'fst$j': 'Int_int_prod_int_prod$' > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_244, type, 'fun_app$ak': ('Int_int_fun$' * $int) > $int).
% 18.49/13.54 tff(func_def_245, type, 'collect$g': 'Int_int_prod_bool_fun$' > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_246, type, 'pair$s': ('A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod$') > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$').
% 18.49/13.54 tff(func_def_247, type, 'plus$v': ('Int_int_prod_int_prod$' * 'Int_int_prod_int_prod$') > 'Int_int_prod_int_prod$').
% 18.49/13.54 tff(func_def_248, type, 'splice$a': ('A_iarray_list_list$' * 'A_iarray_list_list$') > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_249, type, 'pair$w': ('A_iarray_iarray_list$' * 'A_iarray_iarray_list$') > 'A_iarray_iarray_list_a_iarray_iarray_list_prod$').
% 18.49/13.54 tff(func_def_250, type, 'lex$b': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$').
% 18.49/13.54 tff(func_def_251, type, 'pair$v': ('Int_list$' * 'Int_list$') > 'Int_list_int_list_prod$').
% 18.49/13.54 tff(func_def_252, type, 'is_zero_iarray$': 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_253, type, 'size_prod$a': ('Int_nat_fun$' * 'Int_nat_fun$' * 'Int_int_prod$') > 'Nat$').
% 18.49/13.54 tff(func_def_254, type, 'fun_app$be': ('A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' * 'A_iarray_list$') > 'A_iarray_list_a_iarray_list_bool_fun_fun$').
% 18.49/13.54 tff(func_def_255, type, 'iarray_to_matrix$': 'A_iarray_iarray$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_256, type, 'fun_app$am': ('A_iarray_list_int_fun$' * 'A_iarray_list$') > $int).
% 18.49/13.54 tff(func_def_257, type, 'pair$l': ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_258, type, 'inverse_matrix$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$').
% 18.49/13.54 tff(func_def_259, type, 'fst$i': 'Int_set_int_set_prod$' > 'Int_set$').
% 18.49/13.54 tff(func_def_260, type, 'fst$': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$').
% 18.49/13.54 tff(func_def_261, type, 'nrows_iarray$': 'A_iarray_iarray_nat_fun$').
% 18.49/13.54 tff(func_def_262, type, 'fun_app$z': ('A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_iarray_iarray_option$') > 'A_iarray_iarray_option_bool_fun$').
% 18.49/13.54 tff(func_def_263, type, 'pair$f': ($int * 'A_iarray_iarray$') > 'Int_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_264, type, 'fun_app$aw': ('A_iarray_iarray_option_nat_fun$' * 'A_iarray_iarray_option$') > 'Nat$').
% 18.49/13.54 tff(func_def_265, type, 'uun$': 'A_iarray_set$' > 'A_iarray_bool_fun$').
% 18.49/13.54 tff(func_def_266, type, 'uub$': 'Nat_a_iarray_prod_bool_fun$' > 'Nat_a_iarray_prod_bool_fun$').
% 18.49/13.54 tff(func_def_267, type, 'similar_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$').
% 18.49/13.54 tff(func_def_268, type, 'case_option$a': (tlbool * 'A_iarray_iarray_bool_fun$') > 'A_iarray_iarray_option_bool_fun$').
% 18.49/13.54 tff(func_def_269, type, 'zero$g': 'Int_int_prod_int_int_prod_prod$').
% 18.49/13.54 tff(func_def_270, type, 'pair$u': ('Nat$' * 'A_iarray$') > 'Nat_a_iarray_prod$').
% 18.49/13.54 tff(func_def_271, type, 'image2$a': ('Int_set$' * 'Int_int_fun$' * 'Int_int_fun$') > 'Int_int_prod_set$').
% 18.49/13.54 tff(func_def_272, type, 'uup$': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$').
% 18.49/13.54 tff(func_def_273, type, 'the$a': 'A_iarray_iarray_option$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_274, type, 'some$': 'A_iarray_iarray$' > 'A_iarray_iarray_option$').
% 18.49/13.54 tff(func_def_275, type, 'size_option$': 'A_iarray_iarray_nat_fun$' > 'A_iarray_iarray_option_nat_fun$').
% 18.49/13.54 tff(func_def_276, type, 'zero$e': 'Int_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_277, type, 'fun_app$y': ('A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_iarray_iarray_option$') > 'A_n_vec_n_vec_option_bool_fun$').
% 18.49/13.54 tff(func_def_278, type, 'pair$r': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$').
% 18.49/13.54 tff(func_def_279, type, 'zero$c': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$').
% 18.49/13.54 tff(func_def_280, type, 'image2$h': ('Int_set$' * 'Int_a_iarray_iarray_fun$' * 'Int_a_iarray_iarray_fun$') > 'A_iarray_iarray_a_iarray_iarray_prod_set$').
% 18.49/13.54 tff(func_def_281, type, 'fun_app$q': ('A_iarray_iarray_nat_fun$' * 'A_iarray_iarray$') > 'Nat$').
% 18.49/13.54 tff(func_def_282, type, 'fun_app$p': ('A_iarray_list_a_iarray_list_fun$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_283, type, 'fun_app$ac': ('Int_int_prod_int_fun$' * 'Int_int_prod$') > $int).
% 18.49/13.54 tff(func_def_284, type, 'swap$c': 'Int_int_prod$' > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_285, type, 'zero$f': 'Int_int_prod_int_prod$').
% 18.49/13.54 tff(func_def_286, type, 'append$a': ('Int_list$' * 'Int_list$') > 'Int_list$').
% 18.49/13.54 tff(func_def_287, type, 'size_option$a': 'A_n_vec_n_vec_nat_fun$' > 'A_n_vec_n_vec_option_nat_fun$').
% 18.49/13.54 tff(func_def_288, type, 'nil$a': 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_289, type, 'fstOp$b': ('A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$') > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$').
% 18.49/13.54 tff(func_def_290, type, 'fun_app$i': ('A_iarray_list_a_iarray_list_bool_fun_fun$' * 'A_iarray_list$') > 'A_iarray_list_bool_fun$').
% 18.49/13.54 tff(func_def_291, type, 'the$': 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_292, type, 'size$d': 'A_n_vec_n_vec_option$' > 'Nat$').
% 18.49/13.54 tff(func_def_293, type, 'plus$g': ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.54 tff(func_def_294, type, 'enumerate$b': ('Nat$' * 'A_iarray_list_list$') > 'Nat_a_iarray_list_prod_list$').
% 18.49/13.54 tff(func_def_295, type, 'plus$f': ('A_iarray_set$' * 'A_iarray_set$') > 'A_iarray_set$').
% 18.49/13.54 tff(func_def_296, type, 'matrix_matrix_mult_iarray$': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_297, type, 'splice$': ('Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_298, type, 'fun_app$u': ('Nat_a_iarray_prod_list_nat_fun$' * 'Nat_a_iarray_prod_list$') > 'Nat$').
% 18.49/13.54 tff(func_def_299, type, 'vec_to_iarray$': 'A_n_vec_n_vec$' > 'A_n_vec_iarray$').
% 18.49/13.54 tff(func_def_300, type, 'snd$g': 'Int_int_int_prod_prod$' > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_301, type, 'pair$i': ('Int_set$' * 'Int_set$') > 'Int_set_int_set_prod$').
% 18.49/13.54 tff(func_def_302, type, 'lexord$b': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$').
% 18.49/13.54 tff(func_def_303, type, 'snd$b': 'Int_int_prod_int_fun$').
% 18.49/13.54 tff(func_def_304, type, 'plus$c': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_305, type, 'size_list$': ('A_iarray_nat_fun$' * 'A_iarray_list$') > 'Nat$').
% 18.49/13.54 tff(func_def_310, type, sK5: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_311, type, sK6: 'A_iarray_iarray_option$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_312, type, sK7: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_313, type, sK8: 'A_iarray_iarray_option$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_314, type, sK9: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_315, type, sK10: 'A_iarray_iarray_option$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_316, type, sK11: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec_option$').
% 18.49/13.54 tff(func_def_317, type, sK12: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_318, type, sK13: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray_option$').
% 18.49/13.54 tff(func_def_319, type, sK14: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_320, type, sK15: 'Nat$' > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_321, type, sK16: 'Nat$' > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_322, type, sK17: 'Nat$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_323, type, sK18: ('A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_324, type, sK19: ('A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_325, type, sK20: ('A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_326, type, sK21: ('A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_327, type, sK22: ('A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_328, type, sK23: ('A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_329, type, sK24: ('A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_330, type, sK25: ('A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_331, type, sK26: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_332, type, sK27: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec_option$').
% 18.49/13.54 tff(func_def_333, type, sK28: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_334, type, sK29: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray_option$').
% 18.49/13.54 tff(func_def_335, type, sK30: ('A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec_option$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_336, type, sK31: ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_337, type, sK32: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.54 tff(func_def_338, type, sK33: ('A_iarray_bool_fun$' * 'A_iarray_bool_fun$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_339, type, sK34: ('A_iarray$' * 'A_iarray_set$' * 'A_iarray_set$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_340, type, sK35: ('A_iarray$' * 'A_iarray_set$' * 'A_iarray_set$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_341, type, sK36: ('Nat$' * 'Nat_set$' * 'Nat_set$') > 'Nat$').
% 18.49/13.54 tff(func_def_342, type, sK37: ('Nat$' * 'Nat_set$' * 'Nat_set$') > 'Nat$').
% 18.49/13.54 tff(func_def_343, type, sK38: ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_344, type, sK39: ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 18.49/13.54 tff(func_def_345, type, sK40: ('A_iarray_iarray$' * 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_346, type, sK41: ('A_iarray_iarray$' * 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_347, type, sK42: ('Int_set$' * 'Int_set_set$' * 'Int_set_set$') > 'Int_set$').
% 18.49/13.54 tff(func_def_348, type, sK43: ('Int_set$' * 'Int_set_set$' * 'Int_set_set$') > 'Int_set$').
% 18.49/13.54 tff(func_def_349, type, sK44: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_350, type, sK45: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_351, type, sK46: ('Int_int_prod$' * 'Int_int_prod_set$' * 'Int_int_prod_set$') > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_352, type, sK47: ('Int_int_prod$' * 'Int_int_prod_set$' * 'Int_int_prod_set$') > 'Int_int_prod$').
% 18.49/13.54 tff(func_def_353, type, sK48: ($int * 'Int_set$' * 'Int_set$') > $int).
% 18.49/13.54 tff(func_def_354, type, sK49: ($int * 'Int_set$' * 'Int_set$') > $int).
% 18.49/13.54 tff(func_def_355, type, sK50: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_356, type, sK51: 'Int_int_prod$' > $int).
% 18.49/13.54 tff(func_def_357, type, sK52: 'Int_int_prod$' > $int).
% 18.49/13.54 tff(func_def_358, type, sK53: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_359, type, sK54: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_360, type, sK55: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_361, type, sK56: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_362, type, sK57: 'A_iarray_a_iarray_prod$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_363, type, sK58: 'A_iarray_a_iarray_prod$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_364, type, sK59: 'Int_int_prod$' > $int).
% 18.49/13.54 tff(func_def_365, type, sK60: 'Int_int_prod$' > $int).
% 18.49/13.54 tff(func_def_366, type, sK61: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_367, type, sK62: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_368, type, sK63: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_369, type, sK64: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_370, type, sK65: 'A_iarray_a_iarray_prod$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_371, type, sK66: 'A_iarray_a_iarray_prod$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_372, type, sK67: 'Int_int_prod_bool_fun$' > $int).
% 18.49/13.54 tff(func_def_373, type, sK68: 'Int_int_prod_bool_fun$' > $int).
% 18.49/13.54 tff(func_def_374, type, sK69: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_375, type, sK70: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_376, type, sK71: 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_377, type, sK72: 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_378, type, sK73: 'A_iarray_a_iarray_prod_bool_fun$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_379, type, sK74: 'A_iarray_a_iarray_prod_bool_fun$' > 'A_iarray$').
% 18.49/13.54 tff(func_def_380, type, sK75: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_381, type, sK76: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_382, type, sK77: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_383, type, sK78: ('A_iarray_list$' * 'A_iarray_list_a_iarray_list_prod$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_384, type, sK79: ('A_iarray$' * 'A_iarray_a_iarray_prod$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_385, type, sK80: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_386, type, sK81: ($int * 'Int_int_prod$') > $int).
% 18.49/13.54 tff(func_def_387, type, sK82: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_388, type, sK83: ('A_iarray_list$' * 'A_iarray_list_a_iarray_list_prod$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_389, type, sK84: ('A_iarray$' * 'A_iarray_a_iarray_prod$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_390, type, sK85: ('A_n_vec_n_vec$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_391, type, sK86: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 18.49/13.54 tff(func_def_392, type, sK87: ($int * 'Int_int_prod$') > $int).
% 18.49/13.54 tff(func_def_393, type, sK88: ('A_n_vec_n_vec$' * 'Nat$') > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_394, type, sK89: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 18.49/13.54 tff(func_def_395, type, sK90: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_396, type, sK91: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_397, type, sK92: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_398, type, sK93: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_399, type, sK94: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_400, type, sK95: 'Nat$' > 'Nat$').
% 18.49/13.54 tff(func_def_401, type, sK96: 'Nat_bool_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_402, type, sK97: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_403, type, sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_404, type, sK99: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_405, type, sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_406, type, sK101: 'Nat_bool_fun$' > 'Nat$').
% 18.49/13.54 tff(func_def_407, type, sK102: 'Nat$' > 'Nat$').
% 18.49/13.54 tff(func_def_408, type, sK103: ('Nat_a_iarray_prod_list$' * 'Nat$') > 'Nat_a_iarray_prod$').
% 18.49/13.54 tff(func_def_409, type, sK104: ('Nat_a_iarray_prod_list$' * 'Nat$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.54 tff(func_def_410, type, sK105: ('A_iarray_list_list$' * 'Nat$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_411, type, sK106: ('A_iarray_list_list$' * 'Nat$') > 'A_iarray_list_list$').
% 18.49/13.54 tff(func_def_412, type, sK107: ('A_iarray_list$' * 'Nat$') > 'A_iarray$').
% 18.49/13.54 tff(func_def_413, type, sK108: ('A_iarray_list$' * 'Nat$') > 'A_iarray_list$').
% 18.49/13.54 tff(func_def_414, type, sK109: ('Nat$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod$').
% 18.49/13.55 tff(func_def_415, type, sK110: ('Nat$' * 'Nat_a_iarray_prod_list$') > 'Nat_a_iarray_prod_list$').
% 18.49/13.55 tff(func_def_416, type, sK111: ('Nat$' * 'A_iarray_list_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_417, type, sK112: ('Nat$' * 'A_iarray_list_list$') > 'A_iarray_list_list$').
% 18.49/13.55 tff(func_def_418, type, sK113: ('Nat$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_419, type, sK114: ('Nat$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_420, type, sK115: 'Int_int_prod_set$' > $int).
% 18.49/13.55 tff(func_def_421, type, sK116: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$').
% 18.49/13.55 tff(func_def_422, type, sK117: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_423, type, sK118: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_424, type, sK119: 'Int_int_prod_set$' > $int).
% 18.49/13.55 tff(func_def_425, type, sK120: 'Int_int_prod_set$' > $int).
% 18.49/13.55 tff(func_def_426, type, sK121: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$').
% 18.49/13.55 tff(func_def_427, type, sK122: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$').
% 18.49/13.55 tff(func_def_428, type, sK123: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_429, type, sK124: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_430, type, sK125: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_431, type, sK126: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_432, type, sK127: ('Int_list$' * $int * 'Int_list$' * 'Int_int_prod_set$') > $int).
% 18.49/13.55 tff(func_def_433, type, sK128: ('Int_list$' * $int * 'Int_list$' * 'Int_int_prod_set$') > 'Int_list$').
% 18.49/13.55 tff(func_def_434, type, sK129: ('A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray$').
% 18.49/13.55 tff(func_def_435, type, sK130: ('A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray_list$').
% 18.49/13.55 tff(func_def_436, type, sK131: ('A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_437, type, sK132: ('A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$') > 'A_iarray_list_list$').
% 18.49/13.55 tff(func_def_438, type, sK133: ('A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_439, type, sK134: ('A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_440, type, sK135: ($int * 'Int_list$' * 'Int_list$' * 'Int_int_prod_set$') > $int).
% 18.49/13.55 tff(func_def_441, type, sK136: ($int * 'Int_list$' * 'Int_list$' * 'Int_int_prod_set$') > 'Int_list$').
% 18.49/13.55 tff(func_def_442, type, sK137: ('A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray$').
% 18.49/13.55 tff(func_def_443, type, sK138: ('A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$') > 'A_iarray_iarray_list$').
% 18.49/13.55 tff(func_def_444, type, sK139: ('A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_445, type, sK140: ('A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$') > 'A_iarray_list_list$').
% 18.49/13.55 tff(func_def_446, type, sK141: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_447, type, sK142: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_448, type, sK143: 'A_iarray_list$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_449, type, sK144: 'A_iarray_list$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_450, type, sK145: ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_451, type, sK146: ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_452, type, sK147: ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_453, type, sK148: ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_454, type, sK149: ('A_iarray_list$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_455, type, sK150: ('A_iarray_list$' * 'Nat$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_456, type, sK151: ('A_iarray_list$' * 'Nat$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_457, type, sK152: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_458, type, sK153: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_459, type, sK154: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_460, type, sK155: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_461, type, sK156: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_462, type, sK157: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_463, type, sK158: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_464, type, sK159: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_465, type, sK160: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_466, type, sK161: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_467, type, sK162: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_468, type, sK163: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_469, type, sK164: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_470, type, sK165: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_471, type, sK166: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_472, type, sK167: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_473, type, sK168: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$').
% 18.49/13.55 tff(func_def_474, type, sK169: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_475, type, sK170: ('A_iarray_list$' * 'A_iarray_bool_fun$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_476, type, sK171: ('A_iarray_list$' * 'A_iarray_bool_fun$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_477, type, sK172: ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_478, type, sK173: ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_479, type, sK174: ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_480, type, sK175: ('A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_bool_fun$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_481, type, sK176: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_482, type, sK177: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_483, type, sK178: ('A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_484, type, sK179: ('A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_485, type, sK180: ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_486, type, sK181: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_487, type, sK182: ('A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_488, type, sK183: ('A_iarray_bool_fun$' * 'A_iarray_list$') > 'A_iarray$').
% 18.49/13.55 tff(func_def_489, type, sK184: ('A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_490, type, sK185: ('A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$') > 'A_iarray_list$').
% 18.49/13.55 tff(func_def_491, type, sK186: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(func_def_492, type, sK187: 'Nat$' > 'Nat$').
% 18.49/13.55 tff(func_def_493, type, sK188: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_494, type, sK189: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_495, type, sK190: 'Nat$' > 'Nat$').
% 18.49/13.55 tff(func_def_496, type, sK191: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_497, type, sK192: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_498, type, sK193: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(func_def_499, type, sK194: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(func_def_500, type, sK195: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(func_def_501, type, sK196: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(func_def_502, type, sK197: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_503, type, sK198: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 18.49/13.55 tff(func_def_504, type, sK199: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.55 tff(func_def_505, type, sK200: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.55 tff(func_def_506, type, sK201: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.55 tff(func_def_507, type, sK202: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 18.49/13.55 tff(func_def_508, type, sK203: ('Nat$' * 'Nat$') > 'Nat$').
% 18.49/13.55 tff(f23,conjecture,(
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) => (('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))) & ('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$'))) & ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) => (('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'none$' = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))) & ('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'none$' = 'none$')))),
% 18.49/13.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture22)).
% 18.49/13.55
% 18.49/13.55 tff(f24,negated_conjecture,(
% 18.49/13.55 ~(('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) => (('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))) & ('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$'))) & ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) => (('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'none$' = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))) & ('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) => 'none$' = 'none$'))))),
% 18.49/13.55 inference(negated_conjecture,[status(cth)],[f23])).
% 18.49/13.55
% 18.49/13.55 tff(f195,axiom,(
% 18.49/13.55 ! [X0 : 'A_n_vec_n_vec$'] : 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0)))),
% 18.49/13.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193)).
% 18.49/13.55
% 18.49/13.55 tff(f206,axiom,(
% 18.49/13.55 ! [X0 : 'A_iarray_iarray$'] : 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) = 'gauss_Jordan_iarrays$'(X0)),
% 18.49/13.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204)).
% 18.49/13.55
% 18.49/13.55 tff(f207,axiom,(
% 18.49/13.55 ! [X0 : 'A_n_vec_n_vec$'] : ? [X1 : 'A_n_vec_n_vec$'] : ('fun_app$o'('invertible$',X1) & 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0))),
% 18.49/13.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205)).
% 18.49/13.55
% 18.49/13.55 tff(f275,axiom,(
% 18.49/13.55 ! [X0 : 'A_n_vec_n_vec$'] : 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'gauss_Jordan$'(X0)),
% 18.49/13.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273)).
% 18.49/13.55
% 18.49/13.55 tff(f777,plain,(
% 18.49/13.55 ((('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$'))))))) | ('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))))) & 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))) | ((('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$'))))))) | ('none$' != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))))) & 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))))),
% 18.49/13.55 inference(ennf_transformation,[],[f24])).
% 18.49/13.55
% 18.49/13.55 tff(f1197,plain,(
% 18.49/13.55 ! [X0 : 'A_n_vec_n_vec$'] : ('fun_app$o'('invertible$',sK50(X0)) & 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK50(X0),X0))),
% 18.49/13.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(X1,sK50(X0))],[f207])).
% 18.49/13.55
% 18.49/13.55 tff(f1535,plain,(
% 18.49/13.55 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) | sP0),
% 18.49/13.55 inference(cnf_transformation,[],[f1072])).
% 18.49/13.55
% 18.49/13.55 tff(f1827,plain,(
% 18.49/13.55 ( ! [X0 : 'A_n_vec_n_vec$'] : ('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0)))) )),
% 18.49/13.55 inference(cnf_transformation,[],[f195])).
% 18.49/13.55
% 18.49/13.55 tff(f1838,plain,(
% 18.49/13.55 ( ! [X0 : 'A_iarray_iarray$'] : ('gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0))) )),
% 18.49/13.55 inference(cnf_transformation,[],[f206])).
% 18.49/13.55
% 18.49/13.55 tff(f1839,plain,(
% 18.49/13.55 ( ! [X0 : 'A_n_vec_n_vec$'] : ('gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK50(X0),X0)) )),
% 18.49/13.55 inference(cnf_transformation,[],[f1197])).
% 18.49/13.55
% 18.49/13.55 tff(f1934,plain,(
% 18.49/13.55 ( ! [X0 : 'A_n_vec_n_vec$'] : ('gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) )),
% 18.49/13.55 inference(cnf_transformation,[],[f275])).
% 18.49/13.55
% 18.49/13.55 tff(f2640,plain,(
% 18.49/13.55 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) | sP0),
% 18.49/13.55 inference(definition_unfolding,[],[f1535,f1838])).
% 18.49/13.55
% 18.49/13.55 tff(f2681,plain,(
% 18.49/13.55 ( ! [X0 : 'A_n_vec_n_vec$'] : ('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK50(X0),X0)) )),
% 18.49/13.55 inference(definition_unfolding,[],[f1934,f1839])).
% 18.49/13.55
% 18.49/13.55 tcf(c_105,plain,
% 18.49/13.55 (~sP0|'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(cnf_transformation,[],[f3053])).
% 18.49/13.55
% 18.49/13.55 tcf(c_108,negated_conjecture,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 sP0),
% 18.49/13.55 inference(cnf_transformation,[],[f3058])).
% 18.49/13.55
% 18.49/13.55 tcf(c_110,negated_conjecture,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 sP0),
% 18.49/13.55 inference(cnf_transformation,[],[f2640])).
% 18.49/13.55
% 18.49/13.55 tcf(c_359,negated_conjecture,![X0_'A_n_vec_n_vec':'A_n_vec_n_vec$']:
% 18.49/13.55 ('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0_'A_n_vec_n_vec'))) = 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0_'A_n_vec_n_vec')))),
% 18.49/13.55 inference(cnf_transformation,[],[f1827])).
% 18.49/13.55
% 18.49/13.55 tcf(c_439,negated_conjecture,![X0_'A_n_vec_n_vec':'A_n_vec_n_vec$']:
% 18.49/13.55 ('matrix_matrix_mult$'(sK50(X0_'A_n_vec_n_vec'),X0_'A_n_vec_n_vec') = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0_'A_n_vec_n_vec'))),
% 18.49/13.55 inference(cnf_transformation,[],[f2681])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1933,plain,
% 18.49/13.55 (sP0|'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(prop_impl_just,[status(thm)],[c_108])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1934,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 sP0),
% 18.49/13.55 inference(renaming,[status(thm)],[c_1933])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1935,plain,
% 18.49/13.55 (~sP0|'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(prop_impl_just,[status(thm)],[c_105])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1939,plain,
% 18.49/13.55 (sP0|'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(prop_impl_just,[status(thm)],[c_110])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1940,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 sP0),
% 18.49/13.55 inference(renaming,[status(thm)],[c_1939])).
% 18.49/13.55
% 18.49/13.55 tcf(c_8323,plain,![X0_'A_n_vec_n_vec':'A_n_vec_n_vec$']:
% 18.49/13.55 ('matrix_to_iarray$'('matrix_matrix_mult$'(sK50(X0_'A_n_vec_n_vec'),X0_'A_n_vec_n_vec')) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0_'A_n_vec_n_vec')))),
% 18.49/13.55 inference(demodulation,[status(thm)],[c_359,c_439])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9637,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 sP0),
% 18.49/13.55 inference(demodulation,[status(thm)],[c_1940,c_8323])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9770,plain,
% 18.49/13.55 (sP0),
% 18.49/13.55 inference(forward_subsumption_resolution,[status(thm)],[c_1934,c_9637])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9773,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(forward_subsumption_resolution,[status(thm)],[c_1935,c_9770])).
% 18.49/13.55
% 18.49/13.55 tff(f1071,definition,(
% 18.49/13.55 ((('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$'))))))) | ('none$' != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))))) & 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))) | ~ sP0),
% 18.49/13.55 introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction])).
% 18.49/13.55 tff(f1072,plain,(
% 18.49/13.55 ((('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$'))))))) | ('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))))) & 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))) | sP0),
% 18.49/13.55 inference(definition_folding,[],[f777,f1071])).
% 18.49/13.55
% 18.49/13.55 tff(f1101,plain,(
% 18.49/13.55 ((('some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$'))))))) | ('none$' != 'none$' & 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))))) & 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))) | ~sP0),
% 18.49/13.55 inference(nnf_transformation,[],[f1071])).
% 18.49/13.55
% 18.49/13.55 tff(f1530,plain,(
% 18.49/13.55 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) | ~sP0),
% 18.49/13.55 inference(cnf_transformation,[],[f1101])).
% 18.49/13.55
% 18.49/13.55 tff(f2636,plain,(
% 18.49/13.55 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) | ~sP0),
% 18.49/13.55 inference(definition_unfolding,[],[f1530,f1838])).
% 18.49/13.55
% 18.49/13.55 tcf(c_106,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 ~sP0),
% 18.49/13.55 inference(cnf_transformation,[],[f2636])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1937,plain,
% 18.49/13.55 (~sP0|'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(prop_impl_just,[status(thm)],[c_106])).
% 18.49/13.55
% 18.49/13.55 tcf(c_1938,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))|
% 18.49/13.55 ~sP0),
% 18.49/13.55 inference(renaming,[status(thm)],[c_1937])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9869,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(forward_subsumption_resolution,[status(thm)],[c_1938,c_9770])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9870,plain,
% 18.49/13.55 ('fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))),
% 18.49/13.55 inference(demodulation,[status(thm)],[c_9869,c_8323,c_9773])).
% 18.49/13.55
% 18.49/13.55 tcf(c_9871,plain,
% 18.49/13.55 ($false),
% 18.49/13.55 inference(equality_resolution_simp,[status(thm)],[c_9870])).
% 18.49/13.55
% 18.49/13.55
% 18.49/13.55 % SZS output end CNFRefutation for theBenchmark.p
% 18.49/13.55
% 18.49/13.55
%------------------------------------------------------------------------------