%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP339_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:49:27 PM UTC 2026
% Result : Theorem 12.19s 2.86s
% Output : CNFRefutation 12.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP339_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 18:24:42 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.48 Running TFA theorem proving
% 0.17/0.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.50
% 0.17/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.50
% 0.17/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 12.19/2.86 % SZS status Started for theBenchmark.p
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_65080:40.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/7sswbdve 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/7sswbdve_error
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_66020:200.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/7skyfv1h 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/7skyfv1h_error
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_65511:44.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/u734sm8k 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/u734sm8k_error
% 12.19/2.86 ERROR - "ProverProcess:heur/schedule_none:304.999972820282" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/yz4sxwlk 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/yz4sxwlk_error
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_65520:11.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/kmviez8u 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/kmviez8u_error
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_65097:3.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/qjb0ttdw 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/qjb0ttdw_error
% 12.19/2.86 ERROR - "ProverProcess:heur/vip_64741:92.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 12.19/2.86 Fatal error: exception Failure("undefined enum value")
% 12.19/2.86 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/j0kncj_y 2>> /export/starexec/sandbox2/tmp/iprover_out_u7o6qm9l/j0kncj_y_error
% 12.19/2.86 % SZS status Theorem for theBenchmark.p
% 12.19/2.86
% 12.19/2.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.19/2.86
% 12.19/2.86 % ------ iProver source info
% 12.19/2.86
% 12.19/2.86 % git: date: 2026-07-19 20:42:38 +0200
% 12.19/2.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.19/2.86 % git: non_committed_changes: false
% 12.19/2.86
% 12.19/2.86 % ------ Parsing...
% 12.19/2.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.19/2.86
% 12.19/2.86 % ------ Preprocessing...%
% 12.19/2.86
% 12.19/2.86 % SZS status Theorem for theBenchmark.p
% 12.19/2.86
% 12.19/2.86 % SZS output start CNFRefutation for theBenchmark.p
% 12.19/2.86
% 12.19/2.86 tff(func_def_0, type, 'snd$g': 'Int_nat_prod$' > 'Nat$').
% 12.19/2.86 tff(pred_def_1, type, 'fun_app$n': ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$') > $o).
% 12.19/2.86 tff(pred_def_2, type, 'fun_app$f': ('Int_nat_prod_bool_fun$' * 'Int_nat_prod$') > $o).
% 12.19/2.86 tff(pred_def_3, type, 'fun_app$p': ('A_b_vec_c_vec_bool_fun$' * 'A_b_vec_c_vec$') > $o).
% 12.19/2.86 tff(pred_def_4, type, 'fun_app$g': ('Int_int_prod_bool_fun$' * 'Int_int_prod$') > $o).
% 12.19/2.86 tff(pred_def_5, type, 'fun_app$j': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > $o).
% 12.19/2.86 tff(pred_def_6, type, 'fun_app$d': ('Nat_nat_prod_bool_fun$' * 'Nat_nat_prod$') > $o).
% 12.19/2.86 tff(pred_def_7, type, 'fun_app$e': ('Nat_int_prod_bool_fun$' * 'Nat_int_prod$') > $o).
% 12.19/2.86 tff(pred_def_8, type, 'fun_app$i': ('Nat_a_b_vec_c_vec_prod_bool_fun$' * 'Nat_a_b_vec_c_vec_prod$') > $o).
% 12.19/2.86 tff(pred_def_9, type, 'fun_app$k': ('Nat_a_iarray_iarray_prod_bool_fun$' * 'Nat_a_iarray_iarray_prod$') > $o).
% 12.19/2.86 tff(pred_def_10, type, 'fun_app$x': ('Int_bool_fun$' * $int) > $o).
% 12.19/2.86 tff(pred_def_11, type, 'fun_app$h': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > $o).
% 12.19/2.86 tff(pred_def_12, type, 'fun_app$c': ('Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$') > $o).
% 12.19/2.86 tff(pred_def_13, type, 'fun_app$s': ('Nat_bool_fun$' * 'Nat$') > $o).
% 12.19/2.86 tff(func_def_14, type, 'fun_app$q': ('Nat_a_b_vec_c_vec_bool_fun_fun$' * 'Nat$') > 'A_b_vec_c_vec_bool_fun$').
% 12.19/2.86 tff(func_def_15, type, 'a$a': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(pred_def_16, type, sP0: ($int * $int * $int) > $o).
% 12.19/2.86 tff(pred_def_17, type, sP1: ($int * $int * $int) > $o).
% 12.19/2.86 tff(pred_def_18, type, sP2: ($int * $int * $int) > $o).
% 12.19/2.86 tff(func_def_19, type, 'pair$h': ($int * $int) > 'Int_int_prod$').
% 12.19/2.86 tff(func_def_20, type, 'fun_app$o': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$') > 'A_iarray_iarray_bool_fun$').
% 12.19/2.86 tff(func_def_21, type, 'pair$a': ('Nat$' * 'A_b_vec_c_vec$') > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_22, type, 'snd$h': 'Int_int_prod$' > $int).
% 12.19/2.86 tff(func_def_23, type, 'fst$e': 'Nat_nat_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_24, type, 'fst$k': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_25, type, 'fun_app$': ('Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' * 'Nat$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_26, type, 'foldl$': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_list$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_27, type, 'nrows$': 'A_b_vec_c_vec$' > 'Nat$').
% 12.19/2.86 tff(func_def_28, type, 'pair$f': ('Nat$' * $int) > 'Nat_int_prod$').
% 12.19/2.86 tff(func_def_29, type, 'snd$e': 'Nat_nat_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_30, type, 'zero$a': 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_31, type, 'fun_app$r': ('Nat_a_iarray_iarray_bool_fun_fun$' * 'Nat$') > 'A_iarray_iarray_bool_fun$').
% 12.19/2.86 tff(func_def_32, type, 'fun_app$m': ('A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray$') > 'Nat_a_iarray_iarray_prod_bool_fun$').
% 12.19/2.86 tff(func_def_33, type, 'pair$l': ('A_c_vec_c_vec$' * 'A_b_vec_c_vec$') > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_34, type, 'fun_app$t': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 12.19/2.86 tff(func_def_35, type, 'snd$a': 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_36, type, 'pair$j': ('A_c_vec_c_vec$' * 'Nat_a_c_vec_c_vec_prod$') > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_37, type, 'of_nat$': 'Nat_int_fun$').
% 12.19/2.86 tff(func_def_38, type, 'one$': 'A$').
% 12.19/2.86 tff(func_def_39, type, 'upt$': ('Nat$' * 'Nat$') > 'Nat_list$').
% 12.19/2.86 tff(func_def_40, type, 'nrows$a': 'A_c_vec_c_vec$' > 'Nat$').
% 12.19/2.86 tff(func_def_41, type, 'fst$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_42, type, 'fst$a': 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_43, type, 'snd$b': 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_44, type, 'fst$g': 'Int_nat_prod$' > $int).
% 12.19/2.86 tff(func_def_45, type, 'zero$b': 'Int_nat_prod$').
% 12.19/2.86 tff(func_def_46, type, 'less$': 'Nat_nat_bool_fun_fun$').
% 12.19/2.86 tff(func_def_47, type, 'nrows_iarray$': 'A_iarray_iarray$' > 'Nat$').
% 12.19/2.86 tff(func_def_48, type, 'pair$i': ('Nat$' * 'A_iarray$') > 'Nat_a_iarray_prod$').
% 12.19/2.86 tff(func_def_49, type, tltrue: tlbool).
% 12.19/2.86 tff(func_def_50, type, 'gauss_Jordan_column_k_PA$a': ('A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$') > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_51, type, 'plus$f': ('Nat_a_iarray_iarray_prod$' * 'Nat_a_iarray_iarray_prod$') > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_52, type, 'plus$': 'Nat$' > 'Nat_nat_fun$').
% 12.19/2.86 tff(func_def_53, type, 'fun_app$a': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$').
% 12.19/2.86 tff(func_def_54, type, 'snd$f': 'Nat_int_prod$' > $int).
% 12.19/2.86 tff(func_def_55, type, 'pair$c': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_56, type, 'plus$k': ('Nat_nat_prod$' * 'Nat_nat_prod$') > 'Nat_nat_prod$').
% 12.19/2.86 tff(func_def_57, type, 'gauss_Jordan_column_k_iarrays_PA$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$').
% 12.19/2.86 tff(func_def_58, type, 'one$a': 'Nat$').
% 12.19/2.86 tff(func_def_59, type, 'fst$i': 'Nat_a_iarray_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_60, type, 'plus$j': ('Nat_int_prod$' * 'Nat_int_prod$') > 'Nat_int_prod$').
% 12.19/2.86 tff(func_def_61, type, 'zero$i': 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_62, type, 'fun_app$v': ('Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' * 'Nat$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 12.19/2.86 tff(func_def_63, type, 'fst$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_64, type, 'fun_app$y': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 12.19/2.86 tff(func_def_65, type, 'fst$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_66, type, 'ncols$': 'A_b_vec_c_vec$' > 'Nat$').
% 12.19/2.86 tff(func_def_67, type, 'fst$b': 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_68, type, 'fun_app$u': ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_69, type, 'vector_all_zero_from_index$': 'Nat_a_iarray_prod_bool_fun$').
% 12.19/2.86 tff(func_def_70, type, 'plus$l': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_71, type, 'plus$c': ('Nat_a_b_vec_c_vec_prod$' * 'Nat_a_b_vec_c_vec_prod$') > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_72, type, 'matrix_to_iarray$a': 'A_b_vec_c_vec$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_73, type, 'plus$d': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 12.19/2.86 tff(func_def_74, type, 'zero$h': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_75, type, 'pair$k': ('Nat$' * 'A_c_vec_c_vec$') > 'Nat_a_c_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_76, type, 'column_iarray$': ('Nat$' * 'A_iarray_iarray$') > 'A_iarray$').
% 12.19/2.86 tff(func_def_77, type, 'fun_app$w': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$').
% 12.19/2.86 tff(func_def_78, type, 'zero$j': 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_79, type, 'divides_aux$': 'Int_int_prod_bool_fun$').
% 12.19/2.86 tff(func_def_80, type, 'less_eq$': 'Nat_nat_bool_fun_fun$').
% 12.19/2.86 tff(func_def_81, type, 'snd$i': 'Nat_a_iarray_prod$' > 'A_iarray$').
% 12.19/2.86 tff(func_def_82, type, 'plus$e': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_83, type, 'zero$c': 'Nat_a_c_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_84, type, 'zero$': 'A$').
% 12.19/2.86 tff(func_def_85, type, 'matrix_to_iarray$': 'A_c_vec_c_vec$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_86, type, 'plus$i': ('A_b_vec_c_vec$' * 'A_b_vec_c_vec$') > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_87, type, 'plus$g': ('Int_int_prod$' * 'Int_int_prod$') > 'Int_int_prod$').
% 12.19/2.86 tff(func_def_88, type, tlfalse: tlbool).
% 12.19/2.86 tff(func_def_89, type, 'zero$g': 'Int_int_prod$').
% 12.19/2.86 tff(func_def_90, type, 'nat$': $int > 'Nat$').
% 12.19/2.86 tff(func_def_91, type, 'fst$h': 'Int_int_prod$' > $int).
% 12.19/2.86 tff(func_def_92, type, 'zero$e': 'Nat_nat_prod$').
% 12.19/2.86 tff(func_def_93, type, 'zero$f': 'Nat_int_prod$').
% 12.19/2.86 tff(func_def_94, type, 'snd$l': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_95, type, 'pair$': ('A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_96, type, 'gauss_Jordan_upt_k_iarrays_PA$': ('A_iarray_iarray$' * 'Nat$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_97, type, 'suc$': 'Nat_nat_fun$').
% 12.19/2.86 tff(func_def_98, type, 'plus$a': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 12.19/2.86 tff(func_def_99, type, 'pair$g': ($int * 'Nat$') > 'Int_nat_prod$').
% 12.19/2.86 tff(func_def_100, type, 'fun_app$b': ('Nat_int_fun$' * 'Nat$') > $int).
% 12.19/2.86 tff(func_def_101, type, 'fst$j': 'Nat_a_c_vec_c_vec_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_102, type, 'zero$d': 'Nat$').
% 12.19/2.86 tff(func_def_103, type, 'a$': 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_104, type, 'ka$': 'Nat$').
% 12.19/2.86 tff(func_def_105, type, 'snd$j': 'Nat_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_106, type, 'plus$b': ('A_c_vec_c_vec$' * 'A_c_vec_c_vec$') > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_107, type, 'mat_iarray$': ('A$' * 'Nat$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_108, type, 'k$': 'Nat$').
% 12.19/2.86 tff(func_def_109, type, 'snd$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_110, type, 'snd$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_111, type, 'snd$k': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_116, type, sK3: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_117, type, sK4: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$').
% 12.19/2.86 tff(func_def_118, type, sK5: 'Nat_nat_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_119, type, sK6: 'Nat_nat_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_120, type, sK7: 'Nat_int_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_121, type, sK8: 'Nat_int_prod_bool_fun$' > $int).
% 12.19/2.86 tff(func_def_122, type, sK9: 'Int_nat_prod_bool_fun$' > $int).
% 12.19/2.86 tff(func_def_123, type, sK10: 'Int_nat_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_124, type, sK11: 'Int_int_prod_bool_fun$' > $int).
% 12.19/2.86 tff(func_def_125, type, sK12: 'Int_int_prod_bool_fun$' > $int).
% 12.19/2.86 tff(func_def_126, type, sK13: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_127, type, sK14: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_128, type, sK15: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_129, type, sK16: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_130, type, sK17: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_131, type, sK18: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_132, type, sK19: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_133, type, sK20: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_134, type, sK21: 'Int_int_prod$' > $int).
% 12.19/2.86 tff(func_def_135, type, sK22: 'Int_int_prod$' > $int).
% 12.19/2.86 tff(func_def_136, type, sK23: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_137, type, sK24: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_138, type, sK25: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_139, type, sK26: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_140, type, sK27: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_141, type, sK28: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_142, type, sK29: 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_143, type, sK30: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_144, type, sK31: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_145, type, sK32: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_146, type, sK33: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_147, type, sK34: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_148, type, sK35: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_149, type, sK36: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_150, type, sK37: 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_151, type, sK38: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_152, type, sK39: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_153, type, sK40: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_154, type, sK41: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_155, type, sK42: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_156, type, sK43: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_157, type, sK44: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_158, type, sK45: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_159, type, sK46: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_160, type, sK47: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_161, type, sK48: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_162, type, sK49: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat$').
% 12.19/2.86 tff(func_def_163, type, sK50: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_164, type, sK51: 'Nat_int_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_165, type, sK52: 'Nat_int_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_166, type, sK53: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_167, type, sK54: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_168, type, sK55: 'Nat_int_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_169, type, sK56: 'Nat_int_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_170, type, sK57: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_171, type, sK58: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_172, type, sK59: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_173, type, sK60: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_174, type, sK61: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_175, type, sK62: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_176, type, sK63: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_177, type, sK64: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_178, type, sK65: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_179, type, sK66: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_180, type, sK67: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_181, type, sK68: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_182, type, sK69: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_183, type, sK70: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_184, type, sK71: 'Nat_nat_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_185, type, sK72: 'Nat_nat_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_186, type, sK73: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_187, type, sK74: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_188, type, sK75: 'Nat$' > 'Nat$').
% 12.19/2.86 tff(func_def_189, type, sK76: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_190, type, sK77: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_191, type, sK78: 'Nat$' > 'Nat$').
% 12.19/2.86 tff(func_def_192, type, sK79: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_193, type, sK80: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_194, type, sK81: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_195, type, sK82: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_196, type, sK83: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_197, type, sK84: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_198, type, sK85: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_199, type, sK86: 'Nat$' > 'Nat$').
% 12.19/2.86 tff(func_def_200, type, sK87: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_201, type, sK88: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_202, type, sK89: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_203, type, sK90: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_204, type, sK91: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_205, type, sK92: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_206, type, sK93: 'Nat$' > 'Nat$').
% 12.19/2.86 tff(func_def_207, type, sK94: 'Nat$' > 'Nat$').
% 12.19/2.86 tff(func_def_208, type, sK95: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_209, type, sK96: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 12.19/2.86 tff(func_def_210, type, sK97: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_211, type, sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_212, type, sK99: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_213, type, sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_214, type, sK101: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_215, type, sK102: 'Nat_bool_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_216, type, sK103: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_217, type, sK104: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_218, type, sK105: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_219, type, sK106: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_220, type, sK107: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_221, type, sK108: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_222, type, sK109: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_223, type, sK110: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_224, type, sK111: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_225, type, sK112: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_226, type, sK113: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_227, type, sK114: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_228, type, sK115: $int > $int).
% 12.19/2.86 tff(func_def_229, type, sK116: $int > $int).
% 12.19/2.86 tff(func_def_230, type, sK117: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_231, type, sK118: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_232, type, sK119: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_233, type, sK120: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_234, type, sK121: 'Int_int_bool_fun_fun$' > $int).
% 12.19/2.86 tff(func_def_235, type, sK122: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_236, type, sK123: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_237, type, sK124: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_238, type, sK125: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_239, type, sK126: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_240, type, sK127: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_241, type, sK128: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_242, type, sK129: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_243, type, sK130: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_244, type, sK131: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_245, type, sK132: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_246, type, sK133: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_247, type, sK134: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_248, type, sK135: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_249, type, sK136: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_250, type, sK137: 'Int_int_fun$' > $int).
% 12.19/2.86 tff(func_def_251, type, sK138: ('A_c_vec_c_vec$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'Nat_a_b_vec_c_vec_prod$').
% 12.19/2.86 tff(func_def_252, type, sK139: ('A_iarray_iarray$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'Nat_a_iarray_iarray_prod$').
% 12.19/2.86 tff(func_def_253, type, sK140: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_254, type, sK141: ('Nat$' * 'Nat_a_b_vec_c_vec_prod$') > 'A_b_vec_c_vec$').
% 12.19/2.86 tff(func_def_255, type, sK142: ('Nat$' * 'Nat_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_256, type, sK143: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_257, type, sK144: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_258, type, sK145: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_259, type, sK146: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_260, type, sK147: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_261, type, sK148: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_262, type, sK149: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_263, type, sK150: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_264, type, sK151: ('Nat$' * 'Nat$') > 'Nat$').
% 12.19/2.86 tff(func_def_265, type, sK152: 'Nat_nat_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_266, type, sK153: 'Nat_nat_fun$' > 'Nat$').
% 12.19/2.86 tff(func_def_267, type, sK154: ('Nat_a_b_vec_c_vec_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'A_c_vec_c_vec$').
% 12.19/2.86 tff(func_def_268, type, sK155: ('Nat_a_iarray_iarray_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_269, type, sK156: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 12.19/2.86 tff(func_def_270, type, sK157: ('A_b_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$') > 'Nat$').
% 12.19/2.86 tff(func_def_271, type, sK158: ('A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$') > 'Nat$').
% 12.19/2.86 tff(f1,conjecture,(
% 12.19/2.86 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture0)).
% 12.19/2.86
% 12.19/2.86 tff(f2,negated_conjecture,(
% 12.19/2.86 ~ 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 inference(negated_conjecture,[status(cth)],[f1])).
% 12.19/2.86
% 12.19/2.86 tff(f3,axiom,(
% 12.19/2.86 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum($sum('fun_app$b'('of_nat$','ka$'),1),1)))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 12.19/2.86
% 12.19/2.86 tff(f133,axiom,(
% 12.19/2.86 ! [X0 : 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : X0 = 'pair$'('fst$'(X0),'snd$'(X0))),
% 12.19/2.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131)).
% 12.19/2.86
% 12.19/2.86 tff(f136,axiom,(
% 12.19/2.86 ! [X0 : 'Nat_a_b_vec_c_vec_prod$'] : X0 = 'pair$a'('fst$a'(X0),'snd$a'(X0))),
% 12.19/2.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134)).
% 12.19/2.86
% 12.19/2.86 tff(f799,plain,(
% 12.19/2.86 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 12.19/2.86 introduced(definition,[],[tha_commutativity])).
% 12.19/2.86 tff(f800,plain,(
% 12.19/2.86 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2))) )),
% 12.19/2.86 introduced(definition,[],[tha_associativity])).
% 12.19/2.86 tff(f801,plain,(
% 12.19/2.86 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 12.19/2.86 introduced(definition,[],[tha_right_identity])).
% 12.19/2.86 tff(f802,plain,(
% 12.19/2.86 ( ! [X0 : $int,X1 : $int] : ($uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0))) )),
% 12.19/2.86 introduced(definition,[],[tha_inverse_op_op_inverses])).
% 12.19/2.86 tff(f803,plain,(
% 12.19/2.86 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 12.19/2.86 introduced(definition,[],[tha_inverse_op_unit])).
% 12.19/2.86 tff(f804,plain,(
% 12.19/2.86 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 12.19/2.86 introduced(definition,[],[tha_non-reflexivity])).
% 12.19/2.86 tff(f805,plain,(
% 12.19/2.86 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
% 12.19/2.86 introduced(definition,[],[tha_transitivity])).
% 12.19/2.86 tff(f806,plain,(
% 12.19/2.86 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 12.19/2.86 introduced(definition,[],[tha_order_totality])).
% 12.19/2.86 tff(f807,plain,(
% 12.19/2.86 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 12.19/2.86 introduced(definition,[],[tha_order_monotonicity])).
% 12.19/2.86 tff(f808,plain,(
% 12.19/2.86 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
% 12.19/2.86 introduced(definition,[],[tha_order_plus_one_dichotomy])).
% 12.19/2.86 tff(f809,plain,(
% 12.19/2.86 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 12.19/2.86 introduced(definition,[],[tha_minus_minus_x])).
% 12.19/2.86 tff(f810,plain,(
% 12.19/2.86 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
% 12.19/2.86 introduced(definition,[],[tha_extra_integer_ordering])).
% 12.19/2.86 tff(f811,plain,(
% 12.19/2.86 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 inference(flattening,[],[f2])).
% 12.19/2.86
% 12.19/2.86 tff(f1700,plain,(
% 12.19/2.86 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 inference(cnf_transformation,[],[f811])).
% 12.19/2.86
% 12.19/2.86 tff(f1701,plain,(
% 12.19/2.86 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum($sum('fun_app$b'('of_nat$','ka$'),1),1))))))),
% 12.19/2.86 inference(cnf_transformation,[],[f3])).
% 12.19/2.86
% 12.19/2.86 tff(f1886,plain,(
% 12.19/2.86 ( ! [X0 : 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : ('pair$'('fst$'(X0),'snd$'(X0)) = X0) )),
% 12.19/2.86 inference(cnf_transformation,[],[f133])).
% 12.19/2.86
% 12.19/2.86 tff(f1889,plain,(
% 12.19/2.86 ( ! [X0 : 'Nat_a_b_vec_c_vec_prod$'] : ('pair$a'('fst$a'(X0),'snd$a'(X0)) = X0) )),
% 12.19/2.86 inference(cnf_transformation,[],[f136])).
% 12.19/2.86
% 12.19/2.86 tcf(c_59,negated_conjecture,![X0_int:$int,X1_int:$int,X2_int:$int]:
% 12.19/2.86 ($sum($sum(X0_int,X1_int),X2_int) = $sum(X0_int,$sum(X1_int,X2_int))),
% 12.19/2.86 inference(cnf_transformation,[],[f800])).
% 12.19/2.86
% 12.19/2.86 tcf(c_60,negated_conjecture,![X0_int:$int,X1_int:$int]:
% 12.19/2.86 ($sum(X0_int,X1_int) = $sum(X1_int,X0_int)),
% 12.19/2.86 inference(cnf_transformation,[],[f799])).
% 12.19/2.86
% 12.19/2.86 tcf(c_61,negated_conjecture,
% 12.19/2.86 ('matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 12.19/2.86 inference(cnf_transformation,[],[f1700])).
% 12.19/2.86
% 12.19/2.86 tcf(c_62,negated_conjecture,
% 12.19/2.86 ('matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum($sum('fun_app$b'('of_nat$','ka$'),1),1))))))),
% 12.19/2.86 inference(cnf_transformation,[],[f1701])).
% 12.19/2.86
% 12.19/2.86 tcf(c_219,negated_conjecture,![X0_'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod':'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$']:
% 12.19/2.86 ('pair$'('fst$'(X0_'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod'),'snd$'(X0_'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod')) = X0_'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod'),
% 12.19/2.86 inference(cnf_transformation,[],[f1886])).
% 12.19/2.86
% 12.19/2.86 tcf(c_222,negated_conjecture,![X0_'Nat_a_b_vec_c_vec_prod':'Nat_a_b_vec_c_vec_prod$']:
% 12.19/2.86 ('pair$a'('fst$a'(X0_'Nat_a_b_vec_c_vec_prod'),'snd$a'(X0_'Nat_a_b_vec_c_vec_prod')) = X0_'Nat_a_b_vec_c_vec_prod'),
% 12.19/2.86 inference(cnf_transformation,[],[f1889])).
% 12.19/2.86
% 12.19/2.86 tcf(c_1282,negated_conjecture,
% 12.19/2.86 ('matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),
% 12.19/2.86 inference(theory_normalisation,[status(thm)],[c_61,c_59,c_60])).
% 12.19/2.86
% 12.19/2.86 tcf(c_1283,negated_conjecture,
% 12.19/2.86 ('matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,$sum(1,'fun_app$b'('of_nat$','ka$'))))))))),
% 12.19/2.86 inference(theory_normalisation,[status(thm)],[c_62,c_59,c_60])).
% 12.19/2.86
% 12.19/2.86 tcf(c_6582,plain,
% 12.19/2.86 ('matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,$sum(1,'fun_app$b'('of_nat$','ka$')))))))) != 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,$sum(1,'fun_app$b'('of_nat$','ka$'))))))))),
% 12.19/2.86 inference(demodulation,[status(thm)],[c_1282,c_222,c_219,c_1283])).
% 12.19/2.86
% 12.19/2.86 tcf(c_6583,plain,
% 12.19/2.86 ($false),
% 12.19/2.86 inference(equality_resolution_simp,[status(thm)],[c_6582])).
% 12.19/2.86
% 12.19/2.86
% 12.19/2.86 % SZS output end CNFRefutation for theBenchmark.p
% 12.19/2.86
% 12.19/2.86
%------------------------------------------------------------------------------