0.04/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_iprover 120 /export/starexec/sandbox2/benchmark/theBenchmark.p THM 0.11/0.33 % Computer : n005.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 960 0.11/0.33 % WCLimit : 120 0.11/0.33 % DateTime : Wed Jul 30 16:37:49 EDT 2025 0.11/0.33 % CPUTime : 0.41/0.61 Running TFA theorem proving 0.41/0.61 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core-casc.sh -l tptp -s tfa_schedule -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.41/0.61 0.41/0.61 % ======== iProver multi-core TPTP/SMT ========= 0.41/0.61 0.41/0.62 % Detected problem language: tptp 0.41/0.63 % Checking... 0.73/1.35 % Proving... 531.96/68.69 % SZS status Started for theBenchmark.p 531.96/68.69 % SZS status Theorem for theBenchmark.p 531.96/68.69 531.96/68.69 %---------------- iProver v3.9.3 (pre CASC 2025/SMT-COMP 2025) ----------------% 531.96/68.69 531.96/68.69 % ------ iProver source info 531.96/68.69 531.96/68.69 % git: date: 2025-07-21 10:15:00 +0000 531.96/68.69 % git: sha1: d7ebeb21b290b8724a1e08b4c4a533d26e8c009f 531.96/68.69 % git: non_committed_changes: true 531.96/68.69 531.96/68.69 % ------ Parsing... 531.96/68.69 % ------ Clausification by vclausify_rel & Parsing by iProver...% 531.96/68.69 % ------ Proving... 531.96/68.69 % ------ Problem Properties 531.96/68.69 531.96/68.69 % 531.96/68.69 % clauses 929 531.96/68.69 % conjectures 3 531.96/68.69 % EPR 292 531.96/68.69 % Horn 612 531.96/68.69 % unary 179 531.96/68.69 % binary 297 531.96/68.69 % lits 2290 531.96/68.69 % lits eq 320 531.96/68.69 % fd_pure 1 531.96/68.69 % fd_pseudo 0 531.96/68.69 % fd_cond 21 531.96/68.69 % fd_pseudo_cond 73 531.96/68.69 % AC symbols 1 531.96/68.69 531.96/68.69 % % ------ Input Options Time Limit: Unbounded 531.96/68.69 531.96/68.69 531.96/68.69 % % ------ 531.96/68.69 % Current options: 531.96/68.69 % ------ 531.96/68.69 531.96/68.69 531.96/68.69 % 531.96/68.69 531.96/68.69 % ------ Proving... 531.96/68.69 % 531.96/68.69 531.96/68.69 % SZS status Theorem for theBenchmark.p 531.96/68.69 531.96/68.69 % % SZS output start CNFRefutation for theBenchmark.p 531.96/68.69 531.96/68.69 tff(func_def_0, type, 'uua$': 'Int_int_bool_fun_fun$'). 531.96/68.69 tff(pred_def_1, type, 'less_eq$': ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > $o). 531.96/68.69 tff(pred_def_2, type, 'less$': ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > $o). 531.96/68.69 tff(pred_def_3, type, 'less$a': ('A_ltln_bool_fun$' * 'A_ltln_bool_fun$') > $o). 531.96/68.69 tff(pred_def_4, type, 'equivp$': 'A_ltln_a_ltln_bool_fun_fun$' > $o). 531.96/68.69 tff(pred_def_5, type, 'fun_app$': ('Int_bool_fun$' * $int) > $o). 531.96/68.69 tff(pred_def_6, type, 'member$': ('A_ltln$' * 'A_ltln_set$') > $o). 531.96/68.69 tff(pred_def_7, type, 'af_congruent$': 'A_ltln_a_ltln_bool_fun_fun$' > $o). 531.96/68.69 tff(pred_def_8, type, 'ltl_equivalence$': 'A_ltln_a_ltln_bool_fun_fun$' > $o). 531.96/68.69 tff(pred_def_9, type, 'fun_app$b': ('A_ltln_bool_fun$' * 'A_ltln$') > $o). 531.96/68.69 tff(pred_def_10, type, 'transition_functions$': ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$') > $o). 531.96/68.69 tff(pred_def_11, type, 'af_congruent_axioms$': 'A_ltln_a_ltln_bool_fun_fun$' > $o). 531.96/68.69 tff(pred_def_12, type, 'fun_app$l': ('Nat_bool_fun$' * 'Nat$') > $o). 531.96/68.69 tff(pred_def_13, type, 'fun_app$w': ('A_set_list_bool_fun$' * 'A_set_list$') > $o). 531.96/68.69 tff(pred_def_14, type, 'less_eq$a': ('A_ltln_bool_fun$' * 'A_ltln_bool_fun$') > $o). 531.96/68.69 tff(func_def_15, type, 'mu_LTL$': 'A_ltln_set$'). 531.96/68.69 tff(func_def_16, type, 'fun_app$d': ('A_set_list_a_ltln_fun$' * 'A_set_list$') > 'A_ltln$'). 531.96/68.69 tff(pred_def_17, type, sP0: ($int * $int * $int) > $o). 531.96/68.69 tff(pred_def_18, type, sP1: ($int * $int * $int) > $o). 531.96/68.69 tff(pred_def_19, type, sP2: ($int * $int * $int) > $o). 531.96/68.69 tff(func_def_20, type, 'collect$': 'A_ltln_bool_fun$' > 'A_ltln_set$'). 531.96/68.69 tff(func_def_21, type, 'fun_app$x': ('A_set_list_a_set_list_bool_fun_fun$' * 'A_set_list$') > 'A_set_list_bool_fun$'). 531.96/68.69 tff(func_def_22, type, 'fun_app$c': ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$') > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_23, type, 'fun_app$s': ('Int_int_fun$' * $int) > $int). 531.96/68.69 tff(func_def_24, type, tltrue: tlbool). 531.96/68.69 tff(func_def_25, type, 'af_letter_F$': 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$'). 531.96/68.69 tff(func_def_26, type, 'ltl_prop_equiv$': 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_27, type, 'ltl_const_equiv$': 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_28, type, 'fun_app$y': ('A_set_list_a_set_list_list_fun$' * 'A_set_list$') > 'A_set_list_list$'). 531.96/68.69 tff(func_def_29, type, 'eq$': 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_30, type, 'until_ltln$': 'A_ltln$' > 'A_ltln_a_ltln_fun$'). 531.96/68.69 tff(func_def_31, type, 'fun_app$j': ('A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$') > 'A_set_a_ltln_fun$'). 531.96/68.69 tff(func_def_32, type, 'foldl$': ('A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$') > 'A_set_list_a_ltln_fun$'). 531.96/68.69 tff(func_def_33, type, 'ltl_lang_equiv$': 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_34, type, 'fun_app$u': ('A_ltln_a_ltln_bool_fun_fun_int_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > $int). 531.96/68.69 tff(func_def_35, type, 'fun_app$k': ('A_set_list_a_set_list_fun$' * 'A_set_list$') > 'A_set_list$'). 531.96/68.69 tff(func_def_36, type, 'fun_app$e': ('A_ltln_a_ltln_fun$' * 'A_ltln$') > 'A_ltln$'). 531.96/68.69 tff(func_def_37, type, 'true_ltln$': 'A_ltln$'). 531.96/68.69 tff(func_def_38, type, 'fun_app$o': ('A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_39, type, 'ltl_prop_implies$': 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_40, type, 'semantics_ltln$': 'Nat_a_set_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_41, type, 'n_lists$': 'Nat$' > 'A_set_list_a_set_list_list_fun$'). 531.96/68.69 tff(func_def_42, type, tlfalse: tlbool). 531.96/68.69 tff(func_def_43, type, 'fun_app$ab': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$'). 531.96/68.69 tff(func_def_44, type, 'fun_app$v': ('A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_45, type, 'nat$': $int > 'Nat$'). 531.96/68.69 tff(func_def_46, type, 'fun_app$q': ('A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' * 'A_ltln_bool_fun$') > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_47, type, 'fun_app$aa': ('Nat_a_ltln_a_ltln_bool_fun_fun_fun$' * 'Nat$') > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_48, type, 'nu_LTL$': 'A_ltln_set$'). 531.96/68.69 tff(func_def_49, type, 'fun_app$n': ('Int_a_ltln_bool_fun_fun$' * $int) > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_50, type, 'fun_app$z': ('Nat_a_set_fun$' * 'Nat$') > 'A_set$'). 531.96/68.69 tff(func_def_51, type, 'fun_app$r': ('A_ltln_bool_fun_a_ltln_bool_fun_fun$' * 'A_ltln_bool_fun$') > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_52, type, 'subsequence$': ('Nat_a_set_fun$' * 'Nat$') > 'Nat_a_set_list_fun$'). 531.96/68.69 tff(func_def_53, type, 'fun_app$t': ('Int_a_ltln_a_ltln_bool_fun_fun_fun$' * $int) > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_54, type, 'af_letter_G$': 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$'). 531.96/68.69 tff(func_def_55, type, 'fun_app$i': ('A_set_a_ltln_fun$' * 'A_set$') > 'A_ltln$'). 531.96/68.69 tff(func_def_56, type, 'release_ltln$': 'A_ltln$' > 'A_ltln_a_ltln_fun$'). 531.96/68.69 tff(func_def_57, type, 'phi$': 'A_ltln$'). 531.96/68.69 tff(func_def_62, type, sK3: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_63, type, sK4: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_64, type, sK5: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_65, type, sK6: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_66, type, sK7: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_67, type, sK8: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_68, type, sK9: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_69, type, sK10: 'A_set_list_list$' > 'A_set$'). 531.96/68.69 tff(func_def_70, type, sK11: 'A_set_list_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_71, type, sK12: 'A_set_list_list$' > 'A_set_list_list$'). 531.96/68.69 tff(func_def_72, type, sK13: 'A_set_list_list$' > 'A_set_list_list$'). 531.96/68.69 tff(func_def_73, type, sK14: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_74, type, sK15: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_75, type, sK16: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_76, type, sK17: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_77, type, sK18: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_78, type, sK19: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_79, type, sK20: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_80, type, sK21: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_81, type, sK22: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_82, type, sK23: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_83, type, sK24: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$'). 531.96/68.69 tff(func_def_84, type, sK25: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$'). 531.96/68.69 tff(func_def_85, type, sK26: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_86, type, sK27: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_87, type, sK28: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_88, type, sK29: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_89, type, sK30: 'Nat_int_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_90, type, sK31: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_91, type, sK32: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_92, type, sK33: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln$'). 531.96/68.69 tff(func_def_93, type, sK34: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln$'). 531.96/68.69 tff(func_def_94, type, sK35: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_95, type, sK36: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_96, type, sK37: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_97, type, sK38: $int > $int). 531.96/68.69 tff(func_def_98, type, sK39: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_99, type, sK40: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_100, type, sK41: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_101, type, sK42: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_102, type, sK43: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_103, type, sK44: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_104, type, sK45: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_105, type, sK46: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_106, type, sK47: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_107, type, sK48: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_108, type, sK49: ('A_ltln_bool_fun$' * 'A_ltln_bool_fun$') > 'A_ltln$'). 531.96/68.69 tff(func_def_109, type, sK50: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_110, type, sK51: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_111, type, sK52: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_112, type, sK53: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_113, type, sK54: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_114, type, sK55: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_115, type, sK56: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_116, type, sK57: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_117, type, sK58: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_118, type, sK59: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_119, type, sK60: ('Nat_bool_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_120, type, sK61: 'Nat_bool_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_121, type, sK62: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_122, type, sK63: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_123, type, sK64: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_124, type, sK65: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_125, type, sK66: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_126, type, sK67: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_127, type, sK68: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_128, type, sK69: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_129, type, sK70: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_130, type, sK71: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_131, type, sK72: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_132, type, sK73: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_133, type, sK74: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_134, type, sK75: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_135, type, sK76: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_136, type, sK77: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_137, type, sK78: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_138, type, sK79: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_139, type, sK80: 'A_set_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_140, type, sK81: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_141, type, sK82: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_142, type, sK83: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_143, type, sK84: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_144, type, sK85: 'A_set_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_145, type, sK86: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_146, type, sK87: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln$'). 531.96/68.69 tff(func_def_147, type, sK88: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_148, type, sK89: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_149, type, sK90: ('A_set_list$' * 'A_ltln$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_150, type, sK91: ('A_set_list$' * 'A_ltln$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_151, type, sK92: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_152, type, sK93: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_153, type, sK94: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_154, type, sK95: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_155, type, sK96: ('A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_156, type, sK97: ('A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_157, type, sK98: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$'). 531.96/68.69 tff(func_def_158, type, sK99: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$'). 531.96/68.69 tff(func_def_159, type, sK100: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_160, type, sK101: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_161, type, sK102: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_162, type, sK103: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_163, type, sK104: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_164, type, sK105: ('A_set_list$' * 'A_set_list$' * 'A_set_list$' * 'A_set_list$') > 'A_set_list$'). 531.96/68.69 tff(func_def_165, type, sK106: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_166, type, sK107: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_167, type, sK108: 'Nat_int_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_168, type, sK109: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_169, type, sK110: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_170, type, sK111: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_171, type, sK112: 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_172, type, sK113: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_173, type, sK114: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_174, type, sK115: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_175, type, sK116: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_176, type, sK117: 'Nat_nat_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_177, type, sK118: 'Nat_nat_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_178, type, sK119: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_179, type, sK120: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_180, type, sK121: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_181, type, sK122: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_182, type, sK123: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_183, type, sK124: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_184, type, sK125: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_185, type, sK126: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_186, type, sK127: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_187, type, sK128: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_188, type, sK129: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_189, type, sK130: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_190, type, sK131: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_191, type, sK132: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_192, type, sK133: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_193, type, sK134: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_194, type, sK135: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_195, type, sK136: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_196, type, sK137: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_197, type, sK138: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_198, type, sK139: 'A_set_list_a_set_list_bool_fun_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_199, type, sK140: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_200, type, sK141: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_201, type, sK142: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_202, type, sK143: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_203, type, sK144: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_204, type, sK145: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_205, type, sK146: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_206, type, sK147: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_207, type, sK148: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_208, type, sK149: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_209, type, sK150: ('A_set_list$' * 'A_ltln$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_210, type, sK151: ('A_set_list$' * 'A_ltln$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_211, type, sK152: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_212, type, sK153: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_213, type, sK154: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_214, type, sK155: 'Nat_bool_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_215, type, sK156: ('Nat_bool_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_216, type, sK157: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_217, type, sK158: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_218, type, sK159: 'Nat$'). 531.96/68.69 tff(func_def_219, type, sK160: 'Nat$'). 531.96/68.69 tff(func_def_220, type, sK161: 'A_set_list_bool_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_221, type, sK162: 'A_set_list_bool_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_222, type, sK163: 'A_set_list_bool_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_223, type, sK164: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_224, type, sK165: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_225, type, sK166: 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_226, type, sK167: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_227, type, sK168: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_228, type, sK169: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_229, type, sK170: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_230, type, sK171: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_231, type, sK172: ('A_ltln$' * 'A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_232, type, sK173: ('A_ltln$' * 'A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_233, type, sK174: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_234, type, sK175: 'A_set_list_bool_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_235, type, sK176: 'A_set_list_bool_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_236, type, sK177: 'A_set_list_bool_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_237, type, sK178: 'A_set_list_bool_fun$' > 'A_set$'). 531.96/68.69 tff(func_def_238, type, sK179: 'A_set_list_bool_fun$' > 'A_set_list$'). 531.96/68.69 tff(func_def_239, type, sK180: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_240, type, sK181: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_241, type, sK182: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_242, type, sK183: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_243, type, sK184: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_244, type, sK185: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_245, type, sK186: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_246, type, sK187: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_247, type, sK188: 'A_set_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_248, type, sK189: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_249, type, sK190: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_250, type, sK191: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_251, type, sK192: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_252, type, sK193: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_253, type, sK194: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_254, type, sK195: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_255, type, sK196: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_256, type, sK197: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_257, type, sK198: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_258, type, sK199: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_259, type, sK200: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_260, type, sK201: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_261, type, sK202: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_262, type, sK203: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_263, type, sK204: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_264, type, sK205: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_265, type, sK206: 'Int_int_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_266, type, sK207: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_267, type, sK208: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_268, type, sK209: 'Nat_bool_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_269, type, sK210: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_270, type, sK211: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_271, type, sK212: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_272, type, sK213: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_273, type, sK214: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_274, type, sK215: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_275, type, sK216: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_276, type, sK217: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_277, type, sK218: 'A_set_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_278, type, sK219: ('Nat$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_279, type, sK220: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_280, type, sK221: 'A_ltln_bool_fun_int_fun$' > 'A_ltln_bool_fun$'). 531.96/68.69 tff(func_def_281, type, sK222: ('Nat$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_282, type, sK223: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_283, type, sK224: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_284, type, sK225: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_285, type, sK226: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_286, type, sK227: 'A_set_list$' > 'A_set$'). 531.96/68.69 tff(func_def_287, type, sK228: 'A_set_list$' > 'A_set_list$'). 531.96/68.69 tff(func_def_288, type, sK229: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_289, type, sK230: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_290, type, sK231: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_291, type, sK232: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_292, type, sK233: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_293, type, sK234: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$') > 'A_ltln$'). 531.96/68.69 tff(func_def_294, type, sK235: 'Nat$' > 'Nat$'). 531.96/68.69 tff(func_def_295, type, sK236: 'Nat$'). 531.96/68.69 tff(func_def_296, type, sK237: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_297, type, sK238: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_298, type, sK239: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_299, type, sK240: ('A_ltln$' * 'A_ltln$') > 'Nat_a_set_fun$'). 531.96/68.69 tff(func_def_300, type, sK241: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_301, type, sK242: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_302, type, sK243: 'Nat_int_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_303, type, sK244: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_304, type, sK245: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_305, type, sK246: ('A_ltln$' * 'A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_306, type, sK247: ('A_ltln$' * 'A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_307, type, sK248: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_308, type, sK249: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_309, type, sK250: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_310, type, sK251: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_311, type, sK252: ('A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_312, type, sK253: ('A_set_list$' * 'A_ltln$') > 'A_set_list$'). 531.96/68.69 tff(func_def_313, type, sK254: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_314, type, sK255: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_315, type, sK256: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_316, type, sK257: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_317, type, sK258: 'Nat_nat_bool_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_318, type, sK259: 'Nat_nat_bool_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_319, type, sK260: 'Nat_nat_bool_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_320, type, sK261: 'Nat_nat_bool_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_321, type, sK262: 'Nat_nat_bool_fun_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_322, type, sK263: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_323, type, sK264: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_324, type, sK265: ('A_set$' * 'A_set_list$' * 'A_set_list$' * 'A_set_list$') > 'A_set_list$'). 531.96/68.69 tff(func_def_325, type, sK266: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_326, type, sK267: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int). 531.96/68.69 tff(func_def_327, type, sK268: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_328, type, sK269: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_329, type, sK270: 'Nat_bool_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_330, type, sK271: 'Nat_bool_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_331, type, sK272: ('Nat_bool_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_332, type, sK273: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_333, type, sK274: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_334, type, sK275: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_335, type, sK276: ('A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_336, type, sK277: 'Nat_int_fun$' > 'Nat$'). 531.96/68.69 tff(func_def_337, type, sK278: ('A_ltln$' * 'Nat_a_set_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_338, type, sK279: ('A_ltln$' * 'Nat_a_set_fun$' * 'Nat$') > 'Nat$'). 531.96/68.69 tff(func_def_339, type, sK280: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_340, type, sK281: ('Nat$' * 'Nat_bool_fun$') > 'Nat$'). 531.96/68.69 tff(func_def_341, type, sK282: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_342, type, sK283: 'Int_a_ltln_bool_fun_fun$' > $int). 531.96/68.69 tff(func_def_343, type, sK284: $int > $int). 531.96/68.69 tff(func_def_344, type, sK285: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_345, type, sK286: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$'). 531.96/68.69 tff(func_def_346, type, sK287: ('A_set_list$' * 'A_set_list$' * 'A_set$' * 'A_set_list$') > 'A_set_list$'). 531.96/68.69 tff(func_def_347, type, sK288: 'Int_int_fun$' > $int). 531.96/68.69 tff(func_def_348, type, sK289: 'Int_int_fun$' > $int). 531.96/68.69 tff(f19,axiom,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$',X2 : 'A_ltln$',X3 : 'A_ltln$'] : (('less_eq$'(X0,X1) & 'fun_app$b'('fun_app$c'(X0,X2),X3)) => 'fun_app$b'('fun_app$c'(X1,X2),X3))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361)). 531.96/68.69 531.96/68.69 tff(f25,axiom,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : (('member$'(X1,'nu_LTL$') & 'ltl_equivalence$'(X0)) => ('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) <=> ? [X3 : 'Nat$'] : ! [X4 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128)). 531.96/68.69 531.96/68.69 tff(f89,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ('member$'(X0,'nu_LTL$') => ('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) <=> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134)). 531.96/68.69 531.96/68.69 tff(f118,axiom,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'A_ltln$',X3 : 'A_ltln_a_ltln_bool_fun_fun$'] : (('less_eq$'(X0,X3) & 'fun_app$b'('fun_app$c'(X0,X1),X2)) => 'fun_app$b'('fun_app$c'(X3,X1),X2))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360)). 531.96/68.69 531.96/68.69 tff(f156,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$')) => ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$'))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12)). 531.96/68.69 531.96/68.69 tff(f183,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$',X2 : 'A_ltln$'] : (('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) & 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X2)) => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358)). 531.96/68.69 531.96/68.69 tff(f220,axiom,( 531.96/68.69 'member$'('phi$','nu_LTL$')), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9)). 531.96/68.69 531.96/68.69 tff(f271,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') => ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$')))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13)). 531.96/68.69 531.96/68.69 tff(f314,conjecture,( 531.96/68.69 ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') <=> ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$'))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture2)). 531.96/68.69 531.96/68.69 tff(f315,negated_conjecture,( 531.96/68.69 ~(? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') <=> ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$')))), 531.96/68.69 inference(negated_conjecture,[status(cth)],[f314])). 531.96/68.69 531.96/68.69 tff(f377,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('eq$',X0),X1) => 'fun_app$b'('fun_app$c'('eq$',X1),X0))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4)). 531.96/68.69 531.96/68.69 tff(f434,axiom,( 531.96/68.69 'ltl_equivalence$'('ltl_lang_equiv$')), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479)). 531.96/68.69 531.96/68.69 tff(f446,axiom,( 531.96/68.69 ! [X0 : 'Nat_a_set_fun$'] : ('fun_app$b'('semantics_ltln$'(X0),'false_ltln$') <=> $false)), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143)). 531.96/68.69 531.96/68.69 tff(f509,axiom,( 531.96/68.69 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) <=> ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92)). 531.96/68.69 531.96/68.69 tff(f518,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X0))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356)). 531.96/68.69 531.96/68.69 tff(f519,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : (! [X2 : 'Nat_a_set_fun$'] : ('fun_app$b'('semantics_ltln$'(X2),X1) <=> 'fun_app$b'('semantics_ltln$'(X2),X0)) <=> 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476)). 531.96/68.69 531.96/68.69 tff(f558,axiom,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ('member$'(X0,'nu_LTL$') => ('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) <=> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112)). 531.96/68.69 531.96/68.69 tff(f595,axiom,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : (X0 = X1 <=> ('less_eq$'(X1,X0) & 'less_eq$'(X0,X1)))), 531.96/68.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269)). 531.96/68.69 531.96/68.69 tff(f802,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$')) => ? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$'))), 531.96/68.69 inference(rectify,[],[f156])). 531.96/68.69 531.96/68.69 tff(f821,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') => ? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$')))), 531.96/68.69 inference(rectify,[],[f271])). 531.96/68.69 531.96/68.69 tff(f824,plain,( 531.96/68.69 ~(? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') <=> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) => ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$')))), 531.96/68.69 inference(rectify,[],[f315])). 531.96/68.69 531.96/68.69 tff(f850,plain,( 531.96/68.69 ! [X0 : 'Nat_a_set_fun$'] : ~'fun_app$b'('semantics_ltln$'(X0),'false_ltln$')), 531.96/68.69 inference(true_and_false_elimination,[],[f446])). 531.96/68.69 531.96/68.69 tff(f851,plain,( 531.96/68.69 ! [X0 : 'Nat_a_set_fun$'] : ~'fun_app$b'('semantics_ltln$'(X0),'false_ltln$')), 531.96/68.69 inference(flattening,[],[f850])). 531.96/68.69 531.96/68.69 tff(f912,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$',X2 : 'A_ltln$',X3 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'(X1,X2),X3) | (~'less_eq$'(X0,X1) | ~'fun_app$b'('fun_app$c'(X0,X2),X3)))), 531.96/68.69 inference(ennf_transformation,[],[f19])). 531.96/68.69 531.96/68.69 tff(f913,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$',X2 : 'A_ltln$',X3 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'(X1,X2),X3) | ~'less_eq$'(X0,X1) | ~'fun_app$b'('fun_app$c'(X0,X2),X3))), 531.96/68.69 inference(flattening,[],[f912])). 531.96/68.69 531.96/68.69 tff(f921,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) <=> ? [X3 : 'Nat$'] : ! [X4 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')) | (~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0)))), 531.96/68.69 inference(ennf_transformation,[],[f25])). 531.96/68.69 531.96/68.69 tff(f922,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) <=> ? [X3 : 'Nat$'] : ! [X4 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')) | ~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0))), 531.96/68.69 inference(flattening,[],[f921])). 531.96/68.69 531.96/68.69 tff(f980,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) <=> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(ennf_transformation,[],[f89])). 531.96/68.69 531.96/68.69 tff(f1007,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'A_ltln$',X3 : 'A_ltln_a_ltln_bool_fun_fun$'] : ('fun_app$b'('fun_app$c'(X3,X1),X2) | (~'less_eq$'(X0,X3) | ~'fun_app$b'('fun_app$c'(X0,X1),X2)))), 531.96/68.69 inference(ennf_transformation,[],[f118])). 531.96/68.69 531.96/68.69 tff(f1008,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'A_ltln$',X3 : 'A_ltln_a_ltln_bool_fun_fun$'] : ('fun_app$b'('fun_app$c'(X3,X1),X2) | ~'less_eq$'(X0,X3) | ~'fun_app$b'('fun_app$c'(X0,X1),X2))), 531.96/68.69 inference(flattening,[],[f1007])). 531.96/68.69 531.96/68.69 tff(f1046,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') & $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))))), 531.96/68.69 inference(ennf_transformation,[],[f802])). 531.96/68.69 531.96/68.69 tff(f1070,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$',X2 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2) | (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X2)))), 531.96/68.69 inference(ennf_transformation,[],[f183])). 531.96/68.69 531.96/68.69 tff(f1071,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$',X2 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X2))), 531.96/68.69 inference(flattening,[],[f1070])). 531.96/68.69 531.96/68.69 tff(f1155,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$'))), 531.96/68.69 inference(ennf_transformation,[],[f821])). 531.96/68.69 531.96/68.69 tff(f1203,plain,( 531.96/68.69 ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') <~> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)))), 531.96/68.69 inference(ennf_transformation,[],[f824])). 531.96/68.69 531.96/68.69 tff(f1253,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('eq$',X1),X0) | ~'fun_app$b'('fun_app$c'('eq$',X0),X1))), 531.96/68.69 inference(ennf_transformation,[],[f377])). 531.96/68.69 531.96/68.69 tff(f1397,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X0) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1))), 531.96/68.69 inference(ennf_transformation,[],[f518])). 531.96/68.69 531.96/68.69 tff(f1435,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) <=> ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(ennf_transformation,[],[f558])). 531.96/68.69 531.96/68.69 tff(f1523,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) | ! [X3 : 'Nat$'] : ? [X4 : 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')) & (? [X3 : 'Nat$'] : ! [X4 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))))) | ~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0))), 531.96/68.69 inference(nnf_transformation,[],[f922])). 531.96/68.69 531.96/68.69 tff(f1524,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) | ! [X3 : 'Nat$'] : ? [X4 : 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')) & (? [X5 : 'Nat$'] : ! [X6 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X5),X6))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))))) | ~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0))), 531.96/68.69 inference(rectify,[],[f1523])). 531.96/68.69 531.96/68.69 tff(f1525,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$',X3 : 'Nat$'] : (? [X4 : 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$') => 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),sK14(X0,X1,X2,X3)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1526,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : (? [X5 : 'Nat$'] : ! [X6 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X5),X6))),'false_ltln$') => ! [X6 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,sK15(X0,X1,X2)),X6))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1527,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X2 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) | ! [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),sK14(X0,X1,X2,X3)))),'false_ltln$')) & (! [X6 : 'Nat$'] : ~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,sK15(X0,X1,X2)),X6))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))))) | ~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f1524,f1526,f1525])). 531.96/68.69 531.96/68.69 tff(f1577,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) & (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(nnf_transformation,[],[f980])). 531.96/68.69 531.96/68.69 tff(f1578,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) & (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(rectify,[],[f1577])). 531.96/68.69 531.96/68.69 tff(f1579,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X2 : 'Nat$'] : (? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK41(X0,X1,X2)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1580,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') => ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK42(X0,X1)),X5))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1581,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK41(X0,X1,X2)))),'false_ltln$')) & (! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK42(X0,X1)),X5))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f1578,f1580,f1579])). 531.96/68.69 531.96/68.69 tff(f1650,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') | ! [X4 : 'Nat$'] : ? [X5 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') & $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))))), 531.96/68.69 inference(rectify,[],[f1046])). 531.96/68.69 531.96/68.69 tff(f1651,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') => ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK71(X0,X1)),X3))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1652,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X4 : 'Nat$'] : (? [X5 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') & $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))) => ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),sK72(X0,X1,X4)))),'false_ltln$') & $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',sK72(X0,X1,X4)))))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1653,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK71(X0,X1)),X3))),'false_ltln$') | ! [X4 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),sK72(X0,X1,X4)))),'false_ltln$') & $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',sK72(X0,X1,X4)))))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f1650,f1652,f1651])). 531.96/68.69 531.96/68.69 tff(f1759,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))) | ! [X4 : 'Nat$'] : ? [X5 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$'))), 531.96/68.69 inference(rectify,[],[f1155])). 531.96/68.69 531.96/68.69 tff(f1760,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))) => ! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK128(X0,X1)),'fun_app$g'('of_nat$',X3))))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1761,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X4 : 'Nat$'] : (? [X5 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),sK129(X0,X1,X4)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1762,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK128(X0,X1)),'fun_app$g'('of_nat$',X3))) | ! [X4 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),sK129(X0,X1,X4)))),'false_ltln$'))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129])],[f1759,f1761,f1760])). 531.96/68.69 531.96/68.69 tff(f1804,plain,( 531.96/68.69 (! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$') & $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))) | ! [X0 : 'Nat$'] : ? [X1 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')) & (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))) | ? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$'))), 531.96/68.69 inference(nnf_transformation,[],[f1203])). 531.96/68.69 531.96/68.69 tff(f1805,plain,( 531.96/68.69 (! [X0 : 'Nat$'] : ? [X1 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$') & $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),X3))),'false_ltln$')) & (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))) | ? [X6 : 'Nat$'] : ! [X7 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X6),X7))),'false_ltln$'))), 531.96/68.69 inference(rectify,[],[f1804])). 531.96/68.69 531.96/68.69 tff(f1806,plain,( 531.96/68.69 ! [X0 : 'Nat$'] : (? [X1 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$') & $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1))) => ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0)))),'false_ltln$') & $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',sK157(X0)))))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1807,plain,( 531.96/68.69 ! [X2 : 'Nat$'] : (? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),X3))),'false_ltln$') => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),sK158(X2)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1808,plain,( 531.96/68.69 ? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))) => ! [X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',X5)))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1809,plain,( 531.96/68.69 ? [X6 : 'Nat$'] : ! [X7 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X6),X7))),'false_ltln$') => ! [X7 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X7))),'false_ltln$')), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1810,plain,( 531.96/68.69 (! [X0 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0)))),'false_ltln$') & $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',sK157(X0)))) | ! [X2 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),sK158(X2)))),'false_ltln$')) & (! [X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',X5))) | ! [X7 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X7))),'false_ltln$'))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK157,sK158,sK159,sK160])],[f1805,f1809,f1808,f1807,f1806])). 531.96/68.69 531.96/68.69 tff(f1966,plain,( 531.96/68.69 ('fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) | ! [X0 : 'Nat$'] : ? [X1 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')) & (? [X0 : 'Nat$'] : ! [X1 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))))), 531.96/68.69 inference(nnf_transformation,[],[f509])). 531.96/68.69 531.96/68.69 tff(f1967,plain,( 531.96/68.69 ('fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) | ! [X0 : 'Nat$'] : ? [X1 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')) & (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),X3))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))))), 531.96/68.69 inference(rectify,[],[f1966])). 531.96/68.69 531.96/68.69 tff(f1968,plain,( 531.96/68.69 ! [X0 : 'Nat$'] : (? [X1 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') => 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK235(X0)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1969,plain,( 531.96/68.69 ? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),X3))),'false_ltln$') => ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK236),X3))),'false_ltln$')), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1970,plain,( 531.96/68.69 ('fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) | ! [X0 : 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK235(X0)))),'false_ltln$')) & (! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK236),X3))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK235,sK236])],[f1967,f1969,f1968])). 531.96/68.69 531.96/68.69 tff(f1986,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ((! [X2 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X2),X1) | ~'fun_app$b'('semantics_ltln$'(X2),X0)) & ('fun_app$b'('semantics_ltln$'(X2),X0) | ~'fun_app$b'('semantics_ltln$'(X2),X1))) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1)) & ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ? [X2 : 'Nat_a_set_fun$'] : ((~'fun_app$b'('semantics_ltln$'(X2),X0) | ~'fun_app$b'('semantics_ltln$'(X2),X1)) & ('fun_app$b'('semantics_ltln$'(X2),X0) | 'fun_app$b'('semantics_ltln$'(X2),X1)))))), 531.96/68.69 inference(nnf_transformation,[],[f519])). 531.96/68.69 531.96/68.69 tff(f1987,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ((! [X2 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X2),X1) | ~'fun_app$b'('semantics_ltln$'(X2),X0)) & ('fun_app$b'('semantics_ltln$'(X2),X0) | ~'fun_app$b'('semantics_ltln$'(X2),X1))) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1)) & ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ? [X3 : 'Nat_a_set_fun$'] : ((~'fun_app$b'('semantics_ltln$'(X3),X0) | ~'fun_app$b'('semantics_ltln$'(X3),X1)) & ('fun_app$b'('semantics_ltln$'(X3),X0) | 'fun_app$b'('semantics_ltln$'(X3),X1)))))), 531.96/68.69 inference(rectify,[],[f1986])). 531.96/68.69 531.96/68.69 tff(f1988,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : (? [X3 : 'Nat_a_set_fun$'] : ((~'fun_app$b'('semantics_ltln$'(X3),X0) | ~'fun_app$b'('semantics_ltln$'(X3),X1)) & ('fun_app$b'('semantics_ltln$'(X3),X0) | 'fun_app$b'('semantics_ltln$'(X3),X1))) => ((~'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X0) | ~'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X1)) & ('fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X0) | 'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X1))))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f1989,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ((! [X2 : 'Nat_a_set_fun$'] : (('fun_app$b'('semantics_ltln$'(X2),X1) | ~'fun_app$b'('semantics_ltln$'(X2),X0)) & ('fun_app$b'('semantics_ltln$'(X2),X0) | ~'fun_app$b'('semantics_ltln$'(X2),X1))) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1)) & ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ((~'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X0) | ~'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X1)) & ('fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X0) | 'fun_app$b'('semantics_ltln$'(sK240(X0,X1)),X1)))))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK240])],[f1987,f1988])). 531.96/68.69 531.96/68.69 tff(f2023,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) & (? [X2 : 'Nat$'] : ! [X3 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(nnf_transformation,[],[f1435])). 531.96/68.69 531.96/68.69 tff(f2024,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : ? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')) & (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(rectify,[],[f2023])). 531.96/68.69 531.96/68.69 tff(f2025,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X2 : 'Nat$'] : (? [X3 : 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') => 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK263(X0,X1,X2)))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f2026,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : (? [X4 : 'Nat$'] : ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') => ! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK264(X0,X1)),X5))),'false_ltln$'))), 531.96/68.69 introduced(choice_axiom,[])). 531.96/68.69 531.96/68.69 tff(f2027,plain,( 531.96/68.69 ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ((('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ! [X2 : 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK263(X0,X1,X2)))),'false_ltln$')) & (! [X5 : 'Nat$'] : ~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK264(X0,X1)),X5))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))))) | ~'member$'(X0,'nu_LTL$'))), 531.96/68.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK263,sK264])],[f2024,f2026,f2025])). 531.96/68.69 531.96/68.69 tff(f2055,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : ((X0 = X1 | (~'less_eq$'(X1,X0) | ~'less_eq$'(X0,X1))) & (('less_eq$'(X1,X0) & 'less_eq$'(X0,X1)) | X0 != X1))), 531.96/68.69 inference(nnf_transformation,[],[f595])). 531.96/68.69 531.96/68.69 tff(f2056,plain,( 531.96/68.69 ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : ((X0 = X1 | ~'less_eq$'(X1,X0) | ~'less_eq$'(X0,X1)) & (('less_eq$'(X1,X0) & 'less_eq$'(X0,X1)) | X0 != X1))), 531.96/68.69 inference(flattening,[],[f2055])). 531.96/68.69 531.96/68.69 tff(f2118,plain,( 531.96/68.69 ( ! [X2 : 'A_ltln$',X3 : 'A_ltln$',X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : ('fun_app$b'('fun_app$c'(X1,X2),X3) | ~'less_eq$'(X0,X1) | ~'fun_app$b'('fun_app$c'(X0,X2),X3)) )), 531.96/68.69 inference(cnf_transformation,[],[f913])). 531.96/68.69 531.96/68.69 tff(f2126,plain,( 531.96/68.69 ( ! [X2 : 'Nat_a_set_fun$',X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$',X6 : 'Nat$'] : (~'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,sK15(X0,X1,X2)),X6))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) | ~'member$'(X1,'nu_LTL$') | ~'ltl_equivalence$'(X0)) )), 531.96/68.69 inference(cnf_transformation,[],[f1527])). 531.96/68.69 531.96/68.69 tff(f2221,plain,( 531.96/68.69 ( ! [X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK42(X0,X1)),X5))),'false_ltln$') | ~'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | ~'member$'(X0,'nu_LTL$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1581])). 531.96/68.69 531.96/68.69 tff(f2274,plain,( 531.96/68.69 ( ! [X2 : 'A_ltln$',X3 : 'A_ltln_a_ltln_bool_fun_fun$',X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'(X3,X1),X2) | ~'less_eq$'(X0,X3) | ~'fun_app$b'('fun_app$c'(X0,X1),X2)) )), 531.96/68.69 inference(cnf_transformation,[],[f1008])). 531.96/68.69 531.96/68.69 tff(f2334,plain,( 531.96/68.69 ( ! [X3 : 'Nat$',X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X4 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK71(X0,X1)),X3))),'false_ltln$') | $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',sK72(X0,X1,X4)))) )), 531.96/68.69 inference(cnf_transformation,[],[f1653])). 531.96/68.69 531.96/68.69 tff(f2335,plain,( 531.96/68.69 ( ! [X3 : 'Nat$',X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X4 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK71(X0,X1)),X3))),'false_ltln$') | 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),sK72(X0,X1,X4)))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1653])). 531.96/68.69 531.96/68.69 tff(f2378,plain,( 531.96/68.69 ( ! [X2 : 'A_ltln$',X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X2)) )), 531.96/68.69 inference(cnf_transformation,[],[f1071])). 531.96/68.69 531.96/68.69 tff(f2446,plain,( 531.96/68.69 'member$'('phi$','nu_LTL$')), 531.96/68.69 inference(cnf_transformation,[],[f220])). 531.96/68.69 531.96/68.69 tff(f2513,plain,( 531.96/68.69 ( ! [X3 : 'Nat$',X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$',X4 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK128(X0,X1)),'fun_app$g'('of_nat$',X3)) | 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),sK129(X0,X1,X4)))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1762])). 531.96/68.69 531.96/68.69 tff(f2582,plain,( 531.96/68.69 ( ! [X7 : 'Nat$',X5 : 'Nat$'] : (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X5))),'false_ltln$') | ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',X5)) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X7))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1810])). 531.96/68.69 531.96/68.69 tff(f2583,plain,( 531.96/68.69 ( ! [X2 : 'Nat$',X0 : 'Nat$'] : ($less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',sK157(X0))) | 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),sK158(X2)))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1810])). 531.96/68.69 531.96/68.69 tff(f2584,plain,( 531.96/68.69 ( ! [X2 : 'Nat$',X0 : 'Nat$'] : ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0)))),'false_ltln$') | 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X2),sK158(X2)))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1810])). 531.96/68.69 531.96/68.69 tff(f2677,plain,( 531.96/68.69 ( ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('eq$',X1),X0) | ~'fun_app$b'('fun_app$c'('eq$',X0),X1)) )), 531.96/68.69 inference(cnf_transformation,[],[f1253])). 531.96/68.69 531.96/68.69 tff(f2756,plain,( 531.96/68.69 'ltl_equivalence$'('ltl_lang_equiv$')), 531.96/68.69 inference(cnf_transformation,[],[f434])). 531.96/68.69 531.96/68.69 tff(f2772,plain,( 531.96/68.69 ( ! [X0 : 'Nat_a_set_fun$'] : (~'fun_app$b'('semantics_ltln$'(X0),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f851])). 531.96/68.69 531.96/68.69 tff(f2877,plain,( 531.96/68.69 ( ! [X0 : 'Nat$'] : ('fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) | 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK235(X0)))),'false_ltln$')) )), 531.96/68.69 inference(cnf_transformation,[],[f1970])). 531.96/68.69 531.96/68.69 tff(f2894,plain,( 531.96/68.69 ( ! [X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X0) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1)) )), 531.96/68.69 inference(cnf_transformation,[],[f1397])). 531.96/68.69 531.96/68.69 tff(f2898,plain,( 531.96/68.69 ( ! [X2 : 'Nat_a_set_fun$',X0 : 'A_ltln$',X1 : 'A_ltln$'] : ('fun_app$b'('semantics_ltln$'(X2),X1) | ~'fun_app$b'('semantics_ltln$'(X2),X0) | ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X1)) )), 531.96/68.69 inference(cnf_transformation,[],[f1989])). 531.96/68.69 531.96/68.69 tff(f2959,plain,( 531.96/68.69 ( ! [X2 : 'Nat$',X0 : 'A_ltln$',X1 : 'Nat_a_set_fun$'] : ('fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) | 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK263(X0,X1,X2)))),'false_ltln$') | ~'member$'(X0,'nu_LTL$')) )), 531.96/68.69 inference(cnf_transformation,[],[f2027])). 531.96/68.69 531.96/68.69 tff(f3016,plain,( 531.96/68.69 ( ! [X0 : 'A_ltln_a_ltln_bool_fun_fun$',X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : ('less_eq$'(X0,X1) | X0 != X1) )), 531.96/68.69 inference(cnf_transformation,[],[f2056])). 531.96/68.69 531.96/68.69 tff(f3232,plain,( 531.96/68.69 ( ! [X1 : 'A_ltln_a_ltln_bool_fun_fun$'] : ('less_eq$'(X1,X1)) )), 531.96/68.69 inference(equality_resolution,[],[f3016])). 531.96/68.69 531.96/68.69 tcf(c_83,plain,![X0_'A_ltln':'A_ltln$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$',X1_'A_ltln':'A_ltln$',X1_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln'),X1_'A_ltln')| 531.96/68.69 ~'less_eq$'(X0_'A_ltln_a_ltln_bool_fun_fun',X1_'A_ltln_a_ltln_bool_fun_fun')| 531.96/68.69 'fun_app$b'('fun_app$c'(X1_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln'),X1_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2118])). 531.96/68.69 531.96/68.69 tcf(c_92,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',sK15(X0_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln',X0_'Nat_a_set_fun')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')))| 531.96/68.69 ~'member$'(X0_'A_ltln','nu_LTL$')|~'ltl_equivalence$'(X0_'A_ltln_a_ltln_bool_fun_fun')), 531.96/68.69 inference(cnf_transformation,[],[f2126])). 531.96/68.69 531.96/68.69 tcf(c_180,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',sK42(X0_'A_ltln',X0_'Nat_a_set_fun')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')))| 531.96/68.69 ~'member$'(X0_'A_ltln','nu_LTL$')), 531.96/68.69 inference(cnf_transformation,[],[f2221])). 531.96/68.69 531.96/68.69 tcf(c_231,plain,![X0_'A_ltln':'A_ltln$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$',X1_'A_ltln':'A_ltln$',X1_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln'),X1_'A_ltln')| 531.96/68.69 ~'less_eq$'(X0_'A_ltln_a_ltln_bool_fun_fun',X1_'A_ltln_a_ltln_bool_fun_fun')| 531.96/68.69 'fun_app$b'('fun_app$c'(X1_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln'),X1_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2274])). 531.96/68.69 531.96/68.69 tcf(c_288,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',sK71(X0_'A_ltln',X0_'Nat_a_set_fun')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0_'A_ltln'),'fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun','nat$'(0)),sK72(X0_'A_ltln',X0_'Nat_a_set_fun',X1_'Nat')))),'false_ltln$')), 531.96/68.69 inference(cnf_transformation,[],[f2335])). 531.96/68.69 531.96/68.69 tcf(c_289,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',sK71(X0_'A_ltln',X0_'Nat_a_set_fun')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK72(X0_'A_ltln',X0_'Nat_a_set_fun',X1_'Nat')))), 531.96/68.69 inference(cnf_transformation,[],[f2334])). 531.96/68.69 531.96/68.69 tcf(c_327,plain,![X0_'A_ltln':'A_ltln$',X1_'A_ltln':'A_ltln$',X2_'A_ltln':'A_ltln$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),X1_'A_ltln')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1_'A_ltln'),X2_'A_ltln')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),X2_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2378])). 531.96/68.69 531.96/68.69 tcf(c_394,plain, 531.96/68.69 ('member$'('phi$','nu_LTL$')), 531.96/68.69 inference(cnf_transformation,[],[f2446])). 531.96/68.69 531.96/68.69 tcf(c_459,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0_'A_ltln'),'fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun','nat$'(0)),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK128(X0_'A_ltln',X0_'Nat_a_set_fun')),'fun_app$g'('of_nat$',X0_'Nat'))| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',X1_'Nat'),sK129(X0_'A_ltln',X0_'Nat_a_set_fun',X1_'Nat')))),'false_ltln$')), 531.96/68.69 inference(cnf_transformation,[],[f2513])). 531.96/68.69 531.96/68.69 tcf(c_522,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X1_'Nat'),sK158(X1_'Nat')))),'false_ltln$')), 531.96/68.69 inference(cnf_transformation,[],[f2584])). 531.96/68.69 531.96/68.69 tcf(c_523,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat')))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))), 531.96/68.69 inference(cnf_transformation,[],[f2583])). 531.96/68.69 531.96/68.69 tcf(c_524,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X1_'Nat'))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',X0_'Nat'))), 531.96/68.69 inference(cnf_transformation,[],[f2582])). 531.96/68.69 531.96/68.69 tcf(c_614,plain,![X0_'A_ltln':'A_ltln$',X1_'A_ltln':'A_ltln$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$',X0_'A_ltln'),X1_'A_ltln')|'fun_app$b'('fun_app$c'('eq$',X1_'A_ltln'),X0_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2677])). 531.96/68.69 531.96/68.69 tcf(c_686,plain, 531.96/68.69 ('ltl_equivalence$'('ltl_lang_equiv$')), 531.96/68.69 inference(cnf_transformation,[],[f2756])). 531.96/68.69 531.96/68.69 tcf(c_700,plain,![X0_'Nat_a_set_fun':'Nat_a_set_fun$']: 531.96/68.69 (~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'false_ltln$')), 531.96/68.69 inference(cnf_transformation,[],[f2772])). 531.96/68.69 531.96/68.69 tcf(c_796,plain,![X0_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK235(X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))), 531.96/68.69 inference(cnf_transformation,[],[f2877])). 531.96/68.69 531.96/68.69 tcf(c_812,plain,![X0_'A_ltln':'A_ltln$',X1_'A_ltln':'A_ltln$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),X1_'A_ltln')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1_'A_ltln'),X0_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2894])). 531.96/68.69 531.96/68.69 tcf(c_813,plain,![X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'A_ltln':'A_ltln$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),X1_'A_ltln')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),X0_'A_ltln')|'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),X1_'A_ltln')), 531.96/68.69 inference(cnf_transformation,[],[f2898])). 531.96/68.69 531.96/68.69 tcf(c_875,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$']: 531.96/68.69 (~'member$'(X0_'A_ltln','nu_LTL$')|'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')),'fun_app$f'('subsequence$'(X0_'Nat_a_set_fun',X0_'Nat'),sK263(X0_'A_ltln',X0_'Nat_a_set_fun',X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0_'A_ltln')))), 531.96/68.69 inference(cnf_transformation,[],[f2959])). 531.96/68.69 531.96/68.69 tcf(c_933,plain,![X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 ('less_eq$'(X0_'A_ltln_a_ltln_bool_fun_fun',X0_'A_ltln_a_ltln_bool_fun_fun')), 531.96/68.69 inference(cnf_transformation,[],[f3232])). 531.96/68.69 531.96/68.69 tcf(c_1063,plain, 531.96/68.69 ('less_eq$'('eq$','eq$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_933])). 531.96/68.69 531.96/68.69 tcf(c_1410,plain,![X0_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK15('ltl_lang_equiv$','phi$','w$')),sK158(sK15('ltl_lang_equiv$','phi$','w$'))))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_522])). 531.96/68.69 531.96/68.69 tcf(c_1421,plain,![X0_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK42('phi$','w$')),sK158(sK42('phi$','w$'))))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',X0_'Nat'),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_523])). 531.96/68.69 531.96/68.69 tcf(c_1422,plain, 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK42('phi$','w$')),sK158(sK42('phi$','w$'))))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK157(sK159)))), 531.96/68.69 inference(instantiation,[status(thm)],[c_1421])). 531.96/68.69 531.96/68.69 tcf(c_1500,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK15('ltl_lang_equiv$','phi$','w$')),sK158(sK15('ltl_lang_equiv$','phi$','w$'))))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))| 531.96/68.69 ~'member$'('phi$','nu_LTL$')|~'ltl_equivalence$'('ltl_lang_equiv$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_92])). 531.96/68.69 531.96/68.69 tcf(c_1501,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK42('phi$','w$')),sK158(sK42('phi$','w$'))))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))| 531.96/68.69 ~'member$'('phi$','nu_LTL$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_180])). 531.96/68.69 531.96/68.69 tcf(c_44866,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X1_'Nat'))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_524])). 531.96/68.69 531.96/68.69 tcf(c_45221,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK158(sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_44866])). 531.96/68.69 531.96/68.69 tcf(c_45222,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',sK159)))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK158(sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',sK159)))), 531.96/68.69 inference(instantiation,[status(thm)],[c_45221])). 531.96/68.69 531.96/68.69 tcf(c_45251,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK235(sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_44866])). 531.96/68.69 531.96/68.69 tcf(c_45252,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',sK159)))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK235(sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',sK159)))), 531.96/68.69 inference(instantiation,[status(thm)],[c_45251])). 531.96/68.69 531.96/68.69 tcf(c_69551,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','false_ltln$'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))), 531.96/68.69 inference(resolution,[status(thm)],[c_812,c_523])). 531.96/68.69 531.96/68.69 tcf(c_69655,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','false_ltln$'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X1_'Nat'),sK158(X1_'Nat'))))), 531.96/68.69 inference(resolution,[status(thm)],[c_812,c_522])). 531.96/68.69 531.96/68.69 tcf(c_98180,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','false_ltln$'),'fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat')))| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat'))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_614])). 531.96/68.69 531.96/68.69 tcf(c_98188,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),X1_'Nat'))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_524])). 531.96/68.69 531.96/68.69 tcf(c_98558,plain,![X0_'Nat':'Nat$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$',X1_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~'less_eq$'(X0_'A_ltln_a_ltln_bool_fun_fun',X1_'A_ltln_a_ltln_bool_fun_fun')| 531.96/68.69 'fun_app$b'('fun_app$c'(X1_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat'))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_83])). 531.96/68.69 531.96/68.69 tcf(c_98767,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'member$'('phi$','nu_LTL$')|'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK263('phi$','w$',X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_875])). 531.96/68.69 531.96/68.69 tcf(c_99657,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK129('phi$','w$',sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_98188])). 531.96/68.69 531.96/68.69 tcf(c_99658,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(sK159)))),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK129('phi$','w$',sK160)))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK157(sK159)))), 531.96/68.69 inference(instantiation,[status(thm)],[c_99657])). 531.96/68.69 531.96/68.69 tcf(c_101211,plain,![X0_'Nat':'Nat$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'less_eq$'('eq$',X0_'A_ltln_a_ltln_bool_fun_fun')|'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_98558])). 531.96/68.69 531.96/68.69 tcf(c_105326,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','false_ltln$'),'fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat'))))| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_98180])). 531.96/68.69 531.96/68.69 tcf(c_105349,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',X1_'Nat')))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_288])). 531.96/68.69 531.96/68.69 tcf(c_107245,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),X0_'Nat'))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK72('phi$','w$',X1_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_289])). 531.96/68.69 531.96/68.69 tcf(c_108996,plain, 531.96/68.69 (~'member$'('phi$','nu_LTL$')|'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),sK263('phi$','w$',sK71('phi$','w$'))))),'false_ltln$')| 531.96/68.69 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_98767])). 531.96/68.69 531.96/68.69 tcf(c_111757,plain,![X0_'Nat':'Nat$']: 531.96/68.69 ('fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK158(sK160)))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_522])). 531.96/68.69 531.96/68.69 tcf(c_111939,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X0_'Nat'))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK128('phi$','w$')),'fun_app$g'('of_nat$',X0_'Nat'))| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK129('phi$','w$',sK160)))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_459])). 531.96/68.69 531.96/68.69 tcf(c_111963,plain, 531.96/68.69 ('fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK235(sK160)))),'false_ltln$')| 531.96/68.69 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_796])). 531.96/68.69 531.96/68.69 tcf(c_117677,plain,![X0_'Nat':'Nat$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'less_eq$'('eq$',X0_'A_ltln_a_ltln_bool_fun_fun')|'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','false_ltln$'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X1_'Nat'),sK158(X1_'Nat'))))), 531.96/68.69 inference(resolution,[status(thm)],[c_231,c_69655])). 531.96/68.69 531.96/68.69 tcf(c_130844,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),sK263('phi$','w$',sK71('phi$','w$'))))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',X0_'Nat')))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_105349])). 531.96/68.69 531.96/68.69 tcf(c_130845,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),sK263('phi$','w$',sK71('phi$','w$'))))),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK72('phi$','w$',sK159)))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_130844])). 531.96/68.69 531.96/68.69 tcf(c_140681,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),sK263('phi$','w$',sK71('phi$','w$'))))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',X0_'Nat'),'fun_app$g'('of_nat$',sK72('phi$','w$',X0_'Nat')))), 531.96/68.69 inference(instantiation,[status(thm)],[c_107245])). 531.96/68.69 531.96/68.69 tcf(c_140682,plain, 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK71('phi$','w$')),sK263('phi$','w$',sK71('phi$','w$'))))),'false_ltln$')| 531.96/68.69 $less('fun_app$g'('of_nat$',sK159),'fun_app$g'('of_nat$',sK72('phi$','w$',sK159)))), 531.96/68.69 inference(instantiation,[status(thm)],[c_140681])). 531.96/68.69 531.96/68.69 tcf(c_151809,plain,![X0_'Nat':'Nat$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))| 531.96/68.69 'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'false_ltln$')), 531.96/68.69 inference(resolution,[status(thm)],[c_813,c_523])). 531.96/68.69 531.96/68.69 tcf(c_152885,plain,![X0_'Nat':'Nat$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 ($less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))), 531.96/68.69 inference(global_subsumption_just, 531.96/68.69 [status(thm)], 531.96/68.69 [c_151809,c_700,c_151809])). 531.96/68.69 531.96/68.69 tcf(c_152886,plain,![X0_'Nat':'Nat$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))), 531.96/68.69 inference(renaming,[status(thm)],[c_152885])). 531.96/68.69 531.96/68.69 tcf(c_153217,plain,![X0_'Nat':'Nat$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 ('fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~'less_eq$'('eq$',X0_'A_ltln_a_ltln_bool_fun_fun')), 531.96/68.69 inference(global_subsumption_just, 531.96/68.69 [status(thm)], 531.96/68.69 [c_117677,c_686,c_394,c_1410,c_1500,c_45222,c_101211,c_108996, 531.96/68.69 c_111757,c_130845,c_140682])). 531.96/68.69 531.96/68.69 tcf(c_153218,plain,![X0_'Nat':'Nat$',X0_'A_ltln_a_ltln_bool_fun_fun':'A_ltln_a_ltln_bool_fun_fun$']: 531.96/68.69 (~'less_eq$'('eq$',X0_'A_ltln_a_ltln_bool_fun_fun')|'fun_app$b'('fun_app$c'(X0_'A_ltln_a_ltln_bool_fun_fun','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')), 531.96/68.69 inference(renaming,[status(thm)],[c_153217])). 531.96/68.69 531.96/68.69 tcf(c_153219,plain, 531.96/68.69 (~'less_eq$'('eq$','eq$')|'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(sK159)))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_153218])). 531.96/68.69 531.96/68.69 tcf(c_153268,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'less_eq$'('eq$','eq$')|'fun_app$b'('fun_app$c'('eq$','false_ltln$'),'fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat'))))), 531.96/68.69 inference(resolution,[status(thm)],[c_153218,c_614])). 531.96/68.69 531.96/68.69 tcf(c_159732,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK157(X0_'Nat')))),'false_ltln$')| 531.96/68.69 ~$less('fun_app$g'('of_nat$',sK128('phi$','w$')),'fun_app$g'('of_nat$',sK157(X0_'Nat')))| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK160),sK129('phi$','w$',sK160)))),'false_ltln$')), 531.96/68.69 inference(instantiation,[status(thm)],[c_111939])). 531.96/68.69 531.96/68.69 tcf(c_221763,plain, 531.96/68.69 ('fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))), 531.96/68.69 inference(global_subsumption_just, 531.96/68.69 [status(thm)], 531.96/68.69 [c_796,c_394,c_45252,c_108996,c_111963,c_130845,c_140682])). 531.96/68.69 531.96/68.69 tcf(c_227530,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),'false_ltln$')| 531.96/68.69 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))), 531.96/68.69 inference(resolution,[status(thm)],[c_327,c_69551])). 531.96/68.69 531.96/68.69 tcf(c_246679,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$',X1_'Nat':'Nat$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),X0_'A_ltln')|'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0_'Nat'),sK158(X0_'Nat'))))| 531.96/68.69 $less('fun_app$g'('of_nat$',X1_'Nat'),'fun_app$g'('of_nat$',sK157(X1_'Nat')))), 531.96/68.69 inference(resolution,[status(thm)],[c_227530,c_813])). 531.96/68.69 531.96/68.69 tcf(c_250520,plain,![X0_'Nat':'Nat$',X0_'A_ltln':'A_ltln$',X0_'Nat_a_set_fun':'Nat_a_set_fun$']: 531.96/68.69 (~'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0_'A_ltln'),'false_ltln$')| 531.96/68.69 ~'fun_app$b'('semantics_ltln$'(X0_'Nat_a_set_fun'),X0_'A_ltln')|$less('fun_app$g'('of_nat$',X0_'Nat'),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(backward_subsumption_resolution, 531.96/68.69 [status(thm)], 531.96/68.69 [c_246679,c_152886])). 531.96/68.69 531.96/68.69 tcf(c_250631,plain,![X0_'Nat':'Nat$']: 531.96/68.69 ($less('fun_app$g'('of_nat$',X0_'Nat'),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(global_subsumption_just, 531.96/68.69 [status(thm)], 531.96/68.69 [c_250520,c_394,c_1421,c_1501,c_45252,c_108996,c_111963, 531.96/68.69 c_130845,c_140682])). 531.96/68.69 531.96/68.69 tcf(c_798709,plain,![X0_'Nat':'Nat$',X1_'Nat':'Nat$']: 531.96/68.69 (~$less('fun_app$g'('of_nat$',sK128('phi$','w$')),'fun_app$g'('of_nat$',sK157(X0_'Nat')))| 531.96/68.69 ~'less_eq$'('eq$','eq$')|'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X1_'Nat'),sK129('phi$','w$',X1_'Nat')))),'false_ltln$')), 531.96/68.69 inference(resolution,[status(thm)],[c_459,c_153218])). 531.96/68.69 531.96/68.69 tcf(c_798940,plain,![X0_'Nat':'Nat$']: 531.96/68.69 (~$less('fun_app$g'('of_nat$',sK128('phi$','w$')),'fun_app$g'('of_nat$',sK157(X0_'Nat')))), 531.96/68.69 inference(global_subsumption_just, 531.96/68.69 [status(thm)], 531.96/68.69 [c_798709,c_1063,c_394,c_1422,c_1501,c_99658,c_105326,c_153219, 531.96/68.69 c_153268,c_159732,c_221763])). 531.96/68.69 531.96/68.69 tcf(c_798967,plain, 531.96/68.69 ($false), 531.96/68.69 inference(resolution,[status(thm)],[c_798940,c_250631])). 531.96/68.69 531.96/68.69 531.96/68.69 % % SZS output end CNFRefutation for theBenchmark.p 531.96/68.69 531.96/68.69 531.96/68.79 EOF