%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 04:11:54 EDT 2023 % Result : Theorem 144.07s 19.76s % Output : Proof 192.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n016.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sun Aug 27 15:08:13 EDT 2023 % 0.14/0.37 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 15.35/2.93 Prover 1: Preprocessing ... % 15.35/2.94 Prover 4: Preprocessing ... % 16.78/3.04 Prover 2: Preprocessing ... % 16.78/3.04 Prover 0: Preprocessing ... % 16.78/3.04 Prover 5: Preprocessing ... % 17.20/3.12 Prover 3: Preprocessing ... % 17.80/3.17 Prover 6: Preprocessing ... % 41.15/6.29 Prover 3: Warning: ignoring some quantifiers % 41.15/6.32 Prover 1: Warning: ignoring some quantifiers % 42.17/6.40 Prover 3: Constructing countermodel ... % 42.17/6.42 Prover 6: Proving ... % 42.17/6.53 Prover 1: Constructing countermodel ... % 46.38/7.00 Prover 0: Proving ... % 46.87/7.11 Prover 4: Warning: ignoring some quantifiers % 48.81/7.33 Prover 5: Proving ... % 49.64/7.46 Prover 4: Constructing countermodel ... % 52.29/7.93 Prover 2: Proving ... % 99.66/14.00 Prover 5: stopped % 99.66/14.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 105.91/14.75 Prover 7: Preprocessing ... % 109.98/15.27 Prover 2: stopped % 109.98/15.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 113.61/15.78 Prover 7: Warning: ignoring some quantifiers % 114.55/15.92 Prover 7: Constructing countermodel ... % 115.36/16.02 Prover 1: stopped % 115.91/16.03 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.68/16.15 Prover 8: Preprocessing ... % 120.05/16.60 Prover 9: Preprocessing ... % 122.95/17.14 Prover 8: Warning: ignoring some quantifiers % 124.86/17.27 Prover 8: Constructing countermodel ... % 129.88/17.91 Prover 6: stopped % 129.88/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.25/18.22 Prover 9: Warning: ignoring some quantifiers % 133.17/18.31 Prover 9: Constructing countermodel ... % 135.98/18.71 Prover 10: Preprocessing ... % 141.69/19.48 Prover 10: Warning: ignoring some quantifiers % 142.37/19.55 Prover 10: Constructing countermodel ... % 144.07/19.76 Prover 9: proved (3726ms) % 144.07/19.76 % 144.07/19.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 144.07/19.76 % 144.07/19.77 Prover 3: stopped % 144.07/19.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 144.07/19.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 144.07/19.84 Prover 0: stopped % 144.07/19.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 154.54/21.29 Prover 16: Preprocessing ... % 154.54/21.33 Prover 13: Preprocessing ... % 156.30/21.38 Prover 11: Preprocessing ... % 162.09/22.11 Prover 16: Warning: ignoring some quantifiers % 162.74/22.18 Prover 16: Constructing countermodel ... % 168.11/22.87 Prover 13: Warning: ignoring some quantifiers % 168.11/22.94 Prover 11: Warning: ignoring some quantifiers % 169.03/23.02 Prover 13: Constructing countermodel ... % 169.34/23.08 Prover 11: Constructing countermodel ... % 176.67/24.01 Prover 16: stopped % 176.67/24.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 181.70/24.82 Prover 19: Preprocessing ... % 186.83/25.44 Prover 4: Found proof (size 493) % 186.83/25.45 Prover 4: proved (24782ms) % 186.83/25.45 Prover 11: stopped % 186.83/25.45 Prover 7: stopped % 186.83/25.45 Prover 10: stopped % 186.83/25.45 Prover 8: stopped % 186.83/25.45 Prover 13: stopped % 188.91/25.92 Prover 19: Warning: ignoring some quantifiers % 189.09/26.00 Prover 19: Constructing countermodel ... % 189.09/26.02 Prover 19: stopped % 189.09/26.02 % 189.09/26.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 189.09/26.02 % 189.40/26.20 % SZS output start Proof for theBenchmark % 189.40/26.22 Assumptions after simplification: % 189.40/26.22 --------------------------------- % 189.40/26.22 % 189.40/26.22 (axiom12) % 190.01/26.24 A_ltln_a_ltln_fun$(normalise$) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ( ~ % 190.01/26.24 (fun_app$d(normalise$, v0) = v1) | ~ A_ltln$(v0) | ? [v2: A_ltln_set$] : % 190.01/26.24 ? [v3: A_ltln_set$] : (nested_prop_atoms$(v1) = v2 & nested_prop_atoms$(v0) % 190.01/26.24 = v3 & less_eq$(v2, v3) = 0 & A_ltln_set$(v3) & A_ltln_set$(v2))) & ! % 190.01/26.24 [v0: A_ltln$] : ! [v1: A_ltln_set$] : ( ~ (nested_prop_atoms$(v0) = v1) | ~ % 190.01/26.24 A_ltln$(v0) | ? [v2: A_ltln$] : ? [v3: A_ltln_set$] : % 190.01/26.24 (fun_app$d(normalise$, v0) = v2 & nested_prop_atoms$(v2) = v3 & less_eq$(v3, % 190.01/26.24 v1) = 0 & A_ltln$(v2) & A_ltln_set$(v3))) % 190.01/26.24 % 190.01/26.24 (axiom135) % 190.01/26.24 gF_advice_congruent$(eq$, normalise$) = 0 & A_ltln_a_ltln_bool_fun_fun$(eq$) & % 190.01/26.24 A_ltln_a_ltln_fun$(normalise$) % 190.01/26.24 % 190.01/26.24 (axiom136) % 190.01/26.24 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.24 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : % 190.01/26.24 (af_letter_F$(eq$) = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.01/26.24 [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_set_list$] : ! [v4: % 190.01/26.24 A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : ! [v6: % 190.01/26.24 A_ltln$] : ( ~ (foldl$(v4, v2) = v5) | ~ (fun_app$s(v5, v3) = v6) | ~ % 190.01/26.24 (fun_app$c(v0, v1) = v4) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 190.01/26.24 A_set_list$(v3) | ? [v7: A_ltln_bool_fun$] : ? [v8: any] : ? [v9: % 190.01/26.24 A_set_list_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln_bool_fun$] % 190.01/26.24 : ? [v12: any] : (foldl$(af_letter$, v2) = v9 & fun_app$s(v9, v3) = v10 & % 190.01/26.24 fun_app$e(eq$, v10) = v11 & fun_app$e(eq$, v6) = v7 & fun_app$(v11, % 190.01/26.24 true_ltln$) = v12 & fun_app$(v7, true_ltln$) = v8 & % 190.01/26.24 A_set_list_a_ltln_fun$(v9) & A_ltln$(v10) & A_ltln_bool_fun$(v11) & % 190.01/26.24 A_ltln_bool_fun$(v7) & ( ~ (v8 = 0) | v12 = 0)))) % 190.01/26.24 % 190.01/26.24 (axiom137) % 190.01/26.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ! [v0: A_ltln$] : ! [v1: A_set$] % 190.01/26.25 : ! [v2: A_set_a_ltln_fun$] : ! [v3: A_ltln$] : ( ~ (fun_app$b(af_letter$, % 190.01/26.25 v0) = v2) | ~ (fun_app$a(v2, v1) = v3) | ~ A_ltln$(v0) | ~ A_set$(v1) % 190.01/26.25 | ? [v4: A_ltln_set$] : ? [v5: A_ltln_set$] : (nested_prop_atoms$(v3) = v4 % 190.01/26.25 & nested_prop_atoms$(v0) = v5 & less_eq$(v4, v5) = 0 & A_ltln_set$(v5) & % 190.01/26.25 A_ltln_set$(v4))) % 190.01/26.25 % 190.01/26.25 (axiom146) % 190.01/26.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.01/26.25 A_set_list_a_ltln_fun$] : (foldl$(af_letter$, true_ltln$) = v0 & % 190.01/26.25 A_set_list_a_ltln_fun$(v0) & ! [v1: A_set_list$] : ! [v2: A_ltln$] : (v2 = % 190.01/26.25 true_ltln$ | ~ (fun_app$s(v0, v1) = v2) | ~ A_set_list$(v1))) % 190.01/26.25 % 190.01/26.25 (axiom147) % 190.01/26.25 ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 190.01/26.25 int] : (v2 = 0 | ~ (transition_functions_size$(v0, v1) = v2) | ~ % 190.01/26.25 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v3: any] : % 190.01/26.25 ? [v4: any] : (transition_functions_size_axioms$(v1) = v4 & % 190.01/26.25 transition_functions$(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! % 190.01/26.25 [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: any] % 190.01/26.25 : ( ~ (transition_functions$(v0, v1) = v2) | ~ % 190.01/26.25 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v3: any] : % 190.01/26.25 ? [v4: any] : (transition_functions_size_axioms$(v1) = v4 & % 190.01/26.25 transition_functions_size$(v0, v1) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 190.01/26.25 0)))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 190.01/26.25 A_ltln_a_ltln_fun$] : ( ~ (transition_functions$(v0, v1) = 0) | ~ % 190.01/26.25 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v2: any] : % 190.01/26.25 ? [v3: any] : (transition_functions_size_axioms$(v1) = v2 & % 190.01/26.25 transition_functions_size$(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! % 190.01/26.25 [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ( ~ % 190.01/26.25 (transition_functions_size$(v0, v1) = 0) | ~ % 190.01/26.25 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | % 190.01/26.25 (transition_functions_size_axioms$(v1) = 0 & transition_functions$(v0, v1) = % 190.01/26.25 0)) % 190.01/26.25 % 190.01/26.25 (axiom158) % 190.01/26.26 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.01/26.26 A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) % 190.01/26.26 & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 190.01/26.26 [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_set$] : ! [v6: % 190.01/26.26 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v7: % 190.01/26.26 A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_set_a_ltln_fun$] : ! [v9: % 190.01/26.26 A_ltln$] : ( ~ (transition_functions$(v1, v2) = 0) | ~ (fun_app$c(v6, v3) % 190.01/26.26 = v7) | ~ (fun_app$b(v7, v4) = v8) | ~ (fun_app$a(v8, v5) = v9) | ~ % 190.01/26.26 (af_letter_F$(v1) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.01/26.26 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | % 190.01/26.26 ? [v10: A_ltln_bool_fun$] : ? [v11: any] : ? [v12: A_ltln$] : ? [v13: % 190.01/26.26 A_set_a_ltln_fun$] : ? [v14: A_ltln$] : (fun_app$b(af_letter$, v4) = % 190.01/26.26 v13 & fun_app$a(v13, v5) = v14 & fun_app$e(v1, v4) = v10 & fun_app$d(v0, % 190.01/26.26 v3) = v12 & fun_app$(v10, true_ltln$) = v11 & A_ltln$(v14) & % 190.01/26.26 A_ltln$(v12) & A_ltln_bool_fun$(v10) & A_set_a_ltln_fun$(v13) & ( ~ (v11 % 190.01/26.26 = 0) | v12 = v9) & (v14 = v9 | v11 = 0))) & ! [v1: % 190.01/26.26 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.01/26.26 A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_set$] : ! [v6: A_ltln$] : ! [v7: % 190.01/26.26 A_set_a_ltln_fun$] : ! [v8: A_ltln$] : ( ~ (transition_functions$(v1, v2) % 190.01/26.26 = 0) | ~ (fun_app$b(af_letter$, v4) = v7) | ~ (fun_app$a(v7, v5) = v8) % 190.01/26.26 | ~ (fun_app$d(v0, v3) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.01/26.26 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | % 190.01/26.26 ? [v9: A_ltln_bool_fun$] : ? [v10: any] : ? [v11: % 190.01/26.26 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v12: % 190.01/26.26 A_ltln_a_set_a_ltln_fun_fun$] : ? [v13: A_set_a_ltln_fun$] : ? [v14: % 190.01/26.26 A_ltln$] : (fun_app$c(v11, v3) = v12 & fun_app$b(v12, v4) = v13 & % 190.01/26.26 fun_app$a(v13, v5) = v14 & af_letter_F$(v1) = v11 & fun_app$e(v1, v4) = % 190.01/26.26 v9 & fun_app$(v9, true_ltln$) = v10 & A_ltln_a_set_a_ltln_fun_fun$(v12) % 190.01/26.26 & A_ltln$(v14) & A_ltln_bool_fun$(v9) & A_set_a_ltln_fun$(v13) & % 190.01/26.26 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v11) & ( ~ (v10 = 0) | v14 = v6) % 190.01/26.26 & (v14 = v8 | v10 = 0)))) % 190.01/26.26 % 190.01/26.26 (axiom160) % 190.01/26.26 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln$(true_ltln$) & ? [v0: % 190.01/26.26 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.01/26.26 (af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.01/26.26 A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.01/26.26 [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: % 190.01/26.26 A_set_list$] : ! [v6: A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: % 190.01/26.26 A_set_list_a_ltln_fun$] : ! [v8: A_set_list_a_set_list_fun$] : ! [v9: % 190.01/26.26 A_set_list$] : ! [v10: A_ltln$] : ( ~ (append$(v4) = v8) | ~ % 190.01/26.26 (fun_app$t(v8, v5) = v9) | ~ (foldl$(v6, v3) = v7) | ~ (fun_app$s(v7, % 190.01/26.26 v9) = v10) | ~ (fun_app$c(v0, v2) = v6) | ~ A_ltln$(v3) | ~ % 190.01/26.26 A_ltln$(v2) | ~ A_set_list$(v5) | ~ A_set_list$(v4) | ? [v11: A_ltln$] % 190.01/26.26 : ? [v12: A_ltln$] : ? [v13: A_set_list_a_ltln_fun$] : ? [v14: A_ltln$] % 190.01/26.27 : (foldl$(v6, v12) = v13 & fun_app$s(v13, v5) = v14 & fun_app$s(v7, v4) = % 190.01/26.27 v11 & fun_app$d(v1, v2) = v12 & A_set_list_a_ltln_fun$(v13) & % 190.01/26.27 A_ltln$(v14) & A_ltln$(v12) & A_ltln$(v11) & ( ~ (v12 = v11) | v14 = % 190.01/26.27 v10)))) % 190.01/26.27 % 190.01/26.27 (axiom161) % 190.01/26.27 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.27 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : % 190.01/26.27 (af_letter_F$(eq$) = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.01/26.27 [v1: A_set_list$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.01/26.27 A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : ! [v6: % 190.01/26.27 A_ltln$] : ( ~ (foldl$(v4, v3) = v5) | ~ (fun_app$s(v5, v1) = v6) | ~ % 190.01/26.27 (fun_app$c(v0, v2) = v4) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.01/26.27 A_set_list$(v1) | ? [v7: A_set_list_a_ltln_fun$] : ? [v8: A_ltln$] : ? % 190.01/26.27 [v9: A_set_list$] : ? [v10: A_set_list$] : ? [v11: % 190.01/26.27 A_set_list_a_set_list_fun$] : ? [v12: A_set_list$] : ? [v13: A_ltln$] % 190.01/26.27 : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : (A_set_list$(v10) & % 190.01/26.27 A_set_list$(v9) & ((v15 = 0 & v12 = v1 & append$(v9) = v11 & % 190.01/26.27 fun_app$t(v11, v10) = v1 & fun_app$s(v5, v9) = v13 & fun_app$e(eq$, % 190.01/26.27 v13) = v14 & fun_app$(v14, true_ltln$) = 0 & A_ltln$(v13) & % 190.01/26.27 A_ltln_bool_fun$(v14) & A_set_list_a_set_list_fun$(v11)) | (v8 = v6 % 190.01/26.27 & foldl$(af_letter$, v3) = v7 & fun_app$s(v7, v1) = v6 & % 190.01/26.27 A_set_list_a_ltln_fun$(v7) & A_ltln$(v6)))))) % 190.01/26.27 % 190.01/26.27 (axiom162) % 190.01/26.27 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.27 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : % 190.01/26.27 (af_letter_F$(eq$) = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.01/26.27 [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_ltln$] : ! [v4: % 190.01/26.27 A_set_list_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_bool_fun$] : % 190.01/26.27 ! [v7: A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_set_list_a_ltln_fun$] : ( ~ % 190.01/26.27 (foldl$(v7, v1) = v8) | ~ (foldl$(af_letter$, v1) = v4) | ~ % 190.01/26.27 (fun_app$s(v4, v2) = v5) | ~ (fun_app$c(v0, v3) = v7) | ~ % 190.01/26.27 (fun_app$e(eq$, v5) = v6) | ~ (fun_app$(v6, true_ltln$) = 0) | ~ % 190.01/26.27 A_ltln$(v3) | ~ A_ltln$(v1) | ~ A_set_list$(v2) | ? [v9: A_set_list$] : % 190.01/26.27 ? [v10: A_set_list$] : ? [v11: A_set_list_a_set_list_fun$] : ? [v12: % 190.01/26.27 A_ltln$] : ? [v13: A_ltln_bool_fun$] : (append$(v9) = v11 & % 190.01/26.27 fun_app$t(v11, v10) = v2 & fun_app$s(v8, v9) = v12 & fun_app$e(eq$, v12) % 190.01/26.27 = v13 & fun_app$(v13, true_ltln$) = 0 & A_ltln$(v12) & A_set_list$(v10) % 190.01/26.27 & A_set_list$(v9) & A_ltln_bool_fun$(v13) & % 190.01/26.27 A_set_list_a_set_list_fun$(v11)))) % 190.01/26.27 % 190.01/26.27 (axiom163) % 190.01/26.28 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.28 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : % 190.01/26.28 (af_letter_F$(eq$) = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.01/26.28 [v1: A_set_list$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.01/26.28 A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : ! [v6: % 190.01/26.28 A_ltln$] : ( ~ (foldl$(v4, v2) = v5) | ~ (fun_app$s(v5, v1) = v6) | ~ % 190.01/26.28 (fun_app$c(v0, v3) = v4) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.01/26.28 A_set_list$(v1) | ? [v7: A_set_list_a_ltln_fun$] : ? [v8: A_ltln$] : ? % 190.01/26.28 [v9: A_set_list$] : ? [v10: A_set_list$] : ? [v11: % 190.01/26.28 A_set_list_a_set_list_fun$] : ? [v12: A_set_list$] : ? [v13: A_ltln$] % 190.01/26.28 : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : (foldl$(af_letter$, v2) = % 190.01/26.28 v7 & fun_app$s(v7, v1) = v8 & A_set_list_a_ltln_fun$(v7) & A_ltln$(v8) & % 190.01/26.28 A_set_list$(v10) & A_set_list$(v9) & (v8 = v6 | (v15 = 0 & v12 = v1 & % 190.01/26.28 append$(v9) = v11 & fun_app$t(v11, v10) = v1 & fun_app$s(v7, v9) = % 190.01/26.28 v13 & fun_app$e(eq$, v13) = v14 & fun_app$(v14, true_ltln$) = 0 & % 190.01/26.28 A_ltln$(v13) & A_ltln_bool_fun$(v14) & % 190.01/26.28 A_set_list_a_set_list_fun$(v11)))))) % 190.01/26.28 % 190.01/26.28 (axiom164) % 190.01/26.28 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.28 A_ltln$(true_ltln$) & ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: % 190.01/26.28 A_set_list$] : ! [v3: A_set_list_a_ltln_fun$] : ! [v4: % 190.01/26.28 A_set_list_a_set_list_fun$] : ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ % 190.01/26.28 (append$(v1) = v4) | ~ (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, % 190.01/26.28 v0) = v3) | ~ (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ % 190.01/26.28 A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: % 190.01/26.28 A_ltln_bool_fun$] : ? [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: % 190.01/26.28 any] : (fun_app$s(v3, v1) = v7 & fun_app$e(eq$, v7) = v8 & fun_app$e(eq$, % 190.01/26.28 v6) = v10 & fun_app$(v10, true_ltln$) = v11 & fun_app$(v8, true_ltln$) = % 190.01/26.28 v9 & A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 % 190.01/26.28 = 0) | v11 = 0))) % 190.01/26.28 % 190.01/26.28 (axiom175) % 190.01/26.29 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 190.01/26.29 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.01/26.29 A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: % 190.01/26.29 A_set_list$] : ! [v6: A_set_list$] : ! [v7: % 190.01/26.29 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.01/26.29 A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : ! [v10: % 190.01/26.29 A_set_list_a_set_list_fun$] : ! [v11: A_set_list$] : ! [v12: A_ltln$] : % 190.01/26.29 ( ~ (append$(v5) = v10) | ~ (fun_app$t(v10, v6) = v11) | ~ % 190.01/26.29 (transition_functions$(v1, v2) = 0) | ~ (foldl$(v8, v4) = v9) | ~ % 190.01/26.29 (fun_app$s(v9, v11) = v12) | ~ (fun_app$c(v7, v3) = v8) | ~ % 190.01/26.29 (af_letter_F$(v1) = v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.01/26.29 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set_list$(v6) | ~ A_set_list$(v5) | % 190.01/26.29 ~ A_ltln_a_ltln_fun$(v2) | ? [v13: A_ltln$] : ? [v14: A_ltln$] : ? % 190.01/26.29 [v15: A_set_list_a_ltln_fun$] : ? [v16: A_ltln$] : (foldl$(v8, v14) = v15 % 190.01/26.29 & fun_app$s(v15, v6) = v16 & fun_app$s(v9, v5) = v13 & fun_app$d(v0, v3) % 190.01/26.29 = v14 & A_set_list_a_ltln_fun$(v15) & A_ltln$(v16) & A_ltln$(v14) & % 190.01/26.29 A_ltln$(v13) & ( ~ (v14 = v13) | v16 = v12))) & ! [v1: % 190.01/26.29 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.01/26.29 A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_set_list$] : ! [v6: A_set_list$] % 190.01/26.29 : ! [v7: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.01/26.29 A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : ! [v10: % 190.01/26.29 A_ltln$] : ! [v11: A_set_list_a_ltln_fun$] : ! [v12: A_ltln$] : ( ~ % 190.01/26.29 (transition_functions$(v1, v2) = 0) | ~ (foldl$(v8, v10) = v11) | ~ % 190.01/26.29 (foldl$(v8, v4) = v9) | ~ (fun_app$s(v11, v6) = v12) | ~ (fun_app$s(v9, % 190.01/26.29 v5) = v10) | ~ (fun_app$c(v7, v3) = v8) | ~ (af_letter_F$(v1) = v7) % 190.01/26.29 | ~ (fun_app$d(v0, v3) = v10) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.01/26.29 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set_list$(v6) | ~ A_set_list$(v5) | % 190.01/26.29 ~ A_ltln_a_ltln_fun$(v2) | ? [v13: A_set_list_a_set_list_fun$] : ? [v14: % 190.01/26.29 A_set_list$] : (append$(v5) = v13 & fun_app$t(v13, v6) = v14 & % 190.01/26.29 fun_app$s(v9, v14) = v12 & A_ltln$(v12) & A_set_list$(v14) & % 190.01/26.29 A_set_list_a_set_list_fun$(v13)))) % 190.01/26.29 % 190.01/26.29 (axiom178) % 190.01/26.29 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.01/26.29 A_ltln$(false_ltln$) & ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: % 190.01/26.29 A_set_list$] : ! [v3: A_set_list_a_ltln_fun$] : ! [v4: % 190.01/26.29 A_set_list_a_set_list_fun$] : ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ % 190.01/26.29 (append$(v1) = v4) | ~ (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, % 190.01/26.29 v0) = v3) | ~ (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ % 190.01/26.29 A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: % 190.01/26.29 A_ltln_bool_fun$] : ? [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: % 190.01/26.29 any] : (fun_app$s(v3, v1) = v7 & fun_app$e(eq$, v7) = v8 & fun_app$e(eq$, % 190.01/26.29 v6) = v10 & fun_app$(v10, false_ltln$) = v11 & fun_app$(v8, false_ltln$) % 190.01/26.29 = v9 & A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ % 190.01/26.29 (v9 = 0) | v11 = 0))) % 190.01/26.29 % 190.01/26.29 (axiom188) % 190.01/26.29 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.01/26.29 A_ltln$(false_ltln$) & tlbool(tltrue) & ? [v0: A_set_list_a_ltln_fun$] : ? % 190.01/26.29 [v1: A_set_list_a_ltln_fun$] : (foldl$(af_letter$, true_ltln$) = v0 & % 190.01/26.29 foldl$(af_letter$, false_ltln$) = v1 & A_set_list_a_ltln_fun$(v1) & % 190.01/26.29 A_set_list_a_ltln_fun$(v0) & ? [v2: tlbool] : ! [v3: A_set_list$] : ! % 190.01/26.29 [v4: A_ltln$] : (v4 = false_ltln$ | v2 = tltrue | ~ (fun_app$s(v1, v3) = % 190.01/26.29 v4) | ~ A_set_list$(v3) | ~ tlbool(v2)) & ! [v2: A_set_list$] : ! % 190.01/26.29 [v3: A_ltln$] : (v3 = true_ltln$ | ~ (fun_app$s(v0, v2) = v3) | ~ % 190.01/26.29 A_set_list$(v2))) % 190.01/26.29 % 190.01/26.29 (axiom189) % 190.01/26.29 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.01/26.29 A_ltln$(false_ltln$) & tlbool(tltrue) & ? [v0: A_set_list_a_ltln_fun$] : ? % 190.01/26.29 [v1: A_set_list_a_ltln_fun$] : (foldl$(af_letter$, true_ltln$) = v1 & % 190.01/26.29 foldl$(af_letter$, false_ltln$) = v0 & A_set_list_a_ltln_fun$(v1) & % 190.01/26.29 A_set_list_a_ltln_fun$(v0) & ? [v2: tlbool] : ! [v3: A_set_list$] : ! % 190.01/26.29 [v4: A_ltln$] : (v4 = true_ltln$ | v2 = tltrue | ~ (fun_app$s(v1, v3) = v4) % 190.01/26.29 | ~ A_set_list$(v3) | ~ tlbool(v2)) & ! [v2: A_set_list$] : ! [v3: % 190.01/26.29 A_ltln$] : (v3 = false_ltln$ | ~ (fun_app$s(v0, v2) = v3) | ~ % 190.01/26.29 A_set_list$(v2))) % 190.01/26.29 % 190.01/26.29 (axiom216) % 190.01/26.30 ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 190.01/26.30 int] : (v2 = 0 | ~ (gF_advice_congruent$(v0, v1) = v2) | ~ % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v3: any] : % 190.01/26.30 ? [v4: any] : (gF_advice_congruent_axioms$(v0, v1) = v4 & % 190.01/26.30 ltl_equivalence$(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: any] : % 190.01/26.30 ( ~ (gF_advice_congruent_axioms$(v0, v1) = v2) | ~ % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v3: any] : % 190.01/26.30 ? [v4: any] : (gF_advice_congruent$(v0, v1) = v3 & ltl_equivalence$(v0) = % 190.01/26.30 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ( ~ % 190.01/26.30 (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? [v2: any] : % 190.01/26.30 ? [v3: any] : (gF_advice_congruent$(v0, v1) = v3 & ltl_equivalence$(v0) = % 190.01/26.30 v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! % 190.01/26.30 [v1: A_ltln_a_ltln_fun$] : ( ~ (gF_advice_congruent$(v0, v1) = 0) | ~ % 190.01/26.30 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | % 190.01/26.30 (gF_advice_congruent_axioms$(v0, v1) = 0 & ltl_equivalence$(v0) = 0)) % 190.01/26.30 % 190.01/26.30 (axiom229) % 190.30/26.30 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 190.30/26.30 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 190.30/26.30 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 190.30/26.30 ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! [v8: int] : (v8 = 0 | ~ % 190.30/26.30 (semantics_ltln$(v1) = v4) | ~ (until_ltln$(v2) = v5) | ~ (fun_app$d(v5, % 190.30/26.30 v3) = v6) | ~ (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v4, v7) = v8) | % 190.30/26.30 ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v9: A_ltln$] % 190.30/26.30 : ? [v10: int] : ( ~ (v10 = 0) & fun_app$d(v0, v3) = v9 & fun_app$(v4, % 190.30/26.30 v9) = v10 & A_ltln$(v9))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 190.30/26.30 : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 190.30/26.30 : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (semantics_ltln$(v1) = v4) | ~ % 190.30/26.30 (until_ltln$(v2) = v5) | ~ (fun_app$d(v5, v3) = v6) | ~ (fun_app$d(v0, % 190.30/26.30 v6) = v7) | ~ (fun_app$(v4, v7) = 0) | ~ Nat_a_set_fun$(v1) | ~ % 190.30/26.30 A_ltln$(v3) | ~ A_ltln$(v2) | ? [v8: A_ltln$] : (fun_app$d(v0, v3) = v8 % 190.30/26.30 & fun_app$(v4, v8) = 0 & A_ltln$(v8)))) % 190.30/26.30 % 190.30/26.30 (axiom241) % 190.30/26.30 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.30/26.30 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.30/26.30 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.30/26.30 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln_set$] : ! [v3: Nat_a_set_fun$] : ! % 190.30/26.30 [v4: A_ltln$] : ! [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ( ~ % 190.30/26.30 (semantics_ltln$(v3) = v5) | ~ (gF_advice$(v4, v2) = v6) | ~ % 190.30/26.30 (fun_app$(v5, v6) = 0) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ % 190.30/26.30 A_ltln_set$(v2) | ? [v7: int] : ? [v8: A_ltln$] : ? [v9: int] : ? % 190.30/26.30 [v10: A_ltln$] : ? [v11: A_ltln$] : ? [v12: int] : (A_ltln$(v8) & ((v9 = % 190.30/26.30 0 & ~ (v12 = 0) & fun_app$d(v1, v8) = v10 & fun_app$d(v0, v10) = % 190.30/26.30 v11 & member$(v8, v2) = 0 & fun_app$(v5, v11) = v12 & A_ltln$(v11) & % 190.30/26.30 A_ltln$(v10)) | (v7 = 0 & fun_app$(v5, v4) = 0))))) % 190.30/26.30 % 190.30/26.30 (axiom251) % 190.30/26.30 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.30/26.30 A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) % 190.30/26.30 & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_set_list$] : ! % 190.30/26.30 [v4: A_set_list$] : ! [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ! [v7: % 190.30/26.30 A_set_list_a_ltln_fun$] : ! [v8: A_set_list_a_set_list_fun$] : ! [v9: % 190.30/26.30 A_set_list$] : ! [v10: A_ltln$] : ! [v11: int] : (v11 = 0 | ~ % 190.30/26.30 (semantics_ltln$(v1) = v5) | ~ (append$(v4) = v8) | ~ (fun_app$t(v8, v3) % 190.30/26.30 = v9) | ~ (foldl$(af_letter$, v6) = v7) | ~ (fun_app$s(v7, v9) = v10) % 190.30/26.30 | ~ (fun_app$d(v0, v2) = v6) | ~ (fun_app$(v5, v10) = v11) | ~ % 190.30/26.30 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ A_set_list$(v4) | ~ % 190.30/26.30 A_set_list$(v3) | ? [v12: A_ltln$] : ? [v13: int] : ( ~ (v13 = 0) & % 190.30/26.30 fun_app$s(v7, v3) = v12 & fun_app$(v5, v12) = v13 & A_ltln$(v12)))) % 190.30/26.30 % 190.30/26.30 (axiom257) % 190.30/26.31 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.30/26.31 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & A_ltln_set$(mu_LTL$) & ? [v0: % 190.30/26.31 A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.30/26.31 (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.30/26.31 A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: % 190.30/26.31 Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 190.30/26.31 A_ltln$] : ! [v7: any] : ( ~ (semantics_ltln$(v3) = v4) | ~ % 190.30/26.31 (fun_app$d(v1, v2) = v5) | ~ (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, % 190.30/26.31 v6) = v7) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? % 190.30/26.31 [v9: A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = % 190.30/26.31 v9 & member$(v2, mu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) % 190.30/26.31 & ( ~ (v8 = 0) | (( ~ (v7 = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? % 190.30/26.31 [v12: Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? % 190.30/26.31 [v15: A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.30/26.31 fun_app$s(v9, v13) = v14 & fun_app$e(eq$, v14) = v15 & % 190.30/26.31 fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.30/26.31 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 % 190.30/26.31 = 0 | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 190.30/26.31 (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.30/26.31 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.30/26.31 (v15 = 0) & fun_app$s(v9, v12) = v13 & fun_app$e(eq$, v13) = % 190.30/26.31 v14 & fun_app$(v14, true_ltln$) = v15 & A_ltln$(v13) & % 190.30/26.31 A_ltln_bool_fun$(v14))))))))) % 190.30/26.31 % 190.30/26.31 (axiom258) % 190.30/26.31 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.30/26.31 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & A_ltln_set$(nu_LTL$) & ? [v0: % 190.30/26.31 A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.30/26.31 (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 190.30/26.31 A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: % 190.30/26.31 Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 190.30/26.31 A_ltln$] : ! [v7: any] : ( ~ (semantics_ltln$(v3) = v4) | ~ % 190.30/26.31 (fun_app$d(v1, v2) = v5) | ~ (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, % 190.30/26.31 v6) = v7) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? % 190.30/26.31 [v9: A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = % 190.30/26.31 v9 & member$(v2, nu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) % 190.30/26.31 & ( ~ (v8 = 0) | (( ~ (v7 = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] % 190.30/26.31 : ( ~ (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.30/26.31 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.30/26.31 (v15 = 0) & fun_app$s(v9, v12) = v13 & fun_app$e(eq$, v13) = % 190.30/26.31 v14 & fun_app$(v14, false_ltln$) = v15 & A_ltln$(v13) & % 190.30/26.31 A_ltln_bool_fun$(v14)))) & (v7 = 0 | ? [v11: Nat$] : ( ~ % 190.30/26.31 Nat$(v11) | ? [v12: Nat$] : ? [v13: A_set_list$] : ? [v14: % 190.30/26.31 A_ltln$] : ? [v15: A_ltln_bool_fun$] : (subsequence$(v3, v11, % 190.30/26.31 v12) = v13 & fun_app$s(v9, v13) = v14 & fun_app$e(eq$, v14) % 190.30/26.31 = v15 & fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 190.30/26.31 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12))))))))) % 190.30/26.31 % 190.30/26.31 (axiom26) % 190.30/26.31 transition_functions_size$(eq$, normalise$) = 0 & % 190.30/26.31 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_ltln_fun$(normalise$) % 190.30/26.31 % 190.30/26.31 (axiom272) % 190.30/26.31 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.30/26.31 A_ltln$(false_ltln$) & A_ltln_set$(mu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.30/26.31 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.30/26.31 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.30/26.31 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln_a_ltln_bool_fun_fun$] : ! [v3: % 190.30/26.31 A_ltln$] : ! [v4: Nat_a_set_fun$] : ! [v5: A_ltln_bool_fun$] : ! [v6: % 190.30/26.31 A_ltln$] : ! [v7: A_ltln$] : ! [v8: any] : ( ~ (semantics_ltln$(v4) = % 190.30/26.31 v5) | ~ (ltl_equivalence$(v2) = 0) | ~ (fun_app$d(v1, v3) = v6) | ~ % 190.30/26.31 (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v5, v7) = v8) | ~ % 190.30/26.31 A_ltln_a_ltln_bool_fun_fun$(v2) | ~ Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | % 190.30/26.31 ? [v9: any] : ? [v10: A_set_list_a_ltln_fun$] : ? [v11: Nat$] : % 190.39/26.31 (foldl$(af_letter$, v6) = v10 & member$(v3, mu_LTL$) = v9 & % 190.39/26.31 A_set_list_a_ltln_fun$(v10) & Nat$(v11) & ( ~ (v9 = 0) | (( ~ (v8 = 0) | % 190.39/26.31 ? [v12: Nat$] : ( ~ Nat$(v12) | ? [v13: Nat$] : ? [v14: % 190.39/26.31 A_set_list$] : ? [v15: A_ltln$] : ? [v16: A_ltln_bool_fun$] % 190.39/26.31 : (subsequence$(v4, v12, v13) = v14 & fun_app$s(v10, v14) = v15 % 190.39/26.31 & fun_app$e(v2, v15) = v16 & fun_app$(v16, true_ltln$) = 0 & % 190.39/26.31 A_ltln$(v15) & A_set_list$(v14) & A_ltln_bool_fun$(v16) & % 190.39/26.31 Nat$(v13)))) & (v8 = 0 | ! [v12: Nat$] : ! [v13: % 190.39/26.31 A_set_list$] : ( ~ (subsequence$(v4, v11, v12) = v13) | ~ % 190.39/26.31 Nat$(v12) | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : ? % 190.39/26.31 [v16: int] : ( ~ (v16 = 0) & fun_app$s(v10, v13) = v14 & % 190.39/26.32 fun_app$e(v2, v14) = v15 & fun_app$(v15, true_ltln$) = v16 & % 190.39/26.32 A_ltln$(v14) & A_ltln_bool_fun$(v15))))))))) % 190.39/26.32 % 190.39/26.32 (axiom273) % 190.39/26.32 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.39/26.32 A_ltln$(false_ltln$) & A_ltln_set$(nu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.39/26.32 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v1 & % 190.39/26.32 until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 190.39/26.32 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln_a_ltln_bool_fun_fun$] : ! [v3: % 190.39/26.32 A_ltln$] : ! [v4: Nat_a_set_fun$] : ! [v5: A_ltln_bool_fun$] : ! [v6: % 190.39/26.32 A_ltln$] : ! [v7: A_ltln$] : ! [v8: any] : ( ~ (semantics_ltln$(v4) = % 190.39/26.32 v5) | ~ (ltl_equivalence$(v2) = 0) | ~ (fun_app$d(v1, v3) = v6) | ~ % 190.39/26.32 (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v5, v7) = v8) | ~ % 190.39/26.32 A_ltln_a_ltln_bool_fun_fun$(v2) | ~ Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | % 190.39/26.32 ? [v9: any] : ? [v10: A_set_list_a_ltln_fun$] : ? [v11: Nat$] : % 190.39/26.32 (foldl$(af_letter$, v6) = v10 & member$(v3, nu_LTL$) = v9 & % 190.39/26.32 A_set_list_a_ltln_fun$(v10) & Nat$(v11) & ( ~ (v9 = 0) | (( ~ (v8 = 0) | % 190.39/26.32 ! [v12: Nat$] : ! [v13: A_set_list$] : ( ~ (subsequence$(v4, % 190.39/26.32 v11, v12) = v13) | ~ Nat$(v12) | ? [v14: A_ltln$] : ? % 190.39/26.32 [v15: A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = 0) & % 190.39/26.32 fun_app$s(v10, v13) = v14 & fun_app$e(v2, v14) = v15 & % 190.39/26.32 fun_app$(v15, false_ltln$) = v16 & A_ltln$(v14) & % 190.39/26.32 A_ltln_bool_fun$(v15)))) & (v8 = 0 | ? [v12: Nat$] : ( ~ % 190.39/26.32 Nat$(v12) | ? [v13: Nat$] : ? [v14: A_set_list$] : ? [v15: % 190.39/26.32 A_ltln$] : ? [v16: A_ltln_bool_fun$] : (subsequence$(v4, v12, % 190.39/26.32 v13) = v14 & fun_app$s(v10, v14) = v15 & fun_app$e(v2, v15) % 190.39/26.32 = v16 & fun_app$(v16, false_ltln$) = 0 & A_ltln$(v15) & % 190.39/26.32 A_set_list$(v14) & A_ltln_bool_fun$(v16) & Nat$(v13))))))))) % 190.39/26.32 % 190.39/26.32 (axiom296) % 190.39/26.33 A_ltln_a_ltln_bool_fun_fun$(eq$) & Nat_int_fun$(of_nat$) & % 190.39/26.33 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.39/26.33 A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? % 190.39/26.33 [v2: Nat$] : (nat$(0) = v2 & af_letter_F$(eq$) = v1 & until_ltln$(true_ltln$) % 190.39/26.33 = v0 & Nat$(v2) & A_ltln_a_ltln_fun$(v0) & % 190.39/26.33 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v1) & ? [v3: Nat_a_set_fun$] : ! % 190.39/26.33 [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_set_a_ltln_fun_fun$] : % 190.39/26.33 ! [v7: A_set_list_a_ltln_fun$] : ! [v8: Nat$] : ! [v9: int] : ( ~ % 190.39/26.33 (fun_app$y(of_nat$, v8) = v9) | ~ (foldl$(v6, v5) = v7) | ~ % 190.39/26.33 (fun_app$c(v1, v4) = v6) | ~ (fun_app$d(v0, v4) = v5) | ~ % 190.39/26.33 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v8) | ? [v10: % 190.39/26.33 A_set_list_a_ltln_fun$] : ? [v11: Nat$] : ? [v12: Nat$] : ? [v13: % 190.39/26.33 int] : ? [v14: A_set_list$] : ? [v15: A_ltln$] : ? [v16: % 190.39/26.33 A_ltln_bool_fun$] : ? [v17: int] : (Nat$(v12) & Nat$(v11) & ((v17 = 0 & % 190.39/26.33 $lesseq(1, $difference(v13, v9)) & fun_app$y(of_nat$, v12) = v13 & % 190.39/26.33 subsequence$(v3, v2, v12) = v14 & fun_app$s(v7, v14) = v15 & % 190.39/26.33 fun_app$e(eq$, v15) = v16 & fun_app$(v16, true_ltln$) = 0 & % 190.39/26.33 A_ltln$(v15) & A_set_list$(v14) & A_ltln_bool_fun$(v16)) | % 190.39/26.33 (foldl$(af_letter$, v5) = v10 & A_set_list_a_ltln_fun$(v10) & ! [v18: % 190.39/26.33 Nat$] : ! [v19: A_set_list$] : ( ~ (subsequence$(v3, v11, v18) = % 190.39/26.33 v19) | ~ Nat$(v18) | ? [v20: A_ltln$] : ? [v21: % 190.39/26.33 A_ltln_bool_fun$] : ? [v22: int] : ( ~ (v22 = 0) & % 190.39/26.33 fun_app$s(v10, v19) = v20 & fun_app$e(eq$, v20) = v21 & % 190.39/26.33 fun_app$(v21, true_ltln$) = v22 & A_ltln$(v20) & % 190.39/26.33 A_ltln_bool_fun$(v21))))))) & ? [v3: Nat_a_set_fun$] : ! [v4: % 190.39/26.33 A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_set_list_a_ltln_fun$] : ( ~ % 190.39/26.33 (foldl$(af_letter$, v5) = v6) | ~ (fun_app$d(v0, v4) = v5) | ~ % 190.39/26.33 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ? [v7: % 190.39/26.33 A_ltln_a_set_a_ltln_fun_fun$] : ? [v8: A_set_list_a_ltln_fun$] : ? % 190.39/26.33 [v9: Nat$] : (Nat$(v9) & ( ! [v10: Nat$] : ! [v11: A_set_list$] : ( ~ % 190.39/26.33 (subsequence$(v3, v9, v10) = v11) | ~ Nat$(v10) | ? [v12: A_ltln$] % 190.39/26.33 : ? [v13: A_ltln_bool_fun$] : ? [v14: int] : ( ~ (v14 = 0) & % 190.39/26.33 fun_app$s(v6, v11) = v12 & fun_app$e(eq$, v12) = v13 & % 190.39/26.33 fun_app$(v13, true_ltln$) = v14 & A_ltln$(v12) & % 190.39/26.33 A_ltln_bool_fun$(v13))) | (foldl$(v7, v5) = v8 & fun_app$c(v1, v4) % 190.39/26.33 = v7 & A_set_list_a_ltln_fun$(v8) & A_ltln_a_set_a_ltln_fun_fun$(v7) % 190.39/26.33 & ! [v10: Nat$] : ! [v11: int] : ( ~ (fun_app$y(of_nat$, v10) = % 190.39/26.33 v11) | ~ Nat$(v10) | ? [v12: Nat$] : ? [v13: int] : ? [v14: % 190.39/26.33 A_set_list$] : ? [v15: A_ltln$] : ? [v16: A_ltln_bool_fun$] : % 190.39/26.33 ($lesseq(1, $difference(v13, v11)) & fun_app$y(of_nat$, v12) = v13 % 190.39/26.33 & subsequence$(v3, v2, v12) = v14 & fun_app$s(v8, v14) = v15 & % 190.39/26.33 fun_app$e(eq$, v15) = v16 & fun_app$(v16, true_ltln$) = 0 & % 190.39/26.33 A_ltln$(v15) & A_set_list$(v14) & A_ltln_bool_fun$(v16) & % 190.39/26.33 Nat$(v12)))))))) % 190.39/26.33 % 190.39/26.33 (axiom30) % 190.39/26.33 ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : % 190.39/26.33 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_bool_fun$] : ! % 190.39/26.33 [v6: int] : (v6 = 0 | ~ (fun_app$e(v0, v2) = v5) | ~ (fun_app$e(v0, v1) = % 190.39/26.33 v4) | ~ (fun_app$(v5, v3) = 0) | ~ (fun_app$(v4, v3) = v6) | ~ % 190.39/26.33 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.39/26.33 A_ltln$(v1) | ? [v7: any] : ? [v8: any] : (ltl_equivalence$(v0) = v7 & % 190.39/26.33 fun_app$(v4, v2) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: % 190.39/26.33 A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 190.39/26.33 A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: int] : (v5 = 0 | ~ % 190.39/26.33 (fun_app$e(v0, v1) = v4) | ~ (fun_app$(v4, v3) = v5) | ~ (fun_app$(v4, v2) % 190.39/26.33 = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ % 190.39/26.33 A_ltln$(v2) | ~ A_ltln$(v1) | ? [v6: any] : ? [v7: A_ltln_bool_fun$] : ? % 190.39/26.33 [v8: any] : (ltl_equivalence$(v0) = v6 & fun_app$e(v0, v2) = v7 & % 190.39/26.33 fun_app$(v7, v3) = v8 & A_ltln_bool_fun$(v7) & ( ~ (v8 = 0) | ~ (v6 = % 190.39/26.33 0)))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln$] : ! % 190.39/26.33 [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.39/26.33 A_ltln_bool_fun$] : ( ~ (fun_app$e(v0, v2) = v5) | ~ (fun_app$e(v0, v1) = % 190.39/26.33 v4) | ~ (fun_app$(v5, v3) = 0) | ~ (fun_app$(v4, v2) = 0) | ~ % 190.39/26.33 A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.39/26.33 A_ltln$(v1) | ? [v6: any] : ? [v7: any] : (ltl_equivalence$(v0) = v6 & % 190.39/26.33 fun_app$(v4, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))) % 190.39/26.33 % 190.39/26.33 (axiom307) % 190.39/26.33 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ % 190.39/26.33 (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: % 190.39/26.33 any] : (less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v1 = v0) & ( ~ (v1 = v0) | % 190.39/26.33 v3 = 0))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = v0 | ~ % 190.39/26.33 (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | less$(v0, % 190.39/26.33 v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: int] : (v1 = 0 | ~ % 190.39/26.33 (less_eq$(v0, v0) = v1) | ~ A_ltln_set$(v0) | less$(v0, v0) = 0) % 190.39/26.33 % 190.39/26.33 (axiom313) % 190.39/26.34 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ % 190.39/26.34 (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: % 190.39/26.34 any] : ? [v4: any] : (less_eq$(v1, v0) = v4 & less_eq$(v0, v1) = v3 & ( ~ % 190.39/26.34 (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 190.39/26.34 [v2: int] : (v2 = 0 | ~ (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ % 190.39/26.34 A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v4 & % 190.39/26.34 less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : % 190.39/26.34 ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ (less_eq$(v1, v0) = v2) | ~ % 190.39/26.34 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : % 190.39/26.34 (less$(v0, v1) = v3 & less_eq$(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & ~ % 190.39/26.34 (v2 = 0))))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: % 190.39/26.34 any] : ( ~ (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 190.39/26.34 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v4 % 190.39/26.34 & ( ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: A_ltln_set$] : ! % 190.39/26.34 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.34 A_ltln_set$(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_eq$(v1, v0) = v2 & % 190.39/26.34 less_eq$(v0, v1) = 0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ % 190.39/26.34 (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: % 190.39/26.34 any] : ? [v3: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v2 & (v3 = % 190.39/26.34 0 | v2 = 0))) % 190.39/26.34 % 190.39/26.34 (axiom317) % 190.39/26.34 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | v1 = v0 % 190.39/26.34 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? % 190.39/26.34 [v3: int] : ( ~ (v3 = 0) & less_eq$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : % 190.39/26.34 ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ (less_eq$(v0, v1) = v2) | ~ % 190.39/26.34 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 190.39/26.34 less$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = % 190.39/26.34 v0 | ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 190.39/26.34 less$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: int] : (v1 = 0 | ~ % 190.39/26.34 (less_eq$(v0, v0) = v1) | ~ A_ltln_set$(v0)) & ! [v0: A_ltln_set$] : ! % 190.39/26.34 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.34 A_ltln_set$(v0) | less_eq$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: % 190.39/26.34 MultipleValueBool] : ( ~ (less$(v0, v0) = v1) | ~ A_ltln_set$(v0) | % 190.39/26.34 less_eq$(v0, v0) = 0) % 190.39/26.34 % 190.39/26.34 (axiom329) % 190.39/26.34 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ % 190.39/26.34 (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: % 190.39/26.34 any] : ? [v4: any] : (less_eq$(v1, v0) = v4 & less_eq$(v0, v1) = v3 & ( ~ % 190.39/26.34 (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 190.39/26.34 [v2: int] : (v2 = 0 | ~ (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ % 190.39/26.34 A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v4 & % 190.39/26.34 less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : % 190.39/26.34 ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ (less_eq$(v1, v0) = v2) | ~ % 190.39/26.34 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : % 190.39/26.34 (less$(v0, v1) = v3 & less_eq$(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & ~ % 190.39/26.34 (v2 = 0))))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: % 190.39/26.34 any] : ( ~ (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 190.39/26.34 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v4 % 190.39/26.34 & ( ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: A_ltln_set$] : ! % 190.39/26.34 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.34 A_ltln_set$(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_eq$(v1, v0) = v2 & % 190.39/26.34 less_eq$(v0, v1) = 0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ % 190.39/26.34 (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: % 190.39/26.34 any] : ? [v3: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v2 & (v3 = % 190.39/26.34 0 | v2 = 0))) % 190.39/26.34 % 190.39/26.34 (axiom33) % 190.39/26.35 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = v0 | ~ (less_eq$(v1, v0) % 190.39/26.35 = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: int] : ( ~ (v2 = % 190.39/26.35 0) & less_eq$(v0, v1) = v2)) & ! [v0: A_ltln_set$] : ! [v1: % 190.39/26.35 A_ltln_set$] : ( ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.35 A_ltln_set$(v0) | ? [v2: any] : (less_eq$(v1, v0) = v2 & ( ~ (v2 = 0) | v1 % 190.39/26.35 = v0) & ( ~ (v1 = v0) | v2 = 0))) % 190.39/26.35 % 190.39/26.35 (axiom332) % 190.39/26.35 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | v1 = v0 % 190.39/26.35 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? % 190.39/26.35 [v3: int] : ( ~ (v3 = 0) & less_eq$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : % 190.39/26.35 ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ (less_eq$(v0, v1) = v2) | ~ % 190.39/26.35 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 190.39/26.35 less$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = % 190.39/26.35 v0 | ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 190.39/26.35 less$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: int] : (v1 = 0 | ~ % 190.39/26.35 (less_eq$(v0, v0) = v1) | ~ A_ltln_set$(v0)) & ! [v0: A_ltln_set$] : ! % 190.39/26.35 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.35 A_ltln_set$(v0) | less_eq$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: % 190.39/26.35 MultipleValueBool] : ( ~ (less$(v0, v0) = v1) | ~ A_ltln_set$(v0) | % 190.39/26.35 less_eq$(v0, v0) = 0) % 190.39/26.35 % 190.39/26.35 (axiom344) % 190.39/26.35 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ % 190.39/26.35 (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: % 190.39/26.35 any] : ? [v4: any] : (less_eq$(v1, v0) = v4 & less_eq$(v0, v1) = v3 & ( ~ % 190.39/26.35 (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 190.39/26.35 [v2: int] : (v2 = 0 | ~ (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ % 190.39/26.35 A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v4 & % 190.39/26.35 less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : % 190.39/26.35 ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ (less_eq$(v1, v0) = v2) | ~ % 190.39/26.35 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : % 190.39/26.35 (less$(v0, v1) = v3 & less_eq$(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & ~ % 190.39/26.35 (v2 = 0))))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: % 190.39/26.35 any] : ( ~ (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 190.39/26.35 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v4 % 190.39/26.35 & ( ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: A_ltln_set$] : ! % 190.39/26.35 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.35 A_ltln_set$(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_eq$(v1, v0) = v2 & % 190.39/26.35 less_eq$(v0, v1) = 0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ % 190.39/26.35 (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: % 190.39/26.35 any] : ? [v3: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v2 & (v3 = % 190.39/26.35 0 | v2 = 0))) % 190.39/26.35 % 190.39/26.35 (axiom353) % 190.39/26.36 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | v1 = v0 % 190.39/26.36 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? % 190.39/26.36 [v3: int] : ( ~ (v3 = 0) & less_eq$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : % 190.39/26.36 ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ (less_eq$(v0, v1) = v2) | ~ % 190.39/26.36 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 190.39/26.36 less$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = % 190.39/26.36 v0 | ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 190.39/26.36 less$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: int] : (v1 = 0 | ~ % 190.39/26.36 (less_eq$(v0, v0) = v1) | ~ A_ltln_set$(v0)) & ! [v0: A_ltln_set$] : ! % 190.39/26.36 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.36 A_ltln_set$(v0) | less_eq$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: % 190.39/26.36 MultipleValueBool] : ( ~ (less$(v0, v0) = v1) | ~ A_ltln_set$(v0) | % 190.39/26.36 less_eq$(v0, v0) = 0) % 190.39/26.36 % 190.39/26.36 (axiom439) % 190.39/26.36 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.39/26.36 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v1 & % 190.39/26.36 until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 190.39/26.36 A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 190.39/26.36 A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: Nat_a_set_fun$] : % 190.39/26.36 ! [v8: A_ltln_bool_fun$] : ! [v9: int] : (v9 = 0 | ~ (suffix$(v2, v3) = % 190.39/26.36 v7) | ~ (semantics_ltln$(v7) = v8) | ~ (fun_app$d(v1, v4) = v5) | ~ % 190.39/26.36 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v8, v6) = v9) | ~ % 190.39/26.36 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? [v10: % 190.39/26.36 A_ltln_bool_fun$] : ? [v11: int] : ( ~ (v11 = 0) & semantics_ltln$(v3) % 190.39/26.36 = v10 & fun_app$(v10, v6) = v11 & A_ltln_bool_fun$(v10))) & ! [v2: % 190.39/26.36 Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.36 Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: % 190.39/26.36 A_ltln$] : ( ~ (suffix$(v2, v3) = v5) | ~ (semantics_ltln$(v5) = v6) | ~ % 190.39/26.36 (fun_app$d(v1, v4) = v7) | ~ (fun_app$d(v0, v7) = v8) | ~ (fun_app$(v6, % 190.39/26.36 v8) = 0) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? % 190.39/26.36 [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & fun_app$(v9, v8) = 0 % 190.39/26.36 & A_ltln_bool_fun$(v9)))) % 190.39/26.36 % 190.39/26.36 (axiom440) % 190.39/26.36 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.39/26.36 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.39/26.36 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.39/26.36 A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 190.39/26.36 A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: Nat_a_set_fun$] : % 190.39/26.36 ! [v8: A_ltln_bool_fun$] : ! [v9: int] : (v9 = 0 | ~ (suffix$(v2, v3) = % 190.39/26.36 v7) | ~ (semantics_ltln$(v7) = v8) | ~ (fun_app$d(v1, v4) = v5) | ~ % 190.39/26.36 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v8, v6) = v9) | ~ % 190.39/26.36 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? [v10: % 190.39/26.36 A_ltln_bool_fun$] : ? [v11: int] : ( ~ (v11 = 0) & semantics_ltln$(v3) % 190.39/26.36 = v10 & fun_app$(v10, v6) = v11 & A_ltln_bool_fun$(v10))) & ! [v2: % 190.39/26.36 Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.36 Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: % 190.39/26.36 A_ltln$] : ( ~ (suffix$(v2, v3) = v5) | ~ (semantics_ltln$(v5) = v6) | ~ % 190.39/26.36 (fun_app$d(v1, v4) = v7) | ~ (fun_app$d(v0, v7) = v8) | ~ (fun_app$(v6, % 190.39/26.36 v8) = 0) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? % 190.39/26.36 [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & fun_app$(v9, v8) = 0 % 190.39/26.36 & A_ltln_bool_fun$(v9)))) % 190.39/26.36 % 190.39/26.36 (axiom445) % 190.39/26.38 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 190.39/26.38 Nat$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.39/26.38 A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.38 A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! [v8: % 190.39/26.38 A_ltln_bool_fun$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ! [v11: int] : % 190.39/26.38 (v11 = 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (gF_advice$(v9, % 190.39/26.38 v5) = v10) | ~ (gF_advice$(v6, v5) = v7) | ~ (fun_app$e(v1, v7) = % 190.39/26.38 v8) | ~ (fun_app$d(v2, v4) = v9) | ~ (fun_app$d(v2, v3) = v6) | ~ % 190.39/26.38 (fun_app$(v8, v10) = v11) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.39/26.38 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_ltln_set$(v5) | ~ % 190.39/26.38 A_ltln_a_ltln_fun$(v2) | ? [v12: A_ltln_bool_fun$] : ? [v13: int] : ( ~ % 190.39/26.38 (v13 = 0) & fun_app$e(v1, v3) = v12 & fun_app$(v12, v4) = v13 & % 190.39/26.38 A_ltln_bool_fun$(v12))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.39/26.38 A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.38 A_ltln_set$] : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: % 190.39/26.38 A_ltln$] : ! [v9: int] : (v9 = 0 | ~ (gF_advice_congruent_axioms$(v1, % 190.39/26.38 v2) = 0) | ~ (semantics_ltln$(v3) = v6) | ~ (gF_advice$(v7, v5) = % 190.39/26.38 v8) | ~ (fun_app$d(v2, v4) = v7) | ~ (fun_app$(v6, v8) = v9) | ~ % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 190.39/26.38 ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v10: A_ltln$] : ? % 190.39/26.38 [v11: int] : ( ~ (v11 = 0) & gF_advice$(v4, v5) = v10 & fun_app$(v6, v10) % 190.39/26.38 = v11 & A_ltln$(v10))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.39/26.38 A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.38 A_ltln_set$] : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: % 190.39/26.38 A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 190.39/26.38 (semantics_ltln$(v3) = v6) | ~ (gF_advice$(v7, v5) = v8) | ~ % 190.39/26.38 (fun_app$d(v2, v4) = v7) | ~ (fun_app$(v6, v8) = 0) | ~ % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 190.39/26.38 ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v9: % 190.39/26.38 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : ? [v11: Nat_a_set_fun$] : ? % 190.39/26.38 [v12: A_ltln_bool_fun$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? % 190.39/26.38 [v15: A_ltln$] : (suffix$(v10, v3) = v11 & subsequence$(v3, v0, v10) = v13 % 190.39/26.38 & semantics_ltln$(v11) = v12 & gF_advice$(v14, v5) = v15 & % 190.39/26.38 foldl$(af_letter$, v4) = v9 & fun_app$s(v9, v13) = v14 & fun_app$(v12, % 190.39/26.38 v15) = 0 & A_set_list_a_ltln_fun$(v9) & Nat_a_set_fun$(v11) & % 190.39/26.38 A_ltln$(v15) & A_ltln$(v14) & A_set_list$(v13) & A_ltln_bool_fun$(v12) & % 190.39/26.38 Nat$(v10))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.39/26.38 A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 190.39/26.38 A_ltln_set$] : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ( ~ % 190.39/26.38 (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (semantics_ltln$(v3) = v6) % 190.39/26.38 | ~ (gF_advice$(v4, v5) = v7) | ~ (fun_app$(v6, v7) = 0) | ~ % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 190.39/26.38 ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v8: A_ltln$] : ? % 190.39/26.38 [v9: A_ltln$] : (gF_advice$(v8, v5) = v9 & fun_app$d(v2, v4) = v8 & % 190.39/26.38 fun_app$(v6, v9) = 0 & A_ltln$(v9) & A_ltln$(v8))) & ! [v1: % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.39/26.38 A_ltln$] : ! [v4: A_ltln_bool_fun$] : ( ~ % 190.39/26.38 (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$e(v1, v3) = v4) | % 190.39/26.38 ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 190.39/26.38 A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln$] : (fun_app$d(v2, v3) = v5 & % 190.39/26.38 fun_app$(v4, v5) = 0 & A_ltln$(v5))) & ! [v1: % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.39/26.38 A_ltln$] : ! [v4: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = % 190.39/26.38 0) | ~ (fun_app$d(v2, v3) = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | % 190.39/26.38 ~ A_ltln$(v3) | ~ A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln_bool_fun$] : % 190.39/26.38 (fun_app$e(v1, v3) = v5 & fun_app$(v5, v4) = 0 & A_ltln_bool_fun$(v5))) & % 190.39/26.38 ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.39/26.38 int] : (v3 = 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = v3) | ~ % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | ? [v4: % 190.39/26.38 A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? [v7: % 190.39/26.38 A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? [v10: A_ltln$] % 190.39/26.38 : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? % 190.39/26.38 [v14: int] : ? [v15: Nat_a_set_fun$] : ? [v16: A_ltln$] : ? [v17: % 190.39/26.38 A_ltln_set$] : ? [v18: A_ltln_bool_fun$] : ? [v19: A_ltln$] : ? [v20: % 190.39/26.38 A_ltln$] : ? [v21: int] : ? [v22: A_set_list_a_ltln_fun$] : ? [v23: % 190.39/26.38 Nat_a_set_fun$] : ? [v24: A_ltln$] : ? [v25: A_ltln_set$] : ? [v26: % 190.39/26.38 A_ltln_bool_fun$] : ? [v27: A_ltln$] : ? [v28: int] : ? [v29: % 190.39/26.38 A_ltln$] : ? [v30: A_ltln$] : ? [v31: int] : ? [v32: A_ltln$] : ? % 190.39/26.38 [v33: A_ltln_bool_fun$] : ? [v34: A_ltln$] : ? [v35: int] : % 190.39/26.38 (Nat_a_set_fun$(v23) & Nat_a_set_fun$(v15) & A_ltln$(v32) & A_ltln$(v24) & % 190.39/26.38 A_ltln$(v16) & A_ltln$(v5) & A_ltln$(v4) & A_ltln_set$(v25) & % 190.39/26.38 A_ltln_set$(v17) & A_ltln_set$(v6) & ((v28 = 0 & ~ (v31 = 0) & % 190.39/26.38 semantics_ltln$(v23) = v26 & gF_advice$(v29, v25) = v30 & % 190.39/26.38 gF_advice$(v24, v25) = v27 & fun_app$d(v2, v24) = v29 & % 190.39/26.38 fun_app$(v26, v30) = v31 & fun_app$(v26, v27) = 0 & A_ltln$(v30) & % 190.39/26.38 A_ltln$(v29) & A_ltln$(v27) & A_ltln_bool_fun$(v26)) | (v21 = 0 & % 190.39/26.38 semantics_ltln$(v15) = v18 & gF_advice$(v19, v17) = v20 & % 190.39/26.38 foldl$(af_letter$, v16) = v22 & fun_app$d(v2, v16) = v19 & % 190.39/26.38 fun_app$(v18, v20) = 0 & A_set_list_a_ltln_fun$(v22) & A_ltln$(v20) % 190.39/26.38 & A_ltln$(v19) & A_ltln_bool_fun$(v18) & ! [v36: Nat$] : ! [v37: % 190.39/26.38 Nat_a_set_fun$] : ( ~ (suffix$(v36, v15) = v37) | ~ Nat$(v36) | % 190.39/26.38 ? [v38: A_ltln_bool_fun$] : ? [v39: A_set_list$] : ? [v40: % 190.39/26.38 A_ltln$] : ? [v41: A_ltln$] : ? [v42: int] : ( ~ (v42 = 0) & % 190.39/26.38 subsequence$(v15, v0, v36) = v39 & semantics_ltln$(v37) = v38 & % 190.39/26.38 gF_advice$(v40, v17) = v41 & fun_app$s(v22, v39) = v40 & % 190.39/26.38 fun_app$(v38, v41) = v42 & A_ltln$(v41) & A_ltln$(v40) & % 190.39/26.38 A_set_list$(v39) & A_ltln_bool_fun$(v38))) & ! [v36: Nat$] : ! % 190.39/26.38 [v37: A_set_list$] : ( ~ (subsequence$(v15, v0, v36) = v37) | ~ % 190.39/26.38 Nat$(v36) | ? [v38: Nat_a_set_fun$] : ? [v39: A_ltln_bool_fun$] % 190.39/26.38 : ? [v40: A_ltln$] : ? [v41: A_ltln$] : ? [v42: int] : ( ~ (v42 % 190.39/26.38 = 0) & suffix$(v36, v15) = v38 & semantics_ltln$(v38) = v39 & % 190.39/26.38 gF_advice$(v40, v17) = v41 & fun_app$s(v22, v37) = v40 & % 190.39/26.38 fun_app$(v39, v41) = v42 & Nat_a_set_fun$(v38) & A_ltln$(v41) & % 190.39/26.38 A_ltln$(v40) & A_ltln_bool_fun$(v39)))) | (v8 = 0 & ~ (v14 = 0) % 190.39/26.38 & gF_advice$(v12, v6) = v13 & gF_advice$(v9, v6) = v10 & % 190.39/26.38 fun_app$e(v1, v10) = v11 & fun_app$e(v1, v4) = v7 & fun_app$d(v2, % 190.39/26.38 v5) = v12 & fun_app$d(v2, v4) = v9 & fun_app$(v11, v13) = v14 & % 190.39/26.38 fun_app$(v7, v5) = 0 & A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v10) & % 190.39/26.38 A_ltln$(v9) & A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7)) | ( ~ % 190.39/26.38 (v35 = 0) & fun_app$e(v1, v32) = v33 & fun_app$d(v2, v32) = v34 & % 190.39/26.38 fun_app$(v33, v34) = v35 & A_ltln$(v34) & A_ltln_bool_fun$(v33)))))) % 190.39/26.38 % 190.39/26.38 (axiom448) % 190.39/26.38 Nat_int_fun$(of_nat$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.39/26.38 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? [v1: Nat$] : (nat$(0) = % 190.39/26.38 v1 & until_ltln$(true_ltln$) = v0 & Nat$(v1) & A_ltln_a_ltln_fun$(v0) & ? % 190.39/26.38 [v2: Nat_a_set_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : ! [v4: % 190.39/26.38 A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: % 190.39/26.38 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.39/26.38 A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : ! [v10: % 190.39/26.38 Nat$] : ! [v11: int] : ( ~ (fun_app$y(of_nat$, v10) = v11) | ~ % 190.39/26.38 (transition_functions$(v3, v4) = 0) | ~ (foldl$(v8, v6) = v9) | ~ % 190.39/26.38 (fun_app$c(v7, v5) = v8) | ~ (af_letter_F$(v3) = v7) | ~ (fun_app$d(v0, % 190.39/26.38 v5) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v3) | ~ Nat_a_set_fun$(v2) % 190.39/26.38 | ~ A_ltln$(v5) | ~ Nat$(v10) | ~ A_ltln_a_ltln_fun$(v4) | ? [v12: % 190.39/26.38 A_set_list_a_ltln_fun$] : ? [v13: Nat$] : ? [v14: Nat$] : ? [v15: % 190.39/26.38 int] : ? [v16: A_set_list$] : ? [v17: A_ltln$] : ? [v18: % 190.39/26.38 A_ltln_bool_fun$] : ? [v19: int] : (Nat$(v14) & Nat$(v13) & ((v19 = 0 & % 190.39/26.38 $lesseq(1, $difference(v15, v11)) & fun_app$y(of_nat$, v14) = v15 & % 190.39/26.38 subsequence$(v2, v1, v14) = v16 & fun_app$s(v9, v16) = v17 & % 190.39/26.38 fun_app$e(v3, v17) = v18 & fun_app$(v18, true_ltln$) = 0 & % 190.39/26.38 A_ltln$(v17) & A_set_list$(v16) & A_ltln_bool_fun$(v18)) | % 190.39/26.38 (foldl$(af_letter$, v6) = v12 & A_set_list_a_ltln_fun$(v12) & ! [v20: % 190.39/26.38 Nat$] : ! [v21: A_set_list$] : ( ~ (subsequence$(v2, v13, v20) = % 190.39/26.38 v21) | ~ Nat$(v20) | ? [v22: A_ltln$] : ? [v23: % 190.39/26.38 A_ltln_bool_fun$] : ? [v24: int] : ( ~ (v24 = 0) & % 190.39/26.38 fun_app$s(v12, v21) = v22 & fun_app$e(v3, v22) = v23 & % 190.39/26.38 fun_app$(v23, true_ltln$) = v24 & A_ltln$(v22) & % 190.39/26.38 A_ltln_bool_fun$(v23))))))) & ? [v2: Nat_a_set_fun$] : ! [v3: % 190.39/26.38 A_ltln_a_ltln_bool_fun_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 190.39/26.38 A_ltln$] : ! [v6: A_ltln$] : ! [v7: A_set_list_a_ltln_fun$] : ( ~ % 190.39/26.38 (transition_functions$(v3, v4) = 0) | ~ (foldl$(af_letter$, v6) = v7) | % 190.39/26.38 ~ (fun_app$d(v0, v5) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v3) | ~ % 190.39/26.38 Nat_a_set_fun$(v2) | ~ A_ltln$(v5) | ~ A_ltln_a_ltln_fun$(v4) | ? [v8: % 190.39/26.38 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v9: % 190.39/26.38 A_ltln_a_set_a_ltln_fun_fun$] : ? [v10: A_set_list_a_ltln_fun$] : ? % 190.39/26.38 [v11: Nat$] : (Nat$(v11) & ( ! [v12: Nat$] : ! [v13: A_set_list$] : ( ~ % 190.39/26.38 (subsequence$(v2, v11, v12) = v13) | ~ Nat$(v12) | ? [v14: % 190.39/26.38 A_ltln$] : ? [v15: A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = % 190.39/26.38 0) & fun_app$s(v7, v13) = v14 & fun_app$e(v3, v14) = v15 & % 190.39/26.38 fun_app$(v15, true_ltln$) = v16 & A_ltln$(v14) & % 190.39/26.38 A_ltln_bool_fun$(v15))) | (foldl$(v9, v6) = v10 & fun_app$c(v8, % 190.39/26.38 v5) = v9 & af_letter_F$(v3) = v8 & A_set_list_a_ltln_fun$(v10) & % 190.39/26.38 A_ltln_a_set_a_ltln_fun_fun$(v9) & % 190.39/26.38 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v8) & ! [v12: Nat$] : ! % 190.39/26.38 [v13: int] : ( ~ (fun_app$y(of_nat$, v12) = v13) | ~ Nat$(v12) | ? % 190.39/26.38 [v14: Nat$] : ? [v15: int] : ? [v16: A_set_list$] : ? [v17: % 190.39/26.38 A_ltln$] : ? [v18: A_ltln_bool_fun$] : ($lesseq(1, % 190.39/26.38 $difference(v15, v13)) & fun_app$y(of_nat$, v14) = v15 & % 190.39/26.38 subsequence$(v2, v1, v14) = v16 & fun_app$s(v10, v16) = v17 & % 190.39/26.38 fun_app$e(v3, v17) = v18 & fun_app$(v18, true_ltln$) = 0 & % 190.39/26.38 A_ltln$(v17) & A_set_list$(v16) & A_ltln_bool_fun$(v18) & % 190.39/26.38 Nat$(v14)))))))) % 190.39/26.38 % 190.39/26.38 (axiom451) % 190.39/26.39 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.39 A_ltln_a_ltln_bool_fun_fun$(eq$) & Nat_int_fun$(of_nat$) & % 190.39/26.39 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.39/26.39 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: A_ltln_a_ltln_fun$] : ? % 190.39/26.39 [v2: Nat$] : (nat$(0) = v2 & af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) % 190.39/26.39 = v1 & Nat$(v2) & A_ltln_a_ltln_fun$(v1) & % 190.39/26.39 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ? [v3: Nat_a_set_fun$] : ! % 190.39/26.39 [v4: A_ltln$] : ! [v5: A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_ltln$] : % 190.39/26.39 ! [v7: A_set_list_a_ltln_fun$] : ( ~ (foldl$(v5, v6) = v7) | ~ % 190.39/26.39 (fun_app$c(v0, v4) = v5) | ~ (fun_app$d(v1, v4) = v6) | ~ % 190.39/26.39 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ? [v8: A_set_list_a_ltln_fun$] : ? % 190.39/26.39 [v9: Nat$] : ? [v10: int] : (Nat$(v9) & ((fun_app$y(of_nat$, v9) = v10 & % 190.39/26.39 ! [v11: Nat$] : ! [v12: int] : ( ~ ($lesseq(1, $difference(v12, % 190.39/26.39 v10))) | ~ (fun_app$y(of_nat$, v11) = v12) | ~ Nat$(v11) | % 190.39/26.39 ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.39/26.39 A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = 0) & % 190.39/26.39 subsequence$(v3, v2, v11) = v13 & fun_app$s(v7, v13) = v14 & % 190.39/26.39 fun_app$e(eq$, v14) = v15 & fun_app$(v15, true_ltln$) = v16 & % 190.39/26.39 A_ltln$(v14) & A_set_list$(v13) & A_ltln_bool_fun$(v15))) & ! % 190.39/26.39 [v11: Nat$] : ! [v12: A_set_list$] : ( ~ (subsequence$(v3, v2, v11) % 190.39/26.39 = v12) | ~ Nat$(v11) | ? [v13: int] : ? [v14: A_ltln$] : ? % 190.39/26.39 [v15: A_ltln_bool_fun$] : ? [v16: any] : (fun_app$y(of_nat$, v11) % 190.39/26.39 = v13 & fun_app$s(v7, v12) = v14 & fun_app$e(eq$, v14) = v15 & % 190.39/26.39 fun_app$(v15, true_ltln$) = v16 & A_ltln$(v14) & % 190.39/26.39 A_ltln_bool_fun$(v15) & ( ~ (v16 = 0) | ~ ($lesseq(1, % 190.39/26.39 $difference(v13, v10))))))) | (foldl$(af_letter$, v6) = v8 % 190.39/26.39 & A_set_list_a_ltln_fun$(v8) & ? [v11: Nat$] : ( ~ Nat$(v11) | ? % 190.39/26.39 [v12: Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.39/26.39 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.39/26.39 fun_app$s(v8, v13) = v14 & fun_app$e(ltl_lang_equiv$, v14) = v15 % 190.39/26.39 & fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.39/26.39 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12))))))) & ? % 190.39/26.39 [v3: Nat_a_set_fun$] : ? [v4: Nat$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : % 190.39/26.39 ! [v7: A_set_list_a_ltln_fun$] : ( ~ (foldl$(af_letter$, v6) = v7) | ~ % 190.39/26.39 (fun_app$d(v1, v5) = v6) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v5) | ~ % 190.39/26.39 Nat$(v4) | ? [v8: A_ltln_a_set_a_ltln_fun_fun$] : ? [v9: % 190.39/26.39 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : ? [v11: int] : ? [v12: % 190.39/26.39 Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.39/26.39 A_ltln_bool_fun$] : ? [v16: int] : (Nat$(v12) & Nat$(v10) & ((v16 = 0 & % 190.39/26.39 subsequence$(v3, v4, v12) = v13 & fun_app$s(v7, v13) = v14 & % 190.39/26.39 fun_app$e(ltl_lang_equiv$, v14) = v15 & fun_app$(v15, true_ltln$) = % 190.39/26.39 0 & A_ltln$(v14) & A_set_list$(v13) & A_ltln_bool_fun$(v15)) | % 190.39/26.39 (fun_app$y(of_nat$, v10) = v11 & foldl$(v8, v6) = v9 & fun_app$c(v0, % 190.39/26.39 v5) = v8 & A_set_list_a_ltln_fun$(v9) & % 190.39/26.39 A_ltln_a_set_a_ltln_fun_fun$(v8) & ! [v17: Nat$] : ! [v18: int] : % 190.39/26.39 ( ~ ($lesseq(1, $difference(v18, v11))) | ~ (fun_app$y(of_nat$, % 190.39/26.39 v17) = v18) | ~ Nat$(v17) | ? [v19: A_set_list$] : ? [v20: % 190.39/26.39 A_ltln$] : ? [v21: A_ltln_bool_fun$] : ? [v22: int] : ( ~ (v22 % 190.39/26.39 = 0) & subsequence$(v3, v2, v17) = v19 & fun_app$s(v9, v19) = % 190.39/26.39 v20 & fun_app$e(eq$, v20) = v21 & fun_app$(v21, true_ltln$) = % 190.39/26.39 v22 & A_ltln$(v20) & A_set_list$(v19) & A_ltln_bool_fun$(v21))) % 190.39/26.39 & ! [v17: Nat$] : ! [v18: A_set_list$] : ( ~ (subsequence$(v3, v2, % 190.39/26.39 v17) = v18) | ~ Nat$(v17) | ? [v19: int] : ? [v20: A_ltln$] % 190.39/26.39 : ? [v21: A_ltln_bool_fun$] : ? [v22: any] : (fun_app$y(of_nat$, % 190.39/26.39 v17) = v19 & fun_app$s(v9, v18) = v20 & fun_app$e(eq$, v20) = % 190.39/26.39 v21 & fun_app$(v21, true_ltln$) = v22 & A_ltln$(v20) & % 190.39/26.39 A_ltln_bool_fun$(v21) & ( ~ (v22 = 0) | ~ ($lesseq(1, % 190.39/26.39 $difference(v19, v11))))))))))) % 190.39/26.39 % 190.39/26.39 (axiom460) % 190.39/26.39 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ % 190.39/26.39 (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: % 190.39/26.39 any] : ? [v4: any] : (less_eq$(v1, v0) = v4 & less_eq$(v0, v1) = v3 & ( ~ % 190.39/26.39 (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 190.39/26.39 [v2: int] : (v2 = 0 | ~ (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ % 190.39/26.39 A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v4 & % 190.39/26.39 less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: A_ltln_set$] : % 190.39/26.39 ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ (less_eq$(v1, v0) = v2) | ~ % 190.39/26.39 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: any] : ? [v4: any] : % 190.39/26.39 (less$(v0, v1) = v3 & less_eq$(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & ~ % 190.39/26.39 (v2 = 0))))) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: % 190.39/26.39 any] : ( ~ (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 190.39/26.39 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v4 % 190.39/26.39 & ( ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: A_ltln_set$] : ! % 190.39/26.39 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.39 A_ltln_set$(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_eq$(v1, v0) = v2 & % 190.39/26.39 less_eq$(v0, v1) = 0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ % 190.39/26.39 (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: % 190.39/26.39 any] : ? [v3: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v2 & (v3 = % 190.39/26.39 0 | v2 = 0))) % 190.39/26.39 % 190.39/26.39 (axiom462) % 190.39/26.40 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | v1 = v0 % 190.39/26.40 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? % 190.39/26.40 [v3: int] : ( ~ (v3 = 0) & less_eq$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : % 190.39/26.40 ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | ~ (less_eq$(v0, v1) = v2) | ~ % 190.39/26.40 A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 190.39/26.40 less$(v0, v1) = v3)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : (v1 = % 190.39/26.40 v0 | ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 190.39/26.40 less$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: int] : (v1 = 0 | ~ % 190.39/26.40 (less_eq$(v0, v0) = v1) | ~ A_ltln_set$(v0)) & ! [v0: A_ltln_set$] : ! % 190.39/26.40 [v1: A_ltln_set$] : ( ~ (less$(v0, v1) = 0) | ~ A_ltln_set$(v1) | ~ % 190.39/26.40 A_ltln_set$(v0) | less_eq$(v0, v1) = 0) & ! [v0: A_ltln_set$] : ! [v1: % 190.39/26.40 MultipleValueBool] : ( ~ (less$(v0, v0) = v1) | ~ A_ltln_set$(v0) | % 190.39/26.40 less_eq$(v0, v0) = 0) % 190.39/26.40 % 190.39/26.40 (axiom480) % 190.39/26.40 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.40 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(false_ltln$) & ! [v0: % 190.39/26.40 A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! [v3: % 190.39/26.40 A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : ! [v5: % 190.39/26.40 A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ (fun_app$t(v4, % 190.39/26.40 v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v3, v5) = % 190.39/26.40 v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: % 190.39/26.40 A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: % 190.39/26.40 A_ltln_bool_fun$] : ? [v11: any] : (fun_app$s(v3, v1) = v7 & % 190.39/26.40 fun_app$e(ltl_lang_equiv$, v7) = v8 & fun_app$e(ltl_lang_equiv$, v6) = v10 % 190.39/26.40 & fun_app$(v10, false_ltln$) = v11 & fun_app$(v8, false_ltln$) = v9 & % 190.39/26.40 A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) % 190.39/26.40 | v11 = 0))) % 190.39/26.40 % 190.39/26.40 (axiom481) % 190.39/26.40 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.40 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ! [v0: % 190.39/26.40 A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! [v3: % 190.39/26.40 A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : ! [v5: % 190.39/26.40 A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ (fun_app$t(v4, % 190.39/26.40 v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v3, v5) = % 190.39/26.40 v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: % 190.39/26.40 A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: % 190.39/26.40 A_ltln_bool_fun$] : ? [v11: any] : (fun_app$s(v3, v1) = v7 & % 190.39/26.40 fun_app$e(ltl_lang_equiv$, v7) = v8 & fun_app$e(ltl_lang_equiv$, v6) = v10 % 190.39/26.40 & fun_app$(v10, true_ltln$) = v11 & fun_app$(v8, true_ltln$) = v9 & % 190.39/26.40 A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) % 190.39/26.40 | v11 = 0))) % 190.39/26.40 % 190.39/26.40 (axiom484) % 190.39/26.40 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.40 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.39/26.40 A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) % 190.39/26.40 & ! [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_set_list$] : ! [v4: % 190.39/26.40 A_ltln$] : ! [v5: A_set_list_a_ltln_fun$] : ! [v6: % 190.39/26.40 A_set_list_a_set_list_fun$] : ! [v7: A_set_list$] : ! [v8: A_ltln$] : ( % 190.39/26.40 ~ (append$(v3) = v6) | ~ (fun_app$t(v6, v2) = v7) | ~ % 190.39/26.40 (foldl$(af_letter$, v4) = v5) | ~ (fun_app$s(v5, v7) = v8) | ~ % 190.39/26.40 (fun_app$d(v0, v1) = v4) | ~ A_ltln$(v1) | ~ A_set_list$(v3) | ~ % 190.39/26.40 A_set_list$(v2) | ? [v9: A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: % 190.39/26.40 any] : ? [v12: A_ltln_bool_fun$] : ? [v13: any] : (fun_app$s(v5, v2) = % 190.39/26.40 v9 & fun_app$e(ltl_lang_equiv$, v9) = v10 & fun_app$e(ltl_lang_equiv$, % 190.39/26.40 v8) = v12 & fun_app$(v12, true_ltln$) = v13 & fun_app$(v10, % 190.39/26.40 true_ltln$) = v11 & A_ltln$(v9) & A_ltln_bool_fun$(v12) & % 190.39/26.40 A_ltln_bool_fun$(v10) & ( ~ (v11 = 0) | v13 = 0)))) % 190.39/26.40 % 190.39/26.40 (axiom493) % 190.39/26.40 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.40 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.39/26.40 A_ltln$(false_ltln$) & A_ltln_set$(mu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.39/26.40 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.39/26.40 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.39/26.40 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.39/26.40 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.39/26.40 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.39/26.40 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.39/26.40 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.39/26.40 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.39/26.40 & member$(v2, mu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.39/26.40 ~ (v8 = 0) | (( ~ (v7 = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: % 190.39/26.40 Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.39/26.40 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.39/26.40 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_lang_equiv$, v14) = % 190.39/26.40 v15 & fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.39/26.40 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 % 190.39/26.40 = 0 | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 190.39/26.40 (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.39/26.40 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.39/26.40 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.39/26.40 fun_app$e(ltl_lang_equiv$, v13) = v14 & fun_app$(v14, % 190.39/26.40 true_ltln$) = v15 & A_ltln$(v13) & % 190.39/26.40 A_ltln_bool_fun$(v14))))))))) % 190.39/26.40 % 190.39/26.40 (axiom494) % 190.39/26.40 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & % 190.39/26.40 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.39/26.40 A_ltln$(false_ltln$) & A_ltln_set$(nu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.39/26.40 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v1 & % 190.39/26.40 until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 190.39/26.40 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.39/26.40 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.39/26.40 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.39/26.40 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.39/26.40 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.39/26.41 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.39/26.41 & member$(v2, nu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.39/26.41 ~ (v8 = 0) | (( ~ (v7 = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : % 190.39/26.41 ( ~ (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.39/26.41 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.39/26.41 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.39/26.41 fun_app$e(ltl_lang_equiv$, v13) = v14 & fun_app$(v14, % 190.39/26.41 false_ltln$) = v15 & A_ltln$(v13) & A_ltln_bool_fun$(v14)))) % 190.39/26.41 & (v7 = 0 | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? % 190.39/26.41 [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.39/26.41 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.39/26.41 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_lang_equiv$, v14) = % 190.39/26.41 v15 & fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 190.39/26.41 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12))))))))) % 190.39/26.41 % 190.39/26.41 (axiom496) % 190.39/26.41 A_ltln_a_ltln_bool_fun_fun$(ltl_lang_equiv$) & Nat_int_fun$(of_nat$) & % 190.39/26.41 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ? [v0: % 190.39/26.41 A_ltln_a_ltln_fun$] : ? [v1: Nat$] : (nat$(0) = v1 & % 190.39/26.41 until_ltln$(true_ltln$) = v0 & Nat$(v1) & A_ltln_a_ltln_fun$(v0) & ? [v2: % 190.39/26.41 Nat_a_set_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : ! [v4: % 190.39/26.41 A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: % 190.39/26.41 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v7: % 190.39/26.41 A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_ltln$] : ! [v9: % 190.39/26.41 A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v3, v4) = 0) | ~ % 190.39/26.41 (foldl$(v7, v8) = v9) | ~ (fun_app$c(v6, v5) = v7) | ~ (af_letter_F$(v3) % 190.39/26.41 = v6) | ~ (fun_app$d(v0, v5) = v8) | ~ A_ltln_a_ltln_bool_fun_fun$(v3) % 190.39/26.41 | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v5) | ~ A_ltln_a_ltln_fun$(v4) | ? % 190.39/26.41 [v10: A_set_list_a_ltln_fun$] : ? [v11: Nat$] : ? [v12: int] : % 190.39/26.41 (Nat$(v11) & ((fun_app$y(of_nat$, v11) = v12 & ! [v13: Nat$] : ! [v14: % 190.39/26.41 int] : ( ~ ($lesseq(1, $difference(v14, v12))) | ~ % 190.39/26.41 (fun_app$y(of_nat$, v13) = v14) | ~ Nat$(v13) | ? [v15: % 190.39/26.41 A_set_list$] : ? [v16: A_ltln$] : ? [v17: A_ltln_bool_fun$] : % 190.39/26.41 ? [v18: int] : ( ~ (v18 = 0) & subsequence$(v2, v1, v13) = v15 & % 190.39/26.41 fun_app$s(v9, v15) = v16 & fun_app$e(v3, v16) = v17 & % 190.39/26.41 fun_app$(v17, true_ltln$) = v18 & A_ltln$(v16) & % 190.39/26.41 A_set_list$(v15) & A_ltln_bool_fun$(v17))) & ! [v13: Nat$] : ! % 190.39/26.41 [v14: A_set_list$] : ( ~ (subsequence$(v2, v1, v13) = v14) | ~ % 190.39/26.41 Nat$(v13) | ? [v15: int] : ? [v16: A_ltln$] : ? [v17: % 190.39/26.41 A_ltln_bool_fun$] : ? [v18: any] : (fun_app$y(of_nat$, v13) = % 190.39/26.41 v15 & fun_app$s(v9, v14) = v16 & fun_app$e(v3, v16) = v17 & % 190.39/26.41 fun_app$(v17, true_ltln$) = v18 & A_ltln$(v16) & % 190.39/26.41 A_ltln_bool_fun$(v17) & ( ~ (v18 = 0) | ~ ($lesseq(1, % 190.39/26.41 $difference(v15, v12))))))) | (foldl$(af_letter$, v8) = % 190.39/26.41 v10 & A_set_list_a_ltln_fun$(v10) & ? [v13: Nat$] : ( ~ Nat$(v13) | % 190.39/26.41 ? [v14: Nat$] : ? [v15: A_set_list$] : ? [v16: A_ltln$] : ? % 190.39/26.41 [v17: A_ltln_bool_fun$] : (subsequence$(v2, v13, v14) = v15 & % 190.39/26.41 fun_app$s(v10, v15) = v16 & fun_app$e(ltl_lang_equiv$, v16) = % 190.39/26.41 v17 & fun_app$(v17, true_ltln$) = 0 & A_ltln$(v16) & % 190.39/26.41 A_set_list$(v15) & A_ltln_bool_fun$(v17) & Nat$(v14))))))) & ? % 190.39/26.41 [v2: Nat_a_set_fun$] : ? [v3: Nat$] : ! [v4: A_ltln_a_ltln_bool_fun_fun$] % 190.39/26.41 : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! % 190.39/26.41 [v8: A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v4, v5) = 0) | ~ % 190.39/26.41 (foldl$(af_letter$, v7) = v8) | ~ (fun_app$d(v0, v6) = v7) | ~ % 190.39/26.41 A_ltln_a_ltln_bool_fun_fun$(v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v6) | % 190.39/26.41 ~ Nat$(v3) | ~ A_ltln_a_ltln_fun$(v5) | ? [v9: % 190.39/26.41 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v10: % 190.39/26.41 A_ltln_a_set_a_ltln_fun_fun$] : ? [v11: A_set_list_a_ltln_fun$] : ? % 190.39/26.41 [v12: Nat$] : ? [v13: int] : ? [v14: Nat$] : ? [v15: A_set_list$] : ? % 190.39/26.41 [v16: A_ltln$] : ? [v17: A_ltln_bool_fun$] : ? [v18: int] : (Nat$(v14) & % 190.39/26.41 Nat$(v12) & ((v18 = 0 & subsequence$(v2, v3, v14) = v15 & fun_app$s(v8, % 190.39/26.41 v15) = v16 & fun_app$e(ltl_lang_equiv$, v16) = v17 & fun_app$(v17, % 190.39/26.41 true_ltln$) = 0 & A_ltln$(v16) & A_set_list$(v15) & % 190.39/26.41 A_ltln_bool_fun$(v17)) | (fun_app$y(of_nat$, v12) = v13 & % 190.39/26.41 foldl$(v10, v7) = v11 & fun_app$c(v9, v6) = v10 & af_letter_F$(v4) = % 190.39/26.41 v9 & A_set_list_a_ltln_fun$(v11) & A_ltln_a_set_a_ltln_fun_fun$(v10) % 190.39/26.41 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v9) & ! [v19: Nat$] : ! % 190.39/26.41 [v20: int] : ( ~ ($lesseq(1, $difference(v20, v13))) | ~ % 190.39/26.41 (fun_app$y(of_nat$, v19) = v20) | ~ Nat$(v19) | ? [v21: % 190.39/26.41 A_set_list$] : ? [v22: A_ltln$] : ? [v23: A_ltln_bool_fun$] : % 190.39/26.41 ? [v24: int] : ( ~ (v24 = 0) & subsequence$(v2, v1, v19) = v21 & % 190.39/26.41 fun_app$s(v11, v21) = v22 & fun_app$e(v4, v22) = v23 & % 190.39/26.41 fun_app$(v23, true_ltln$) = v24 & A_ltln$(v22) & % 190.39/26.41 A_set_list$(v21) & A_ltln_bool_fun$(v23))) & ! [v19: Nat$] : ! % 190.39/26.41 [v20: A_set_list$] : ( ~ (subsequence$(v2, v1, v19) = v20) | ~ % 190.39/26.41 Nat$(v19) | ? [v21: int] : ? [v22: A_ltln$] : ? [v23: % 190.39/26.41 A_ltln_bool_fun$] : ? [v24: any] : (fun_app$y(of_nat$, v19) = % 190.39/26.41 v21 & fun_app$s(v11, v20) = v22 & fun_app$e(v4, v22) = v23 & % 190.39/26.41 fun_app$(v23, true_ltln$) = v24 & A_ltln$(v22) & % 190.39/26.41 A_ltln_bool_fun$(v23) & ( ~ (v24 = 0) | ~ ($lesseq(1, % 190.39/26.41 $difference(v21, v13))))))))))) % 190.39/26.41 % 190.39/26.41 (axiom502) % 190.39/26.41 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.39/26.41 A_ltln$(false_ltln$) & A_set_list$(nil$) & A_ltln_a_ltln_fun$(normalise$) & ? % 190.39/26.41 [v0: A_ltln_set_a_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun_fun$] : % 190.39/26.41 (af_letter_nu$(eq$, normalise$) = v0 & % 190.39/26.41 A_ltln_set_a_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun_fun$(v0) & ! % 190.39/26.41 [v1: A_ltln_set$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.39/26.41 A_set_list$] : ! [v5: A_set$] : ! [v6: % 190.39/26.41 A_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun$] : ! [v7: % 190.39/26.41 A_ltln_a_ltln_prod$] : ! [v8: A_set_list_a_ltln_a_ltln_prod_fun$] : ! % 190.39/26.41 [v9: A_set_list_a_set_list_fun$] : ! [v10: A_set_list$] : ! [v11: % 190.39/26.41 A_set_list$] : ! [v12: A_ltln_a_ltln_prod$] : ( ~ (cons$(v5, nil$) = v10) % 190.39/26.41 | ~ (fun_app$v(v0, v1) = v6) | ~ (pair$(v2, v3) = v7) | ~ (foldl$a(v6, % 190.39/26.41 v7) = v8) | ~ (fun_app$u(v8, v11) = v12) | ~ (append$(v4) = v9) | ~ % 190.39/26.41 (fun_app$t(v9, v10) = v11) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.39/26.41 A_set_list$(v4) | ~ A_ltln_set$(v1) | ~ A_set$(v5) | ? [v13: % 190.39/26.41 A_ltln_a_ltln_prod$] : ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 190.39/26.41 ? [v16: any] : ? [v17: A_ltln$] : ? [v18: A_set_list_a_ltln_fun$] : ? % 190.39/26.41 [v19: A_ltln$] : ? [v20: A_ltln$] : ? [v21: A_ltln$] : (snd$(v13) = v14 % 190.39/26.41 & snd$(v12) = v17 & fun_app$u(v8, v4) = v13 & gF_advice$(v20, v1) = v21 % 190.39/26.41 & foldl$(af_letter$, v2) = v18 & fun_app$s(v18, v11) = v19 & % 190.39/26.41 fun_app$e(eq$, v14) = v15 & fun_app$d(normalise$, v19) = v20 & % 190.39/26.41 fun_app$(v15, false_ltln$) = v16 & A_set_list_a_ltln_fun$(v18) & % 190.39/26.41 A_ltln$(v21) & A_ltln$(v20) & A_ltln$(v19) & A_ltln$(v17) & A_ltln$(v14) % 190.39/26.41 & A_ltln_bool_fun$(v15) & A_ltln_a_ltln_prod$(v13) & ( ~ (v16 = 0) | v21 % 190.39/26.41 = v17)))) % 190.39/26.41 % 190.39/26.41 (axiom516) % 190.39/26.41 A_set_list$(nil$) & ! [v0: A_set_list$] : ! [v1: A_set_list_a_set_list_fun$] % 190.39/26.41 : ( ~ (append$(v0) = v1) | ~ A_set_list$(v0) | fun_app$t(v1, nil$) = v0) % 190.39/26.41 % 190.39/26.41 (axiom517) % 190.39/26.41 A_set_list$(nil$) & ! [v0: A_set_list$] : ! [v1: A_set_list_a_set_list_fun$] % 190.39/26.41 : ( ~ (append$(v0) = v1) | ~ A_set_list$(v0) | fun_app$t(v1, nil$) = v0) % 190.39/26.41 % 190.39/26.41 (axiom519) % 190.39/26.41 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln$(true_ltln$) & A_set_list$(nil$) & % 190.39/26.41 ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: A_ltln_a_ltln_fun$] % 190.39/26.41 : (af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.39/26.41 A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! % 190.39/26.41 [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: A_set$] : % 190.39/26.41 ! [v6: A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_list_a_ltln_fun$] : ! % 190.39/26.41 [v8: A_set_list_a_set_list_fun$] : ! [v9: A_set_list$] : ! [v10: % 190.39/26.42 A_set_list$] : ! [v11: A_ltln$] : ( ~ (cons$(v5, nil$) = v9) | ~ % 190.39/26.42 (append$(v4) = v8) | ~ (fun_app$t(v8, v9) = v10) | ~ (foldl$(v6, v3) = % 190.39/26.42 v7) | ~ (fun_app$s(v7, v10) = v11) | ~ (fun_app$c(v0, v2) = v6) | ~ % 190.39/26.42 A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_set_list$(v4) | ~ A_set$(v5) | ? % 190.39/26.42 [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: any] : ? [v15: % 190.39/26.42 A_ltln$] : (fun_app$s(v7, v4) = v12 & fun_app$e(eq$, v12) = v13 & % 190.39/26.42 fun_app$d(v1, v2) = v15 & fun_app$(v13, true_ltln$) = v14 & A_ltln$(v15) % 190.39/26.42 & A_ltln$(v12) & A_ltln_bool_fun$(v13) & ( ~ (v14 = 0) | v15 = v11)))) % 190.39/26.42 % 190.39/26.42 (axiom547) % 190.88/26.42 A_set_list$(nil$) & ! [v0: A_ltln_a_set_a_ltln_fun_fun$] : ! [v1: A_ltln$] : % 190.88/26.42 ! [v2: A_set_list_a_ltln_fun$] : ( ~ (foldl$(v0, v1) = v2) | ~ % 190.88/26.42 A_ltln_a_set_a_ltln_fun_fun$(v0) | ~ A_ltln$(v1) | fun_app$s(v2, nil$) = % 190.88/26.42 v1) % 190.88/26.42 % 190.88/26.42 (axiom549) % 190.88/26.42 A_set_list$(nil$) & ? [v0: A_set_list_a_set_list_fun$] : (append$(nil$) = v0 % 190.88/26.42 & A_set_list_a_set_list_fun$(v0) & ! [v1: A_set_list$] : ! [v2: % 190.88/26.42 A_set_list$] : (v2 = v1 | ~ (fun_app$t(v0, v1) = v2) | ~ % 190.88/26.42 A_set_list$(v1))) % 190.88/26.42 % 190.88/26.42 (axiom550) % 190.88/26.42 A_set_list$(nil$) & ? [v0: A_set_list_a_set_list_fun$] : (append$(nil$) = v0 % 190.88/26.42 & A_set_list_a_set_list_fun$(v0) & ! [v1: A_set_list$] : ! [v2: % 190.88/26.42 A_set_list$] : (v2 = v1 | ~ (fun_app$t(v0, v1) = v2) | ~ % 190.88/26.42 A_set_list$(v1))) % 190.88/26.42 % 190.88/26.42 (axiom551) % 190.88/26.42 A_set_list$(nil$) & ? [v0: A_set_list_a_set_list_fun$] : (append$(nil$) = v0 % 190.88/26.42 & A_set_list_a_set_list_fun$(v0) & ! [v1: A_set_list$] : ! [v2: % 190.88/26.42 A_set_list$] : (v2 = v1 | ~ (fun_app$t(v0, v1) = v2) | ~ % 190.88/26.42 A_set_list$(v1))) % 190.88/26.42 % 190.88/26.42 (axiom554) % 190.88/26.42 A_ltln$(true_ltln$) & A_set_list$(nil$) & ? [v0: A_ltln_a_ltln_fun$] : % 190.88/26.42 (until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 190.88/26.42 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.88/26.42 A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_set_list$] : ! [v6: A_set$] : ! % 190.88/26.42 [v7: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.88/26.42 A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : ! [v10: % 190.88/26.42 A_set_list_a_set_list_fun$] : ! [v11: A_set_list$] : ! [v12: % 190.88/26.42 A_set_list$] : ! [v13: A_ltln$] : ( ~ (cons$(v6, nil$) = v11) | ~ % 190.88/26.42 (append$(v5) = v10) | ~ (fun_app$t(v10, v11) = v12) | ~ % 190.88/26.42 (transition_functions$(v1, v2) = 0) | ~ (foldl$(v8, v4) = v9) | ~ % 190.88/26.42 (fun_app$s(v9, v12) = v13) | ~ (fun_app$c(v7, v3) = v8) | ~ % 190.88/26.42 (af_letter_F$(v1) = v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 190.88/26.42 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set_list$(v5) | ~ A_set$(v6) | ~ % 190.88/26.42 A_ltln_a_ltln_fun$(v2) | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 190.88/26.42 ? [v16: any] : ? [v17: A_ltln$] : (fun_app$s(v9, v5) = v14 & % 190.88/26.42 fun_app$e(v1, v14) = v15 & fun_app$d(v0, v3) = v17 & fun_app$(v15, % 190.88/26.42 true_ltln$) = v16 & A_ltln$(v17) & A_ltln$(v14) & % 190.88/26.42 A_ltln_bool_fun$(v15) & ( ~ (v16 = 0) | v17 = v13)))) % 190.88/26.42 % 190.88/26.42 (axiom569) % 190.88/26.42 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 190.88/26.42 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 190.88/26.42 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 190.88/26.42 ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | ~ (semantics_ltln$(v1) = v4) | % 190.88/26.42 ~ (until_ltln$(v2) = v5) | ~ (fun_app$d(v5, v3) = v6) | ~ (fun_app$(v4, % 190.88/26.42 v6) = v7) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 190.88/26.42 ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: any] : ? [v11: % 190.88/26.42 A_ltln$] : ? [v12: any] : (weakUntil_ltln$(v2) = v8 & fun_app$d(v8, v3) % 190.88/26.42 = v9 & fun_app$d(v0, v3) = v11 & fun_app$(v4, v11) = v12 & fun_app$(v4, % 190.88/26.42 v9) = v10 & A_ltln$(v11) & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & ( ~ % 190.88/26.42 (v12 = 0) | ~ (v10 = 0)))) & ! [v1: Nat_a_set_fun$] : ! [v2: % 190.88/26.42 A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.88/26.42 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v5) | % 190.88/26.42 ~ (semantics_ltln$(v1) = v4) | ~ (fun_app$d(v5, v3) = v6) | ~ % 190.88/26.42 (fun_app$(v4, v6) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 190.88/26.42 A_ltln$(v2) | ? [v7: A_ltln$] : ? [v8: any] : ? [v9: % 190.88/26.42 A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: any] : % 190.88/26.42 (until_ltln$(v2) = v9 & fun_app$d(v9, v3) = v10 & fun_app$d(v0, v3) = v7 & % 190.88/26.42 fun_app$(v4, v10) = v11 & fun_app$(v4, v7) = v8 & A_ltln$(v10) & % 190.88/26.42 A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & ( ~ (v8 = 0) | v11 = 0)))) % 190.88/26.42 % 190.88/26.42 (axiom578) % 190.88/26.42 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 190.88/26.42 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 190.88/26.42 ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : % 190.88/26.42 ! [v6: int] : (v6 = 0 | ~ (strongRelease_ltln$(v2) = v4) | ~ % 190.88/26.42 (semantics_ltln$(v1) = v3) | ~ (fun_app$d(v4, true_ltln$) = v5) | ~ % 190.88/26.42 (fun_app$(v3, v5) = v6) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v7: % 190.88/26.42 A_ltln$] : ? [v8: int] : ( ~ (v8 = 0) & fun_app$d(v0, v2) = v7 & % 190.88/26.42 fun_app$(v3, v7) = v8 & A_ltln$(v7))) & ! [v1: Nat_a_set_fun$] : ! % 190.88/26.42 [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: int] % 190.88/26.42 : (v5 = 0 | ~ (semantics_ltln$(v1) = v3) | ~ (fun_app$d(v0, v2) = v4) | ~ % 190.88/26.42 (fun_app$(v3, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v6: % 190.88/26.42 A_ltln_a_ltln_fun$] : ? [v7: A_ltln$] : ? [v8: int] : ( ~ (v8 = 0) & % 190.88/26.42 strongRelease_ltln$(v2) = v6 & fun_app$d(v6, true_ltln$) = v7 & % 190.88/26.42 fun_app$(v3, v7) = v8 & A_ltln$(v7) & A_ltln_a_ltln_fun$(v6))) & ! [v1: % 190.88/26.42 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 190.88/26.42 A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = % 190.88/26.42 v4) | ~ (semantics_ltln$(v1) = v3) | ~ (fun_app$d(v4, true_ltln$) = % 190.88/26.42 v5) | ~ (fun_app$(v3, v5) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) % 190.88/26.42 | ? [v6: A_ltln$] : (fun_app$d(v0, v2) = v6 & fun_app$(v3, v6) = 0 & % 190.88/26.42 A_ltln$(v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 190.88/26.42 A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (semantics_ltln$(v1) = v3) | ~ % 190.88/26.42 (fun_app$d(v0, v2) = v4) | ~ (fun_app$(v3, v4) = 0) | ~ % 190.88/26.42 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v5: A_ltln_a_ltln_fun$] : ? % 190.88/26.42 [v6: A_ltln$] : (strongRelease_ltln$(v2) = v5 & fun_app$d(v5, true_ltln$) % 190.88/26.42 = v6 & fun_app$(v3, v6) = 0 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5)))) % 190.88/26.42 % 190.88/26.42 (axiom587) % 190.88/26.43 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 190.88/26.43 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 190.88/26.43 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 190.88/26.43 ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | ~ (strongRelease_ltln$(v2) = v5) % 190.88/26.43 | ~ (semantics_ltln$(v1) = v4) | ~ (fun_app$d(v5, v3) = v6) | ~ % 190.88/26.43 (fun_app$(v4, v6) = v7) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 190.88/26.43 A_ltln$(v2) | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: % 190.88/26.43 any] : ? [v11: A_ltln$] : ? [v12: any] : (release_ltln$(v2) = v8 & % 190.88/26.43 fun_app$d(v8, v3) = v9 & fun_app$d(v0, v2) = v11 & fun_app$(v4, v11) = % 190.88/26.43 v12 & fun_app$(v4, v9) = v10 & A_ltln$(v11) & A_ltln$(v9) & % 190.88/26.43 A_ltln_a_ltln_fun$(v8) & ( ~ (v12 = 0) | ~ (v10 = 0)))) & ! [v1: % 190.88/26.43 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.43 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 190.88/26.43 (semantics_ltln$(v1) = v4) | ~ (release_ltln$(v2) = v5) | ~ % 190.88/26.43 (fun_app$d(v5, v3) = v6) | ~ (fun_app$(v4, v6) = 0) | ~ % 190.88/26.43 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v7: A_ltln$] : % 190.88/26.43 ? [v8: any] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 190.88/26.43 any] : (strongRelease_ltln$(v2) = v9 & fun_app$d(v9, v3) = v10 & % 190.88/26.43 fun_app$d(v0, v2) = v7 & fun_app$(v4, v10) = v11 & fun_app$(v4, v7) = v8 % 190.88/26.43 & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & ( ~ (v8 = 0) | % 190.88/26.43 v11 = 0)))) % 190.88/26.43 % 190.88/26.43 (axiom588) % 190.88/26.43 A_set_list$(nil$) & A_set_list_list$(nil$a) & ? [v0: Nat$] : ? [v1: % 190.88/26.43 A_set_list_a_set_list_list_fun$] : ? [v2: A_set_list_list$] : (n_lists$(v0) % 190.88/26.43 = v1 & cons$a(nil$, nil$a) = v2 & nat$(0) = v0 & Nat$(v0) & % 190.88/26.43 A_set_list_list$(v2) & A_set_list_a_set_list_list_fun$(v1) & ! [v3: % 190.88/26.43 A_set_list$] : ! [v4: A_set_list_list$] : (v4 = v2 | ~ (fun_app$ae(v1, % 190.88/26.43 v3) = v4) | ~ A_set_list$(v3))) % 190.88/26.43 % 190.88/26.43 (axiom589) % 190.88/26.43 A_ltln_a_ltln_bool_fun_fun$(ltl_prop_equiv$) & % 190.88/26.43 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.88/26.43 A_ltln$(false_ltln$) & A_ltln_set$(nu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.88/26.43 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v1 & % 190.88/26.43 until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.43 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.88/26.43 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.88/26.43 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.43 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.43 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.43 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.88/26.43 & member$(v2, nu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.88/26.43 ~ (v8 = 0) | (( ~ (v7 = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : % 190.88/26.43 ( ~ (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.88/26.43 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.88/26.43 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.88/26.43 fun_app$e(ltl_prop_equiv$, v13) = v14 & fun_app$(v14, % 190.88/26.43 false_ltln$) = v15 & A_ltln$(v13) & A_ltln_bool_fun$(v14)))) % 190.88/26.43 & (v7 = 0 | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? % 190.88/26.43 [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.43 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.88/26.43 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_prop_equiv$, v14) = % 190.88/26.43 v15 & fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.43 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12))))))))) % 190.88/26.43 % 190.88/26.43 (axiom590) % 190.88/26.43 A_ltln_a_ltln_bool_fun_fun$(ltl_prop_equiv$) & % 190.88/26.43 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.88/26.43 A_ltln$(false_ltln$) & A_ltln_set$(mu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.88/26.43 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.88/26.43 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.43 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.88/26.43 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.88/26.43 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.43 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.43 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.43 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.88/26.43 & member$(v2, mu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.88/26.43 ~ (v8 = 0) | (( ~ (v7 = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: % 190.88/26.43 Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.43 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.88/26.43 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_prop_equiv$, v14) = % 190.88/26.43 v15 & fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.43 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 % 190.88/26.43 = 0 | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 190.88/26.43 (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.88/26.43 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.88/26.43 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.88/26.43 fun_app$e(ltl_prop_equiv$, v13) = v14 & fun_app$(v14, % 190.88/26.43 true_ltln$) = v15 & A_ltln$(v13) & % 190.88/26.43 A_ltln_bool_fun$(v14))))))))) % 190.88/26.43 % 190.88/26.43 (axiom604) % 190.88/26.43 A_ltln_a_ltln_bool_fun_fun$(ltl_prop_equiv$) & % 190.88/26.43 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(false_ltln$) & ! [v0: % 190.88/26.43 A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! [v3: % 190.88/26.43 A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : ! [v5: % 190.88/26.43 A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ (fun_app$t(v4, % 190.88/26.43 v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v3, v5) = % 190.88/26.43 v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: % 190.88/26.43 A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: % 190.88/26.43 A_ltln_bool_fun$] : ? [v11: any] : (fun_app$s(v3, v1) = v7 & % 190.88/26.43 fun_app$e(ltl_prop_equiv$, v7) = v8 & fun_app$e(ltl_prop_equiv$, v6) = v10 % 190.88/26.43 & fun_app$(v10, false_ltln$) = v11 & fun_app$(v8, false_ltln$) = v9 & % 190.88/26.43 A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) % 190.88/26.43 | v11 = 0))) % 190.88/26.43 % 190.88/26.43 (axiom605) % 190.88/26.43 A_ltln_a_ltln_bool_fun_fun$(ltl_prop_equiv$) & % 190.88/26.43 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & ! [v0: % 190.88/26.43 A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! [v3: % 190.88/26.43 A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : ! [v5: % 190.88/26.43 A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ (fun_app$t(v4, % 190.88/26.43 v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v3, v5) = % 190.88/26.43 v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ A_set_list$(v1) | ? [v7: % 190.88/26.43 A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: % 190.88/26.43 A_ltln_bool_fun$] : ? [v11: any] : (fun_app$s(v3, v1) = v7 & % 190.88/26.43 fun_app$e(ltl_prop_equiv$, v7) = v8 & fun_app$e(ltl_prop_equiv$, v6) = v10 % 190.88/26.43 & fun_app$(v10, true_ltln$) = v11 & fun_app$(v8, true_ltln$) = v9 & % 190.88/26.43 A_ltln$(v7) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) % 190.88/26.43 | v11 = 0))) % 190.88/26.43 % 190.88/26.43 (axiom615) % 190.88/26.43 A_ltln_a_ltln_bool_fun_fun$(ltl_const_equiv$) & % 190.88/26.43 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.88/26.43 A_ltln$(false_ltln$) & A_ltln_set$(mu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.88/26.43 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 190.88/26.43 until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.43 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.88/26.43 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.88/26.43 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.43 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.43 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.43 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.88/26.43 & member$(v2, mu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.88/26.43 ~ (v8 = 0) | (( ~ (v7 = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: % 190.88/26.43 Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.43 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.88/26.43 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_const_equiv$, v14) = % 190.88/26.43 v15 & fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.43 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 % 190.88/26.43 = 0 | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 190.88/26.43 (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.88/26.43 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.88/26.43 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.88/26.43 fun_app$e(ltl_const_equiv$, v13) = v14 & fun_app$(v14, % 190.88/26.43 true_ltln$) = v15 & A_ltln$(v13) & % 190.88/26.43 A_ltln_bool_fun$(v14))))))))) % 190.88/26.43 % 190.88/26.43 (axiom616) % 190.88/26.44 A_ltln_a_ltln_bool_fun_fun$(ltl_const_equiv$) & % 190.88/26.44 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln$(true_ltln$) & % 190.88/26.44 A_ltln$(false_ltln$) & A_ltln_set$(nu_LTL$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 190.88/26.44 [v1: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v1 & % 190.88/26.44 until_ltln$(true_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.44 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 190.88/26.44 [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] % 190.88/26.44 : ( ~ (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.44 (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.44 Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.44 A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, v5) = v9 % 190.88/26.44 & member$(v2, nu_LTL$) = v8 & A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( % 190.88/26.44 ~ (v8 = 0) | (( ~ (v7 = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : % 190.88/26.44 ( ~ (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? [v13: % 190.88/26.44 A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : ( ~ % 190.88/26.44 (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.88/26.44 fun_app$e(ltl_const_equiv$, v13) = v14 & fun_app$(v14, % 190.88/26.44 false_ltln$) = v15 & A_ltln$(v13) & A_ltln_bool_fun$(v14)))) % 190.88/26.44 & (v7 = 0 | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? % 190.88/26.44 [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.44 A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 190.88/26.44 fun_app$s(v9, v13) = v14 & fun_app$e(ltl_const_equiv$, v14) = % 190.88/26.44 v15 & fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.44 A_set_list$(v13) & A_ltln_bool_fun$(v15) & Nat$(v12))))))))) % 190.88/26.44 % 190.88/26.44 (axiom640) % 190.88/26.44 A_ltln_a_ltln_bool_fun_fun$(ltl_const_equiv$) & % 190.88/26.44 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ! [v0: A_ltln$] : ! [v1: A_ltln$] % 190.88/26.44 : ! [v2: A_set_list$] : ! [v3: A_set_list_a_ltln_fun$] : ! [v4: A_ltln$] : % 190.88/26.44 ! [v5: A_ltln_bool_fun$] : ! [v6: A_set_list_a_ltln_fun$] : ! [v7: A_ltln$] % 190.88/26.44 : ! [v8: int] : (v8 = 0 | ~ (foldl$(af_letter$, v1) = v6) | ~ % 190.88/26.44 (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v6, v2) = v7) | ~ % 190.88/26.44 (fun_app$s(v3, v2) = v4) | ~ (fun_app$e(ltl_const_equiv$, v4) = v5) | ~ % 190.88/26.44 (fun_app$(v5, v7) = v8) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | ~ % 190.88/26.44 A_set_list$(v2) | ? [v9: A_ltln_bool_fun$] : ? [v10: int] : ( ~ (v10 = 0) % 190.88/26.44 & fun_app$e(ltl_const_equiv$, v0) = v9 & fun_app$(v9, v1) = v10 & % 190.88/26.44 A_ltln_bool_fun$(v9))) % 190.88/26.44 % 190.88/26.44 (axiom641) % 190.88/26.44 A_ltln_a_ltln_bool_fun_fun$(ltl_const_equiv$) & % 190.88/26.44 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ! [v0: A_ltln$] : ! [v1: A_ltln$] % 190.88/26.44 : ! [v2: A_set_list$] : ! [v3: A_set_list_a_ltln_fun$] : ! [v4: A_ltln$] : % 190.88/26.44 ! [v5: A_ltln_bool_fun$] : ! [v6: A_set_list_a_ltln_fun$] : ! [v7: A_ltln$] % 190.88/26.44 : ! [v8: int] : (v8 = 0 | ~ (foldl$(af_letter$, v1) = v6) | ~ % 190.88/26.44 (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v6, v2) = v7) | ~ % 190.88/26.44 (fun_app$s(v3, v2) = v4) | ~ (fun_app$e(ltl_const_equiv$, v4) = v5) | ~ % 190.88/26.44 (fun_app$(v5, v7) = v8) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | ~ % 190.88/26.44 A_set_list$(v2) | ? [v9: A_ltln_bool_fun$] : ? [v10: int] : ( ~ (v10 = 0) % 190.88/26.44 & fun_app$e(ltl_const_equiv$, v0) = v9 & fun_app$(v9, v1) = v10 & % 190.88/26.44 A_ltln_bool_fun$(v9))) % 190.88/26.44 % 190.88/26.44 (axiom7) % 190.88/26.44 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & % 190.88/26.44 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? % 190.88/26.44 [v1: A_ltln_a_ltln_fun$] : (af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = % 190.88/26.44 v1 & A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & % 190.88/26.44 ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set$] : ! [v5: % 190.88/26.44 A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_set_a_ltln_fun$] : ! [v7: % 190.88/26.44 A_ltln$] : ( ~ (fun_app$c(v0, v2) = v5) | ~ (fun_app$b(v5, v3) = v6) | ~ % 190.88/26.44 (fun_app$a(v6, v4) = v7) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_set$(v4) % 190.88/26.44 | ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: A_set_a_ltln_fun$] : % 190.88/26.44 ? [v11: A_ltln$] : (fun_app$b(af_letter$, v3) = v10 & fun_app$a(v10, v4) % 190.88/26.44 = v11 & fun_app$e(eq$, v3) = v8 & fun_app$(v8, true_ltln$) = v9 & % 190.88/26.44 A_ltln$(v11) & A_ltln_bool_fun$(v8) & A_set_a_ltln_fun$(v10) & (v11 = v7 % 190.88/26.44 | v9 = 0))) & ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set$] : % 190.88/26.44 ! [v5: A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_set_a_ltln_fun$] : ! [v7: % 190.88/26.44 A_ltln$] : ( ~ (fun_app$c(v0, v2) = v5) | ~ (fun_app$b(v5, v3) = v6) | ~ % 190.88/26.44 (fun_app$a(v6, v4) = v7) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_set$(v4) % 190.88/26.44 | ? [v8: A_ltln_bool_fun$] : ? [v9: any] : ? [v10: A_ltln$] : % 190.88/26.44 (fun_app$e(eq$, v3) = v8 & fun_app$d(v1, v2) = v10 & fun_app$(v8, % 190.88/26.44 true_ltln$) = v9 & A_ltln$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) % 190.88/26.44 | v10 = v7)))) % 190.88/26.44 % 190.88/26.44 (axiom91) % 190.88/26.44 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: % 190.88/26.44 int] : (v3 = 0 | ~ (less_eq$(v2, v1) = v3) | ~ (less_eq$(v2, v0) = 0) | ~ % 190.88/26.44 A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v4: int] : ( % 190.88/26.44 ~ (v4 = 0) & less_eq$(v0, v1) = v4)) & ! [v0: A_ltln_set$] : ! [v1: % 190.88/26.44 A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: int] : (v3 = 0 | ~ % 190.88/26.44 (less_eq$(v2, v1) = v3) | ~ (less_eq$(v0, v1) = 0) | ~ A_ltln_set$(v2) | % 190.88/26.44 ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 190.88/26.44 less_eq$(v2, v0) = v4)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 190.88/26.44 [v2: A_ltln_set$] : ( ~ (less_eq$(v2, v0) = 0) | ~ (less_eq$(v0, v1) = 0) | % 190.88/26.44 ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | less_eq$(v2, % 190.88/26.44 v1) = 0) % 190.88/26.44 % 190.88/26.44 (conjecture1) % 190.88/26.44 A_ltln_a_ltln_bool_fun_fun$(eq$) & A_ltln$(phi$) & A_ltln$(true_ltln$) & % 190.88/26.44 A_ltln$(psi$) & A_set$(nu$) & ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] % 190.88/26.44 : ? [v1: A_ltln_a_set_a_ltln_fun_fun$] : ? [v2: A_set_a_ltln_fun$] : ? [v3: % 190.88/26.44 A_ltln$] : ? [v4: A_ltln_set$] : ? [v5: A_ltln_a_ltln_fun$] : ? [v6: % 190.88/26.44 A_ltln$] : ? [v7: A_ltln_set$] : ? [v8: int] : ( ~ (v8 = 0) & % 190.88/26.44 fun_app$c(v0, phi$) = v1 & fun_app$b(v1, psi$) = v2 & fun_app$a(v2, nu$) = % 190.88/26.44 v3 & af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = v5 & fun_app$d(v5, % 190.88/26.44 phi$) = v6 & nested_prop_atoms$(v6) = v7 & nested_prop_atoms$(v3) = v4 & % 190.88/26.44 less_eq$(v4, v7) = v8 & A_ltln_a_set_a_ltln_fun_fun$(v1) & A_ltln$(v6) & % 190.88/26.44 A_ltln$(v3) & A_ltln_set$(v7) & A_ltln_set$(v4) & A_set_a_ltln_fun$(v2) & % 190.88/26.44 A_ltln_a_ltln_fun$(v5) & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0)) % 190.88/26.44 % 190.88/26.44 (hypothesis2) % 190.88/26.44 A_ltln$(phi$) & A_ltln$(true_ltln$) & A_ltln$(psi$) & ? [v0: A_ltln_set$] : % 190.88/26.44 ? [v1: A_ltln_a_ltln_fun$] : ? [v2: A_ltln$] : ? [v3: A_ltln_set$] : % 190.88/26.44 (until_ltln$(true_ltln$) = v1 & fun_app$d(v1, phi$) = v2 & % 190.88/26.44 nested_prop_atoms$(v2) = v3 & nested_prop_atoms$(psi$) = v0 & less_eq$(v0, % 190.88/26.44 v3) = 0 & A_ltln$(v2) & A_ltln_set$(v3) & A_ltln_set$(v0) & % 190.88/26.44 A_ltln_a_ltln_fun$(v1)) % 190.88/26.44 % 190.88/26.44 (function-axioms) % 190.88/26.46 ! [v0: A_set_list$] : ! [v1: A_set_list$] : ! [v2: Nat$] : ! [v3: Nat$] : % 190.88/26.46 ! [v4: Nat_a_set_fun$] : (v1 = v0 | ~ (subsequence$(v4, v3, v2) = v1) | ~ % 190.88/26.46 (subsequence$(v4, v3, v2) = v0)) & ! [v0: A_set_list_list$] : ! [v1: % 190.88/26.46 A_set_list_list$] : ! [v2: A_set_list$] : ! [v3: % 190.88/26.46 A_set_list_a_set_list_list_fun$] : (v1 = v0 | ~ (fun_app$ae(v3, v2) = v1) | % 190.88/26.46 ~ (fun_app$ae(v3, v2) = v0)) & ! [v0: A_set$] : ! [v1: A_set$] : ! [v2: % 190.88/26.46 Nat$] : ! [v3: Nat_a_set_fun$] : (v1 = v0 | ~ (fun_app$ad(v3, v2) = v1) | % 190.88/26.46 ~ (fun_app$ad(v3, v2) = v0)) & ! [v0: A_set_list_list$] : ! [v1: % 190.88/26.46 A_set_list_list$] : ! [v2: A_set_list_list$] : ! [v3: A_set_list$] : (v1 = % 190.88/26.46 v0 | ~ (cons$a(v3, v2) = v1) | ~ (cons$a(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_set_list_bool_fun$] : ! [v1: A_set_list_bool_fun$] : ! [v2: A_set_list$] % 190.88/26.46 : ! [v3: A_set_list_a_set_list_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$ac(v3, % 190.88/26.46 v2) = v1) | ~ (fun_app$ac(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 190.88/26.46 ! [v1: MultipleValueBool] : ! [v2: A_set_list$] : ! [v3: % 190.88/26.46 A_set_list_bool_fun$] : (v1 = v0 | ~ (fun_app$ab(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$ab(v3, v2) = v0)) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: Nat$] : ! [v3: % 190.88/26.46 Nat_a_ltln_a_ltln_bool_fun_fun_fun$] : (v1 = v0 | ~ (fun_app$aa(v3, v2) = % 190.88/26.46 v1) | ~ (fun_app$aa(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: % 190.88/26.46 A_ltln_set$] : ! [v2: Nat$] : ! [v3: Nat_a_ltln_set_fun$] : (v1 = v0 | ~ % 190.88/26.46 (fun_app$z(v3, v2) = v1) | ~ (fun_app$z(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_set_list$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! [v3: A_set$] % 190.88/26.46 : (v1 = v0 | ~ (cons$(v3, v2) = v1) | ~ (cons$(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = % 190.88/26.46 v0 | ~ (less$a(v3, v2) = v1) | ~ (less$a(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: A_ltln_set$] : ! % 190.88/26.46 [v3: A_ltln_set$] : (v1 = v0 | ~ (less$(v3, v2) = v1) | ~ (less$(v3, v2) = % 190.88/26.46 v0)) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : ! [v2: % 190.88/26.46 Nat_a_set_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (suffix$(v3, v2) = v1) | ~ % 190.88/26.46 (suffix$(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! % 190.88/26.46 [v3: Nat_int_fun$] : (v1 = v0 | ~ (fun_app$y(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$y(v3, v2) = v0)) & ! [v0: A_set_a_ltln_a_ltln_prod_fun$] : ! [v1: % 190.88/26.46 A_set_a_ltln_a_ltln_prod_fun$] : ! [v2: A_ltln_a_ltln_prod$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (fun_app$x(v3, v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_a_ltln_prod$] : ! [v1: A_ltln_a_ltln_prod$] : ! [v2: A_set$] : ! % 190.88/26.46 [v3: A_set_a_ltln_a_ltln_prod_fun$] : (v1 = v0 | ~ (fun_app$w(v3, v2) = v1) | % 190.88/26.46 ~ (fun_app$w(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 190.88/26.46 MultipleValueBool] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (gF_advice_congruent_axioms$(v3, v2) = v1) | ~ % 190.88/26.46 (gF_advice_congruent_axioms$(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_set_a_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun_fun$] : ! % 190.88/26.46 [v1: A_ltln_set_a_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun_fun$] : ! % 190.88/26.46 [v2: A_ltln_a_ltln_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | % 190.88/26.46 ~ (af_letter_nu$(v3, v2) = v1) | ~ (af_letter_nu$(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun$] : ! [v2: A_ltln_set$] % 190.88/26.46 : ! [v3: A_ltln_set_a_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun_fun$] % 190.88/26.46 : (v1 = v0 | ~ (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_a_ltln_prod$] : ! [v1: A_ltln_a_ltln_prod$] : ! [v2: A_ltln$] : % 190.88/26.46 ! [v3: A_ltln$] : (v1 = v0 | ~ (pair$(v3, v2) = v1) | ~ (pair$(v3, v2) = % 190.88/26.46 v0)) & ! [v0: A_set_list_a_ltln_a_ltln_prod_fun$] : ! [v1: % 190.88/26.46 A_set_list_a_ltln_a_ltln_prod_fun$] : ! [v2: A_ltln_a_ltln_prod$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_prod_a_set_a_ltln_a_ltln_prod_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (foldl$a(v3, v2) = v1) | ~ (foldl$a(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_a_ltln_prod$] : ! [v1: A_ltln_a_ltln_prod$] : ! [v2: A_set_list$] : % 190.88/26.46 ! [v3: A_set_list_a_ltln_a_ltln_prod_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) % 190.88/26.46 = v1) | ~ (fun_app$u(v3, v2) = v0)) & ! [v0: A_set_list$] : ! [v1: % 190.88/26.46 A_set_list$] : ! [v2: A_set_list$] : ! [v3: A_set_list_a_set_list_fun$] : % 190.88/26.46 (v1 = v0 | ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln$] : % 190.88/26.46 (v1 = v0 | ~ (gF_advice$(v3, v2) = v1) | ~ (gF_advice$(v3, v2) = v0)) & ! % 190.88/26.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (transition_functions$(v3, v2) = v1) | ~ (transition_functions$(v3, v2) = % 190.88/26.46 v0)) & ! [v0: A_set_list_a_ltln_fun$] : ! [v1: A_set_list_a_ltln_fun$] : % 190.88/26.46 ! [v2: A_ltln$] : ! [v3: A_ltln_a_set_a_ltln_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (foldl$(v3, v2) = v1) | ~ (foldl$(v3, v2) = v0)) & ! [v0: A_ltln$] : ! % 190.88/26.46 [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_set_list_a_ltln_fun$] : (v1 = % 190.88/26.46 v0 | ~ (fun_app$s(v3, v2) = v1) | ~ (fun_app$s(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (gF_advice_congruent$(v3, v2) = v1) | ~ (gF_advice_congruent$(v3, v2) = % 190.88/26.46 v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! % 190.88/26.46 [v3: Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$r(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 190.88/26.46 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~ % 190.88/26.46 (fun_app$q(v3, v2) = v1) | ~ (fun_app$q(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: A_ltln_bool_fun$] : % 190.88/26.46 ! [v3: A_ltln_bool_fun_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$p(v3, % 190.88/26.46 v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: A_ltln_bool_fun$] : % 190.88/26.46 ! [v1: A_ltln_bool_fun$] : ! [v2: int] : ! [v3: Int_a_ltln_bool_fun_fun$] : % 190.88/26.46 (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 190.88/26.46 [v2: A_ltln_a_ltln_bool_fun_fun$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (fun_app$n(v3, v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_a_ltln_bool_fun_fun$] : % 190.88/26.46 ! [v3: A_ltln_a_ltln_bool_fun_fun_a_ltln_set_fun$] : (v1 = v0 | ~ % 190.88/26.46 (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 190.88/26.46 [v2: A_ltln_set$] : ! [v3: A_ltln_set_a_ltln_a_ltln_bool_fun_fun_fun$] : (v1 % 190.88/26.46 = v0 | ~ (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: % 190.88/26.46 int] : ! [v1: int] : ! [v2: A_ltln_a_ltln_bool_fun_fun$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun_int_fun$] : (v1 = v0 | ~ (fun_app$k(v3, v2) = % 190.88/26.46 v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] % 190.88/26.46 : ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: int] : ! [v3: % 190.88/26.46 Int_a_ltln_a_ltln_bool_fun_fun_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = % 190.88/26.46 v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: % 190.88/26.46 A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln_set_a_ltln_set_fun$] : % 190.88/26.46 (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : ! [v3: % 190.88/26.46 Int_a_ltln_set_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$h(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 190.88/26.46 A_ltln_set$] : ! [v3: A_ltln_set_int_fun$] : (v1 = v0 | ~ (fun_app$g(v3, % 190.88/26.46 v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : % 190.88/26.46 ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) % 190.88/26.46 | ~ (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 190.88/26.46 MultipleValueBool] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (transition_functions_size$(v3, % 190.88/26.46 v2) = v1) | ~ (transition_functions_size$(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = % 190.88/26.46 v0 | ~ (less_eq$b(v3, v2) = v1) | ~ (less_eq$b(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: A_ltln_bool_fun$] % 190.88/26.46 : ! [v3: A_ltln_bool_fun$] : (v1 = v0 | ~ (less_eq$a(v3, v2) = v1) | ~ % 190.88/26.46 (less_eq$a(v3, v2) = v0)) & ! [v0: A_ltln_a_set_a_ltln_fun_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_set_a_ltln_fun_fun$] : ! [v2: A_ltln$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : (v1 = v0 | ~ (fun_app$c(v3, v2) % 190.88/26.46 = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: A_set_a_ltln_fun$] : ! % 190.88/26.46 [v1: A_set_a_ltln_fun$] : ! [v2: A_ltln$] : ! [v3: % 190.88/26.46 A_ltln_a_set_a_ltln_fun_fun$] : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$b(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: % 190.88/26.46 A_set$] : ! [v3: A_set_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = % 190.88/26.46 v1) | ~ (fun_app$a(v3, v2) = v0)) & ! [v0: A_ltln_bool_fun$] : ! [v1: % 190.88/26.46 A_ltln_bool_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] % 190.88/26.46 : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 190.88/26.46 A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~ % 190.88/26.46 (fun_app$d(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 190.88/26.46 MultipleValueBool] : ! [v2: A_ltln_set$] : ! [v3: A_ltln_set$] : (v1 = v0 % 190.88/26.46 | ~ (less_eq$(v3, v2) = v1) | ~ (less_eq$(v3, v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: A_ltln_set$] : ! % 190.88/26.46 [v3: A_ltln$] : (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) = % 190.88/26.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln$] : ! [v3: A_ltln_bool_fun$] : (v1 = v0 | ~ (fun_app$(v3, v2) = v1) % 190.88/26.46 | ~ (fun_app$(v3, v2) = v0)) & ! [v0: A_ltln_a_ltln_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 190.88/26.46 (strongRelease_ltln$(v2) = v1) | ~ (strongRelease_ltln$(v2) = v0)) & ! % 190.88/26.46 [v0: A_set_list_a_set_list_list_fun$] : ! [v1: % 190.88/26.46 A_set_list_a_set_list_list_fun$] : ! [v2: Nat$] : (v1 = v0 | ~ % 190.88/26.46 (n_lists$(v2) = v1) | ~ (n_lists$(v2) = v0)) & ! [v0: A_ltln_a_ltln_fun$] % 190.88/26.46 : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 190.88/26.46 (weakUntil_ltln$(v2) = v1) | ~ (weakUntil_ltln$(v2) = v0)) & ! [v0: % 190.88/26.46 A_set_list_a_set_list_fun$] : ! [v1: A_set_list_a_set_list_fun$] : ! [v2: % 190.88/26.46 Nat$] : (v1 = v0 | ~ (take$(v2) = v1) | ~ (take$(v2) = v0)) & ! [v0: % 190.88/26.46 Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ % 190.88/26.46 (nat$(v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_prod$] : (v1 = v0 | ~ (fst$(v2) = v1) | ~ (fst$(v2) = v0)) & % 190.88/26.46 ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln_a_ltln_prod$] : (v1 = v0 % 190.88/26.46 | ~ (snd$(v2) = v1) | ~ (snd$(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 190.88/26.46 [v1: MultipleValueBool] : ! [v2: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (af_congruent_axioms$(v2) = v1) | ~ (af_congruent_axioms$(v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: Nat_a_set_fun$] : % 190.88/26.46 (v1 = v0 | ~ (semantics_ltln$(v2) = v1) | ~ (semantics_ltln$(v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : % 190.88/26.46 (v1 = v0 | ~ (release_ltln$(v2) = v1) | ~ (release_ltln$(v2) = v0)) & ! % 190.88/26.46 [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (af_letter_G$(v2) = v1) | ~ % 190.88/26.46 (af_letter_G$(v2) = v0)) & ! [v0: A_ltln_set_a_ltln_set_fun$] : ! [v1: % 190.88/26.46 A_ltln_set_a_ltln_set_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 190.88/26.46 (nested_prop_atoms_nu$(v2) = v1) | ~ (nested_prop_atoms_nu$(v2) = v0)) & ! % 190.88/26.46 [v0: A_set_list_a_set_list_fun$] : ! [v1: A_set_list_a_set_list_fun$] : ! % 190.88/26.46 [v2: A_set_list$] : (v1 = v0 | ~ (append$(v2) = v1) | ~ (append$(v2) = v0)) % 190.88/26.46 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (transition_functions_size_axioms$(v2) = % 190.88/26.46 v1) | ~ (transition_functions_size_axioms$(v2) = v0)) & ! [v0: % 190.88/26.46 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_bool_fun$] : (v1 = v0 | % 190.88/26.46 ~ (collect$(v2) = v1) | ~ (collect$(v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (equivp$(v2) = v1) | ~ % 190.88/26.46 (equivp$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 190.88/26.46 MultipleValueBool] : ! [v2: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 190.88/26.46 (ltl_equivalence$(v2) = v1) | ~ (ltl_equivalence$(v2) = v0)) & ! [v0: % 190.88/26.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (af_congruent$(v2) = v1) | ~ % 190.88/26.46 (af_congruent$(v2) = v0)) & ! [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] % 190.88/26.46 : ! [v1: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v2: % 190.88/26.46 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (af_letter_F$(v2) = v1) | ~ % 190.88/26.46 (af_letter_F$(v2) = v0)) & ! [v0: A_ltln_a_ltln_fun$] : ! [v1: % 190.88/26.46 A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ (until_ltln$(v2) = % 190.88/26.46 v1) | ~ (until_ltln$(v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: % 190.88/26.46 A_ltln_set$] : ! [v2: A_ltln$] : (v1 = v0 | ~ (nested_prop_atoms$(v2) = % 190.88/26.46 v1) | ~ (nested_prop_atoms$(v2) = v0)) & ! [v0: A_ltln_bool_fun$] : ! % 190.88/26.46 [v1: A_ltln_bool_fun$] : ! [v2: A_ltln_set$] : (v1 = v0 | ~ (uu$(v2) = v1) | % 190.88/26.46 ~ (uu$(v2) = v0)) % 190.88/26.46 % 190.88/26.46 Further assumptions not needed in the proof: % 190.88/26.46 -------------------------------------------- % 190.88/26.46 axiom0, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, axiom105, % 190.88/26.46 axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112, % 190.88/26.46 axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom120, % 190.88/26.46 axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127, axiom128, % 190.88/26.46 axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134, axiom138, % 190.88/26.46 axiom139, axiom14, axiom140, axiom141, axiom142, axiom143, axiom144, axiom145, % 190.88/26.46 axiom148, axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, % 190.88/26.46 axiom155, axiom156, axiom157, axiom159, axiom16, axiom165, axiom166, axiom167, % 190.88/26.46 axiom168, axiom169, axiom17, axiom170, axiom171, axiom172, axiom173, axiom174, % 190.88/26.46 axiom176, axiom177, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, % 190.88/26.46 axiom184, axiom185, axiom186, axiom187, axiom19, axiom190, axiom191, axiom192, % 190.88/26.46 axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, axiom20, % 190.88/26.46 axiom200, axiom201, axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, % 190.88/26.46 axiom208, axiom209, axiom21, axiom210, axiom211, axiom212, axiom213, axiom214, % 190.88/26.46 axiom215, axiom217, axiom218, axiom219, axiom22, axiom220, axiom221, axiom222, % 190.88/26.46 axiom223, axiom224, axiom225, axiom226, axiom227, axiom228, axiom23, axiom230, % 190.88/26.46 axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, axiom238, % 190.88/26.46 axiom239, axiom24, axiom240, axiom242, axiom243, axiom244, axiom245, axiom246, % 190.88/26.46 axiom247, axiom248, axiom249, axiom25, axiom250, axiom252, axiom253, axiom254, % 190.88/26.46 axiom255, axiom256, axiom259, axiom260, axiom261, axiom262, axiom263, axiom264, % 190.88/26.46 axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270, axiom271, % 190.88/26.46 axiom274, axiom275, axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, % 190.88/26.46 axiom281, axiom282, axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, % 190.88/26.46 axiom289, axiom29, axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, % 190.88/26.46 axiom297, axiom298, axiom299, axiom3, axiom300, axiom301, axiom302, axiom303, % 190.88/26.46 axiom304, axiom305, axiom306, axiom308, axiom309, axiom31, axiom310, axiom311, % 190.88/26.46 axiom312, axiom314, axiom315, axiom316, axiom318, axiom319, axiom32, axiom320, % 190.88/26.46 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328, % 190.88/26.46 axiom330, axiom331, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338, % 190.88/26.46 axiom339, axiom34, axiom340, axiom341, axiom342, axiom343, axiom345, axiom346, % 190.88/26.46 axiom347, axiom348, axiom349, axiom35, axiom350, axiom351, axiom352, axiom354, % 190.88/26.46 axiom355, axiom356, axiom357, axiom358, axiom359, axiom36, axiom360, axiom361, % 190.88/26.46 axiom362, axiom363, axiom364, axiom365, axiom366, axiom367, axiom368, axiom369, % 190.88/26.46 axiom37, axiom370, axiom371, axiom372, axiom373, axiom374, axiom375, axiom376, % 190.88/26.46 axiom377, axiom378, axiom379, axiom38, axiom380, axiom381, axiom382, axiom383, % 190.88/26.46 axiom384, axiom385, axiom386, axiom387, axiom388, axiom389, axiom39, axiom390, % 190.88/26.46 axiom391, axiom392, axiom393, axiom394, axiom395, axiom396, axiom397, axiom398, % 190.88/26.46 axiom399, axiom4, axiom40, axiom400, axiom401, axiom402, axiom403, axiom404, % 190.88/26.46 axiom405, axiom406, axiom407, axiom408, axiom409, axiom41, axiom410, axiom411, % 190.88/26.46 axiom412, axiom413, axiom414, axiom415, axiom416, axiom417, axiom418, axiom419, % 190.88/26.46 axiom42, axiom420, axiom421, axiom422, axiom423, axiom424, axiom425, axiom426, % 190.88/26.46 axiom427, axiom428, axiom429, axiom43, axiom430, axiom431, axiom432, axiom433, % 190.88/26.46 axiom434, axiom435, axiom436, axiom437, axiom438, axiom44, axiom441, axiom442, % 190.88/26.46 axiom443, axiom444, axiom446, axiom447, axiom449, axiom45, axiom450, axiom452, % 190.88/26.46 axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, axiom459, axiom46, % 190.88/26.46 axiom461, axiom463, axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, % 190.88/26.46 axiom47, axiom470, axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, % 190.88/26.46 axiom477, axiom478, axiom479, axiom48, axiom482, axiom483, axiom485, axiom486, % 190.88/26.46 axiom487, axiom488, axiom489, axiom49, axiom490, axiom491, axiom492, axiom495, % 190.88/26.46 axiom497, axiom498, axiom499, axiom5, axiom50, axiom500, axiom501, axiom503, % 190.88/26.46 axiom504, axiom505, axiom506, axiom507, axiom508, axiom509, axiom51, axiom510, % 190.88/26.46 axiom511, axiom512, axiom513, axiom514, axiom515, axiom518, axiom52, axiom520, % 190.88/26.46 axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, axiom528, % 190.88/26.46 axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535, % 190.88/26.46 axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, axiom542, % 190.88/26.46 axiom543, axiom544, axiom545, axiom546, axiom548, axiom55, axiom552, axiom553, % 190.88/26.46 axiom555, axiom556, axiom557, axiom558, axiom559, axiom56, axiom560, axiom561, % 190.88/26.46 axiom562, axiom563, axiom564, axiom565, axiom566, axiom567, axiom568, axiom57, % 190.88/26.46 axiom570, axiom571, axiom572, axiom573, axiom574, axiom575, axiom576, axiom577, % 190.88/26.46 axiom579, axiom58, axiom580, axiom581, axiom582, axiom583, axiom584, axiom585, % 190.88/26.46 axiom586, axiom59, axiom591, axiom592, axiom593, axiom594, axiom595, axiom596, % 190.88/26.46 axiom597, axiom598, axiom599, axiom6, axiom60, axiom600, axiom601, axiom602, % 190.88/26.46 axiom603, axiom606, axiom607, axiom608, axiom609, axiom61, axiom610, axiom611, % 190.88/26.46 axiom612, axiom613, axiom614, axiom617, axiom618, axiom619, axiom62, axiom620, % 190.88/26.46 axiom621, axiom622, axiom623, axiom624, axiom625, axiom626, axiom627, axiom628, % 190.88/26.46 axiom629, axiom63, axiom630, axiom631, axiom632, axiom633, axiom634, axiom635, % 190.88/26.46 axiom636, axiom637, axiom638, axiom639, axiom64, axiom642, axiom643, axiom644, % 190.88/26.46 axiom65, axiom66, axiom67, axiom68, axiom69, axiom70, axiom71, axiom72, axiom73, % 190.88/26.46 axiom74, axiom75, axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81, % 190.88/26.46 axiom82, axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, % 190.88/26.46 axiom90, axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, axiom99, % 190.88/26.46 formula_646, formula_647 % 190.88/26.46 % 190.88/26.46 Those formulas are unsatisfiable: % 190.88/26.46 --------------------------------- % 190.88/26.46 % 190.88/26.46 Begin of proof % 190.88/26.46 | % 190.88/26.46 | ALPHA: (hypothesis2) implies: % 190.88/26.46 | (1) ? [v0: A_ltln_set$] : ? [v1: A_ltln_a_ltln_fun$] : ? [v2: A_ltln$] : % 190.88/26.46 | ? [v3: A_ltln_set$] : (until_ltln$(true_ltln$) = v1 & fun_app$d(v1, % 190.88/26.46 | phi$) = v2 & nested_prop_atoms$(v2) = v3 & nested_prop_atoms$(psi$) % 190.88/26.46 | = v0 & less_eq$(v0, v3) = 0 & A_ltln$(v2) & A_ltln_set$(v3) & % 190.88/26.46 | A_ltln_set$(v0) & A_ltln_a_ltln_fun$(v1)) % 190.88/26.46 | % 190.88/26.46 | ALPHA: (axiom7) implies: % 190.88/26.46 | (2) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: % 190.88/26.46 | A_ltln_a_ltln_fun$] : (af_letter_F$(eq$) = v0 & % 190.88/26.46 | until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.46 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v2: A_ltln$] : ! % 190.88/26.46 | [v3: A_ltln$] : ! [v4: A_set$] : ! [v5: % 190.88/26.46 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_set_a_ltln_fun$] : ! % 190.88/26.46 | [v7: A_ltln$] : ( ~ (fun_app$c(v0, v2) = v5) | ~ (fun_app$b(v5, v3) % 190.88/26.46 | = v6) | ~ (fun_app$a(v6, v4) = v7) | ~ A_ltln$(v3) | ~ % 190.88/26.46 | A_ltln$(v2) | ~ A_set$(v4) | ? [v8: A_ltln_bool_fun$] : ? [v9: % 190.88/26.46 | any] : ? [v10: A_set_a_ltln_fun$] : ? [v11: A_ltln$] : % 190.88/26.46 | (fun_app$b(af_letter$, v3) = v10 & fun_app$a(v10, v4) = v11 & % 190.88/26.46 | fun_app$e(eq$, v3) = v8 & fun_app$(v8, true_ltln$) = v9 & % 190.88/26.46 | A_ltln$(v11) & A_ltln_bool_fun$(v8) & A_set_a_ltln_fun$(v10) & % 190.88/26.46 | (v11 = v7 | v9 = 0))) & ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 190.88/26.46 | [v4: A_set$] : ! [v5: A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: % 190.88/26.46 | A_set_a_ltln_fun$] : ! [v7: A_ltln$] : ( ~ (fun_app$c(v0, v2) = % 190.88/26.46 | v5) | ~ (fun_app$b(v5, v3) = v6) | ~ (fun_app$a(v6, v4) = v7) | % 190.88/26.46 | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_set$(v4) | ? [v8: % 190.88/26.46 | A_ltln_bool_fun$] : ? [v9: any] : ? [v10: A_ltln$] : % 190.88/26.46 | (fun_app$e(eq$, v3) = v8 & fun_app$d(v1, v2) = v10 & fun_app$(v8, % 190.88/26.46 | true_ltln$) = v9 & A_ltln$(v10) & A_ltln_bool_fun$(v8) & ( ~ % 190.88/26.46 | (v9 = 0) | v10 = v7)))) % 190.88/26.46 | % 190.88/26.46 | ALPHA: (axiom12) implies: % 190.88/26.46 | (3) ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ( ~ (nested_prop_atoms$(v0) = % 190.88/26.46 | v1) | ~ A_ltln$(v0) | ? [v2: A_ltln$] : ? [v3: A_ltln_set$] : % 190.88/26.46 | (fun_app$d(normalise$, v0) = v2 & nested_prop_atoms$(v2) = v3 & % 190.88/26.46 | less_eq$(v3, v1) = 0 & A_ltln$(v2) & A_ltln_set$(v3))) % 190.88/26.46 | % 190.88/26.46 | ALPHA: (axiom26) implies: % 190.88/26.46 | (4) transition_functions_size$(eq$, normalise$) = 0 % 190.88/26.46 | % 190.88/26.46 | ALPHA: (axiom30) implies: % 190.88/26.47 | (5) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln$] : ! [v2: % 190.88/26.47 | A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.88/26.47 | int] : (v5 = 0 | ~ (fun_app$e(v0, v1) = v4) | ~ (fun_app$(v4, v3) = % 190.88/26.47 | v5) | ~ (fun_app$(v4, v2) = 0) | ~ % 190.88/26.47 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 190.88/26.47 | ~ A_ltln$(v1) | ? [v6: any] : ? [v7: A_ltln_bool_fun$] : ? [v8: % 190.88/26.47 | any] : (ltl_equivalence$(v0) = v6 & fun_app$e(v0, v2) = v7 & % 190.88/26.47 | fun_app$(v7, v3) = v8 & A_ltln_bool_fun$(v7) & ( ~ (v8 = 0) | ~ % 190.88/26.47 | (v6 = 0)))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom33) implies: % 190.88/26.47 | (6) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ (less_eq$(v0, v1) = % 190.88/26.47 | 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: any] : % 190.88/26.47 | (less_eq$(v1, v0) = v2 & ( ~ (v2 = 0) | v1 = v0) & ( ~ (v1 = v0) | v2 % 190.88/26.47 | = 0))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom91) implies: % 190.88/26.47 | (7) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ( % 190.88/26.47 | ~ (less_eq$(v2, v0) = 0) | ~ (less_eq$(v0, v1) = 0) | ~ % 190.88/26.47 | A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 190.88/26.47 | less_eq$(v2, v1) = 0) % 190.88/26.47 | (8) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ! % 190.88/26.47 | [v3: int] : (v3 = 0 | ~ (less_eq$(v2, v1) = v3) | ~ (less_eq$(v0, v1) % 190.88/26.47 | = 0) | ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 190.88/26.47 | | ? [v4: int] : ( ~ (v4 = 0) & less_eq$(v2, v0) = v4)) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom135) implies: % 190.88/26.47 | (9) gF_advice_congruent$(eq$, normalise$) = 0 % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom136) implies: % 190.88/26.47 | (10) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : (af_letter_F$(eq$) % 190.88/26.47 | = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v1: % 190.88/26.47 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_set_list$] : ! [v4: % 190.88/26.47 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : % 190.88/26.47 | ! [v6: A_ltln$] : ( ~ (foldl$(v4, v2) = v5) | ~ (fun_app$s(v5, v3) % 190.88/26.47 | = v6) | ~ (fun_app$c(v0, v1) = v4) | ~ A_ltln$(v2) | ~ % 190.88/26.47 | A_ltln$(v1) | ~ A_set_list$(v3) | ? [v7: A_ltln_bool_fun$] : ? % 190.88/26.47 | [v8: any] : ? [v9: A_set_list_a_ltln_fun$] : ? [v10: A_ltln$] : % 190.88/26.47 | ? [v11: A_ltln_bool_fun$] : ? [v12: any] : (foldl$(af_letter$, % 190.88/26.47 | v2) = v9 & fun_app$s(v9, v3) = v10 & fun_app$e(eq$, v10) = v11 % 190.88/26.47 | & fun_app$e(eq$, v6) = v7 & fun_app$(v11, true_ltln$) = v12 & % 190.88/26.47 | fun_app$(v7, true_ltln$) = v8 & A_set_list_a_ltln_fun$(v9) & % 190.88/26.47 | A_ltln$(v10) & A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7) & ( % 190.88/26.47 | ~ (v8 = 0) | v12 = 0)))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom137) implies: % 190.88/26.47 | (11) ! [v0: A_ltln$] : ! [v1: A_set$] : ! [v2: A_set_a_ltln_fun$] : ! % 190.88/26.47 | [v3: A_ltln$] : ( ~ (fun_app$b(af_letter$, v0) = v2) | ~ % 190.88/26.47 | (fun_app$a(v2, v1) = v3) | ~ A_ltln$(v0) | ~ A_set$(v1) | ? [v4: % 190.88/26.47 | A_ltln_set$] : ? [v5: A_ltln_set$] : (nested_prop_atoms$(v3) = v4 % 190.88/26.47 | & nested_prop_atoms$(v0) = v5 & less_eq$(v4, v5) = 0 & % 190.88/26.47 | A_ltln_set$(v5) & A_ltln_set$(v4))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom146) implies: % 190.88/26.47 | (12) ? [v0: A_set_list_a_ltln_fun$] : (foldl$(af_letter$, true_ltln$) = v0 % 190.88/26.47 | & A_set_list_a_ltln_fun$(v0) & ! [v1: A_set_list$] : ! [v2: % 190.88/26.47 | A_ltln$] : (v2 = true_ltln$ | ~ (fun_app$s(v0, v1) = v2) | ~ % 190.88/26.47 | A_set_list$(v1))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom147) implies: % 190.88/26.47 | (13) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ( % 190.88/26.47 | ~ (transition_functions_size$(v0, v1) = 0) | ~ % 190.88/26.47 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | % 190.88/26.47 | (transition_functions_size_axioms$(v1) = 0 & % 190.88/26.47 | transition_functions$(v0, v1) = 0)) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom158) implies: % 190.88/26.47 | (14) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 190.88/26.47 | A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 190.88/26.47 | [v2: A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! % 190.88/26.47 | [v5: A_set$] : ! [v6: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! % 190.88/26.47 | [v7: A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_set_a_ltln_fun$] : ! % 190.88/26.47 | [v9: A_ltln$] : ( ~ (transition_functions$(v1, v2) = 0) | ~ % 190.88/26.47 | (fun_app$c(v6, v3) = v7) | ~ (fun_app$b(v7, v4) = v8) | ~ % 190.88/26.47 | (fun_app$a(v8, v5) = v9) | ~ (af_letter_F$(v1) = v6) | ~ % 190.88/26.47 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v4) | ~ A_ltln$(v3) % 190.88/26.47 | | ~ A_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v10: % 190.88/26.47 | A_ltln_bool_fun$] : ? [v11: any] : ? [v12: A_ltln$] : ? [v13: % 190.88/26.47 | A_set_a_ltln_fun$] : ? [v14: A_ltln$] : (fun_app$b(af_letter$, % 190.88/26.47 | v4) = v13 & fun_app$a(v13, v5) = v14 & fun_app$e(v1, v4) = v10 % 190.88/26.47 | & fun_app$d(v0, v3) = v12 & fun_app$(v10, true_ltln$) = v11 & % 190.88/26.47 | A_ltln$(v14) & A_ltln$(v12) & A_ltln_bool_fun$(v10) & % 190.88/26.47 | A_set_a_ltln_fun$(v13) & ( ~ (v11 = 0) | v12 = v9) & (v14 = v9 | % 190.88/26.47 | v11 = 0))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.88/26.47 | A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! % 190.88/26.47 | [v5: A_set$] : ! [v6: A_ltln$] : ! [v7: A_set_a_ltln_fun$] : ! % 190.88/26.47 | [v8: A_ltln$] : ( ~ (transition_functions$(v1, v2) = 0) | ~ % 190.88/26.47 | (fun_app$b(af_letter$, v4) = v7) | ~ (fun_app$a(v7, v5) = v8) | % 190.88/26.47 | ~ (fun_app$d(v0, v3) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | % 190.88/26.47 | ~ A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set$(v5) | ~ % 190.88/26.47 | A_ltln_a_ltln_fun$(v2) | ? [v9: A_ltln_bool_fun$] : ? [v10: any] % 190.88/26.47 | : ? [v11: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v12: % 190.88/26.47 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v13: A_set_a_ltln_fun$] : ? % 190.88/26.47 | [v14: A_ltln$] : (fun_app$c(v11, v3) = v12 & fun_app$b(v12, v4) = % 190.88/26.47 | v13 & fun_app$a(v13, v5) = v14 & af_letter_F$(v1) = v11 & % 190.88/26.47 | fun_app$e(v1, v4) = v9 & fun_app$(v9, true_ltln$) = v10 & % 190.88/26.47 | A_ltln_a_set_a_ltln_fun_fun$(v12) & A_ltln$(v14) & % 190.88/26.47 | A_ltln_bool_fun$(v9) & A_set_a_ltln_fun$(v13) & % 190.88/26.47 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v11) & ( ~ (v10 = 0) | % 190.88/26.47 | v14 = v6) & (v14 = v8 | v10 = 0)))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom160) implies: % 190.88/26.47 | (15) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: % 190.88/26.47 | A_ltln_a_ltln_fun$] : (af_letter_F$(eq$) = v0 & % 190.88/26.47 | until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 190.88/26.47 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v2: A_ltln$] : ! % 190.88/26.47 | [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: A_set_list$] : ! % 190.88/26.47 | [v6: A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_list_a_ltln_fun$] % 190.88/26.47 | : ! [v8: A_set_list_a_set_list_fun$] : ! [v9: A_set_list$] : ! % 190.88/26.47 | [v10: A_ltln$] : ( ~ (append$(v4) = v8) | ~ (fun_app$t(v8, v5) = % 190.88/26.47 | v9) | ~ (foldl$(v6, v3) = v7) | ~ (fun_app$s(v7, v9) = v10) | % 190.88/26.47 | ~ (fun_app$c(v0, v2) = v6) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 190.88/26.47 | A_set_list$(v5) | ~ A_set_list$(v4) | ? [v11: A_ltln$] : ? % 190.88/26.47 | [v12: A_ltln$] : ? [v13: A_set_list_a_ltln_fun$] : ? [v14: % 190.88/26.47 | A_ltln$] : (foldl$(v6, v12) = v13 & fun_app$s(v13, v5) = v14 & % 190.88/26.47 | fun_app$s(v7, v4) = v11 & fun_app$d(v1, v2) = v12 & % 190.88/26.47 | A_set_list_a_ltln_fun$(v13) & A_ltln$(v14) & A_ltln$(v12) & % 190.88/26.47 | A_ltln$(v11) & ( ~ (v12 = v11) | v14 = v10)))) % 190.88/26.47 | % 190.88/26.47 | ALPHA: (axiom161) implies: % 190.88/26.48 | (16) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : (af_letter_F$(eq$) % 190.88/26.48 | = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v1: % 190.88/26.48 | A_set_list$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.48 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : % 190.88/26.48 | ! [v6: A_ltln$] : ( ~ (foldl$(v4, v3) = v5) | ~ (fun_app$s(v5, v1) % 190.88/26.48 | = v6) | ~ (fun_app$c(v0, v2) = v4) | ~ A_ltln$(v3) | ~ % 190.88/26.48 | A_ltln$(v2) | ~ A_set_list$(v1) | ? [v7: A_set_list_a_ltln_fun$] % 190.88/26.48 | : ? [v8: A_ltln$] : ? [v9: A_set_list$] : ? [v10: A_set_list$] % 190.88/26.48 | : ? [v11: A_set_list_a_set_list_fun$] : ? [v12: A_set_list$] : % 190.88/26.48 | ? [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : % 190.88/26.48 | (A_set_list$(v10) & A_set_list$(v9) & ((v15 = 0 & v12 = v1 & % 190.88/26.48 | append$(v9) = v11 & fun_app$t(v11, v10) = v1 & fun_app$s(v5, % 190.88/26.48 | v9) = v13 & fun_app$e(eq$, v13) = v14 & fun_app$(v14, % 190.88/26.48 | true_ltln$) = 0 & A_ltln$(v13) & A_ltln_bool_fun$(v14) & % 190.88/26.48 | A_set_list_a_set_list_fun$(v11)) | (v8 = v6 & % 190.88/26.48 | foldl$(af_letter$, v3) = v7 & fun_app$s(v7, v1) = v6 & % 190.88/26.48 | A_set_list_a_ltln_fun$(v7) & A_ltln$(v6)))))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom162) implies: % 190.88/26.48 | (17) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : (af_letter_F$(eq$) % 190.88/26.48 | = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v1: % 190.88/26.48 | A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.48 | A_set_list_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: % 190.88/26.48 | A_ltln_bool_fun$] : ! [v7: A_ltln_a_set_a_ltln_fun_fun$] : ! % 190.88/26.48 | [v8: A_set_list_a_ltln_fun$] : ( ~ (foldl$(v7, v1) = v8) | ~ % 190.88/26.48 | (foldl$(af_letter$, v1) = v4) | ~ (fun_app$s(v4, v2) = v5) | ~ % 190.88/26.48 | (fun_app$c(v0, v3) = v7) | ~ (fun_app$e(eq$, v5) = v6) | ~ % 190.88/26.48 | (fun_app$(v6, true_ltln$) = 0) | ~ A_ltln$(v3) | ~ A_ltln$(v1) | % 190.88/26.48 | ~ A_set_list$(v2) | ? [v9: A_set_list$] : ? [v10: A_set_list$] % 190.88/26.48 | : ? [v11: A_set_list_a_set_list_fun$] : ? [v12: A_ltln$] : ? % 190.88/26.48 | [v13: A_ltln_bool_fun$] : (append$(v9) = v11 & fun_app$t(v11, v10) % 190.88/26.48 | = v2 & fun_app$s(v8, v9) = v12 & fun_app$e(eq$, v12) = v13 & % 190.88/26.48 | fun_app$(v13, true_ltln$) = 0 & A_ltln$(v12) & A_set_list$(v10) % 190.88/26.48 | & A_set_list$(v9) & A_ltln_bool_fun$(v13) & % 190.88/26.48 | A_set_list_a_set_list_fun$(v11)))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom163) implies: % 190.88/26.48 | (18) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : (af_letter_F$(eq$) % 190.88/26.48 | = v0 & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v1: % 190.88/26.48 | A_set_list$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.48 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : % 190.88/26.48 | ! [v6: A_ltln$] : ( ~ (foldl$(v4, v2) = v5) | ~ (fun_app$s(v5, v1) % 190.88/26.48 | = v6) | ~ (fun_app$c(v0, v3) = v4) | ~ A_ltln$(v3) | ~ % 190.88/26.48 | A_ltln$(v2) | ~ A_set_list$(v1) | ? [v7: A_set_list_a_ltln_fun$] % 190.88/26.48 | : ? [v8: A_ltln$] : ? [v9: A_set_list$] : ? [v10: A_set_list$] % 190.88/26.48 | : ? [v11: A_set_list_a_set_list_fun$] : ? [v12: A_set_list$] : % 190.88/26.48 | ? [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: int] : % 190.88/26.48 | (foldl$(af_letter$, v2) = v7 & fun_app$s(v7, v1) = v8 & % 190.88/26.48 | A_set_list_a_ltln_fun$(v7) & A_ltln$(v8) & A_set_list$(v10) & % 190.88/26.48 | A_set_list$(v9) & (v8 = v6 | (v15 = 0 & v12 = v1 & append$(v9) = % 190.88/26.48 | v11 & fun_app$t(v11, v10) = v1 & fun_app$s(v7, v9) = v13 & % 190.88/26.48 | fun_app$e(eq$, v13) = v14 & fun_app$(v14, true_ltln$) = 0 & % 190.88/26.48 | A_ltln$(v13) & A_ltln_bool_fun$(v14) & % 190.88/26.48 | A_set_list_a_set_list_fun$(v11)))))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom164) implies: % 190.88/26.48 | (19) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 190.88/26.48 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 190.88/26.48 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 190.88/26.48 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 190.88/26.48 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 190.88/26.48 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 190.88/26.48 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 190.88/26.48 | (fun_app$s(v3, v1) = v7 & fun_app$e(eq$, v7) = v8 & fun_app$e(eq$, % 190.88/26.48 | v6) = v10 & fun_app$(v10, true_ltln$) = v11 & fun_app$(v8, % 190.88/26.48 | true_ltln$) = v9 & A_ltln$(v7) & A_ltln_bool_fun$(v10) & % 190.88/26.48 | A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 = 0))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom175) implies: % 190.88/26.48 | (20) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 190.88/26.48 | A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 190.88/26.48 | [v2: A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! % 190.88/26.48 | [v5: A_set_list$] : ! [v6: A_set_list$] : ! [v7: % 190.88/26.48 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.88/26.48 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : % 190.88/26.48 | ! [v10: A_set_list_a_set_list_fun$] : ! [v11: A_set_list$] : ! % 190.88/26.48 | [v12: A_ltln$] : ( ~ (append$(v5) = v10) | ~ (fun_app$t(v10, v6) = % 190.88/26.48 | v11) | ~ (transition_functions$(v1, v2) = 0) | ~ (foldl$(v8, % 190.88/26.48 | v4) = v9) | ~ (fun_app$s(v9, v11) = v12) | ~ (fun_app$c(v7, % 190.88/26.48 | v3) = v8) | ~ (af_letter_F$(v1) = v7) | ~ % 190.88/26.48 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v4) | ~ A_ltln$(v3) % 190.88/26.48 | | ~ A_set_list$(v6) | ~ A_set_list$(v5) | ~ % 190.88/26.48 | A_ltln_a_ltln_fun$(v2) | ? [v13: A_ltln$] : ? [v14: A_ltln$] : % 190.88/26.48 | ? [v15: A_set_list_a_ltln_fun$] : ? [v16: A_ltln$] : (foldl$(v8, % 190.88/26.48 | v14) = v15 & fun_app$s(v15, v6) = v16 & fun_app$s(v9, v5) = % 190.88/26.48 | v13 & fun_app$d(v0, v3) = v14 & A_set_list_a_ltln_fun$(v15) & % 190.88/26.48 | A_ltln$(v16) & A_ltln$(v14) & A_ltln$(v13) & ( ~ (v14 = v13) | % 190.88/26.48 | v16 = v12))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 190.88/26.48 | A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! % 190.88/26.48 | [v5: A_set_list$] : ! [v6: A_set_list$] : ! [v7: % 190.88/26.48 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 190.88/26.48 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : % 190.88/26.48 | ! [v10: A_ltln$] : ! [v11: A_set_list_a_ltln_fun$] : ! [v12: % 190.88/26.48 | A_ltln$] : ( ~ (transition_functions$(v1, v2) = 0) | ~ % 190.88/26.48 | (foldl$(v8, v10) = v11) | ~ (foldl$(v8, v4) = v9) | ~ % 190.88/26.48 | (fun_app$s(v11, v6) = v12) | ~ (fun_app$s(v9, v5) = v10) | ~ % 190.88/26.48 | (fun_app$c(v7, v3) = v8) | ~ (af_letter_F$(v1) = v7) | ~ % 190.88/26.48 | (fun_app$d(v0, v3) = v10) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | % 190.88/26.48 | ~ A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set_list$(v6) | ~ % 190.88/26.48 | A_set_list$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v13: % 190.88/26.48 | A_set_list_a_set_list_fun$] : ? [v14: A_set_list$] : % 190.88/26.48 | (append$(v5) = v13 & fun_app$t(v13, v6) = v14 & fun_app$s(v9, v14) % 190.88/26.48 | = v12 & A_ltln$(v12) & A_set_list$(v14) & % 190.88/26.48 | A_set_list_a_set_list_fun$(v13)))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom178) implies: % 190.88/26.48 | (21) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 190.88/26.48 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 190.88/26.48 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 190.88/26.48 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 190.88/26.48 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 190.88/26.48 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 190.88/26.48 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 190.88/26.48 | (fun_app$s(v3, v1) = v7 & fun_app$e(eq$, v7) = v8 & fun_app$e(eq$, % 190.88/26.48 | v6) = v10 & fun_app$(v10, false_ltln$) = v11 & fun_app$(v8, % 190.88/26.48 | false_ltln$) = v9 & A_ltln$(v7) & A_ltln_bool_fun$(v10) & % 190.88/26.48 | A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 = 0))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom188) implies: % 190.88/26.48 | (22) ? [v0: A_set_list_a_ltln_fun$] : ? [v1: A_set_list_a_ltln_fun$] : % 190.88/26.48 | (foldl$(af_letter$, true_ltln$) = v0 & foldl$(af_letter$, false_ltln$) % 190.88/26.48 | = v1 & A_set_list_a_ltln_fun$(v1) & A_set_list_a_ltln_fun$(v0) & ? % 190.88/26.48 | [v2: tlbool] : ! [v3: A_set_list$] : ! [v4: A_ltln$] : (v4 = % 190.88/26.48 | false_ltln$ | v2 = tltrue | ~ (fun_app$s(v1, v3) = v4) | ~ % 190.88/26.48 | A_set_list$(v3) | ~ tlbool(v2)) & ! [v2: A_set_list$] : ! [v3: % 190.88/26.48 | A_ltln$] : (v3 = true_ltln$ | ~ (fun_app$s(v0, v2) = v3) | ~ % 190.88/26.48 | A_set_list$(v2))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom189) implies: % 190.88/26.48 | (23) ? [v0: A_set_list_a_ltln_fun$] : ? [v1: A_set_list_a_ltln_fun$] : % 190.88/26.48 | (foldl$(af_letter$, true_ltln$) = v1 & foldl$(af_letter$, false_ltln$) % 190.88/26.48 | = v0 & A_set_list_a_ltln_fun$(v1) & A_set_list_a_ltln_fun$(v0) & ? % 190.88/26.48 | [v2: tlbool] : ! [v3: A_set_list$] : ! [v4: A_ltln$] : (v4 = % 190.88/26.48 | true_ltln$ | v2 = tltrue | ~ (fun_app$s(v1, v3) = v4) | ~ % 190.88/26.48 | A_set_list$(v3) | ~ tlbool(v2)) & ! [v2: A_set_list$] : ! [v3: % 190.88/26.48 | A_ltln$] : (v3 = false_ltln$ | ~ (fun_app$s(v0, v2) = v3) | ~ % 190.88/26.48 | A_set_list$(v2))) % 190.88/26.48 | % 190.88/26.48 | ALPHA: (axiom216) implies: % 190.88/26.48 | (24) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ( % 190.88/26.48 | ~ (gF_advice_congruent$(v0, v1) = 0) | ~ % 190.88/26.48 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | % 190.88/26.48 | (gF_advice_congruent_axioms$(v0, v1) = 0 & ltl_equivalence$(v0) = % 190.88/26.48 | 0)) % 190.88/26.48 | % 190.88/26.49 | ALPHA: (axiom229) implies: % 190.88/26.49 | (25) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 190.88/26.49 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.88/26.49 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! % 190.88/26.49 | [v8: int] : (v8 = 0 | ~ (semantics_ltln$(v1) = v4) | ~ % 190.88/26.49 | (until_ltln$(v2) = v5) | ~ (fun_app$d(v5, v3) = v6) | ~ % 190.88/26.49 | (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v4, v7) = v8) | ~ % 190.88/26.49 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v9: % 190.88/26.49 | A_ltln$] : ? [v10: int] : ( ~ (v10 = 0) & fun_app$d(v0, v3) = % 190.88/26.49 | v9 & fun_app$(v4, v9) = v10 & A_ltln$(v9))) & ! [v1: % 190.88/26.49 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.49 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 190.88/26.49 | : ! [v7: A_ltln$] : ( ~ (semantics_ltln$(v1) = v4) | ~ % 190.88/26.49 | (until_ltln$(v2) = v5) | ~ (fun_app$d(v5, v3) = v6) | ~ % 190.88/26.49 | (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v4, v7) = 0) | ~ % 190.88/26.49 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v8: % 190.88/26.49 | A_ltln$] : (fun_app$d(v0, v3) = v8 & fun_app$(v4, v8) = 0 & % 190.88/26.49 | A_ltln$(v8)))) % 190.88/26.49 | % 190.88/26.49 | ALPHA: (axiom241) implies: % 190.88/26.49 | (26) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.88/26.49 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: % 190.88/26.49 | A_ltln_set$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! % 190.88/26.49 | [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ( ~ (semantics_ltln$(v3) % 190.88/26.49 | = v5) | ~ (gF_advice$(v4, v2) = v6) | ~ (fun_app$(v5, v6) = 0) % 190.88/26.49 | | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v2) | ? % 190.88/26.49 | [v7: int] : ? [v8: A_ltln$] : ? [v9: int] : ? [v10: A_ltln$] : % 190.88/26.49 | ? [v11: A_ltln$] : ? [v12: int] : (A_ltln$(v8) & ((v9 = 0 & ~ % 190.88/26.49 | (v12 = 0) & fun_app$d(v1, v8) = v10 & fun_app$d(v0, v10) = % 190.88/26.49 | v11 & member$(v8, v2) = 0 & fun_app$(v5, v11) = v12 & % 190.88/26.49 | A_ltln$(v11) & A_ltln$(v10)) | (v7 = 0 & fun_app$(v5, v4) = % 190.88/26.49 | 0))))) % 190.88/26.49 | % 190.88/26.49 | ALPHA: (axiom251) implies: % 190.88/26.49 | (27) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 190.88/26.49 | : ! [v3: A_set_list$] : ! [v4: A_set_list$] : ! [v5: % 190.88/26.49 | A_ltln_bool_fun$] : ! [v6: A_ltln$] : ! [v7: % 190.88/26.49 | A_set_list_a_ltln_fun$] : ! [v8: A_set_list_a_set_list_fun$] : ! % 190.88/26.49 | [v9: A_set_list$] : ! [v10: A_ltln$] : ! [v11: int] : (v11 = 0 | % 190.88/26.49 | ~ (semantics_ltln$(v1) = v5) | ~ (append$(v4) = v8) | ~ % 190.88/26.49 | (fun_app$t(v8, v3) = v9) | ~ (foldl$(af_letter$, v6) = v7) | ~ % 190.88/26.49 | (fun_app$s(v7, v9) = v10) | ~ (fun_app$d(v0, v2) = v6) | ~ % 190.88/26.49 | (fun_app$(v5, v10) = v11) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) % 190.88/26.49 | | ~ A_set_list$(v4) | ~ A_set_list$(v3) | ? [v12: A_ltln$] : ? % 190.88/26.49 | [v13: int] : ( ~ (v13 = 0) & fun_app$s(v7, v3) = v12 & % 190.88/26.49 | fun_app$(v5, v12) = v13 & A_ltln$(v12)))) % 190.88/26.49 | % 190.88/26.49 | ALPHA: (axiom257) implies: % 190.88/26.49 | (28) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.88/26.49 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 190.88/26.49 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.88/26.49 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 190.88/26.49 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.49 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.49 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.49 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 190.88/26.49 | v5) = v9 & member$(v2, mu_LTL$) = v8 & % 190.88/26.49 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 190.88/26.49 | = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : % 190.88/26.49 | ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.49 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 % 190.88/26.49 | & fun_app$s(v9, v13) = v14 & fun_app$e(eq$, v14) = v15 % 190.88/26.49 | & fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.49 | A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 190.88/26.49 | Nat$(v12)))) & (v7 = 0 | ! [v11: Nat$] : ! [v12: % 190.88/26.49 | A_set_list$] : ( ~ (subsequence$(v3, v10, v11) = v12) | % 190.88/26.49 | ~ Nat$(v11) | ? [v13: A_ltln$] : ? [v14: % 190.88/26.49 | A_ltln_bool_fun$] : ? [v15: int] : ( ~ (v15 = 0) & % 190.88/26.49 | fun_app$s(v9, v12) = v13 & fun_app$e(eq$, v13) = v14 & % 190.88/26.49 | fun_app$(v14, true_ltln$) = v15 & A_ltln$(v13) & % 190.88/26.49 | A_ltln_bool_fun$(v14))))))))) % 190.88/26.49 | % 190.88/26.49 | ALPHA: (axiom258) implies: % 190.88/26.49 | (29) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.88/26.49 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 190.88/26.49 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 190.88/26.49 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 190.88/26.49 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 190.88/26.49 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 190.88/26.49 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 190.88/26.49 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 190.88/26.49 | v5) = v9 & member$(v2, nu_LTL$) = v8 & % 190.88/26.49 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 190.88/26.49 | = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 190.88/26.49 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 190.88/26.49 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 190.88/26.49 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 190.88/26.49 | fun_app$e(eq$, v13) = v14 & fun_app$(v14, false_ltln$) % 190.88/26.49 | = v15 & A_ltln$(v13) & A_ltln_bool_fun$(v14)))) & (v7 % 190.88/26.49 | = 0 | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? % 190.88/26.49 | [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 190.88/26.49 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 % 190.88/26.49 | & fun_app$s(v9, v13) = v14 & fun_app$e(eq$, v14) = v15 % 190.88/26.49 | & fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 190.88/26.49 | A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 190.88/26.49 | Nat$(v12))))))))) % 190.88/26.49 | % 190.88/26.49 | ALPHA: (axiom272) implies: % 190.88/26.49 | (30) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.88/26.49 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 190.88/26.49 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: % 190.88/26.49 | A_ltln_a_ltln_bool_fun_fun$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.49 | Nat_a_set_fun$] : ! [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : % 190.88/26.49 | ! [v7: A_ltln$] : ! [v8: any] : ( ~ (semantics_ltln$(v4) = v5) | ~ % 190.88/26.49 | (ltl_equivalence$(v2) = 0) | ~ (fun_app$d(v1, v3) = v6) | ~ % 190.88/26.49 | (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v5, v7) = v8) | ~ % 190.88/26.49 | A_ltln_a_ltln_bool_fun_fun$(v2) | ~ Nat_a_set_fun$(v4) | ~ % 190.88/26.49 | A_ltln$(v3) | ? [v9: any] : ? [v10: A_set_list_a_ltln_fun$] : ? % 190.88/26.49 | [v11: Nat$] : (foldl$(af_letter$, v6) = v10 & member$(v3, mu_LTL$) % 190.88/26.49 | = v9 & A_set_list_a_ltln_fun$(v10) & Nat$(v11) & ( ~ (v9 = 0) | % 190.88/26.49 | (( ~ (v8 = 0) | ? [v12: Nat$] : ( ~ Nat$(v12) | ? [v13: % 190.88/26.49 | Nat$] : ? [v14: A_set_list$] : ? [v15: A_ltln$] : ? % 190.88/26.49 | [v16: A_ltln_bool_fun$] : (subsequence$(v4, v12, v13) = % 190.88/26.49 | v14 & fun_app$s(v10, v14) = v15 & fun_app$e(v2, v15) = % 190.88/26.49 | v16 & fun_app$(v16, true_ltln$) = 0 & A_ltln$(v15) & % 190.88/26.49 | A_set_list$(v14) & A_ltln_bool_fun$(v16) & % 190.88/26.49 | Nat$(v13)))) & (v8 = 0 | ! [v12: Nat$] : ! [v13: % 190.88/26.50 | A_set_list$] : ( ~ (subsequence$(v4, v11, v12) = v13) | % 190.88/26.50 | ~ Nat$(v12) | ? [v14: A_ltln$] : ? [v15: % 190.88/26.50 | A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = 0) & % 190.88/26.50 | fun_app$s(v10, v13) = v14 & fun_app$e(v2, v14) = v15 & % 190.88/26.50 | fun_app$(v15, true_ltln$) = v16 & A_ltln$(v14) & % 190.88/26.50 | A_ltln_bool_fun$(v15))))))))) % 190.88/26.50 | % 190.88/26.50 | ALPHA: (axiom273) implies: % 190.88/26.50 | (31) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 190.88/26.50 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 190.88/26.50 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: % 190.88/26.50 | A_ltln_a_ltln_bool_fun_fun$] : ! [v3: A_ltln$] : ! [v4: % 190.88/26.50 | Nat_a_set_fun$] : ! [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : % 190.88/26.50 | ! [v7: A_ltln$] : ! [v8: any] : ( ~ (semantics_ltln$(v4) = v5) | ~ % 190.88/26.50 | (ltl_equivalence$(v2) = 0) | ~ (fun_app$d(v1, v3) = v6) | ~ % 190.88/26.50 | (fun_app$d(v0, v6) = v7) | ~ (fun_app$(v5, v7) = v8) | ~ % 190.88/26.50 | A_ltln_a_ltln_bool_fun_fun$(v2) | ~ Nat_a_set_fun$(v4) | ~ % 190.88/26.50 | A_ltln$(v3) | ? [v9: any] : ? [v10: A_set_list_a_ltln_fun$] : ? % 190.88/26.50 | [v11: Nat$] : (foldl$(af_letter$, v6) = v10 & member$(v3, nu_LTL$) % 190.88/26.50 | = v9 & A_set_list_a_ltln_fun$(v10) & Nat$(v11) & ( ~ (v9 = 0) | % 190.88/26.50 | (( ~ (v8 = 0) | ! [v12: Nat$] : ! [v13: A_set_list$] : ( ~ % 190.88/26.50 | (subsequence$(v4, v11, v12) = v13) | ~ Nat$(v12) | ? % 190.88/26.50 | [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : ? [v16: % 190.88/26.50 | int] : ( ~ (v16 = 0) & fun_app$s(v10, v13) = v14 & % 190.88/26.50 | fun_app$e(v2, v14) = v15 & fun_app$(v15, false_ltln$) % 190.88/26.50 | = v16 & A_ltln$(v14) & A_ltln_bool_fun$(v15)))) & (v8 % 190.88/26.50 | = 0 | ? [v12: Nat$] : ( ~ Nat$(v12) | ? [v13: Nat$] : ? % 190.88/26.50 | [v14: A_set_list$] : ? [v15: A_ltln$] : ? [v16: % 190.88/26.50 | A_ltln_bool_fun$] : (subsequence$(v4, v12, v13) = v14 % 190.88/26.50 | & fun_app$s(v10, v14) = v15 & fun_app$e(v2, v15) = v16 % 190.88/26.50 | & fun_app$(v16, false_ltln$) = 0 & A_ltln$(v15) & % 190.88/26.50 | A_set_list$(v14) & A_ltln_bool_fun$(v16) & % 190.88/26.50 | Nat$(v13))))))))) % 190.88/26.50 | % 190.88/26.50 | ALPHA: (axiom296) implies: % 191.22/26.50 | (32) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: % 191.22/26.50 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v2: Nat$] : (nat$(0) % 191.22/26.50 | = v2 & af_letter_F$(eq$) = v1 & until_ltln$(true_ltln$) = v0 & % 191.22/26.50 | Nat$(v2) & A_ltln_a_ltln_fun$(v0) & % 191.22/26.50 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v1) & ? [v3: % 191.22/26.50 | Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.22/26.50 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_list_a_ltln_fun$] : % 191.22/26.50 | ! [v8: Nat$] : ! [v9: int] : ( ~ (fun_app$y(of_nat$, v8) = v9) | ~ % 191.22/26.50 | (foldl$(v6, v5) = v7) | ~ (fun_app$c(v1, v4) = v6) | ~ % 191.22/26.50 | (fun_app$d(v0, v4) = v5) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) % 191.22/26.50 | | ~ Nat$(v8) | ? [v10: A_set_list_a_ltln_fun$] : ? [v11: Nat$] % 191.22/26.50 | : ? [v12: Nat$] : ? [v13: int] : ? [v14: A_set_list$] : ? % 191.22/26.50 | [v15: A_ltln$] : ? [v16: A_ltln_bool_fun$] : ? [v17: int] : % 191.22/26.50 | (Nat$(v12) & Nat$(v11) & ((v17 = 0 & $lesseq(1, $difference(v13, % 191.22/26.50 | v9)) & fun_app$y(of_nat$, v12) = v13 & subsequence$(v3, % 191.22/26.50 | v2, v12) = v14 & fun_app$s(v7, v14) = v15 & fun_app$e(eq$, % 191.22/26.50 | v15) = v16 & fun_app$(v16, true_ltln$) = 0 & A_ltln$(v15) % 191.22/26.50 | & A_set_list$(v14) & A_ltln_bool_fun$(v16)) | % 191.22/26.50 | (foldl$(af_letter$, v5) = v10 & A_set_list_a_ltln_fun$(v10) & % 191.22/26.50 | ! [v18: Nat$] : ! [v19: A_set_list$] : ( ~ % 191.22/26.50 | (subsequence$(v3, v11, v18) = v19) | ~ Nat$(v18) | ? % 191.22/26.50 | [v20: A_ltln$] : ? [v21: A_ltln_bool_fun$] : ? [v22: % 191.22/26.50 | int] : ( ~ (v22 = 0) & fun_app$s(v10, v19) = v20 & % 191.22/26.50 | fun_app$e(eq$, v20) = v21 & fun_app$(v21, true_ltln$) = % 191.22/26.50 | v22 & A_ltln$(v20) & A_ltln_bool_fun$(v21))))))) & ? % 191.22/26.50 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.22/26.50 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(af_letter$, v5) = v6) | ~ % 191.22/26.50 | (fun_app$d(v0, v4) = v5) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) % 191.22/26.50 | | ? [v7: A_ltln_a_set_a_ltln_fun_fun$] : ? [v8: % 191.22/26.50 | A_set_list_a_ltln_fun$] : ? [v9: Nat$] : (Nat$(v9) & ( ! [v10: % 191.22/26.50 | Nat$] : ! [v11: A_set_list$] : ( ~ (subsequence$(v3, v9, % 191.22/26.50 | v10) = v11) | ~ Nat$(v10) | ? [v12: A_ltln$] : ? % 191.22/26.50 | [v13: A_ltln_bool_fun$] : ? [v14: int] : ( ~ (v14 = 0) & % 191.22/26.50 | fun_app$s(v6, v11) = v12 & fun_app$e(eq$, v12) = v13 & % 191.22/26.50 | fun_app$(v13, true_ltln$) = v14 & A_ltln$(v12) & % 191.22/26.50 | A_ltln_bool_fun$(v13))) | (foldl$(v7, v5) = v8 & % 191.22/26.50 | fun_app$c(v1, v4) = v7 & A_set_list_a_ltln_fun$(v8) & % 191.22/26.50 | A_ltln_a_set_a_ltln_fun_fun$(v7) & ! [v10: Nat$] : ! [v11: % 191.22/26.50 | int] : ( ~ (fun_app$y(of_nat$, v10) = v11) | ~ Nat$(v10) % 191.22/26.50 | | ? [v12: Nat$] : ? [v13: int] : ? [v14: A_set_list$] : % 191.22/26.50 | ? [v15: A_ltln$] : ? [v16: A_ltln_bool_fun$] : % 191.22/26.50 | ($lesseq(1, $difference(v13, v11)) & fun_app$y(of_nat$, % 191.22/26.50 | v12) = v13 & subsequence$(v3, v2, v12) = v14 & % 191.22/26.50 | fun_app$s(v8, v14) = v15 & fun_app$e(eq$, v15) = v16 & % 191.22/26.50 | fun_app$(v16, true_ltln$) = 0 & A_ltln$(v15) & % 191.22/26.50 | A_set_list$(v14) & A_ltln_bool_fun$(v16) & % 191.22/26.50 | Nat$(v12)))))))) % 191.22/26.50 | % 191.22/26.50 | ALPHA: (axiom307) implies: % 191.22/26.50 | (33) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | % 191.22/26.50 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 191.22/26.50 | ? [v3: any] : (less_eq$(v0, v1) = v3 & ( ~ (v3 = 0) | v1 = v0) & ( ~ % 191.22/26.50 | (v1 = v0) | v3 = 0))) % 191.22/26.50 | % 191.22/26.50 | ALPHA: (axiom439) implies: % 191.22/26.50 | (34) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.50 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 191.22/26.50 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! % 191.22/26.50 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.22/26.50 | A_ltln$] : ! [v7: Nat_a_set_fun$] : ! [v8: A_ltln_bool_fun$] : % 191.22/26.50 | ! [v9: int] : (v9 = 0 | ~ (suffix$(v2, v3) = v7) | ~ % 191.22/26.50 | (semantics_ltln$(v7) = v8) | ~ (fun_app$d(v1, v4) = v5) | ~ % 191.22/26.50 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v8, v6) = v9) | ~ % 191.22/26.50 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? [v10: % 191.22/26.50 | A_ltln_bool_fun$] : ? [v11: int] : ( ~ (v11 = 0) & % 191.22/26.50 | semantics_ltln$(v3) = v10 & fun_app$(v10, v6) = v11 & % 191.22/26.50 | A_ltln_bool_fun$(v10))) & ! [v2: Nat$] : ! [v3: % 191.22/26.50 | Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] : ! % 191.22/26.50 | [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ % 191.22/26.50 | (suffix$(v2, v3) = v5) | ~ (semantics_ltln$(v5) = v6) | ~ % 191.22/26.50 | (fun_app$d(v1, v4) = v7) | ~ (fun_app$d(v0, v7) = v8) | ~ % 191.22/26.50 | (fun_app$(v6, v8) = 0) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 191.22/26.50 | ~ Nat$(v2) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 % 191.22/26.50 | & fun_app$(v9, v8) = 0 & A_ltln_bool_fun$(v9)))) % 191.22/26.50 | % 191.22/26.50 | ALPHA: (axiom440) implies: % 191.22/26.51 | (35) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.51 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 191.22/26.51 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! % 191.22/26.51 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.22/26.51 | A_ltln$] : ! [v7: Nat_a_set_fun$] : ! [v8: A_ltln_bool_fun$] : % 191.22/26.51 | ! [v9: int] : (v9 = 0 | ~ (suffix$(v2, v3) = v7) | ~ % 191.22/26.51 | (semantics_ltln$(v7) = v8) | ~ (fun_app$d(v1, v4) = v5) | ~ % 191.22/26.51 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v8, v6) = v9) | ~ % 191.22/26.51 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ? [v10: % 191.22/26.51 | A_ltln_bool_fun$] : ? [v11: int] : ( ~ (v11 = 0) & % 191.22/26.51 | semantics_ltln$(v3) = v10 & fun_app$(v10, v6) = v11 & % 191.22/26.51 | A_ltln_bool_fun$(v10))) & ! [v2: Nat$] : ! [v3: % 191.22/26.51 | Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] : ! % 191.22/26.51 | [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ % 191.22/26.51 | (suffix$(v2, v3) = v5) | ~ (semantics_ltln$(v5) = v6) | ~ % 191.22/26.51 | (fun_app$d(v1, v4) = v7) | ~ (fun_app$d(v0, v7) = v8) | ~ % 191.22/26.51 | (fun_app$(v6, v8) = 0) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 191.22/26.51 | ~ Nat$(v2) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 % 191.22/26.51 | & fun_app$(v9, v8) = 0 & A_ltln_bool_fun$(v9)))) % 191.22/26.51 | % 191.22/26.51 | ALPHA: (axiom445) implies: % 191.22/26.51 | (36) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 191.22/26.51 | [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: % 191.22/26.51 | A_ltln$] : ! [v7: A_ltln$] : ! [v8: A_ltln_bool_fun$] : ! [v9: % 191.22/26.51 | A_ltln$] : ! [v10: A_ltln$] : ! [v11: int] : (v11 = 0 | ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (gF_advice$(v9, v5) % 191.22/26.51 | = v10) | ~ (gF_advice$(v6, v5) = v7) | ~ (fun_app$e(v1, v7) = % 191.22/26.51 | v8) | ~ (fun_app$d(v2, v4) = v9) | ~ (fun_app$d(v2, v3) = v6) % 191.22/26.51 | | ~ (fun_app$(v8, v10) = v11) | ~ % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v4) | ~ A_ltln$(v3) % 191.22/26.51 | | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v12: % 191.22/26.51 | A_ltln_bool_fun$] : ? [v13: int] : ( ~ (v13 = 0) & % 191.22/26.51 | fun_app$e(v1, v3) = v12 & fun_app$(v12, v4) = v13 & % 191.22/26.51 | A_ltln_bool_fun$(v12))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : % 191.22/26.51 | ! [v2: A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 191.22/26.51 | A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln_bool_fun$] : ! % 191.22/26.51 | [v7: A_ltln$] : ! [v8: A_ltln$] : ! [v9: int] : (v9 = 0 | ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 191.22/26.51 | (semantics_ltln$(v3) = v6) | ~ (gF_advice$(v7, v5) = v8) | ~ % 191.22/26.51 | (fun_app$d(v2, v4) = v7) | ~ (fun_app$(v6, v8) = v9) | ~ % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 191.22/26.51 | A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? % 191.22/26.51 | [v10: A_ltln$] : ? [v11: int] : ( ~ (v11 = 0) & gF_advice$(v4, % 191.22/26.51 | v5) = v10 & fun_app$(v6, v10) = v11 & A_ltln$(v10))) & ! [v1: % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 191.22/26.51 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 191.22/26.51 | [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 191.22/26.51 | (semantics_ltln$(v3) = v6) | ~ (gF_advice$(v7, v5) = v8) | ~ % 191.22/26.51 | (fun_app$d(v2, v4) = v7) | ~ (fun_app$(v6, v8) = 0) | ~ % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 191.22/26.51 | A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? % 191.22/26.51 | [v9: A_set_list_a_ltln_fun$] : ? [v10: Nat$] : ? [v11: % 191.22/26.51 | Nat_a_set_fun$] : ? [v12: A_ltln_bool_fun$] : ? [v13: % 191.22/26.51 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: A_ltln$] : % 191.22/26.51 | (suffix$(v10, v3) = v11 & subsequence$(v3, v0, v10) = v13 & % 191.22/26.51 | semantics_ltln$(v11) = v12 & gF_advice$(v14, v5) = v15 & % 191.22/26.51 | foldl$(af_letter$, v4) = v9 & fun_app$s(v9, v13) = v14 & % 191.22/26.51 | fun_app$(v12, v15) = 0 & A_set_list_a_ltln_fun$(v9) & % 191.22/26.51 | Nat_a_set_fun$(v11) & A_ltln$(v15) & A_ltln$(v14) & % 191.22/26.51 | A_set_list$(v13) & A_ltln_bool_fun$(v12) & Nat$(v10))) & ! [v1: % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 191.22/26.51 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 191.22/26.51 | [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ( ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 191.22/26.51 | (semantics_ltln$(v3) = v6) | ~ (gF_advice$(v4, v5) = v7) | ~ % 191.22/26.51 | (fun_app$(v6, v7) = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 191.22/26.51 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ % 191.22/26.51 | A_ltln_a_ltln_fun$(v2) | ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 191.22/26.51 | (gF_advice$(v8, v5) = v9 & fun_app$d(v2, v4) = v8 & fun_app$(v6, % 191.22/26.51 | v9) = 0 & A_ltln$(v9) & A_ltln$(v8))) & ! [v1: % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 191.22/26.51 | [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ( ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$e(v1, v3) % 191.22/26.51 | = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 191.22/26.51 | A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln$] : (fun_app$d(v2, v3) = % 191.22/26.51 | v5 & fun_app$(v4, v5) = 0 & A_ltln$(v5))) & ! [v1: % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 191.22/26.51 | [v3: A_ltln$] : ! [v4: A_ltln$] : ( ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$d(v2, v3) % 191.22/26.51 | = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 191.22/26.51 | A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln_bool_fun$] : % 191.22/26.51 | (fun_app$e(v1, v3) = v5 & fun_app$(v5, v4) = 0 & % 191.22/26.51 | A_ltln_bool_fun$(v5))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : % 191.22/26.51 | ! [v2: A_ltln_a_ltln_fun$] : ! [v3: int] : (v3 = 0 | ~ % 191.22/26.51 | (gF_advice_congruent_axioms$(v1, v2) = v3) | ~ % 191.22/26.51 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | ? % 191.22/26.51 | [v4: A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? [v7: % 191.22/26.51 | A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? [v10: % 191.22/26.51 | A_ltln$] : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : ? % 191.22/26.51 | [v13: A_ltln$] : ? [v14: int] : ? [v15: Nat_a_set_fun$] : ? % 191.22/26.51 | [v16: A_ltln$] : ? [v17: A_ltln_set$] : ? [v18: % 191.22/26.51 | A_ltln_bool_fun$] : ? [v19: A_ltln$] : ? [v20: A_ltln$] : ? % 191.22/26.51 | [v21: int] : ? [v22: A_set_list_a_ltln_fun$] : ? [v23: % 191.22/26.51 | Nat_a_set_fun$] : ? [v24: A_ltln$] : ? [v25: A_ltln_set$] : ? % 191.22/26.51 | [v26: A_ltln_bool_fun$] : ? [v27: A_ltln$] : ? [v28: int] : ? % 191.22/26.51 | [v29: A_ltln$] : ? [v30: A_ltln$] : ? [v31: int] : ? [v32: % 191.22/26.51 | A_ltln$] : ? [v33: A_ltln_bool_fun$] : ? [v34: A_ltln$] : ? % 191.22/26.51 | [v35: int] : (Nat_a_set_fun$(v23) & Nat_a_set_fun$(v15) & % 191.22/26.51 | A_ltln$(v32) & A_ltln$(v24) & A_ltln$(v16) & A_ltln$(v5) & % 191.22/26.51 | A_ltln$(v4) & A_ltln_set$(v25) & A_ltln_set$(v17) & % 191.22/26.51 | A_ltln_set$(v6) & ((v28 = 0 & ~ (v31 = 0) & % 191.22/26.51 | semantics_ltln$(v23) = v26 & gF_advice$(v29, v25) = v30 & % 191.22/26.51 | gF_advice$(v24, v25) = v27 & fun_app$d(v2, v24) = v29 & % 191.22/26.51 | fun_app$(v26, v30) = v31 & fun_app$(v26, v27) = 0 & % 191.22/26.51 | A_ltln$(v30) & A_ltln$(v29) & A_ltln$(v27) & % 191.22/26.51 | A_ltln_bool_fun$(v26)) | (v21 = 0 & semantics_ltln$(v15) = % 191.22/26.51 | v18 & gF_advice$(v19, v17) = v20 & foldl$(af_letter$, v16) = % 191.22/26.51 | v22 & fun_app$d(v2, v16) = v19 & fun_app$(v18, v20) = 0 & % 191.22/26.51 | A_set_list_a_ltln_fun$(v22) & A_ltln$(v20) & A_ltln$(v19) & % 191.22/26.51 | A_ltln_bool_fun$(v18) & ! [v36: Nat$] : ! [v37: % 191.22/26.51 | Nat_a_set_fun$] : ( ~ (suffix$(v36, v15) = v37) | ~ % 191.22/26.51 | Nat$(v36) | ? [v38: A_ltln_bool_fun$] : ? [v39: % 191.22/26.51 | A_set_list$] : ? [v40: A_ltln$] : ? [v41: A_ltln$] : % 191.22/26.51 | ? [v42: int] : ( ~ (v42 = 0) & subsequence$(v15, v0, v36) % 191.22/26.51 | = v39 & semantics_ltln$(v37) = v38 & gF_advice$(v40, % 191.22/26.51 | v17) = v41 & fun_app$s(v22, v39) = v40 & fun_app$(v38, % 191.22/26.51 | v41) = v42 & A_ltln$(v41) & A_ltln$(v40) & % 191.22/26.51 | A_set_list$(v39) & A_ltln_bool_fun$(v38))) & ! [v36: % 191.22/26.51 | Nat$] : ! [v37: A_set_list$] : ( ~ (subsequence$(v15, v0, % 191.22/26.51 | v36) = v37) | ~ Nat$(v36) | ? [v38: Nat_a_set_fun$] % 191.22/26.51 | : ? [v39: A_ltln_bool_fun$] : ? [v40: A_ltln$] : ? % 191.22/26.51 | [v41: A_ltln$] : ? [v42: int] : ( ~ (v42 = 0) & % 191.22/26.51 | suffix$(v36, v15) = v38 & semantics_ltln$(v38) = v39 & % 191.22/26.51 | gF_advice$(v40, v17) = v41 & fun_app$s(v22, v37) = v40 & % 191.22/26.51 | fun_app$(v39, v41) = v42 & Nat_a_set_fun$(v38) & % 191.22/26.51 | A_ltln$(v41) & A_ltln$(v40) & A_ltln_bool_fun$(v39)))) | % 191.22/26.51 | (v8 = 0 & ~ (v14 = 0) & gF_advice$(v12, v6) = v13 & % 191.22/26.51 | gF_advice$(v9, v6) = v10 & fun_app$e(v1, v10) = v11 & % 191.22/26.51 | fun_app$e(v1, v4) = v7 & fun_app$d(v2, v5) = v12 & % 191.22/26.51 | fun_app$d(v2, v4) = v9 & fun_app$(v11, v13) = v14 & % 191.22/26.51 | fun_app$(v7, v5) = 0 & A_ltln$(v13) & A_ltln$(v12) & % 191.22/26.51 | A_ltln$(v10) & A_ltln$(v9) & A_ltln_bool_fun$(v11) & % 191.22/26.51 | A_ltln_bool_fun$(v7)) | ( ~ (v35 = 0) & fun_app$e(v1, v32) = % 191.22/26.51 | v33 & fun_app$d(v2, v32) = v34 & fun_app$(v33, v34) = v35 & % 191.22/26.51 | A_ltln$(v34) & A_ltln_bool_fun$(v33)))))) % 191.22/26.51 | % 191.22/26.51 | ALPHA: (axiom448) implies: % 191.22/26.52 | (37) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: Nat$] : (nat$(0) = v1 & % 191.22/26.52 | until_ltln$(true_ltln$) = v0 & Nat$(v1) & A_ltln_a_ltln_fun$(v0) & % 191.22/26.52 | ? [v2: Nat_a_set_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : ! % 191.22/26.52 | [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! % 191.22/26.52 | [v7: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 191.22/26.52 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : % 191.22/26.52 | ! [v10: Nat$] : ! [v11: int] : ( ~ (fun_app$y(of_nat$, v10) = v11) % 191.22/26.52 | | ~ (transition_functions$(v3, v4) = 0) | ~ (foldl$(v8, v6) = % 191.22/26.52 | v9) | ~ (fun_app$c(v7, v5) = v8) | ~ (af_letter_F$(v3) = v7) | % 191.22/26.52 | ~ (fun_app$d(v0, v5) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v3) | % 191.22/26.52 | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v5) | ~ Nat$(v10) | ~ % 191.22/26.52 | A_ltln_a_ltln_fun$(v4) | ? [v12: A_set_list_a_ltln_fun$] : ? % 191.22/26.52 | [v13: Nat$] : ? [v14: Nat$] : ? [v15: int] : ? [v16: % 191.22/26.52 | A_set_list$] : ? [v17: A_ltln$] : ? [v18: A_ltln_bool_fun$] : % 191.22/26.52 | ? [v19: int] : (Nat$(v14) & Nat$(v13) & ((v19 = 0 & $lesseq(1, % 191.22/26.52 | $difference(v15, v11)) & fun_app$y(of_nat$, v14) = v15 & % 191.22/26.52 | subsequence$(v2, v1, v14) = v16 & fun_app$s(v9, v16) = v17 & % 191.22/26.52 | fun_app$e(v3, v17) = v18 & fun_app$(v18, true_ltln$) = 0 & % 191.22/26.52 | A_ltln$(v17) & A_set_list$(v16) & A_ltln_bool_fun$(v18)) | % 191.22/26.52 | (foldl$(af_letter$, v6) = v12 & A_set_list_a_ltln_fun$(v12) & % 191.22/26.52 | ! [v20: Nat$] : ! [v21: A_set_list$] : ( ~ % 191.22/26.52 | (subsequence$(v2, v13, v20) = v21) | ~ Nat$(v20) | ? % 191.22/26.52 | [v22: A_ltln$] : ? [v23: A_ltln_bool_fun$] : ? [v24: % 191.22/26.52 | int] : ( ~ (v24 = 0) & fun_app$s(v12, v21) = v22 & % 191.22/26.52 | fun_app$e(v3, v22) = v23 & fun_app$(v23, true_ltln$) = % 191.22/26.52 | v24 & A_ltln$(v22) & A_ltln_bool_fun$(v23))))))) & ? % 191.22/26.52 | [v2: Nat_a_set_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : ! % 191.22/26.52 | [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! % 191.22/26.52 | [v7: A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v3, v4) = % 191.22/26.52 | 0) | ~ (foldl$(af_letter$, v6) = v7) | ~ (fun_app$d(v0, v5) = % 191.22/26.52 | v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v3) | ~ Nat_a_set_fun$(v2) % 191.22/26.52 | | ~ A_ltln$(v5) | ~ A_ltln_a_ltln_fun$(v4) | ? [v8: % 191.22/26.52 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v9: % 191.22/26.52 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v10: A_set_list_a_ltln_fun$] % 191.22/26.52 | : ? [v11: Nat$] : (Nat$(v11) & ( ! [v12: Nat$] : ! [v13: % 191.22/26.52 | A_set_list$] : ( ~ (subsequence$(v2, v11, v12) = v13) | ~ % 191.22/26.52 | Nat$(v12) | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 191.22/26.52 | ? [v16: int] : ( ~ (v16 = 0) & fun_app$s(v7, v13) = v14 & % 191.22/26.52 | fun_app$e(v3, v14) = v15 & fun_app$(v15, true_ltln$) = v16 % 191.22/26.52 | & A_ltln$(v14) & A_ltln_bool_fun$(v15))) | (foldl$(v9, v6) % 191.22/26.52 | = v10 & fun_app$c(v8, v5) = v9 & af_letter_F$(v3) = v8 & % 191.22/26.52 | A_set_list_a_ltln_fun$(v10) & % 191.22/26.52 | A_ltln_a_set_a_ltln_fun_fun$(v9) & % 191.22/26.52 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v8) & ! [v12: Nat$] % 191.22/26.52 | : ! [v13: int] : ( ~ (fun_app$y(of_nat$, v12) = v13) | ~ % 191.22/26.52 | Nat$(v12) | ? [v14: Nat$] : ? [v15: int] : ? [v16: % 191.22/26.52 | A_set_list$] : ? [v17: A_ltln$] : ? [v18: % 191.22/26.52 | A_ltln_bool_fun$] : ($lesseq(1, $difference(v15, v13)) & % 191.22/26.52 | fun_app$y(of_nat$, v14) = v15 & subsequence$(v2, v1, % 191.22/26.52 | v14) = v16 & fun_app$s(v10, v16) = v17 & fun_app$e(v3, % 191.22/26.52 | v17) = v18 & fun_app$(v18, true_ltln$) = 0 & % 191.22/26.52 | A_ltln$(v17) & A_set_list$(v16) & A_ltln_bool_fun$(v18) % 191.22/26.52 | & Nat$(v14)))))))) % 191.22/26.52 | % 191.22/26.52 | ALPHA: (axiom451) implies: % 191.22/26.52 | (38) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: % 191.22/26.52 | A_ltln_a_ltln_fun$] : ? [v2: Nat$] : (nat$(0) = v2 & % 191.22/26.52 | af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = v1 & Nat$(v2) & % 191.22/26.52 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) % 191.22/26.52 | & ? [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 191.22/26.52 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_ltln$] : ! [v7: % 191.22/26.52 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(v5, v6) = v7) | ~ % 191.22/26.52 | (fun_app$c(v0, v4) = v5) | ~ (fun_app$d(v1, v4) = v6) | ~ % 191.22/26.52 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ? [v8: % 191.22/26.52 | A_set_list_a_ltln_fun$] : ? [v9: Nat$] : ? [v10: int] : % 191.22/26.52 | (Nat$(v9) & ((fun_app$y(of_nat$, v9) = v10 & ! [v11: Nat$] : ! % 191.22/26.52 | [v12: int] : ( ~ ($lesseq(1, $difference(v12, v10))) | ~ % 191.22/26.52 | (fun_app$y(of_nat$, v11) = v12) | ~ Nat$(v11) | ? [v13: % 191.22/26.52 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.52 | A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = 0) & % 191.22/26.52 | subsequence$(v3, v2, v11) = v13 & fun_app$s(v7, v13) = % 191.22/26.52 | v14 & fun_app$e(eq$, v14) = v15 & fun_app$(v15, % 191.22/26.52 | true_ltln$) = v16 & A_ltln$(v14) & A_set_list$(v13) & % 191.22/26.52 | A_ltln_bool_fun$(v15))) & ! [v11: Nat$] : ! [v12: % 191.22/26.52 | A_set_list$] : ( ~ (subsequence$(v3, v2, v11) = v12) | ~ % 191.22/26.52 | Nat$(v11) | ? [v13: int] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.52 | A_ltln_bool_fun$] : ? [v16: any] : (fun_app$y(of_nat$, % 191.22/26.52 | v11) = v13 & fun_app$s(v7, v12) = v14 & fun_app$e(eq$, % 191.22/26.52 | v14) = v15 & fun_app$(v15, true_ltln$) = v16 & % 191.22/26.52 | A_ltln$(v14) & A_ltln_bool_fun$(v15) & ( ~ (v16 = 0) | % 191.22/26.52 | ~ ($lesseq(1, $difference(v13, v10))))))) | % 191.22/26.52 | (foldl$(af_letter$, v6) = v8 & A_set_list_a_ltln_fun$(v8) & ? % 191.22/26.52 | [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? [v13: % 191.22/26.52 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.52 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 & % 191.22/26.52 | fun_app$s(v8, v13) = v14 & fun_app$e(ltl_lang_equiv$, % 191.22/26.52 | v14) = v15 & fun_app$(v15, true_ltln$) = 0 & % 191.22/26.52 | A_ltln$(v14) & A_set_list$(v13) & A_ltln_bool_fun$(v15) % 191.22/26.52 | & Nat$(v12))))))) & ? [v3: Nat_a_set_fun$] : ? [v4: % 191.22/26.52 | Nat$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: % 191.22/26.52 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(af_letter$, v6) = v7) | ~ % 191.22/26.52 | (fun_app$d(v1, v5) = v6) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v5) % 191.22/26.52 | | ~ Nat$(v4) | ? [v8: A_ltln_a_set_a_ltln_fun_fun$] : ? [v9: % 191.22/26.52 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : ? [v11: int] : ? % 191.22/26.52 | [v12: Nat$] : ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.52 | A_ltln_bool_fun$] : ? [v16: int] : (Nat$(v12) & Nat$(v10) & % 191.22/26.52 | ((v16 = 0 & subsequence$(v3, v4, v12) = v13 & fun_app$s(v7, v13) % 191.22/26.52 | = v14 & fun_app$e(ltl_lang_equiv$, v14) = v15 & % 191.22/26.52 | fun_app$(v15, true_ltln$) = 0 & A_ltln$(v14) & % 191.22/26.52 | A_set_list$(v13) & A_ltln_bool_fun$(v15)) | % 191.22/26.52 | (fun_app$y(of_nat$, v10) = v11 & foldl$(v8, v6) = v9 & % 191.22/26.52 | fun_app$c(v0, v5) = v8 & A_set_list_a_ltln_fun$(v9) & % 191.22/26.52 | A_ltln_a_set_a_ltln_fun_fun$(v8) & ! [v17: Nat$] : ! [v18: % 191.22/26.52 | int] : ( ~ ($lesseq(1, $difference(v18, v11))) | ~ % 191.22/26.52 | (fun_app$y(of_nat$, v17) = v18) | ~ Nat$(v17) | ? [v19: % 191.22/26.52 | A_set_list$] : ? [v20: A_ltln$] : ? [v21: % 191.22/26.52 | A_ltln_bool_fun$] : ? [v22: int] : ( ~ (v22 = 0) & % 191.22/26.52 | subsequence$(v3, v2, v17) = v19 & fun_app$s(v9, v19) = % 191.22/26.52 | v20 & fun_app$e(eq$, v20) = v21 & fun_app$(v21, % 191.22/26.52 | true_ltln$) = v22 & A_ltln$(v20) & A_set_list$(v19) & % 191.22/26.52 | A_ltln_bool_fun$(v21))) & ! [v17: Nat$] : ! [v18: % 191.22/26.52 | A_set_list$] : ( ~ (subsequence$(v3, v2, v17) = v18) | ~ % 191.22/26.52 | Nat$(v17) | ? [v19: int] : ? [v20: A_ltln$] : ? [v21: % 191.22/26.52 | A_ltln_bool_fun$] : ? [v22: any] : (fun_app$y(of_nat$, % 191.22/26.52 | v17) = v19 & fun_app$s(v9, v18) = v20 & fun_app$e(eq$, % 191.22/26.52 | v20) = v21 & fun_app$(v21, true_ltln$) = v22 & % 191.22/26.52 | A_ltln$(v20) & A_ltln_bool_fun$(v21) & ( ~ (v22 = 0) | % 191.22/26.52 | ~ ($lesseq(1, $difference(v19, v11))))))))))) % 191.22/26.52 | % 191.22/26.52 | ALPHA: (axiom460) implies: % 191.22/26.52 | (39) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ( ~ (less_eq$(v0, v1) = % 191.22/26.52 | 0) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v2: any] : ? % 191.22/26.52 | [v3: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) = v2 & (v3 = 0 | % 191.22/26.52 | v2 = 0))) % 191.22/26.52 | (40) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ % 191.22/26.52 | (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 191.22/26.52 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v1, v0) % 191.22/26.52 | = v4 & ( ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) % 191.22/26.52 | (41) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: any] : ( ~ % 191.22/26.52 | (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 191.22/26.52 | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v3 & less_eq$(v0, v1) % 191.22/26.52 | = v4 & ( ~ (v3 = 0) | (v4 = 0 & ~ (v2 = 0))))) % 191.22/26.52 | (42) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | % 191.22/26.52 | ~ (less_eq$(v1, v0) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 191.22/26.52 | | ? [v3: any] : ? [v4: any] : (less$(v0, v1) = v4 & less_eq$(v0, % 191.22/26.52 | v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 191.22/26.52 | (43) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | % 191.22/26.52 | ~ (less$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | % 191.22/26.52 | ? [v3: any] : ? [v4: any] : (less_eq$(v1, v0) = v4 & less_eq$(v0, % 191.22/26.52 | v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 191.22/26.52 | % 191.22/26.52 | ALPHA: (axiom462) implies: % 191.22/26.53 | (44) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: int] : (v2 = 0 | % 191.22/26.53 | ~ (less_eq$(v0, v1) = v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) % 191.22/26.53 | | ? [v3: int] : ( ~ (v3 = 0) & less$(v0, v1) = v3)) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom480) implies: % 191.22/26.53 | (45) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 191.22/26.53 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 191.22/26.53 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 191.22/26.53 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 191.22/26.53 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 191.22/26.53 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 191.22/26.53 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 191.22/26.53 | (fun_app$s(v3, v1) = v7 & fun_app$e(ltl_lang_equiv$, v7) = v8 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v6) = v10 & fun_app$(v10, false_ltln$) % 191.22/26.53 | = v11 & fun_app$(v8, false_ltln$) = v9 & A_ltln$(v7) & % 191.22/26.53 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 % 191.22/26.53 | = 0))) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom481) implies: % 191.22/26.53 | (46) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 191.22/26.53 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 191.22/26.53 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 191.22/26.53 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 191.22/26.53 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 191.22/26.53 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 191.22/26.53 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 191.22/26.53 | (fun_app$s(v3, v1) = v7 & fun_app$e(ltl_lang_equiv$, v7) = v8 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v6) = v10 & fun_app$(v10, true_ltln$) = % 191.22/26.53 | v11 & fun_app$(v8, true_ltln$) = v9 & A_ltln$(v7) & % 191.22/26.53 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 % 191.22/26.53 | = 0))) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom484) implies: % 191.22/26.53 | (47) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 191.22/26.53 | A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln$] : ! [v2: A_set_list$] : % 191.22/26.53 | ! [v3: A_set_list$] : ! [v4: A_ltln$] : ! [v5: % 191.22/26.53 | A_set_list_a_ltln_fun$] : ! [v6: A_set_list_a_set_list_fun$] : ! % 191.22/26.53 | [v7: A_set_list$] : ! [v8: A_ltln$] : ( ~ (append$(v3) = v6) | ~ % 191.22/26.53 | (fun_app$t(v6, v2) = v7) | ~ (foldl$(af_letter$, v4) = v5) | ~ % 191.22/26.53 | (fun_app$s(v5, v7) = v8) | ~ (fun_app$d(v0, v1) = v4) | ~ % 191.22/26.53 | A_ltln$(v1) | ~ A_set_list$(v3) | ~ A_set_list$(v2) | ? [v9: % 191.22/26.53 | A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : ? [v12: % 191.22/26.53 | A_ltln_bool_fun$] : ? [v13: any] : (fun_app$s(v5, v2) = v9 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v9) = v10 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v8) = v12 & fun_app$(v12, true_ltln$) % 191.22/26.53 | = v13 & fun_app$(v10, true_ltln$) = v11 & A_ltln$(v9) & % 191.22/26.53 | A_ltln_bool_fun$(v12) & A_ltln_bool_fun$(v10) & ( ~ (v11 = 0) | % 191.22/26.53 | v13 = 0)))) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom493) implies: % 191.22/26.53 | (48) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.53 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 191.22/26.53 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.53 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.53 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.53 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.53 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.53 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.53 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.53 | v5) = v9 & member$(v2, mu_LTL$) = v8 & % 191.22/26.53 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.53 | = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : % 191.22/26.53 | ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.53 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 % 191.22/26.53 | & fun_app$s(v9, v13) = v14 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v14) = v15 & fun_app$(v15, % 191.22/26.53 | true_ltln$) = 0 & A_ltln$(v14) & A_set_list$(v13) & % 191.22/26.53 | A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 = 0 | ! % 191.22/26.53 | [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.53 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.53 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.53 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.53 | true_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.53 | A_ltln_bool_fun$(v14))))))))) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom494) implies: % 191.22/26.53 | (49) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.53 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 191.22/26.53 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.53 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.53 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.53 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.53 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.53 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.53 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.53 | v5) = v9 & member$(v2, nu_LTL$) = v8 & % 191.22/26.53 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.53 | = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.53 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.53 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.53 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.53 | fun_app$e(ltl_lang_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.53 | false_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.53 | A_ltln_bool_fun$(v14)))) & (v7 = 0 | ? [v11: Nat$] : % 191.22/26.53 | ( ~ Nat$(v11) | ? [v12: Nat$] : ? [v13: A_set_list$] : % 191.22/26.53 | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 191.22/26.53 | (subsequence$(v3, v11, v12) = v13 & fun_app$s(v9, v13) = % 191.22/26.53 | v14 & fun_app$e(ltl_lang_equiv$, v14) = v15 & % 191.22/26.53 | fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 191.22/26.53 | A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 191.22/26.53 | Nat$(v12))))))))) % 191.22/26.53 | % 191.22/26.53 | ALPHA: (axiom496) implies: % 191.22/26.54 | (50) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: Nat$] : (nat$(0) = v1 & % 191.22/26.54 | until_ltln$(true_ltln$) = v0 & Nat$(v1) & A_ltln_a_ltln_fun$(v0) & % 191.22/26.54 | ? [v2: Nat_a_set_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : ! % 191.22/26.54 | [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: % 191.22/26.54 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v7: % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_ltln$] : ! [v9: % 191.22/26.54 | A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v3, v4) = 0) % 191.22/26.54 | | ~ (foldl$(v7, v8) = v9) | ~ (fun_app$c(v6, v5) = v7) | ~ % 191.22/26.54 | (af_letter_F$(v3) = v6) | ~ (fun_app$d(v0, v5) = v8) | ~ % 191.22/26.54 | A_ltln_a_ltln_bool_fun_fun$(v3) | ~ Nat_a_set_fun$(v2) | ~ % 191.22/26.54 | A_ltln$(v5) | ~ A_ltln_a_ltln_fun$(v4) | ? [v10: % 191.22/26.54 | A_set_list_a_ltln_fun$] : ? [v11: Nat$] : ? [v12: int] : % 191.22/26.54 | (Nat$(v11) & ((fun_app$y(of_nat$, v11) = v12 & ! [v13: Nat$] : ! % 191.22/26.54 | [v14: int] : ( ~ ($lesseq(1, $difference(v14, v12))) | ~ % 191.22/26.54 | (fun_app$y(of_nat$, v13) = v14) | ~ Nat$(v13) | ? [v15: % 191.22/26.54 | A_set_list$] : ? [v16: A_ltln$] : ? [v17: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v18: int] : ( ~ (v18 = 0) & % 191.22/26.54 | subsequence$(v2, v1, v13) = v15 & fun_app$s(v9, v15) = % 191.22/26.54 | v16 & fun_app$e(v3, v16) = v17 & fun_app$(v17, % 191.22/26.54 | true_ltln$) = v18 & A_ltln$(v16) & A_set_list$(v15) & % 191.22/26.54 | A_ltln_bool_fun$(v17))) & ! [v13: Nat$] : ! [v14: % 191.22/26.54 | A_set_list$] : ( ~ (subsequence$(v2, v1, v13) = v14) | ~ % 191.22/26.54 | Nat$(v13) | ? [v15: int] : ? [v16: A_ltln$] : ? [v17: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v18: any] : (fun_app$y(of_nat$, % 191.22/26.54 | v13) = v15 & fun_app$s(v9, v14) = v16 & fun_app$e(v3, % 191.22/26.54 | v16) = v17 & fun_app$(v17, true_ltln$) = v18 & % 191.22/26.54 | A_ltln$(v16) & A_ltln_bool_fun$(v17) & ( ~ (v18 = 0) | % 191.22/26.54 | ~ ($lesseq(1, $difference(v15, v12))))))) | % 191.22/26.54 | (foldl$(af_letter$, v8) = v10 & A_set_list_a_ltln_fun$(v10) & % 191.22/26.54 | ? [v13: Nat$] : ( ~ Nat$(v13) | ? [v14: Nat$] : ? [v15: % 191.22/26.54 | A_set_list$] : ? [v16: A_ltln$] : ? [v17: % 191.22/26.54 | A_ltln_bool_fun$] : (subsequence$(v2, v13, v14) = v15 & % 191.22/26.54 | fun_app$s(v10, v15) = v16 & fun_app$e(ltl_lang_equiv$, % 191.22/26.54 | v16) = v17 & fun_app$(v17, true_ltln$) = 0 & % 191.22/26.54 | A_ltln$(v16) & A_set_list$(v15) & A_ltln_bool_fun$(v17) % 191.22/26.54 | & Nat$(v14))))))) & ? [v2: Nat_a_set_fun$] : ? [v3: % 191.22/26.54 | Nat$] : ! [v4: A_ltln_a_ltln_bool_fun_fun$] : ! [v5: % 191.22/26.54 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! % 191.22/26.54 | [v8: A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v4, v5) = % 191.22/26.54 | 0) | ~ (foldl$(af_letter$, v7) = v8) | ~ (fun_app$d(v0, v6) = % 191.22/26.54 | v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v4) | ~ Nat_a_set_fun$(v2) % 191.22/26.54 | | ~ A_ltln$(v6) | ~ Nat$(v3) | ~ A_ltln_a_ltln_fun$(v5) | ? % 191.22/26.54 | [v9: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v10: % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v11: A_set_list_a_ltln_fun$] % 191.22/26.54 | : ? [v12: Nat$] : ? [v13: int] : ? [v14: Nat$] : ? [v15: % 191.22/26.54 | A_set_list$] : ? [v16: A_ltln$] : ? [v17: A_ltln_bool_fun$] : % 191.22/26.54 | ? [v18: int] : (Nat$(v14) & Nat$(v12) & ((v18 = 0 & % 191.22/26.54 | subsequence$(v2, v3, v14) = v15 & fun_app$s(v8, v15) = v16 & % 191.22/26.54 | fun_app$e(ltl_lang_equiv$, v16) = v17 & fun_app$(v17, % 191.22/26.54 | true_ltln$) = 0 & A_ltln$(v16) & A_set_list$(v15) & % 191.22/26.54 | A_ltln_bool_fun$(v17)) | (fun_app$y(of_nat$, v12) = v13 & % 191.22/26.54 | foldl$(v10, v7) = v11 & fun_app$c(v9, v6) = v10 & % 191.22/26.54 | af_letter_F$(v4) = v9 & A_set_list_a_ltln_fun$(v11) & % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$(v10) & % 191.22/26.54 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v9) & ! [v19: Nat$] % 191.22/26.54 | : ! [v20: int] : ( ~ ($lesseq(1, $difference(v20, v13))) | % 191.22/26.54 | ~ (fun_app$y(of_nat$, v19) = v20) | ~ Nat$(v19) | ? % 191.22/26.54 | [v21: A_set_list$] : ? [v22: A_ltln$] : ? [v23: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v24: int] : ( ~ (v24 = 0) & % 191.22/26.54 | subsequence$(v2, v1, v19) = v21 & fun_app$s(v11, v21) = % 191.22/26.54 | v22 & fun_app$e(v4, v22) = v23 & fun_app$(v23, % 191.22/26.54 | true_ltln$) = v24 & A_ltln$(v22) & A_set_list$(v21) & % 191.22/26.54 | A_ltln_bool_fun$(v23))) & ! [v19: Nat$] : ! [v20: % 191.22/26.54 | A_set_list$] : ( ~ (subsequence$(v2, v1, v19) = v20) | ~ % 191.22/26.54 | Nat$(v19) | ? [v21: int] : ? [v22: A_ltln$] : ? [v23: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v24: any] : (fun_app$y(of_nat$, % 191.22/26.54 | v19) = v21 & fun_app$s(v11, v20) = v22 & fun_app$e(v4, % 191.22/26.54 | v22) = v23 & fun_app$(v23, true_ltln$) = v24 & % 191.22/26.54 | A_ltln$(v22) & A_ltln_bool_fun$(v23) & ( ~ (v24 = 0) | % 191.22/26.54 | ~ ($lesseq(1, $difference(v21, v13))))))))))) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom502) implies: % 191.22/26.54 | (51) A_ltln_a_ltln_fun$(normalise$) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom517) implies: % 191.22/26.54 | (52) ! [v0: A_set_list$] : ! [v1: A_set_list_a_set_list_fun$] : ( ~ % 191.22/26.54 | (append$(v0) = v1) | ~ A_set_list$(v0) | fun_app$t(v1, nil$) = v0) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom519) implies: % 191.22/26.54 | (53) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: % 191.22/26.54 | A_ltln_a_ltln_fun$] : (af_letter_F$(eq$) = v0 & % 191.22/26.54 | until_ltln$(true_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 191.22/26.54 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0) & ! [v2: A_ltln$] : ! % 191.22/26.54 | [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: A_set$] : ! [v6: % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_list_a_ltln_fun$] : % 191.22/26.54 | ! [v8: A_set_list_a_set_list_fun$] : ! [v9: A_set_list$] : ! [v10: % 191.22/26.54 | A_set_list$] : ! [v11: A_ltln$] : ( ~ (cons$(v5, nil$) = v9) | ~ % 191.22/26.54 | (append$(v4) = v8) | ~ (fun_app$t(v8, v9) = v10) | ~ (foldl$(v6, % 191.22/26.54 | v3) = v7) | ~ (fun_app$s(v7, v10) = v11) | ~ (fun_app$c(v0, % 191.22/26.54 | v2) = v6) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 191.22/26.54 | A_set_list$(v4) | ~ A_set$(v5) | ? [v12: A_ltln$] : ? [v13: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v14: any] : ? [v15: A_ltln$] : % 191.22/26.54 | (fun_app$s(v7, v4) = v12 & fun_app$e(eq$, v12) = v13 & % 191.22/26.54 | fun_app$d(v1, v2) = v15 & fun_app$(v13, true_ltln$) = v14 & % 191.22/26.54 | A_ltln$(v15) & A_ltln$(v12) & A_ltln_bool_fun$(v13) & ( ~ (v14 = % 191.22/26.54 | 0) | v15 = v11)))) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom547) implies: % 191.22/26.54 | (54) ! [v0: A_ltln_a_set_a_ltln_fun_fun$] : ! [v1: A_ltln$] : ! [v2: % 191.22/26.54 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(v0, v1) = v2) | ~ % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$(v0) | ~ A_ltln$(v1) | fun_app$s(v2, % 191.22/26.54 | nil$) = v1) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom551) implies: % 191.22/26.54 | (55) ? [v0: A_set_list_a_set_list_fun$] : (append$(nil$) = v0 & % 191.22/26.54 | A_set_list_a_set_list_fun$(v0) & ! [v1: A_set_list$] : ! [v2: % 191.22/26.54 | A_set_list$] : (v2 = v1 | ~ (fun_app$t(v0, v1) = v2) | ~ % 191.22/26.54 | A_set_list$(v1))) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom554) implies: % 191.22/26.54 | (56) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 191.22/26.54 | A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 191.22/26.54 | [v2: A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! % 191.22/26.54 | [v5: A_set_list$] : ! [v6: A_set$] : ! [v7: % 191.22/26.54 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v8: % 191.22/26.54 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v9: A_set_list_a_ltln_fun$] : % 191.22/26.54 | ! [v10: A_set_list_a_set_list_fun$] : ! [v11: A_set_list$] : ! % 191.22/26.54 | [v12: A_set_list$] : ! [v13: A_ltln$] : ( ~ (cons$(v6, nil$) = v11) % 191.22/26.54 | | ~ (append$(v5) = v10) | ~ (fun_app$t(v10, v11) = v12) | ~ % 191.22/26.54 | (transition_functions$(v1, v2) = 0) | ~ (foldl$(v8, v4) = v9) | % 191.22/26.54 | ~ (fun_app$s(v9, v12) = v13) | ~ (fun_app$c(v7, v3) = v8) | ~ % 191.22/26.54 | (af_letter_F$(v1) = v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 191.22/26.54 | A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_set_list$(v5) | ~ A_set$(v6) % 191.22/26.54 | | ~ A_ltln_a_ltln_fun$(v2) | ? [v14: A_ltln$] : ? [v15: % 191.22/26.54 | A_ltln_bool_fun$] : ? [v16: any] : ? [v17: A_ltln$] : % 191.22/26.54 | (fun_app$s(v9, v5) = v14 & fun_app$e(v1, v14) = v15 & % 191.22/26.54 | fun_app$d(v0, v3) = v17 & fun_app$(v15, true_ltln$) = v16 & % 191.22/26.54 | A_ltln$(v17) & A_ltln$(v14) & A_ltln_bool_fun$(v15) & ( ~ (v16 = % 191.22/26.54 | 0) | v17 = v13)))) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom569) implies: % 191.22/26.54 | (57) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 191.22/26.54 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 191.22/26.54 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.54 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | % 191.22/26.54 | ~ (semantics_ltln$(v1) = v4) | ~ (until_ltln$(v2) = v5) | ~ % 191.22/26.54 | (fun_app$d(v5, v3) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.54 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v8: % 191.22/26.54 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: any] : ? % 191.22/26.54 | [v11: A_ltln$] : ? [v12: any] : (weakUntil_ltln$(v2) = v8 & % 191.22/26.54 | fun_app$d(v8, v3) = v9 & fun_app$d(v0, v3) = v11 & fun_app$(v4, % 191.22/26.54 | v11) = v12 & fun_app$(v4, v9) = v10 & A_ltln$(v11) & % 191.22/26.54 | A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & ( ~ (v12 = 0) | ~ (v10 = % 191.22/26.54 | 0)))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 191.22/26.54 | A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 191.22/26.54 | : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v5) | ~ % 191.22/26.54 | (semantics_ltln$(v1) = v4) | ~ (fun_app$d(v5, v3) = v6) | ~ % 191.22/26.54 | (fun_app$(v4, v6) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | % 191.22/26.54 | ~ A_ltln$(v2) | ? [v7: A_ltln$] : ? [v8: any] : ? [v9: % 191.22/26.54 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: any] : % 191.22/26.54 | (until_ltln$(v2) = v9 & fun_app$d(v9, v3) = v10 & fun_app$d(v0, % 191.22/26.54 | v3) = v7 & fun_app$(v4, v10) = v11 & fun_app$(v4, v7) = v8 & % 191.22/26.54 | A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & ( ~ (v8 = % 191.22/26.54 | 0) | v11 = 0)))) % 191.22/26.54 | % 191.22/26.54 | ALPHA: (axiom578) implies: % 191.22/26.55 | (58) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 191.22/26.55 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 191.22/26.55 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 191.22/26.55 | A_ltln$] : ! [v6: int] : (v6 = 0 | ~ (strongRelease_ltln$(v2) = % 191.22/26.55 | v4) | ~ (semantics_ltln$(v1) = v3) | ~ (fun_app$d(v4, % 191.22/26.55 | true_ltln$) = v5) | ~ (fun_app$(v3, v5) = v6) | ~ % 191.22/26.55 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v7: A_ltln$] : ? [v8: % 191.22/26.55 | int] : ( ~ (v8 = 0) & fun_app$d(v0, v2) = v7 & fun_app$(v3, v7) % 191.22/26.55 | = v8 & A_ltln$(v7))) & ! [v1: Nat_a_set_fun$] : ! [v2: % 191.22/26.55 | A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: % 191.22/26.55 | int] : (v5 = 0 | ~ (semantics_ltln$(v1) = v3) | ~ (fun_app$d(v0, % 191.22/26.55 | v2) = v4) | ~ (fun_app$(v3, v4) = v5) | ~ Nat_a_set_fun$(v1) % 191.22/26.55 | | ~ A_ltln$(v2) | ? [v6: A_ltln_a_ltln_fun$] : ? [v7: A_ltln$] % 191.22/26.55 | : ? [v8: int] : ( ~ (v8 = 0) & strongRelease_ltln$(v2) = v6 & % 191.22/26.55 | fun_app$d(v6, true_ltln$) = v7 & fun_app$(v3, v7) = v8 & % 191.22/26.55 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v6))) & ! [v1: Nat_a_set_fun$] % 191.22/26.55 | : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 191.22/26.55 | A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ % 191.22/26.55 | (strongRelease_ltln$(v2) = v4) | ~ (semantics_ltln$(v1) = v3) | % 191.22/26.55 | ~ (fun_app$d(v4, true_ltln$) = v5) | ~ (fun_app$(v3, v5) = 0) | % 191.22/26.55 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v6: A_ltln$] : % 191.22/26.55 | (fun_app$d(v0, v2) = v6 & fun_app$(v3, v6) = 0 & A_ltln$(v6))) & % 191.22/26.55 | ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 191.22/26.55 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (semantics_ltln$(v1) = % 191.22/26.55 | v3) | ~ (fun_app$d(v0, v2) = v4) | ~ (fun_app$(v3, v4) = 0) | % 191.22/26.55 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v5: % 191.22/26.55 | A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : % 191.22/26.55 | (strongRelease_ltln$(v2) = v5 & fun_app$d(v5, true_ltln$) = v6 & % 191.22/26.55 | fun_app$(v3, v6) = 0 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5)))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom587) implies: % 191.22/26.55 | (59) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 191.22/26.55 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 191.22/26.55 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.55 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | % 191.22/26.55 | ~ (strongRelease_ltln$(v2) = v5) | ~ (semantics_ltln$(v1) = v4) | % 191.22/26.55 | ~ (fun_app$d(v5, v3) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.55 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ? [v8: % 191.22/26.55 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: any] : ? % 191.22/26.55 | [v11: A_ltln$] : ? [v12: any] : (release_ltln$(v2) = v8 & % 191.22/26.55 | fun_app$d(v8, v3) = v9 & fun_app$d(v0, v2) = v11 & fun_app$(v4, % 191.22/26.55 | v11) = v12 & fun_app$(v4, v9) = v10 & A_ltln$(v11) & % 191.22/26.55 | A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & ( ~ (v12 = 0) | ~ (v10 = % 191.22/26.55 | 0)))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 191.22/26.55 | A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 191.22/26.55 | : ! [v6: A_ltln$] : ( ~ (semantics_ltln$(v1) = v4) | ~ % 191.22/26.55 | (release_ltln$(v2) = v5) | ~ (fun_app$d(v5, v3) = v6) | ~ % 191.22/26.55 | (fun_app$(v4, v6) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | % 191.22/26.55 | ~ A_ltln$(v2) | ? [v7: A_ltln$] : ? [v8: any] : ? [v9: % 191.22/26.55 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: any] : % 191.22/26.55 | (strongRelease_ltln$(v2) = v9 & fun_app$d(v9, v3) = v10 & % 191.22/26.55 | fun_app$d(v0, v2) = v7 & fun_app$(v4, v10) = v11 & fun_app$(v4, % 191.22/26.55 | v7) = v8 & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) % 191.22/26.55 | & ( ~ (v8 = 0) | v11 = 0)))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom588) implies: % 191.22/26.55 | (60) A_set_list$(nil$) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom589) implies: % 191.22/26.55 | (61) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.55 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 191.22/26.55 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.55 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.55 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.55 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.55 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.55 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.55 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.55 | v5) = v9 & member$(v2, nu_LTL$) = v8 & % 191.22/26.55 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.55 | = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.55 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.55 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.55 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.55 | fun_app$e(ltl_prop_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.55 | false_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.55 | A_ltln_bool_fun$(v14)))) & (v7 = 0 | ? [v11: Nat$] : % 191.22/26.55 | ( ~ Nat$(v11) | ? [v12: Nat$] : ? [v13: A_set_list$] : % 191.22/26.55 | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 191.22/26.55 | (subsequence$(v3, v11, v12) = v13 & fun_app$s(v9, v13) = % 191.22/26.55 | v14 & fun_app$e(ltl_prop_equiv$, v14) = v15 & % 191.22/26.55 | fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 191.22/26.55 | A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 191.22/26.55 | Nat$(v12))))))))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom590) implies: % 191.22/26.55 | (62) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.55 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 191.22/26.55 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.55 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.55 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.55 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.55 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.55 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.55 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.55 | v5) = v9 & member$(v2, mu_LTL$) = v8 & % 191.22/26.55 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.55 | = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : % 191.22/26.55 | ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.55 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 % 191.22/26.55 | & fun_app$s(v9, v13) = v14 & % 191.22/26.55 | fun_app$e(ltl_prop_equiv$, v14) = v15 & fun_app$(v15, % 191.22/26.55 | true_ltln$) = 0 & A_ltln$(v14) & A_set_list$(v13) & % 191.22/26.55 | A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 = 0 | ! % 191.22/26.55 | [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.55 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.55 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.55 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.55 | fun_app$e(ltl_prop_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.55 | true_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.55 | A_ltln_bool_fun$(v14))))))))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom604) implies: % 191.22/26.55 | (63) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 191.22/26.55 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 191.22/26.55 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 191.22/26.55 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 191.22/26.55 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 191.22/26.55 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 191.22/26.55 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 191.22/26.55 | (fun_app$s(v3, v1) = v7 & fun_app$e(ltl_prop_equiv$, v7) = v8 & % 191.22/26.55 | fun_app$e(ltl_prop_equiv$, v6) = v10 & fun_app$(v10, false_ltln$) % 191.22/26.55 | = v11 & fun_app$(v8, false_ltln$) = v9 & A_ltln$(v7) & % 191.22/26.55 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 % 191.22/26.55 | = 0))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom605) implies: % 191.22/26.55 | (64) ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 191.22/26.55 | [v3: A_set_list_a_ltln_fun$] : ! [v4: A_set_list_a_set_list_fun$] : % 191.22/26.55 | ! [v5: A_set_list$] : ! [v6: A_ltln$] : ( ~ (append$(v1) = v4) | ~ % 191.22/26.55 | (fun_app$t(v4, v2) = v5) | ~ (foldl$(af_letter$, v0) = v3) | ~ % 191.22/26.55 | (fun_app$s(v3, v5) = v6) | ~ A_ltln$(v0) | ~ A_set_list$(v2) | ~ % 191.22/26.55 | A_set_list$(v1) | ? [v7: A_ltln$] : ? [v8: A_ltln_bool_fun$] : ? % 191.22/26.55 | [v9: any] : ? [v10: A_ltln_bool_fun$] : ? [v11: any] : % 191.22/26.55 | (fun_app$s(v3, v1) = v7 & fun_app$e(ltl_prop_equiv$, v7) = v8 & % 191.22/26.55 | fun_app$e(ltl_prop_equiv$, v6) = v10 & fun_app$(v10, true_ltln$) = % 191.22/26.55 | v11 & fun_app$(v8, true_ltln$) = v9 & A_ltln$(v7) & % 191.22/26.55 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v8) & ( ~ (v9 = 0) | v11 % 191.22/26.55 | = 0))) % 191.22/26.55 | % 191.22/26.55 | ALPHA: (axiom615) implies: % 191.22/26.56 | (65) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.56 | (release_ltln$(false_ltln$) = v0 & until_ltln$(true_ltln$) = v1 & % 191.22/26.56 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.56 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.56 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.56 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.56 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.56 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.56 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.56 | v5) = v9 & member$(v2, mu_LTL$) = v8 & % 191.22/26.56 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.56 | = 0) | ? [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : % 191.22/26.56 | ? [v13: A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.22/26.56 | A_ltln_bool_fun$] : (subsequence$(v3, v11, v12) = v13 % 191.22/26.56 | & fun_app$s(v9, v13) = v14 & % 191.22/26.56 | fun_app$e(ltl_const_equiv$, v14) = v15 & fun_app$(v15, % 191.22/26.56 | true_ltln$) = 0 & A_ltln$(v14) & A_set_list$(v13) & % 191.22/26.56 | A_ltln_bool_fun$(v15) & Nat$(v12)))) & (v7 = 0 | ! % 191.22/26.56 | [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.56 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.56 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.56 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.56 | fun_app$e(ltl_const_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.56 | true_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.56 | A_ltln_bool_fun$(v14))))))))) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (axiom616) implies: % 191.22/26.56 | (66) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 191.22/26.56 | (release_ltln$(false_ltln$) = v1 & until_ltln$(true_ltln$) = v0 & % 191.22/26.56 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 191.22/26.56 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 191.22/26.56 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: any] : ( ~ % 191.22/26.56 | (semantics_ltln$(v3) = v4) | ~ (fun_app$d(v1, v2) = v5) | ~ % 191.22/26.56 | (fun_app$d(v0, v5) = v6) | ~ (fun_app$(v4, v6) = v7) | ~ % 191.22/26.56 | Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ? [v8: any] : ? [v9: % 191.22/26.56 | A_set_list_a_ltln_fun$] : ? [v10: Nat$] : (foldl$(af_letter$, % 191.22/26.56 | v5) = v9 & member$(v2, nu_LTL$) = v8 & % 191.22/26.56 | A_set_list_a_ltln_fun$(v9) & Nat$(v10) & ( ~ (v8 = 0) | (( ~ (v7 % 191.22/26.56 | = 0) | ! [v11: Nat$] : ! [v12: A_set_list$] : ( ~ % 191.22/26.56 | (subsequence$(v3, v10, v11) = v12) | ~ Nat$(v11) | ? % 191.22/26.56 | [v13: A_ltln$] : ? [v14: A_ltln_bool_fun$] : ? [v15: % 191.22/26.56 | int] : ( ~ (v15 = 0) & fun_app$s(v9, v12) = v13 & % 191.22/26.56 | fun_app$e(ltl_const_equiv$, v13) = v14 & fun_app$(v14, % 191.22/26.56 | false_ltln$) = v15 & A_ltln$(v13) & % 191.22/26.56 | A_ltln_bool_fun$(v14)))) & (v7 = 0 | ? [v11: Nat$] : % 191.22/26.56 | ( ~ Nat$(v11) | ? [v12: Nat$] : ? [v13: A_set_list$] : % 191.22/26.56 | ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 191.22/26.56 | (subsequence$(v3, v11, v12) = v13 & fun_app$s(v9, v13) = % 191.22/26.56 | v14 & fun_app$e(ltl_const_equiv$, v14) = v15 & % 191.22/26.56 | fun_app$(v15, false_ltln$) = 0 & A_ltln$(v14) & % 191.22/26.56 | A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 191.22/26.56 | Nat$(v12))))))))) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (axiom641) implies: % 191.22/26.56 | (67) A_ltln_a_set_a_ltln_fun_fun$(af_letter$) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (conjecture1) implies: % 191.22/26.56 | (68) A_set$(nu$) % 191.22/26.56 | (69) A_ltln$(psi$) % 191.22/26.56 | (70) A_ltln$(true_ltln$) % 191.22/26.56 | (71) A_ltln$(phi$) % 191.22/26.56 | (72) A_ltln_a_ltln_bool_fun_fun$(eq$) % 191.22/26.56 | (73) ? [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v1: % 191.22/26.56 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v2: A_set_a_ltln_fun$] : ? [v3: % 191.22/26.56 | A_ltln$] : ? [v4: A_ltln_set$] : ? [v5: A_ltln_a_ltln_fun$] : ? % 191.22/26.56 | [v6: A_ltln$] : ? [v7: A_ltln_set$] : ? [v8: int] : ( ~ (v8 = 0) & % 191.22/26.56 | fun_app$c(v0, phi$) = v1 & fun_app$b(v1, psi$) = v2 & fun_app$a(v2, % 191.22/26.56 | nu$) = v3 & af_letter_F$(eq$) = v0 & until_ltln$(true_ltln$) = v5 % 191.22/26.56 | & fun_app$d(v5, phi$) = v6 & nested_prop_atoms$(v6) = v7 & % 191.22/26.56 | nested_prop_atoms$(v3) = v4 & less_eq$(v4, v7) = v8 & % 191.22/26.56 | A_ltln_a_set_a_ltln_fun_fun$(v1) & A_ltln$(v6) & A_ltln$(v3) & % 191.22/26.56 | A_ltln_set$(v7) & A_ltln_set$(v4) & A_set_a_ltln_fun$(v2) & % 191.22/26.56 | A_ltln_a_ltln_fun$(v5) & % 191.22/26.56 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v0)) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (function-axioms) implies: % 191.22/26.56 | (74) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = % 191.22/26.56 | v0 | ~ (nested_prop_atoms$(v2) = v1) | ~ (nested_prop_atoms$(v2) = % 191.22/26.56 | v0)) % 191.22/26.56 | (75) ! [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 191.22/26.56 | A_ltln$] : (v1 = v0 | ~ (until_ltln$(v2) = v1) | ~ % 191.22/26.56 | (until_ltln$(v2) = v0)) % 191.22/26.56 | (76) ! [v0: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v1: % 191.22/26.56 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v2: % 191.22/26.56 | A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (af_letter_F$(v2) = v1) % 191.22/26.56 | | ~ (af_letter_F$(v2) = v0)) % 191.22/26.56 | (77) ! [v0: A_set_list_a_set_list_fun$] : ! [v1: % 191.22/26.56 | A_set_list_a_set_list_fun$] : ! [v2: A_set_list$] : (v1 = v0 | ~ % 191.22/26.56 | (append$(v2) = v1) | ~ (append$(v2) = v0)) % 191.22/26.56 | (78) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 191.22/26.56 | A_ltln_set$] : ! [v3: A_ltln_set$] : (v1 = v0 | ~ (less_eq$(v3, % 191.22/26.56 | v2) = v1) | ~ (less_eq$(v3, v2) = v0)) % 191.22/26.56 | (79) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.22/26.56 | A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~ % 191.22/26.56 | (fun_app$d(v3, v2) = v0)) % 191.22/26.56 | (80) ! [v0: A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: % 191.22/26.56 | A_ltln$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 191.22/26.56 | (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) % 191.22/26.56 | (81) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: % 191.22/26.56 | A_set_list_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | % 191.22/26.56 | ~ (fun_app$s(v3, v2) = v0)) % 191.22/26.56 | (82) ! [v0: A_set_list_a_ltln_fun$] : ! [v1: A_set_list_a_ltln_fun$] : ! % 191.22/26.56 | [v2: A_ltln$] : ! [v3: A_ltln_a_set_a_ltln_fun_fun$] : (v1 = v0 | ~ % 191.22/26.56 | (foldl$(v3, v2) = v1) | ~ (foldl$(v3, v2) = v0)) % 191.22/26.56 | (83) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 191.22/26.56 | A_ltln_set$] : ! [v3: A_ltln_set$] : (v1 = v0 | ~ (less$(v3, v2) = % 191.22/26.56 | v1) | ~ (less$(v3, v2) = v0)) % 191.22/26.56 | % 191.22/26.56 | DELTA: instantiating (55) with fresh symbol all_477_0 gives: % 191.22/26.56 | (84) append$(nil$) = all_477_0 & A_set_list_a_set_list_fun$(all_477_0) & ! % 191.22/26.56 | [v0: A_set_list$] : ! [v1: A_set_list$] : (v1 = v0 | ~ % 191.22/26.56 | (fun_app$t(all_477_0, v0) = v1) | ~ A_set_list$(v0)) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (84) implies: % 191.22/26.56 | (85) append$(nil$) = all_477_0 % 191.22/26.56 | % 191.22/26.56 | DELTA: instantiating (55) with fresh symbol all_485_0 gives: % 191.22/26.56 | (86) append$(nil$) = all_485_0 & A_set_list_a_set_list_fun$(all_485_0) & ! % 191.22/26.56 | [v0: A_set_list$] : ! [v1: A_set_list$] : (v1 = v0 | ~ % 191.22/26.56 | (fun_app$t(all_485_0, v0) = v1) | ~ A_set_list$(v0)) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (86) implies: % 191.22/26.56 | (87) append$(nil$) = all_485_0 % 191.22/26.56 | % 191.22/26.56 | DELTA: instantiating (55) with fresh symbol all_491_0 gives: % 191.22/26.56 | (88) append$(nil$) = all_491_0 & A_set_list_a_set_list_fun$(all_491_0) & ! % 191.22/26.56 | [v0: A_set_list$] : ! [v1: A_set_list$] : (v1 = v0 | ~ % 191.22/26.56 | (fun_app$t(all_491_0, v0) = v1) | ~ A_set_list$(v0)) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (88) implies: % 191.22/26.56 | (89) append$(nil$) = all_491_0 % 191.22/26.56 | % 191.22/26.56 | DELTA: instantiating (12) with fresh symbol all_499_0 gives: % 191.22/26.56 | (90) foldl$(af_letter$, true_ltln$) = all_499_0 & % 191.22/26.56 | A_set_list_a_ltln_fun$(all_499_0) & ! [v0: A_set_list$] : ! [v1: % 191.22/26.56 | A_ltln$] : (v1 = true_ltln$ | ~ (fun_app$s(all_499_0, v0) = v1) | % 191.22/26.56 | ~ A_set_list$(v0)) % 191.22/26.56 | % 191.22/26.56 | ALPHA: (90) implies: % 191.22/26.56 | (91) foldl$(af_letter$, true_ltln$) = all_499_0 % 191.22/26.56 | % 191.22/26.56 | DELTA: instantiating (1) with fresh symbols all_527_0, all_527_1, all_527_2, % 191.22/26.56 | all_527_3 gives: % 191.22/26.57 | (92) until_ltln$(true_ltln$) = all_527_2 & fun_app$d(all_527_2, phi$) = % 191.22/26.57 | all_527_1 & nested_prop_atoms$(all_527_1) = all_527_0 & % 191.22/26.57 | nested_prop_atoms$(psi$) = all_527_3 & less_eq$(all_527_3, all_527_0) % 191.22/26.57 | = 0 & A_ltln$(all_527_1) & A_ltln_set$(all_527_0) & % 191.22/26.57 | A_ltln_set$(all_527_3) & A_ltln_a_ltln_fun$(all_527_2) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (92) implies: % 191.22/26.57 | (93) A_ltln_set$(all_527_3) % 191.22/26.57 | (94) less_eq$(all_527_3, all_527_0) = 0 % 191.22/26.57 | (95) nested_prop_atoms$(psi$) = all_527_3 % 191.22/26.57 | (96) nested_prop_atoms$(all_527_1) = all_527_0 % 191.22/26.57 | (97) fun_app$d(all_527_2, phi$) = all_527_1 % 191.22/26.57 | (98) until_ltln$(true_ltln$) = all_527_2 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (23) with fresh symbols all_535_0, all_535_1 gives: % 191.22/26.57 | (99) foldl$(af_letter$, true_ltln$) = all_535_0 & foldl$(af_letter$, % 191.22/26.57 | false_ltln$) = all_535_1 & A_set_list_a_ltln_fun$(all_535_0) & % 191.22/26.57 | A_set_list_a_ltln_fun$(all_535_1) & ? [v0: tlbool] : ! [v1: % 191.22/26.57 | A_set_list$] : ! [v2: A_ltln$] : (v2 = true_ltln$ | v0 = tltrue | % 191.22/26.57 | ~ (fun_app$s(all_535_0, v1) = v2) | ~ A_set_list$(v1) | ~ % 191.22/26.57 | tlbool(v0)) & ! [v0: A_set_list$] : ! [v1: A_ltln$] : (v1 = % 191.22/26.57 | false_ltln$ | ~ (fun_app$s(all_535_1, v0) = v1) | ~ % 191.22/26.57 | A_set_list$(v0)) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (99) implies: % 191.22/26.57 | (100) foldl$(af_letter$, true_ltln$) = all_535_0 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (22) with fresh symbols all_538_0, all_538_1 gives: % 191.22/26.57 | (101) foldl$(af_letter$, true_ltln$) = all_538_1 & foldl$(af_letter$, % 191.22/26.57 | false_ltln$) = all_538_0 & A_set_list_a_ltln_fun$(all_538_0) & % 191.22/26.57 | A_set_list_a_ltln_fun$(all_538_1) & ? [v0: tlbool] : ! [v1: % 191.22/26.57 | A_set_list$] : ! [v2: A_ltln$] : (v2 = false_ltln$ | v0 = tltrue | % 191.22/26.57 | ~ (fun_app$s(all_538_0, v1) = v2) | ~ A_set_list$(v1) | ~ % 191.22/26.57 | tlbool(v0)) & ! [v0: A_set_list$] : ! [v1: A_ltln$] : (v1 = % 191.22/26.57 | true_ltln$ | ~ (fun_app$s(all_538_1, v0) = v1) | ~ % 191.22/26.57 | A_set_list$(v0)) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (101) implies: % 191.22/26.57 | (102) foldl$(af_letter$, true_ltln$) = all_538_1 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (27) with fresh symbol all_615_0 gives: % 191.22/26.57 | (103) until_ltln$(true_ltln$) = all_615_0 & A_ltln_a_ltln_fun$(all_615_0) & % 191.22/26.57 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_set_list$] : % 191.22/26.57 | ! [v3: A_set_list$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 191.22/26.57 | ! [v6: A_set_list_a_ltln_fun$] : ! [v7: A_set_list_a_set_list_fun$] % 191.22/26.57 | : ! [v8: A_set_list$] : ! [v9: A_ltln$] : ! [v10: int] : (v10 = 0 % 191.22/26.57 | | ~ (semantics_ltln$(v0) = v4) | ~ (append$(v3) = v7) | ~ % 191.22/26.57 | (fun_app$t(v7, v2) = v8) | ~ (foldl$(af_letter$, v5) = v6) | ~ % 191.22/26.57 | (fun_app$s(v6, v8) = v9) | ~ (fun_app$d(all_615_0, v1) = v5) | ~ % 191.22/26.57 | (fun_app$(v4, v9) = v10) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | % 191.22/26.57 | ~ A_set_list$(v3) | ~ A_set_list$(v2) | ? [v11: A_ltln$] : ? % 191.22/26.57 | [v12: int] : ( ~ (v12 = 0) & fun_app$s(v6, v2) = v11 & fun_app$(v4, % 191.22/26.57 | v11) = v12 & A_ltln$(v11))) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (103) implies: % 191.22/26.57 | (104) until_ltln$(true_ltln$) = all_615_0 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (73) with fresh symbols all_624_0, all_624_1, all_624_2, % 191.22/26.57 | all_624_3, all_624_4, all_624_5, all_624_6, all_624_7, all_624_8 gives: % 191.22/26.57 | (105) ~ (all_624_0 = 0) & fun_app$c(all_624_8, phi$) = all_624_7 & % 191.22/26.57 | fun_app$b(all_624_7, psi$) = all_624_6 & fun_app$a(all_624_6, nu$) = % 191.22/26.57 | all_624_5 & af_letter_F$(eq$) = all_624_8 & until_ltln$(true_ltln$) = % 191.22/26.57 | all_624_3 & fun_app$d(all_624_3, phi$) = all_624_2 & % 191.22/26.57 | nested_prop_atoms$(all_624_2) = all_624_1 & % 191.22/26.57 | nested_prop_atoms$(all_624_5) = all_624_4 & less_eq$(all_624_4, % 191.22/26.57 | all_624_1) = all_624_0 & A_ltln_a_set_a_ltln_fun_fun$(all_624_7) & % 191.22/26.57 | A_ltln$(all_624_2) & A_ltln$(all_624_5) & A_ltln_set$(all_624_1) & % 191.22/26.57 | A_ltln_set$(all_624_4) & A_set_a_ltln_fun$(all_624_6) & % 191.22/26.57 | A_ltln_a_ltln_fun$(all_624_3) & % 191.22/26.57 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_624_8) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (105) implies: % 191.22/26.57 | (106) ~ (all_624_0 = 0) % 191.22/26.57 | (107) A_ltln_set$(all_624_4) % 191.22/26.57 | (108) A_ltln_set$(all_624_1) % 191.22/26.57 | (109) less_eq$(all_624_4, all_624_1) = all_624_0 % 191.22/26.57 | (110) nested_prop_atoms$(all_624_5) = all_624_4 % 191.22/26.57 | (111) nested_prop_atoms$(all_624_2) = all_624_1 % 191.22/26.57 | (112) fun_app$d(all_624_3, phi$) = all_624_2 % 191.22/26.57 | (113) until_ltln$(true_ltln$) = all_624_3 % 191.22/26.57 | (114) af_letter_F$(eq$) = all_624_8 % 191.22/26.57 | (115) fun_app$a(all_624_6, nu$) = all_624_5 % 191.22/26.57 | (116) fun_app$b(all_624_7, psi$) = all_624_6 % 191.22/26.57 | (117) fun_app$c(all_624_8, phi$) = all_624_7 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (10) with fresh symbol all_641_0 gives: % 191.22/26.57 | (118) af_letter_F$(eq$) = all_641_0 & % 191.22/26.57 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_641_0) & ! [v0: A_ltln$] % 191.22/26.57 | : ! [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: % 191.22/26.57 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: A_set_list_a_ltln_fun$] : % 191.22/26.57 | ! [v5: A_ltln$] : ( ~ (foldl$(v3, v1) = v4) | ~ (fun_app$s(v4, v2) = % 191.22/26.57 | v5) | ~ (fun_app$c(all_641_0, v0) = v3) | ~ A_ltln$(v1) | ~ % 191.22/26.57 | A_ltln$(v0) | ~ A_set_list$(v2) | ? [v6: A_ltln_bool_fun$] : ? % 191.22/26.57 | [v7: any] : ? [v8: A_set_list_a_ltln_fun$] : ? [v9: A_ltln$] : ? % 191.22/26.57 | [v10: A_ltln_bool_fun$] : ? [v11: any] : (foldl$(af_letter$, v1) = % 191.22/26.57 | v8 & fun_app$s(v8, v2) = v9 & fun_app$e(eq$, v9) = v10 & % 191.22/26.57 | fun_app$e(eq$, v5) = v6 & fun_app$(v10, true_ltln$) = v11 & % 191.22/26.57 | fun_app$(v6, true_ltln$) = v7 & A_set_list_a_ltln_fun$(v8) & % 191.22/26.57 | A_ltln$(v9) & A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v6) & ( ~ % 191.22/26.57 | (v7 = 0) | v11 = 0))) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (118) implies: % 191.22/26.57 | (119) af_letter_F$(eq$) = all_641_0 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (47) with fresh symbol all_650_0 gives: % 191.22/26.57 | (120) until_ltln$(true_ltln$) = all_650_0 & A_ltln_a_ltln_fun$(all_650_0) & % 191.22/26.57 | ! [v0: A_ltln$] : ! [v1: A_set_list$] : ! [v2: A_set_list$] : ! % 191.22/26.57 | [v3: A_ltln$] : ! [v4: A_set_list_a_ltln_fun$] : ! [v5: % 191.22/26.57 | A_set_list_a_set_list_fun$] : ! [v6: A_set_list$] : ! [v7: % 191.22/26.57 | A_ltln$] : ( ~ (append$(v2) = v5) | ~ (fun_app$t(v5, v1) = v6) | % 191.22/26.57 | ~ (foldl$(af_letter$, v3) = v4) | ~ (fun_app$s(v4, v6) = v7) | ~ % 191.22/26.57 | (fun_app$d(all_650_0, v0) = v3) | ~ A_ltln$(v0) | ~ % 191.22/26.57 | A_set_list$(v2) | ~ A_set_list$(v1) | ? [v8: A_ltln$] : ? [v9: % 191.22/26.57 | A_ltln_bool_fun$] : ? [v10: any] : ? [v11: A_ltln_bool_fun$] : % 191.22/26.57 | ? [v12: any] : (fun_app$s(v4, v1) = v8 & fun_app$e(ltl_lang_equiv$, % 191.22/26.57 | v8) = v9 & fun_app$e(ltl_lang_equiv$, v7) = v11 & fun_app$(v11, % 191.22/26.57 | true_ltln$) = v12 & fun_app$(v9, true_ltln$) = v10 & % 191.22/26.57 | A_ltln$(v8) & A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v9) & ( ~ % 191.22/26.57 | (v10 = 0) | v12 = 0))) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (120) implies: % 191.22/26.57 | (121) until_ltln$(true_ltln$) = all_650_0 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (17) with fresh symbol all_668_0 gives: % 191.22/26.57 | (122) af_letter_F$(eq$) = all_668_0 & % 191.22/26.57 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_668_0) & ! [v0: A_ltln$] % 191.22/26.57 | : ! [v1: A_set_list$] : ! [v2: A_ltln$] : ! [v3: % 191.22/26.57 | A_set_list_a_ltln_fun$] : ! [v4: A_ltln$] : ! [v5: % 191.22/26.57 | A_ltln_bool_fun$] : ! [v6: A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: % 191.22/26.57 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(v6, v0) = v7) | ~ % 191.22/26.57 | (foldl$(af_letter$, v0) = v3) | ~ (fun_app$s(v3, v1) = v4) | ~ % 191.22/26.57 | (fun_app$c(all_668_0, v2) = v6) | ~ (fun_app$e(eq$, v4) = v5) | ~ % 191.22/26.57 | (fun_app$(v5, true_ltln$) = 0) | ~ A_ltln$(v2) | ~ A_ltln$(v0) | % 191.22/26.57 | ~ A_set_list$(v1) | ? [v8: A_set_list$] : ? [v9: A_set_list$] : % 191.22/26.57 | ? [v10: A_set_list_a_set_list_fun$] : ? [v11: A_ltln$] : ? [v12: % 191.22/26.57 | A_ltln_bool_fun$] : (append$(v8) = v10 & fun_app$t(v10, v9) = v1 % 191.22/26.57 | & fun_app$s(v7, v8) = v11 & fun_app$e(eq$, v11) = v12 & % 191.22/26.57 | fun_app$(v12, true_ltln$) = 0 & A_ltln$(v11) & A_set_list$(v9) & % 191.22/26.57 | A_set_list$(v8) & A_ltln_bool_fun$(v12) & % 191.22/26.57 | A_set_list_a_set_list_fun$(v10))) % 191.22/26.57 | % 191.22/26.57 | ALPHA: (122) implies: % 191.22/26.57 | (123) af_letter_F$(eq$) = all_668_0 % 191.22/26.57 | % 191.22/26.57 | DELTA: instantiating (26) with fresh symbols all_674_0, all_674_1 gives: % 191.22/26.58 | (124) release_ltln$(false_ltln$) = all_674_1 & until_ltln$(true_ltln$) = % 191.22/26.58 | all_674_0 & A_ltln_a_ltln_fun$(all_674_0) & % 191.22/26.58 | A_ltln_a_ltln_fun$(all_674_1) & ! [v0: A_ltln_set$] : ! [v1: % 191.22/26.58 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! % 191.22/26.58 | [v4: A_ltln$] : ( ~ (semantics_ltln$(v1) = v3) | ~ (gF_advice$(v2, % 191.22/26.58 | v0) = v4) | ~ (fun_app$(v3, v4) = 0) | ~ Nat_a_set_fun$(v1) | % 191.22/26.58 | ~ A_ltln$(v2) | ~ A_ltln_set$(v0) | ? [v5: int] : ? [v6: % 191.22/26.58 | A_ltln$] : ? [v7: int] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 191.22/26.58 | ? [v10: int] : (A_ltln$(v6) & ((v7 = 0 & ~ (v10 = 0) & % 191.22/26.58 | fun_app$d(all_674_0, v6) = v8 & fun_app$d(all_674_1, v8) = v9 % 191.22/26.58 | & member$(v6, v0) = 0 & fun_app$(v3, v9) = v10 & A_ltln$(v9) % 191.22/26.58 | & A_ltln$(v8)) | (v5 = 0 & fun_app$(v3, v2) = 0)))) % 191.22/26.58 | % 191.22/26.58 | ALPHA: (124) implies: % 191.22/26.58 | (125) until_ltln$(true_ltln$) = all_674_0 % 191.22/26.58 | % 191.22/26.58 | DELTA: instantiating (53) with fresh symbols all_683_0, all_683_1 gives: % 191.22/26.58 | (126) af_letter_F$(eq$) = all_683_1 & until_ltln$(true_ltln$) = all_683_0 & % 191.22/26.58 | A_ltln_a_ltln_fun$(all_683_0) & % 191.22/26.58 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_683_1) & ! [v0: A_ltln$] % 191.22/26.58 | : ! [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_set$] : ! [v4: % 191.22/26.58 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] : % 191.22/26.58 | ! [v6: A_set_list_a_set_list_fun$] : ! [v7: A_set_list$] : ! [v8: % 191.22/26.58 | A_set_list$] : ! [v9: A_ltln$] : ( ~ (cons$(v3, nil$) = v7) | ~ % 191.22/26.58 | (append$(v2) = v6) | ~ (fun_app$t(v6, v7) = v8) | ~ (foldl$(v4, % 191.22/26.58 | v1) = v5) | ~ (fun_app$s(v5, v8) = v9) | ~ % 191.22/26.58 | (fun_app$c(all_683_1, v0) = v4) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | % 191.22/26.58 | ~ A_set_list$(v2) | ~ A_set$(v3) | ? [v10: A_ltln$] : ? [v11: % 191.22/26.58 | A_ltln_bool_fun$] : ? [v12: any] : ? [v13: A_ltln$] : % 191.22/26.58 | (fun_app$s(v5, v2) = v10 & fun_app$e(eq$, v10) = v11 & % 191.22/26.58 | fun_app$d(all_683_0, v0) = v13 & fun_app$(v11, true_ltln$) = v12 % 191.22/26.58 | & A_ltln$(v13) & A_ltln$(v10) & A_ltln_bool_fun$(v11) & ( ~ (v12 % 191.22/26.58 | = 0) | v13 = v9))) % 191.22/26.58 | % 191.22/26.58 | ALPHA: (126) implies: % 191.22/26.58 | (127) until_ltln$(true_ltln$) = all_683_0 % 191.22/26.58 | (128) af_letter_F$(eq$) = all_683_1 % 191.22/26.58 | % 191.22/26.58 | DELTA: instantiating (15) with fresh symbols all_686_0, all_686_1 gives: % 191.22/26.58 | (129) af_letter_F$(eq$) = all_686_1 & until_ltln$(true_ltln$) = all_686_0 & % 191.22/26.58 | A_ltln_a_ltln_fun$(all_686_0) & % 191.22/26.58 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_686_1) & ! [v0: A_ltln$] % 191.22/26.58 | : ! [v1: A_ltln$] : ! [v2: A_set_list$] : ! [v3: A_set_list$] : ! % 191.22/26.58 | [v4: A_ltln_a_set_a_ltln_fun_fun$] : ! [v5: A_set_list_a_ltln_fun$] % 191.22/26.58 | : ! [v6: A_set_list_a_set_list_fun$] : ! [v7: A_set_list$] : ! % 191.22/26.58 | [v8: A_ltln$] : ( ~ (append$(v2) = v6) | ~ (fun_app$t(v6, v3) = v7) % 191.22/26.58 | | ~ (foldl$(v4, v1) = v5) | ~ (fun_app$s(v5, v7) = v8) | ~ % 191.22/26.58 | (fun_app$c(all_686_1, v0) = v4) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | % 191.22/26.58 | ~ A_set_list$(v3) | ~ A_set_list$(v2) | ? [v9: A_ltln$] : ? % 191.22/26.58 | [v10: A_ltln$] : ? [v11: A_set_list_a_ltln_fun$] : ? [v12: % 191.22/26.58 | A_ltln$] : (foldl$(v4, v10) = v11 & fun_app$s(v11, v3) = v12 & % 191.22/26.58 | fun_app$s(v5, v2) = v9 & fun_app$d(all_686_0, v0) = v10 & % 191.22/26.58 | A_set_list_a_ltln_fun$(v11) & A_ltln$(v12) & A_ltln$(v10) & % 191.22/26.58 | A_ltln$(v9) & ( ~ (v10 = v9) | v12 = v8))) % 191.22/26.58 | % 191.22/26.58 | ALPHA: (129) implies: % 191.22/26.58 | (130) until_ltln$(true_ltln$) = all_686_0 % 191.22/26.58 | (131) af_letter_F$(eq$) = all_686_1 % 191.56/26.58 | % 191.56/26.58 | DELTA: instantiating (18) with fresh symbol all_698_0 gives: % 191.56/26.58 | (132) af_letter_F$(eq$) = all_698_0 & % 191.56/26.58 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_698_0) & ! [v0: % 191.56/26.58 | A_set_list$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.56/26.58 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: A_set_list_a_ltln_fun$] : % 191.56/26.58 | ! [v5: A_ltln$] : ( ~ (foldl$(v3, v1) = v4) | ~ (fun_app$s(v4, v0) = % 191.56/26.58 | v5) | ~ (fun_app$c(all_698_0, v2) = v3) | ~ A_ltln$(v2) | ~ % 191.56/26.58 | A_ltln$(v1) | ~ A_set_list$(v0) | ? [v6: A_set_list_a_ltln_fun$] % 191.56/26.58 | : ? [v7: A_ltln$] : ? [v8: A_set_list$] : ? [v9: A_set_list$] : % 191.56/26.58 | ? [v10: A_set_list_a_set_list_fun$] : ? [v11: A_set_list$] : ? % 191.56/26.58 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: int] : % 191.56/26.58 | (foldl$(af_letter$, v1) = v6 & fun_app$s(v6, v0) = v7 & % 191.56/26.58 | A_set_list_a_ltln_fun$(v6) & A_ltln$(v7) & A_set_list$(v9) & % 191.56/26.58 | A_set_list$(v8) & (v7 = v5 | (v14 = 0 & v11 = v0 & append$(v8) = % 191.56/26.58 | v10 & fun_app$t(v10, v9) = v0 & fun_app$s(v6, v8) = v12 & % 191.56/26.58 | fun_app$e(eq$, v12) = v13 & fun_app$(v13, true_ltln$) = 0 & % 191.56/26.58 | A_ltln$(v12) & A_ltln_bool_fun$(v13) & % 191.56/26.58 | A_set_list_a_set_list_fun$(v10))))) % 191.56/26.58 | % 191.56/26.58 | ALPHA: (132) implies: % 191.56/26.58 | (133) af_letter_F$(eq$) = all_698_0 % 191.56/26.58 | % 191.56/26.58 | DELTA: instantiating (56) with fresh symbol all_704_0 gives: % 191.56/26.58 | (134) until_ltln$(true_ltln$) = all_704_0 & A_ltln_a_ltln_fun$(all_704_0) & % 191.56/26.58 | ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.58 | ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: % 191.56/26.58 | A_set$] : ! [v6: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! % 191.56/26.58 | [v7: A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_set_list_a_ltln_fun$] % 191.56/26.58 | : ! [v9: A_set_list_a_set_list_fun$] : ! [v10: A_set_list$] : ! % 191.56/26.58 | [v11: A_set_list$] : ! [v12: A_ltln$] : ( ~ (cons$(v5, nil$) = v10) % 191.56/26.58 | | ~ (append$(v4) = v9) | ~ (fun_app$t(v9, v10) = v11) | ~ % 191.56/26.58 | (transition_functions$(v0, v1) = 0) | ~ (foldl$(v7, v3) = v8) | ~ % 191.56/26.58 | (fun_app$s(v8, v11) = v12) | ~ (fun_app$c(v6, v2) = v7) | ~ % 191.56/26.58 | (af_letter_F$(v0) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ % 191.56/26.58 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_set_list$(v4) | ~ A_set$(v5) | % 191.56/26.58 | ~ A_ltln_a_ltln_fun$(v1) | ? [v13: A_ltln$] : ? [v14: % 191.56/26.58 | A_ltln_bool_fun$] : ? [v15: any] : ? [v16: A_ltln$] : % 191.56/26.58 | (fun_app$s(v8, v4) = v13 & fun_app$e(v0, v13) = v14 & % 191.56/26.58 | fun_app$d(all_704_0, v2) = v16 & fun_app$(v14, true_ltln$) = v15 % 191.56/26.58 | & A_ltln$(v16) & A_ltln$(v13) & A_ltln_bool_fun$(v14) & ( ~ (v15 % 191.56/26.58 | = 0) | v16 = v12))) % 191.56/26.58 | % 191.56/26.58 | ALPHA: (134) implies: % 191.56/26.58 | (135) until_ltln$(true_ltln$) = all_704_0 % 191.56/26.58 | % 191.56/26.58 | DELTA: instantiating (16) with fresh symbol all_710_0 gives: % 191.56/26.58 | (136) af_letter_F$(eq$) = all_710_0 & % 191.56/26.58 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_710_0) & ! [v0: % 191.56/26.58 | A_set_list$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.56/26.58 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: A_set_list_a_ltln_fun$] : % 191.56/26.58 | ! [v5: A_ltln$] : ( ~ (foldl$(v3, v2) = v4) | ~ (fun_app$s(v4, v0) = % 191.56/26.58 | v5) | ~ (fun_app$c(all_710_0, v1) = v3) | ~ A_ltln$(v2) | ~ % 191.56/26.58 | A_ltln$(v1) | ~ A_set_list$(v0) | ? [v6: A_set_list_a_ltln_fun$] % 191.56/26.58 | : ? [v7: A_ltln$] : ? [v8: A_set_list$] : ? [v9: A_set_list$] : % 191.56/26.58 | ? [v10: A_set_list_a_set_list_fun$] : ? [v11: A_set_list$] : ? % 191.56/26.58 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: int] : % 191.56/26.58 | (A_set_list$(v9) & A_set_list$(v8) & ((v14 = 0 & v11 = v0 & % 191.56/26.58 | append$(v8) = v10 & fun_app$t(v10, v9) = v0 & fun_app$s(v4, % 191.56/26.58 | v8) = v12 & fun_app$e(eq$, v12) = v13 & fun_app$(v13, % 191.56/26.58 | true_ltln$) = 0 & A_ltln$(v12) & A_ltln_bool_fun$(v13) & % 191.56/26.58 | A_set_list_a_set_list_fun$(v10)) | (v7 = v5 & % 191.56/26.58 | foldl$(af_letter$, v2) = v6 & fun_app$s(v6, v0) = v5 & % 191.56/26.58 | A_set_list_a_ltln_fun$(v6) & A_ltln$(v5))))) % 191.56/26.58 | % 191.56/26.58 | ALPHA: (136) implies: % 191.56/26.58 | (137) af_letter_F$(eq$) = all_710_0 % 191.56/26.58 | % 191.56/26.58 | DELTA: instantiating (25) with fresh symbol all_722_0 gives: % 191.56/26.59 | (138) until_ltln$(true_ltln$) = all_722_0 & A_ltln_a_ltln_fun$(all_722_0) & % 191.56/26.59 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 191.56/26.59 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 191.56/26.59 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | ~ % 191.56/26.59 | (semantics_ltln$(v0) = v3) | ~ (until_ltln$(v1) = v4) | ~ % 191.56/26.59 | (fun_app$d(v4, v2) = v5) | ~ (fun_app$d(all_722_0, v5) = v6) | ~ % 191.56/26.59 | (fun_app$(v3, v6) = v7) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | % 191.56/26.59 | ~ A_ltln$(v1) | ? [v8: A_ltln$] : ? [v9: int] : ( ~ (v9 = 0) & % 191.56/26.59 | fun_app$d(all_722_0, v2) = v8 & fun_app$(v3, v8) = v9 & % 191.56/26.59 | A_ltln$(v8))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! % 191.56/26.59 | [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 191.56/26.59 | A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 191.56/26.59 | (semantics_ltln$(v0) = v3) | ~ (until_ltln$(v1) = v4) | ~ % 191.56/26.59 | (fun_app$d(v4, v2) = v5) | ~ (fun_app$d(all_722_0, v5) = v6) | ~ % 191.56/26.59 | (fun_app$(v3, v6) = 0) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | % 191.56/26.59 | ~ A_ltln$(v1) | ? [v7: A_ltln$] : (fun_app$d(all_722_0, v2) = v7 & % 191.56/26.59 | fun_app$(v3, v7) = 0 & A_ltln$(v7))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (138) implies: % 191.56/26.59 | (139) until_ltln$(true_ltln$) = all_722_0 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (35) with fresh symbols all_728_0, all_728_1 gives: % 191.56/26.59 | (140) release_ltln$(false_ltln$) = all_728_1 & until_ltln$(true_ltln$) = % 191.56/26.59 | all_728_0 & A_ltln_a_ltln_fun$(all_728_0) & % 191.56/26.59 | A_ltln_a_ltln_fun$(all_728_1) & ! [v0: Nat$] : ! [v1: % 191.56/26.59 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.59 | A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ! % 191.56/26.59 | [v7: int] : (v7 = 0 | ~ (suffix$(v0, v1) = v5) | ~ % 191.56/26.59 | (semantics_ltln$(v5) = v6) | ~ (fun_app$d(all_728_0, v2) = v3) | % 191.56/26.59 | ~ (fun_app$d(all_728_1, v3) = v4) | ~ (fun_app$(v6, v4) = v7) | ~ % 191.56/26.59 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | ? [v8: % 191.56/26.59 | A_ltln_bool_fun$] : ? [v9: int] : ( ~ (v9 = 0) & % 191.56/26.59 | semantics_ltln$(v1) = v8 & fun_app$(v8, v4) = v9 & % 191.56/26.59 | A_ltln_bool_fun$(v8))) & ! [v0: Nat$] : ! [v1: Nat_a_set_fun$] % 191.56/26.59 | : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 191.56/26.59 | A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 191.56/26.59 | (suffix$(v0, v1) = v3) | ~ (semantics_ltln$(v3) = v4) | ~ % 191.56/26.59 | (fun_app$d(all_728_0, v2) = v5) | ~ (fun_app$d(all_728_1, v5) = % 191.56/26.59 | v6) | ~ (fun_app$(v4, v6) = 0) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.59 | A_ltln$(v2) | ~ Nat$(v0) | ? [v7: A_ltln_bool_fun$] : % 191.56/26.59 | (semantics_ltln$(v1) = v7 & fun_app$(v7, v6) = 0 & % 191.56/26.59 | A_ltln_bool_fun$(v7))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (140) implies: % 191.56/26.59 | (141) until_ltln$(true_ltln$) = all_728_0 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (34) with fresh symbols all_731_0, all_731_1 gives: % 191.56/26.59 | (142) release_ltln$(false_ltln$) = all_731_0 & until_ltln$(true_ltln$) = % 191.56/26.59 | all_731_1 & A_ltln_a_ltln_fun$(all_731_0) & % 191.56/26.59 | A_ltln_a_ltln_fun$(all_731_1) & ! [v0: Nat$] : ! [v1: % 191.56/26.59 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.59 | A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ! % 191.56/26.59 | [v7: int] : (v7 = 0 | ~ (suffix$(v0, v1) = v5) | ~ % 191.56/26.59 | (semantics_ltln$(v5) = v6) | ~ (fun_app$d(all_731_0, v2) = v3) | % 191.56/26.59 | ~ (fun_app$d(all_731_1, v3) = v4) | ~ (fun_app$(v6, v4) = v7) | ~ % 191.56/26.59 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | ? [v8: % 191.56/26.59 | A_ltln_bool_fun$] : ? [v9: int] : ( ~ (v9 = 0) & % 191.56/26.59 | semantics_ltln$(v1) = v8 & fun_app$(v8, v4) = v9 & % 191.56/26.59 | A_ltln_bool_fun$(v8))) & ! [v0: Nat$] : ! [v1: Nat_a_set_fun$] % 191.56/26.59 | : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 191.56/26.59 | A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 191.56/26.59 | (suffix$(v0, v1) = v3) | ~ (semantics_ltln$(v3) = v4) | ~ % 191.56/26.59 | (fun_app$d(all_731_0, v2) = v5) | ~ (fun_app$d(all_731_1, v5) = % 191.56/26.59 | v6) | ~ (fun_app$(v4, v6) = 0) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.59 | A_ltln$(v2) | ~ Nat$(v0) | ? [v7: A_ltln_bool_fun$] : % 191.56/26.59 | (semantics_ltln$(v1) = v7 & fun_app$(v7, v6) = 0 & % 191.56/26.59 | A_ltln_bool_fun$(v7))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (142) implies: % 191.56/26.59 | (143) until_ltln$(true_ltln$) = all_731_1 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (2) with fresh symbols all_773_0, all_773_1 gives: % 191.56/26.59 | (144) af_letter_F$(eq$) = all_773_1 & until_ltln$(true_ltln$) = all_773_0 & % 191.56/26.59 | A_ltln_a_ltln_fun$(all_773_0) & % 191.56/26.59 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_773_1) & ! [v0: A_ltln$] % 191.56/26.59 | : ! [v1: A_ltln$] : ! [v2: A_set$] : ! [v3: % 191.56/26.59 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: A_set_a_ltln_fun$] : ! % 191.56/26.59 | [v5: A_ltln$] : ( ~ (fun_app$c(all_773_1, v0) = v3) | ~ % 191.56/26.59 | (fun_app$b(v3, v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 191.56/26.59 | A_ltln$(v1) | ~ A_ltln$(v0) | ~ A_set$(v2) | ? [v6: % 191.56/26.59 | A_ltln_bool_fun$] : ? [v7: any] : ? [v8: A_set_a_ltln_fun$] : % 191.56/26.59 | ? [v9: A_ltln$] : (fun_app$b(af_letter$, v1) = v8 & fun_app$a(v8, % 191.56/26.59 | v2) = v9 & fun_app$e(eq$, v1) = v6 & fun_app$(v6, true_ltln$) = % 191.56/26.59 | v7 & A_ltln$(v9) & A_ltln_bool_fun$(v6) & A_set_a_ltln_fun$(v8) & % 191.56/26.59 | (v9 = v5 | v7 = 0))) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! % 191.56/26.59 | [v2: A_set$] : ! [v3: A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: % 191.56/26.59 | A_set_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (fun_app$c(all_773_1, % 191.56/26.59 | v0) = v3) | ~ (fun_app$b(v3, v1) = v4) | ~ (fun_app$a(v4, v2) % 191.56/26.59 | = v5) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | ~ A_set$(v2) | ? [v6: % 191.56/26.59 | A_ltln_bool_fun$] : ? [v7: any] : ? [v8: A_ltln$] : % 191.56/26.59 | (fun_app$e(eq$, v1) = v6 & fun_app$d(all_773_0, v0) = v8 & % 191.56/26.59 | fun_app$(v6, true_ltln$) = v7 & A_ltln$(v8) & % 191.56/26.59 | A_ltln_bool_fun$(v6) & ( ~ (v7 = 0) | v8 = v5))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (144) implies: % 191.56/26.59 | (145) until_ltln$(true_ltln$) = all_773_0 % 191.56/26.59 | (146) af_letter_F$(eq$) = all_773_1 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (49) with fresh symbols all_785_0, all_785_1 gives: % 191.56/26.59 | (147) release_ltln$(false_ltln$) = all_785_0 & until_ltln$(true_ltln$) = % 191.56/26.59 | all_785_1 & A_ltln_a_ltln_fun$(all_785_0) & % 191.56/26.59 | A_ltln_a_ltln_fun$(all_785_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.59 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.59 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.59 | (fun_app$d(all_785_0, v0) = v3) | ~ (fun_app$d(all_785_1, v3) = % 191.56/26.59 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.59 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.59 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, nu_LTL$) = % 191.56/26.59 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.59 | (v5 = 0) | ! [v9: Nat$] : ! [v10: A_set_list$] : ( ~ % 191.56/26.59 | (subsequence$(v1, v8, v9) = v10) | ~ Nat$(v9) | ? [v11: % 191.56/26.59 | A_ltln$] : ? [v12: A_ltln_bool_fun$] : ? [v13: int] : % 191.56/26.59 | ( ~ (v13 = 0) & fun_app$s(v7, v10) = v11 & % 191.56/26.59 | fun_app$e(ltl_lang_equiv$, v11) = v12 & fun_app$(v12, % 191.56/26.59 | false_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.59 | A_ltln_bool_fun$(v12)))) & (v5 = 0 | ? [v9: Nat$] : ( % 191.56/26.59 | ~ Nat$(v9) | ? [v10: Nat$] : ? [v11: A_set_list$] : ? % 191.56/26.59 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : % 191.56/26.59 | (subsequence$(v1, v9, v10) = v11 & fun_app$s(v7, v11) = % 191.56/26.59 | v12 & fun_app$e(ltl_lang_equiv$, v12) = v13 & % 191.56/26.59 | fun_app$(v13, false_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.59 | A_set_list$(v11) & A_ltln_bool_fun$(v13) & % 191.56/26.59 | Nat$(v10)))))))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (147) implies: % 191.56/26.59 | (148) until_ltln$(true_ltln$) = all_785_1 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (66) with fresh symbols all_788_0, all_788_1 gives: % 191.56/26.59 | (149) release_ltln$(false_ltln$) = all_788_0 & until_ltln$(true_ltln$) = % 191.56/26.59 | all_788_1 & A_ltln_a_ltln_fun$(all_788_0) & % 191.56/26.59 | A_ltln_a_ltln_fun$(all_788_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.59 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.59 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.59 | (fun_app$d(all_788_0, v0) = v3) | ~ (fun_app$d(all_788_1, v3) = % 191.56/26.59 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.59 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.59 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, nu_LTL$) = % 191.56/26.59 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.59 | (v5 = 0) | ! [v9: Nat$] : ! [v10: A_set_list$] : ( ~ % 191.56/26.59 | (subsequence$(v1, v8, v9) = v10) | ~ Nat$(v9) | ? [v11: % 191.56/26.59 | A_ltln$] : ? [v12: A_ltln_bool_fun$] : ? [v13: int] : % 191.56/26.59 | ( ~ (v13 = 0) & fun_app$s(v7, v10) = v11 & % 191.56/26.59 | fun_app$e(ltl_const_equiv$, v11) = v12 & fun_app$(v12, % 191.56/26.59 | false_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.59 | A_ltln_bool_fun$(v12)))) & (v5 = 0 | ? [v9: Nat$] : ( % 191.56/26.59 | ~ Nat$(v9) | ? [v10: Nat$] : ? [v11: A_set_list$] : ? % 191.56/26.59 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : % 191.56/26.59 | (subsequence$(v1, v9, v10) = v11 & fun_app$s(v7, v11) = % 191.56/26.59 | v12 & fun_app$e(ltl_const_equiv$, v12) = v13 & % 191.56/26.59 | fun_app$(v13, false_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.59 | A_set_list$(v11) & A_ltln_bool_fun$(v13) & % 191.56/26.59 | Nat$(v10)))))))) % 191.56/26.59 | % 191.56/26.59 | ALPHA: (149) implies: % 191.56/26.59 | (150) until_ltln$(true_ltln$) = all_788_1 % 191.56/26.59 | % 191.56/26.59 | DELTA: instantiating (29) with fresh symbols all_791_0, all_791_1 gives: % 191.56/26.60 | (151) release_ltln$(false_ltln$) = all_791_0 & until_ltln$(true_ltln$) = % 191.56/26.60 | all_791_1 & A_ltln_a_ltln_fun$(all_791_0) & % 191.56/26.60 | A_ltln_a_ltln_fun$(all_791_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.60 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.60 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.60 | (fun_app$d(all_791_0, v0) = v3) | ~ (fun_app$d(all_791_1, v3) = % 191.56/26.60 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.60 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.60 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, nu_LTL$) = % 191.56/26.60 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.60 | (v5 = 0) | ! [v9: Nat$] : ! [v10: A_set_list$] : ( ~ % 191.56/26.60 | (subsequence$(v1, v8, v9) = v10) | ~ Nat$(v9) | ? [v11: % 191.56/26.60 | A_ltln$] : ? [v12: A_ltln_bool_fun$] : ? [v13: int] : % 191.56/26.60 | ( ~ (v13 = 0) & fun_app$s(v7, v10) = v11 & fun_app$e(eq$, % 191.56/26.60 | v11) = v12 & fun_app$(v12, false_ltln$) = v13 & % 191.56/26.60 | A_ltln$(v11) & A_ltln_bool_fun$(v12)))) & (v5 = 0 | ? % 191.56/26.60 | [v9: Nat$] : ( ~ Nat$(v9) | ? [v10: Nat$] : ? [v11: % 191.56/26.60 | A_set_list$] : ? [v12: A_ltln$] : ? [v13: % 191.56/26.60 | A_ltln_bool_fun$] : (subsequence$(v1, v9, v10) = v11 & % 191.56/26.60 | fun_app$s(v7, v11) = v12 & fun_app$e(eq$, v12) = v13 & % 191.56/26.60 | fun_app$(v13, false_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.60 | A_set_list$(v11) & A_ltln_bool_fun$(v13) & % 191.56/26.60 | Nat$(v10)))))))) % 191.56/26.60 | % 191.56/26.60 | ALPHA: (151) implies: % 191.56/26.60 | (152) until_ltln$(true_ltln$) = all_791_1 % 191.56/26.60 | % 191.56/26.60 | DELTA: instantiating (28) with fresh symbols all_794_0, all_794_1 gives: % 191.56/26.60 | (153) release_ltln$(false_ltln$) = all_794_1 & until_ltln$(true_ltln$) = % 191.56/26.60 | all_794_0 & A_ltln_a_ltln_fun$(all_794_0) & % 191.56/26.60 | A_ltln_a_ltln_fun$(all_794_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.60 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.60 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.60 | (fun_app$d(all_794_0, v0) = v3) | ~ (fun_app$d(all_794_1, v3) = % 191.56/26.60 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.60 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.60 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, mu_LTL$) = % 191.56/26.60 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.60 | (v5 = 0) | ? [v9: Nat$] : ( ~ Nat$(v9) | ? [v10: Nat$] : % 191.56/26.60 | ? [v11: A_set_list$] : ? [v12: A_ltln$] : ? [v13: % 191.56/26.60 | A_ltln_bool_fun$] : (subsequence$(v1, v9, v10) = v11 & % 191.56/26.60 | fun_app$s(v7, v11) = v12 & fun_app$e(eq$, v12) = v13 & % 191.56/26.60 | fun_app$(v13, true_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.60 | A_set_list$(v11) & A_ltln_bool_fun$(v13) & Nat$(v10)))) % 191.56/26.60 | & (v5 = 0 | ! [v9: Nat$] : ! [v10: A_set_list$] : ( ~ % 191.56/26.60 | (subsequence$(v1, v8, v9) = v10) | ~ Nat$(v9) | ? [v11: % 191.56/26.60 | A_ltln$] : ? [v12: A_ltln_bool_fun$] : ? [v13: int] : % 191.56/26.60 | ( ~ (v13 = 0) & fun_app$s(v7, v10) = v11 & fun_app$e(eq$, % 191.56/26.60 | v11) = v12 & fun_app$(v12, true_ltln$) = v13 & % 191.56/26.60 | A_ltln$(v11) & A_ltln_bool_fun$(v12)))))))) % 191.56/26.60 | % 191.56/26.60 | ALPHA: (153) implies: % 191.56/26.60 | (154) until_ltln$(true_ltln$) = all_794_0 % 191.56/26.60 | % 191.56/26.60 | DELTA: instantiating (61) with fresh symbols all_797_0, all_797_1 gives: % 191.56/26.60 | (155) release_ltln$(false_ltln$) = all_797_0 & until_ltln$(true_ltln$) = % 191.56/26.60 | all_797_1 & A_ltln_a_ltln_fun$(all_797_0) & % 191.56/26.60 | A_ltln_a_ltln_fun$(all_797_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.60 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.60 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.60 | (fun_app$d(all_797_0, v0) = v3) | ~ (fun_app$d(all_797_1, v3) = % 191.56/26.60 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.60 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.60 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, nu_LTL$) = % 191.56/26.60 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.60 | (v5 = 0) | ! [v9: Nat$] : ! [v10: A_set_list$] : ( ~ % 191.56/26.60 | (subsequence$(v1, v8, v9) = v10) | ~ Nat$(v9) | ? [v11: % 191.56/26.60 | A_ltln$] : ? [v12: A_ltln_bool_fun$] : ? [v13: int] : % 191.56/26.60 | ( ~ (v13 = 0) & fun_app$s(v7, v10) = v11 & % 191.56/26.60 | fun_app$e(ltl_prop_equiv$, v11) = v12 & fun_app$(v12, % 191.56/26.60 | false_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.60 | A_ltln_bool_fun$(v12)))) & (v5 = 0 | ? [v9: Nat$] : ( % 191.56/26.60 | ~ Nat$(v9) | ? [v10: Nat$] : ? [v11: A_set_list$] : ? % 191.56/26.60 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : % 191.56/26.60 | (subsequence$(v1, v9, v10) = v11 & fun_app$s(v7, v11) = % 191.56/26.60 | v12 & fun_app$e(ltl_prop_equiv$, v12) = v13 & % 191.56/26.60 | fun_app$(v13, false_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.60 | A_set_list$(v11) & A_ltln_bool_fun$(v13) & % 191.56/26.60 | Nat$(v10)))))))) % 191.56/26.60 | % 191.56/26.60 | ALPHA: (155) implies: % 191.56/26.60 | (156) until_ltln$(true_ltln$) = all_797_1 % 191.56/26.60 | % 191.56/26.60 | DELTA: instantiating (62) with fresh symbols all_800_0, all_800_1 gives: % 191.56/26.60 | (157) release_ltln$(false_ltln$) = all_800_1 & until_ltln$(true_ltln$) = % 191.56/26.60 | all_800_0 & A_ltln_a_ltln_fun$(all_800_0) & % 191.56/26.60 | A_ltln_a_ltln_fun$(all_800_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.60 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.60 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.60 | (fun_app$d(all_800_0, v0) = v3) | ~ (fun_app$d(all_800_1, v3) = % 191.56/26.60 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.60 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.60 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, mu_LTL$) = % 191.56/26.60 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.60 | (v5 = 0) | ? [v9: Nat$] : ( ~ Nat$(v9) | ? [v10: Nat$] : % 191.56/26.60 | ? [v11: A_set_list$] : ? [v12: A_ltln$] : ? [v13: % 191.56/26.60 | A_ltln_bool_fun$] : (subsequence$(v1, v9, v10) = v11 & % 191.56/26.60 | fun_app$s(v7, v11) = v12 & fun_app$e(ltl_prop_equiv$, % 191.56/26.60 | v12) = v13 & fun_app$(v13, true_ltln$) = 0 & % 191.56/26.60 | A_ltln$(v12) & A_set_list$(v11) & A_ltln_bool_fun$(v13) % 191.56/26.60 | & Nat$(v10)))) & (v5 = 0 | ! [v9: Nat$] : ! [v10: % 191.56/26.60 | A_set_list$] : ( ~ (subsequence$(v1, v8, v9) = v10) | ~ % 191.56/26.60 | Nat$(v9) | ? [v11: A_ltln$] : ? [v12: A_ltln_bool_fun$] % 191.56/26.60 | : ? [v13: int] : ( ~ (v13 = 0) & fun_app$s(v7, v10) = % 191.56/26.60 | v11 & fun_app$e(ltl_prop_equiv$, v11) = v12 & % 191.56/26.60 | fun_app$(v12, true_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.60 | A_ltln_bool_fun$(v12)))))))) % 191.56/26.60 | % 191.56/26.60 | ALPHA: (157) implies: % 191.56/26.60 | (158) until_ltln$(true_ltln$) = all_800_0 % 191.56/26.60 | % 191.56/26.60 | DELTA: instantiating (65) with fresh symbols all_803_0, all_803_1 gives: % 191.56/26.60 | (159) release_ltln$(false_ltln$) = all_803_1 & until_ltln$(true_ltln$) = % 191.56/26.60 | all_803_0 & A_ltln_a_ltln_fun$(all_803_0) & % 191.56/26.60 | A_ltln_a_ltln_fun$(all_803_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.60 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.60 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.60 | (fun_app$d(all_803_0, v0) = v3) | ~ (fun_app$d(all_803_1, v3) = % 191.56/26.60 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.60 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.60 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, mu_LTL$) = % 191.56/26.60 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.60 | (v5 = 0) | ? [v9: Nat$] : ( ~ Nat$(v9) | ? [v10: Nat$] : % 191.56/26.60 | ? [v11: A_set_list$] : ? [v12: A_ltln$] : ? [v13: % 191.56/26.60 | A_ltln_bool_fun$] : (subsequence$(v1, v9, v10) = v11 & % 191.56/26.60 | fun_app$s(v7, v11) = v12 & fun_app$e(ltl_const_equiv$, % 191.56/26.60 | v12) = v13 & fun_app$(v13, true_ltln$) = 0 & % 191.56/26.60 | A_ltln$(v12) & A_set_list$(v11) & A_ltln_bool_fun$(v13) % 191.56/26.60 | & Nat$(v10)))) & (v5 = 0 | ! [v9: Nat$] : ! [v10: % 191.56/26.60 | A_set_list$] : ( ~ (subsequence$(v1, v8, v9) = v10) | ~ % 191.56/26.60 | Nat$(v9) | ? [v11: A_ltln$] : ? [v12: A_ltln_bool_fun$] % 191.56/26.60 | : ? [v13: int] : ( ~ (v13 = 0) & fun_app$s(v7, v10) = % 191.56/26.60 | v11 & fun_app$e(ltl_const_equiv$, v11) = v12 & % 191.56/26.60 | fun_app$(v12, true_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.60 | A_ltln_bool_fun$(v12)))))))) % 191.56/26.60 | % 191.56/26.60 | ALPHA: (159) implies: % 191.56/26.60 | (160) until_ltln$(true_ltln$) = all_803_0 % 191.56/26.60 | % 191.56/26.60 | DELTA: instantiating (48) with fresh symbols all_806_0, all_806_1 gives: % 191.56/26.61 | (161) release_ltln$(false_ltln$) = all_806_1 & until_ltln$(true_ltln$) = % 191.56/26.61 | all_806_0 & A_ltln_a_ltln_fun$(all_806_0) & % 191.56/26.61 | A_ltln_a_ltln_fun$(all_806_1) & ! [v0: A_ltln$] : ! [v1: % 191.56/26.61 | Nat_a_set_fun$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! % 191.56/26.61 | [v4: A_ltln$] : ! [v5: any] : ( ~ (semantics_ltln$(v1) = v2) | ~ % 191.56/26.61 | (fun_app$d(all_806_0, v0) = v3) | ~ (fun_app$d(all_806_1, v3) = % 191.56/26.61 | v4) | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v1) | ~ % 191.56/26.61 | A_ltln$(v0) | ? [v6: any] : ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.61 | [v8: Nat$] : (foldl$(af_letter$, v3) = v7 & member$(v0, mu_LTL$) = % 191.56/26.61 | v6 & A_set_list_a_ltln_fun$(v7) & Nat$(v8) & ( ~ (v6 = 0) | (( ~ % 191.56/26.61 | (v5 = 0) | ? [v9: Nat$] : ( ~ Nat$(v9) | ? [v10: Nat$] : % 191.56/26.61 | ? [v11: A_set_list$] : ? [v12: A_ltln$] : ? [v13: % 191.56/26.61 | A_ltln_bool_fun$] : (subsequence$(v1, v9, v10) = v11 & % 191.56/26.61 | fun_app$s(v7, v11) = v12 & fun_app$e(ltl_lang_equiv$, % 191.56/26.61 | v12) = v13 & fun_app$(v13, true_ltln$) = 0 & % 191.56/26.61 | A_ltln$(v12) & A_set_list$(v11) & A_ltln_bool_fun$(v13) % 191.56/26.61 | & Nat$(v10)))) & (v5 = 0 | ! [v9: Nat$] : ! [v10: % 191.56/26.61 | A_set_list$] : ( ~ (subsequence$(v1, v8, v9) = v10) | ~ % 191.56/26.61 | Nat$(v9) | ? [v11: A_ltln$] : ? [v12: A_ltln_bool_fun$] % 191.56/26.61 | : ? [v13: int] : ( ~ (v13 = 0) & fun_app$s(v7, v10) = % 191.56/26.61 | v11 & fun_app$e(ltl_lang_equiv$, v11) = v12 & % 191.56/26.61 | fun_app$(v12, true_ltln$) = v13 & A_ltln$(v11) & % 191.56/26.61 | A_ltln_bool_fun$(v12)))))))) % 191.56/26.61 | % 191.56/26.61 | ALPHA: (161) implies: % 191.56/26.61 | (162) until_ltln$(true_ltln$) = all_806_0 % 191.56/26.61 | % 191.56/26.61 | DELTA: instantiating (30) with fresh symbols all_812_0, all_812_1 gives: % 191.56/26.61 | (163) release_ltln$(false_ltln$) = all_812_1 & until_ltln$(true_ltln$) = % 191.56/26.61 | all_812_0 & A_ltln_a_ltln_fun$(all_812_0) & % 191.56/26.61 | A_ltln_a_ltln_fun$(all_812_1) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] % 191.56/26.61 | : ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 191.56/26.61 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.56/26.61 | any] : ( ~ (semantics_ltln$(v2) = v3) | ~ (ltl_equivalence$(v0) = % 191.56/26.61 | 0) | ~ (fun_app$d(all_812_0, v1) = v4) | ~ % 191.56/26.61 | (fun_app$d(all_812_1, v4) = v5) | ~ (fun_app$(v3, v5) = v6) | ~ % 191.56/26.61 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 191.56/26.61 | A_ltln$(v1) | ? [v7: any] : ? [v8: A_set_list_a_ltln_fun$] : ? % 191.56/26.61 | [v9: Nat$] : (foldl$(af_letter$, v4) = v8 & member$(v1, mu_LTL$) = % 191.56/26.61 | v7 & A_set_list_a_ltln_fun$(v8) & Nat$(v9) & ( ~ (v7 = 0) | (( ~ % 191.56/26.61 | (v6 = 0) | ? [v10: Nat$] : ( ~ Nat$(v10) | ? [v11: Nat$] % 191.56/26.61 | : ? [v12: A_set_list$] : ? [v13: A_ltln$] : ? [v14: % 191.56/26.61 | A_ltln_bool_fun$] : (subsequence$(v2, v10, v11) = v12 & % 191.56/26.61 | fun_app$s(v8, v12) = v13 & fun_app$e(v0, v13) = v14 & % 191.56/26.61 | fun_app$(v14, true_ltln$) = 0 & A_ltln$(v13) & % 191.56/26.61 | A_set_list$(v12) & A_ltln_bool_fun$(v14) & Nat$(v11)))) % 191.56/26.61 | & (v6 = 0 | ! [v10: Nat$] : ! [v11: A_set_list$] : ( ~ % 191.56/26.61 | (subsequence$(v2, v9, v10) = v11) | ~ Nat$(v10) | ? % 191.56/26.61 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: % 191.56/26.61 | int] : ( ~ (v14 = 0) & fun_app$s(v8, v11) = v12 & % 191.56/26.61 | fun_app$e(v0, v12) = v13 & fun_app$(v13, true_ltln$) = % 191.56/26.61 | v14 & A_ltln$(v12) & A_ltln_bool_fun$(v13)))))))) % 191.56/26.61 | % 191.56/26.61 | ALPHA: (163) implies: % 191.56/26.61 | (164) until_ltln$(true_ltln$) = all_812_0 % 191.56/26.61 | % 191.56/26.61 | DELTA: instantiating (31) with fresh symbols all_815_0, all_815_1 gives: % 191.56/26.61 | (165) release_ltln$(false_ltln$) = all_815_0 & until_ltln$(true_ltln$) = % 191.56/26.61 | all_815_1 & A_ltln_a_ltln_fun$(all_815_0) & % 191.56/26.61 | A_ltln_a_ltln_fun$(all_815_1) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] % 191.56/26.61 | : ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 191.56/26.61 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.56/26.61 | any] : ( ~ (semantics_ltln$(v2) = v3) | ~ (ltl_equivalence$(v0) = % 191.56/26.61 | 0) | ~ (fun_app$d(all_815_0, v1) = v4) | ~ % 191.56/26.61 | (fun_app$d(all_815_1, v4) = v5) | ~ (fun_app$(v3, v5) = v6) | ~ % 191.56/26.61 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 191.56/26.61 | A_ltln$(v1) | ? [v7: any] : ? [v8: A_set_list_a_ltln_fun$] : ? % 191.56/26.61 | [v9: Nat$] : (foldl$(af_letter$, v4) = v8 & member$(v1, nu_LTL$) = % 191.56/26.61 | v7 & A_set_list_a_ltln_fun$(v8) & Nat$(v9) & ( ~ (v7 = 0) | (( ~ % 191.56/26.61 | (v6 = 0) | ! [v10: Nat$] : ! [v11: A_set_list$] : ( ~ % 191.56/26.61 | (subsequence$(v2, v9, v10) = v11) | ~ Nat$(v10) | ? % 191.56/26.61 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: % 191.56/26.61 | int] : ( ~ (v14 = 0) & fun_app$s(v8, v11) = v12 & % 191.56/26.61 | fun_app$e(v0, v12) = v13 & fun_app$(v13, false_ltln$) = % 191.56/26.61 | v14 & A_ltln$(v12) & A_ltln_bool_fun$(v13)))) & (v6 = 0 % 191.56/26.61 | | ? [v10: Nat$] : ( ~ Nat$(v10) | ? [v11: Nat$] : ? % 191.56/26.61 | [v12: A_set_list$] : ? [v13: A_ltln$] : ? [v14: % 191.56/26.61 | A_ltln_bool_fun$] : (subsequence$(v2, v10, v11) = v12 & % 191.56/26.61 | fun_app$s(v8, v12) = v13 & fun_app$e(v0, v13) = v14 & % 191.56/26.61 | fun_app$(v14, false_ltln$) = 0 & A_ltln$(v13) & % 191.56/26.61 | A_set_list$(v12) & A_ltln_bool_fun$(v14) & % 191.56/26.61 | Nat$(v11)))))))) % 191.56/26.61 | % 191.56/26.61 | ALPHA: (165) implies: % 191.56/26.61 | (166) until_ltln$(true_ltln$) = all_815_1 % 191.56/26.61 | % 191.56/26.61 | DELTA: instantiating (57) with fresh symbol all_818_0 gives: % 191.56/26.61 | (167) until_ltln$(true_ltln$) = all_818_0 & A_ltln_a_ltln_fun$(all_818_0) & % 191.56/26.61 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 191.56/26.61 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 191.56/26.61 | A_ltln$] : ! [v6: int] : (v6 = 0 | ~ (semantics_ltln$(v0) = v3) | % 191.56/26.61 | ~ (until_ltln$(v1) = v4) | ~ (fun_app$d(v4, v2) = v5) | ~ % 191.56/26.61 | (fun_app$(v3, v5) = v6) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | % 191.56/26.61 | ~ A_ltln$(v1) | ? [v7: A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? % 191.56/26.61 | [v9: any] : ? [v10: A_ltln$] : ? [v11: any] : % 191.56/26.61 | (weakUntil_ltln$(v1) = v7 & fun_app$d(v7, v2) = v8 & % 191.56/26.61 | fun_app$d(all_818_0, v2) = v10 & fun_app$(v3, v10) = v11 & % 191.56/26.61 | fun_app$(v3, v8) = v9 & A_ltln$(v10) & A_ltln$(v8) & % 191.56/26.61 | A_ltln_a_ltln_fun$(v7) & ( ~ (v11 = 0) | ~ (v9 = 0)))) & ! [v0: % 191.56/26.61 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.56/26.61 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 191.56/26.61 | : ( ~ (weakUntil_ltln$(v1) = v4) | ~ (semantics_ltln$(v0) = v3) | ~ % 191.56/26.61 | (fun_app$d(v4, v2) = v5) | ~ (fun_app$(v3, v5) = 0) | ~ % 191.56/26.61 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ? [v6: % 191.56/26.61 | A_ltln$] : ? [v7: any] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 191.56/26.61 | A_ltln$] : ? [v10: any] : (until_ltln$(v1) = v8 & fun_app$d(v8, % 191.56/26.61 | v2) = v9 & fun_app$d(all_818_0, v2) = v6 & fun_app$(v3, v9) = % 191.56/26.61 | v10 & fun_app$(v3, v6) = v7 & A_ltln$(v9) & A_ltln$(v6) & % 191.56/26.61 | A_ltln_a_ltln_fun$(v8) & ( ~ (v7 = 0) | v10 = 0))) % 191.56/26.61 | % 191.56/26.61 | ALPHA: (167) implies: % 191.56/26.61 | (168) until_ltln$(true_ltln$) = all_818_0 % 191.56/26.61 | % 191.56/26.61 | DELTA: instantiating (59) with fresh symbol all_824_0 gives: % 191.56/26.61 | (169) until_ltln$(true_ltln$) = all_824_0 & A_ltln_a_ltln_fun$(all_824_0) & % 191.56/26.61 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 191.56/26.61 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 191.56/26.61 | A_ltln$] : ! [v6: int] : (v6 = 0 | ~ (strongRelease_ltln$(v1) = % 191.56/26.61 | v4) | ~ (semantics_ltln$(v0) = v3) | ~ (fun_app$d(v4, v2) = v5) % 191.56/26.61 | | ~ (fun_app$(v3, v5) = v6) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.61 | A_ltln$(v2) | ~ A_ltln$(v1) | ? [v7: A_ltln_a_ltln_fun$] : ? % 191.56/26.61 | [v8: A_ltln$] : ? [v9: any] : ? [v10: A_ltln$] : ? [v11: any] : % 191.56/26.61 | (release_ltln$(v1) = v7 & fun_app$d(v7, v2) = v8 & % 191.56/26.61 | fun_app$d(all_824_0, v1) = v10 & fun_app$(v3, v10) = v11 & % 191.56/26.61 | fun_app$(v3, v8) = v9 & A_ltln$(v10) & A_ltln$(v8) & % 191.56/26.61 | A_ltln_a_ltln_fun$(v7) & ( ~ (v11 = 0) | ~ (v9 = 0)))) & ! [v0: % 191.56/26.61 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.56/26.61 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 191.56/26.61 | : ( ~ (semantics_ltln$(v0) = v3) | ~ (release_ltln$(v1) = v4) | ~ % 191.56/26.61 | (fun_app$d(v4, v2) = v5) | ~ (fun_app$(v3, v5) = 0) | ~ % 191.56/26.61 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ? [v6: % 191.56/26.61 | A_ltln$] : ? [v7: any] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 191.56/26.61 | A_ltln$] : ? [v10: any] : (strongRelease_ltln$(v1) = v8 & % 191.56/26.61 | fun_app$d(v8, v2) = v9 & fun_app$d(all_824_0, v1) = v6 & % 191.56/26.61 | fun_app$(v3, v9) = v10 & fun_app$(v3, v6) = v7 & A_ltln$(v9) & % 191.56/26.61 | A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) & ( ~ (v7 = 0) | v10 = 0))) % 191.56/26.61 | % 191.56/26.61 | ALPHA: (169) implies: % 191.56/26.61 | (170) until_ltln$(true_ltln$) = all_824_0 % 191.56/26.61 | % 191.56/26.61 | DELTA: instantiating (58) with fresh symbol all_835_0 gives: % 191.56/26.62 | (171) until_ltln$(true_ltln$) = all_835_0 & A_ltln_a_ltln_fun$(all_835_0) & % 191.56/26.62 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 191.56/26.62 | A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] : ! [v4: A_ltln$] % 191.56/26.62 | : ! [v5: int] : (v5 = 0 | ~ (strongRelease_ltln$(v1) = v3) | ~ % 191.56/26.62 | (semantics_ltln$(v0) = v2) | ~ (fun_app$d(v3, true_ltln$) = v4) | % 191.56/26.62 | ~ (fun_app$(v2, v4) = v5) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) % 191.56/26.62 | | ? [v6: A_ltln$] : ? [v7: int] : ( ~ (v7 = 0) & % 191.56/26.62 | fun_app$d(all_835_0, v1) = v6 & fun_app$(v2, v6) = v7 & % 191.56/26.62 | A_ltln$(v6))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! % 191.56/26.62 | [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ! [v4: int] : (v4 = 0 | % 191.56/26.62 | ~ (semantics_ltln$(v0) = v2) | ~ (fun_app$d(all_835_0, v1) = v3) | % 191.56/26.62 | ~ (fun_app$(v2, v3) = v4) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) % 191.56/26.62 | | ? [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : ? [v7: int] : ( % 191.56/26.62 | ~ (v7 = 0) & strongRelease_ltln$(v1) = v5 & fun_app$d(v5, % 191.56/26.62 | true_ltln$) = v6 & fun_app$(v2, v6) = v7 & A_ltln$(v6) & % 191.56/26.62 | A_ltln_a_ltln_fun$(v5))) & ! [v0: Nat_a_set_fun$] : ! [v1: % 191.56/26.62 | A_ltln$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] % 191.56/26.62 | : ! [v4: A_ltln$] : ( ~ (strongRelease_ltln$(v1) = v3) | ~ % 191.56/26.62 | (semantics_ltln$(v0) = v2) | ~ (fun_app$d(v3, true_ltln$) = v4) | % 191.56/26.62 | ~ (fun_app$(v2, v4) = 0) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | % 191.56/26.62 | ? [v5: A_ltln$] : (fun_app$d(all_835_0, v1) = v5 & fun_app$(v2, % 191.56/26.62 | v5) = 0 & A_ltln$(v5))) & ! [v0: Nat_a_set_fun$] : ! [v1: % 191.56/26.62 | A_ltln$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ( ~ % 191.56/26.62 | (semantics_ltln$(v0) = v2) | ~ (fun_app$d(all_835_0, v1) = v3) | % 191.56/26.62 | ~ (fun_app$(v2, v3) = 0) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | % 191.56/26.62 | ? [v4: A_ltln_a_ltln_fun$] : ? [v5: A_ltln$] : % 191.56/26.62 | (strongRelease_ltln$(v1) = v4 & fun_app$d(v4, true_ltln$) = v5 & % 191.56/26.62 | fun_app$(v2, v5) = 0 & A_ltln$(v5) & A_ltln_a_ltln_fun$(v4))) % 191.56/26.62 | % 191.56/26.62 | ALPHA: (171) implies: % 191.56/26.62 | (172) until_ltln$(true_ltln$) = all_835_0 % 191.56/26.62 | % 191.56/26.62 | DELTA: instantiating (20) with fresh symbol all_841_0 gives: % 191.56/26.62 | (173) until_ltln$(true_ltln$) = all_841_0 & A_ltln_a_ltln_fun$(all_841_0) & % 191.56/26.62 | ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.62 | ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set_list$] : ! [v5: % 191.56/26.62 | A_set_list$] : ! [v6: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : % 191.56/26.62 | ! [v7: A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: % 191.56/26.62 | A_set_list_a_ltln_fun$] : ! [v9: A_set_list_a_set_list_fun$] : ! % 191.56/26.62 | [v10: A_set_list$] : ! [v11: A_ltln$] : ( ~ (append$(v4) = v9) | ~ % 191.56/26.62 | (fun_app$t(v9, v5) = v10) | ~ (transition_functions$(v0, v1) = 0) % 191.56/26.62 | | ~ (foldl$(v7, v3) = v8) | ~ (fun_app$s(v8, v10) = v11) | ~ % 191.56/26.62 | (fun_app$c(v6, v2) = v7) | ~ (af_letter_F$(v0) = v6) | ~ % 191.56/26.62 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 191.56/26.62 | ~ A_set_list$(v5) | ~ A_set_list$(v4) | ~ A_ltln_a_ltln_fun$(v1) % 191.56/26.62 | | ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? [v14: % 191.56/26.62 | A_set_list_a_ltln_fun$] : ? [v15: A_ltln$] : (foldl$(v7, v13) = % 191.56/26.62 | v14 & fun_app$s(v14, v5) = v15 & fun_app$s(v8, v4) = v12 & % 191.56/26.62 | fun_app$d(all_841_0, v2) = v13 & A_set_list_a_ltln_fun$(v14) & % 191.56/26.62 | A_ltln$(v15) & A_ltln$(v13) & A_ltln$(v12) & ( ~ (v13 = v12) | % 191.56/26.62 | v15 = v11))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 191.56/26.62 | A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.62 | A_set_list$] : ! [v5: A_set_list$] : ! [v6: % 191.56/26.62 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v7: % 191.56/26.62 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v8: A_set_list_a_ltln_fun$] : % 191.56/26.62 | ! [v9: A_ltln$] : ! [v10: A_set_list_a_ltln_fun$] : ! [v11: % 191.56/26.62 | A_ltln$] : ( ~ (transition_functions$(v0, v1) = 0) | ~ (foldl$(v7, % 191.56/26.62 | v9) = v10) | ~ (foldl$(v7, v3) = v8) | ~ (fun_app$s(v10, v5) % 191.56/26.62 | = v11) | ~ (fun_app$s(v8, v4) = v9) | ~ (fun_app$c(v6, v2) = % 191.56/26.62 | v7) | ~ (af_letter_F$(v0) = v6) | ~ (fun_app$d(all_841_0, v2) = % 191.56/26.62 | v9) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ % 191.56/26.62 | A_ltln$(v2) | ~ A_set_list$(v5) | ~ A_set_list$(v4) | ~ % 191.56/26.62 | A_ltln_a_ltln_fun$(v1) | ? [v12: A_set_list_a_set_list_fun$] : ? % 191.56/26.62 | [v13: A_set_list$] : (append$(v4) = v12 & fun_app$t(v12, v5) = v13 % 191.56/26.62 | & fun_app$s(v8, v13) = v11 & A_ltln$(v11) & A_set_list$(v13) & % 191.56/26.62 | A_set_list_a_set_list_fun$(v12))) % 191.56/26.62 | % 191.56/26.62 | ALPHA: (173) implies: % 191.56/26.62 | (174) until_ltln$(true_ltln$) = all_841_0 % 191.56/26.62 | % 191.56/26.62 | DELTA: instantiating (14) with fresh symbol all_846_0 gives: % 191.56/26.62 | (175) until_ltln$(true_ltln$) = all_846_0 & A_ltln_a_ltln_fun$(all_846_0) & % 191.56/26.62 | ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.62 | ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set$] : ! [v5: % 191.56/26.62 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v6: % 191.56/26.62 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_a_ltln_fun$] : ! % 191.56/26.62 | [v8: A_ltln$] : ( ~ (transition_functions$(v0, v1) = 0) | ~ % 191.56/26.62 | (fun_app$c(v5, v2) = v6) | ~ (fun_app$b(v6, v3) = v7) | ~ % 191.56/26.62 | (fun_app$a(v7, v4) = v8) | ~ (af_letter_F$(v0) = v5) | ~ % 191.56/26.62 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 191.56/26.62 | ~ A_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? [v9: % 191.56/26.62 | A_ltln_bool_fun$] : ? [v10: any] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.62 | A_set_a_ltln_fun$] : ? [v13: A_ltln$] : (fun_app$b(af_letter$, % 191.56/26.62 | v3) = v12 & fun_app$a(v12, v4) = v13 & fun_app$e(v0, v3) = v9 & % 191.56/26.62 | fun_app$d(all_846_0, v2) = v11 & fun_app$(v9, true_ltln$) = v10 & % 191.56/26.62 | A_ltln$(v13) & A_ltln$(v11) & A_ltln_bool_fun$(v9) & % 191.56/26.62 | A_set_a_ltln_fun$(v12) & ( ~ (v10 = 0) | v11 = v8) & (v13 = v8 | % 191.56/26.62 | v10 = 0))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 191.56/26.62 | A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.62 | A_set$] : ! [v5: A_ltln$] : ! [v6: A_set_a_ltln_fun$] : ! [v7: % 191.56/26.62 | A_ltln$] : ( ~ (transition_functions$(v0, v1) = 0) | ~ % 191.56/26.62 | (fun_app$b(af_letter$, v3) = v6) | ~ (fun_app$a(v6, v4) = v7) | ~ % 191.56/26.62 | (fun_app$d(all_846_0, v2) = v5) | ~ % 191.56/26.62 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 191.56/26.62 | ~ A_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? [v8: % 191.56/26.62 | A_ltln_bool_fun$] : ? [v9: any] : ? [v10: % 191.56/26.62 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v11: % 191.56/26.62 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v12: A_set_a_ltln_fun$] : ? % 191.56/26.62 | [v13: A_ltln$] : (fun_app$c(v10, v2) = v11 & fun_app$b(v11, v3) = % 191.56/26.62 | v12 & fun_app$a(v12, v4) = v13 & af_letter_F$(v0) = v10 & % 191.56/26.62 | fun_app$e(v0, v3) = v8 & fun_app$(v8, true_ltln$) = v9 & % 191.56/26.62 | A_ltln_a_set_a_ltln_fun_fun$(v11) & A_ltln$(v13) & % 191.56/26.62 | A_ltln_bool_fun$(v8) & A_set_a_ltln_fun$(v12) & % 191.56/26.62 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v10) & ( ~ (v9 = 0) | v13 % 191.56/26.62 | = v5) & (v13 = v7 | v9 = 0))) % 191.56/26.62 | % 191.56/26.62 | ALPHA: (175) implies: % 191.56/26.62 | (176) until_ltln$(true_ltln$) = all_846_0 % 191.56/26.62 | (177) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.62 | ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_set$] : ! [v5: % 191.56/26.62 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v6: % 191.56/26.62 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_a_ltln_fun$] : ! % 191.56/26.62 | [v8: A_ltln$] : ( ~ (transition_functions$(v0, v1) = 0) | ~ % 191.56/26.62 | (fun_app$c(v5, v2) = v6) | ~ (fun_app$b(v6, v3) = v7) | ~ % 191.56/26.62 | (fun_app$a(v7, v4) = v8) | ~ (af_letter_F$(v0) = v5) | ~ % 191.56/26.62 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 191.56/26.62 | ~ A_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? [v9: % 191.56/26.62 | A_ltln_bool_fun$] : ? [v10: any] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.62 | A_set_a_ltln_fun$] : ? [v13: A_ltln$] : (fun_app$b(af_letter$, % 191.56/26.62 | v3) = v12 & fun_app$a(v12, v4) = v13 & fun_app$e(v0, v3) = v9 & % 191.56/26.62 | fun_app$d(all_846_0, v2) = v11 & fun_app$(v9, true_ltln$) = v10 & % 191.56/26.62 | A_ltln$(v13) & A_ltln$(v11) & A_ltln_bool_fun$(v9) & % 191.56/26.62 | A_set_a_ltln_fun$(v12) & ( ~ (v10 = 0) | v11 = v8) & (v13 = v8 | % 191.56/26.62 | v10 = 0))) % 191.56/26.62 | % 191.56/26.62 | DELTA: instantiating (32) with fresh symbols all_885_0, all_885_1, all_885_2 % 191.56/26.62 | gives: % 191.56/26.63 | (178) nat$(0) = all_885_0 & af_letter_F$(eq$) = all_885_1 & % 191.56/26.63 | until_ltln$(true_ltln$) = all_885_2 & Nat$(all_885_0) & % 191.56/26.63 | A_ltln_a_ltln_fun$(all_885_2) & % 191.56/26.63 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_885_1) & ? [v0: % 191.56/26.63 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v4: A_set_list_a_ltln_fun$] : % 191.56/26.63 | ! [v5: Nat$] : ! [v6: int] : ( ~ (fun_app$y(of_nat$, v5) = v6) | ~ % 191.56/26.63 | (foldl$(v3, v2) = v4) | ~ (fun_app$c(all_885_1, v1) = v3) | ~ % 191.56/26.63 | (fun_app$d(all_885_2, v1) = v2) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.63 | A_ltln$(v1) | ~ Nat$(v5) | ? [v7: A_set_list_a_ltln_fun$] : ? % 191.56/26.63 | [v8: Nat$] : ? [v9: Nat$] : ? [v10: int] : ? [v11: A_set_list$] % 191.56/26.63 | : ? [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: int] : % 191.56/26.63 | (Nat$(v9) & Nat$(v8) & ((v14 = 0 & $lesseq(1, $difference(v10, v6)) % 191.56/26.63 | & fun_app$y(of_nat$, v9) = v10 & subsequence$(v0, all_885_0, % 191.56/26.63 | v9) = v11 & fun_app$s(v4, v11) = v12 & fun_app$e(eq$, v12) % 191.56/26.63 | = v13 & fun_app$(v13, true_ltln$) = 0 & A_ltln$(v12) & % 191.56/26.63 | A_set_list$(v11) & A_ltln_bool_fun$(v13)) | % 191.56/26.63 | (foldl$(af_letter$, v2) = v7 & A_set_list_a_ltln_fun$(v7) & ! % 191.56/26.63 | [v15: Nat$] : ! [v16: A_set_list$] : ( ~ (subsequence$(v0, % 191.56/26.63 | v8, v15) = v16) | ~ Nat$(v15) | ? [v17: A_ltln$] : ? % 191.56/26.63 | [v18: A_ltln_bool_fun$] : ? [v19: int] : ( ~ (v19 = 0) & % 191.56/26.63 | fun_app$s(v7, v16) = v17 & fun_app$e(eq$, v17) = v18 & % 191.56/26.63 | fun_app$(v18, true_ltln$) = v19 & A_ltln$(v17) & % 191.56/26.63 | A_ltln_bool_fun$(v18))))))) & ? [v0: Nat_a_set_fun$] : % 191.56/26.63 | ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_set_list_a_ltln_fun$] % 191.56/26.63 | : ( ~ (foldl$(af_letter$, v2) = v3) | ~ (fun_app$d(all_885_2, v1) = % 191.56/26.63 | v2) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ? [v4: % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v5: A_set_list_a_ltln_fun$] : % 191.56/26.63 | ? [v6: Nat$] : (Nat$(v6) & ( ! [v7: Nat$] : ! [v8: A_set_list$] : % 191.56/26.63 | ( ~ (subsequence$(v0, v6, v7) = v8) | ~ Nat$(v7) | ? [v9: % 191.56/26.63 | A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: int] : ( ~ % 191.56/26.63 | (v11 = 0) & fun_app$s(v3, v8) = v9 & fun_app$e(eq$, v9) = % 191.56/26.63 | v10 & fun_app$(v10, true_ltln$) = v11 & A_ltln$(v9) & % 191.56/26.63 | A_ltln_bool_fun$(v10))) | (foldl$(v4, v2) = v5 & % 191.56/26.63 | fun_app$c(all_885_1, v1) = v4 & A_set_list_a_ltln_fun$(v5) & % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$(v4) & ! [v7: Nat$] : ! [v8: % 191.56/26.63 | int] : ( ~ (fun_app$y(of_nat$, v7) = v8) | ~ Nat$(v7) | ? % 191.56/26.63 | [v9: Nat$] : ? [v10: int] : ? [v11: A_set_list$] : ? % 191.56/26.63 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ($lesseq(1, % 191.56/26.63 | $difference(v10, v8)) & fun_app$y(of_nat$, v9) = v10 & % 191.56/26.63 | subsequence$(v0, all_885_0, v9) = v11 & fun_app$s(v5, % 191.56/26.63 | v11) = v12 & fun_app$e(eq$, v12) = v13 & fun_app$(v13, % 191.56/26.63 | true_ltln$) = 0 & A_ltln$(v12) & A_set_list$(v11) & % 191.56/26.63 | A_ltln_bool_fun$(v13) & Nat$(v9))))))) % 191.56/26.63 | % 191.56/26.63 | ALPHA: (178) implies: % 191.56/26.63 | (179) until_ltln$(true_ltln$) = all_885_2 % 191.56/26.63 | (180) af_letter_F$(eq$) = all_885_1 % 191.56/26.63 | % 191.56/26.63 | DELTA: instantiating (37) with fresh symbols all_895_0, all_895_1 gives: % 191.56/26.63 | (181) nat$(0) = all_895_0 & until_ltln$(true_ltln$) = all_895_1 & % 191.56/26.63 | Nat$(all_895_0) & A_ltln_a_ltln_fun$(all_895_1) & ? [v0: % 191.56/26.63 | Nat_a_set_fun$] : ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 191.56/26.63 | A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: % 191.56/26.63 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v6: % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v7: A_set_list_a_ltln_fun$] : % 191.56/26.63 | ! [v8: Nat$] : ! [v9: int] : ( ~ (fun_app$y(of_nat$, v8) = v9) | ~ % 191.56/26.63 | (transition_functions$(v1, v2) = 0) | ~ (foldl$(v6, v4) = v7) | ~ % 191.56/26.63 | (fun_app$c(v5, v3) = v6) | ~ (af_letter_F$(v1) = v5) | ~ % 191.56/26.63 | (fun_app$d(all_895_1, v3) = v4) | ~ % 191.56/26.63 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.63 | A_ltln$(v3) | ~ Nat$(v8) | ~ A_ltln_a_ltln_fun$(v2) | ? [v10: % 191.56/26.63 | A_set_list_a_ltln_fun$] : ? [v11: Nat$] : ? [v12: Nat$] : ? % 191.56/26.63 | [v13: int] : ? [v14: A_set_list$] : ? [v15: A_ltln$] : ? [v16: % 191.56/26.63 | A_ltln_bool_fun$] : ? [v17: int] : (Nat$(v12) & Nat$(v11) & % 191.56/26.63 | ((v17 = 0 & $lesseq(1, $difference(v13, v9)) & fun_app$y(of_nat$, % 191.56/26.63 | v12) = v13 & subsequence$(v0, all_895_0, v12) = v14 & % 191.56/26.63 | fun_app$s(v7, v14) = v15 & fun_app$e(v1, v15) = v16 & % 191.56/26.63 | fun_app$(v16, true_ltln$) = 0 & A_ltln$(v15) & % 191.56/26.63 | A_set_list$(v14) & A_ltln_bool_fun$(v16)) | % 191.56/26.63 | (foldl$(af_letter$, v4) = v10 & A_set_list_a_ltln_fun$(v10) & % 191.56/26.63 | ! [v18: Nat$] : ! [v19: A_set_list$] : ( ~ (subsequence$(v0, % 191.56/26.63 | v11, v18) = v19) | ~ Nat$(v18) | ? [v20: A_ltln$] : % 191.56/26.63 | ? [v21: A_ltln_bool_fun$] : ? [v22: int] : ( ~ (v22 = 0) & % 191.56/26.63 | fun_app$s(v10, v19) = v20 & fun_app$e(v1, v20) = v21 & % 191.56/26.63 | fun_app$(v21, true_ltln$) = v22 & A_ltln$(v20) & % 191.56/26.63 | A_ltln_bool_fun$(v21))))))) & ? [v0: Nat_a_set_fun$] : % 191.56/26.63 | ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : % 191.56/26.63 | ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_set_list_a_ltln_fun$] % 191.56/26.63 | : ( ~ (transition_functions$(v1, v2) = 0) | ~ (foldl$(af_letter$, % 191.56/26.63 | v4) = v5) | ~ (fun_app$d(all_895_1, v3) = v4) | ~ % 191.56/26.63 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.63 | A_ltln$(v3) | ~ A_ltln_a_ltln_fun$(v2) | ? [v6: % 191.56/26.63 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v7: % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v8: A_set_list_a_ltln_fun$] : % 191.56/26.63 | ? [v9: Nat$] : (Nat$(v9) & ( ! [v10: Nat$] : ! [v11: A_set_list$] % 191.56/26.63 | : ( ~ (subsequence$(v0, v9, v10) = v11) | ~ Nat$(v10) | ? % 191.56/26.63 | [v12: A_ltln$] : ? [v13: A_ltln_bool_fun$] : ? [v14: int] : % 191.56/26.63 | ( ~ (v14 = 0) & fun_app$s(v5, v11) = v12 & fun_app$e(v1, v12) % 191.56/26.63 | = v13 & fun_app$(v13, true_ltln$) = v14 & A_ltln$(v12) & % 191.56/26.63 | A_ltln_bool_fun$(v13))) | (foldl$(v7, v4) = v8 & % 191.56/26.63 | fun_app$c(v6, v3) = v7 & af_letter_F$(v1) = v6 & % 191.56/26.63 | A_set_list_a_ltln_fun$(v8) & A_ltln_a_set_a_ltln_fun_fun$(v7) % 191.56/26.63 | & A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v6) & ! [v10: % 191.56/26.63 | Nat$] : ! [v11: int] : ( ~ (fun_app$y(of_nat$, v10) = v11) % 191.56/26.63 | | ~ Nat$(v10) | ? [v12: Nat$] : ? [v13: int] : ? [v14: % 191.56/26.63 | A_set_list$] : ? [v15: A_ltln$] : ? [v16: % 191.56/26.63 | A_ltln_bool_fun$] : ($lesseq(1, $difference(v13, v11)) & % 191.56/26.63 | fun_app$y(of_nat$, v12) = v13 & subsequence$(v0, % 191.56/26.63 | all_895_0, v12) = v14 & fun_app$s(v8, v14) = v15 & % 191.56/26.63 | fun_app$e(v1, v15) = v16 & fun_app$(v16, true_ltln$) = 0 % 191.56/26.63 | & A_ltln$(v15) & A_set_list$(v14) & A_ltln_bool_fun$(v16) % 191.56/26.63 | & Nat$(v12))))))) % 191.56/26.63 | % 191.56/26.63 | ALPHA: (181) implies: % 191.56/26.63 | (182) until_ltln$(true_ltln$) = all_895_1 % 191.56/26.63 | % 191.56/26.63 | DELTA: instantiating (38) with fresh symbols all_915_0, all_915_1, all_915_2 % 191.56/26.63 | gives: % 191.56/26.63 | (183) nat$(0) = all_915_0 & af_letter_F$(eq$) = all_915_2 & % 191.56/26.63 | until_ltln$(true_ltln$) = all_915_1 & Nat$(all_915_0) & % 191.56/26.63 | A_ltln_a_ltln_fun$(all_915_1) & % 191.56/26.63 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(all_915_2) & ? [v0: % 191.56/26.63 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 191.56/26.63 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.63 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(v2, v3) = v4) | ~ % 191.56/26.63 | (fun_app$c(all_915_2, v1) = v2) | ~ (fun_app$d(all_915_1, v1) = % 191.56/26.63 | v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ? [v5: % 191.56/26.63 | A_set_list_a_ltln_fun$] : ? [v6: Nat$] : ? [v7: int] : % 191.56/26.63 | (Nat$(v6) & ((fun_app$y(of_nat$, v6) = v7 & ! [v8: Nat$] : ! [v9: % 191.56/26.63 | int] : ( ~ ($lesseq(1, $difference(v9, v7))) | ~ % 191.56/26.63 | (fun_app$y(of_nat$, v8) = v9) | ~ Nat$(v8) | ? [v10: % 191.56/26.63 | A_set_list$] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.63 | A_ltln_bool_fun$] : ? [v13: int] : ( ~ (v13 = 0) & % 191.56/26.63 | subsequence$(v0, all_915_0, v8) = v10 & fun_app$s(v4, % 191.56/26.63 | v10) = v11 & fun_app$e(eq$, v11) = v12 & fun_app$(v12, % 191.56/26.63 | true_ltln$) = v13 & A_ltln$(v11) & A_set_list$(v10) & % 191.56/26.63 | A_ltln_bool_fun$(v12))) & ! [v8: Nat$] : ! [v9: % 191.56/26.63 | A_set_list$] : ( ~ (subsequence$(v0, all_915_0, v8) = v9) | % 191.56/26.63 | ~ Nat$(v8) | ? [v10: int] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.63 | A_ltln_bool_fun$] : ? [v13: any] : (fun_app$y(of_nat$, % 191.56/26.63 | v8) = v10 & fun_app$s(v4, v9) = v11 & fun_app$e(eq$, % 191.56/26.63 | v11) = v12 & fun_app$(v12, true_ltln$) = v13 & % 191.56/26.63 | A_ltln$(v11) & A_ltln_bool_fun$(v12) & ( ~ (v13 = 0) | ~ % 191.56/26.63 | ($lesseq(1, $difference(v10, v7))))))) | % 191.56/26.63 | (foldl$(af_letter$, v3) = v5 & A_set_list_a_ltln_fun$(v5) & ? % 191.56/26.63 | [v8: Nat$] : ( ~ Nat$(v8) | ? [v9: Nat$] : ? [v10: % 191.56/26.63 | A_set_list$] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.63 | A_ltln_bool_fun$] : (subsequence$(v0, v8, v9) = v10 & % 191.56/26.63 | fun_app$s(v5, v10) = v11 & fun_app$e(ltl_lang_equiv$, % 191.56/26.63 | v11) = v12 & fun_app$(v12, true_ltln$) = 0 & % 191.56/26.63 | A_ltln$(v11) & A_set_list$(v10) & A_ltln_bool_fun$(v12) & % 191.56/26.63 | Nat$(v9))))))) & ? [v0: Nat_a_set_fun$] : ? [v1: Nat$] % 191.56/26.63 | : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.63 | A_set_list_a_ltln_fun$] : ( ~ (foldl$(af_letter$, v3) = v4) | ~ % 191.56/26.63 | (fun_app$d(all_915_1, v2) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.63 | A_ltln$(v2) | ~ Nat$(v1) | ? [v5: A_ltln_a_set_a_ltln_fun_fun$] : % 191.56/26.63 | ? [v6: A_set_list_a_ltln_fun$] : ? [v7: Nat$] : ? [v8: int] : ? % 191.56/26.63 | [v9: Nat$] : ? [v10: A_set_list$] : ? [v11: A_ltln$] : ? [v12: % 191.56/26.63 | A_ltln_bool_fun$] : ? [v13: int] : (Nat$(v9) & Nat$(v7) & ((v13 % 191.56/26.63 | = 0 & subsequence$(v0, v1, v9) = v10 & fun_app$s(v4, v10) = % 191.56/26.63 | v11 & fun_app$e(ltl_lang_equiv$, v11) = v12 & fun_app$(v12, % 191.56/26.63 | true_ltln$) = 0 & A_ltln$(v11) & A_set_list$(v10) & % 191.56/26.63 | A_ltln_bool_fun$(v12)) | (fun_app$y(of_nat$, v7) = v8 & % 191.56/26.63 | foldl$(v5, v3) = v6 & fun_app$c(all_915_2, v2) = v5 & % 191.56/26.63 | A_set_list_a_ltln_fun$(v6) & A_ltln_a_set_a_ltln_fun_fun$(v5) % 191.56/26.63 | & ! [v14: Nat$] : ! [v15: int] : ( ~ ($lesseq(1, % 191.56/26.63 | $difference(v15, v8))) | ~ (fun_app$y(of_nat$, v14) = % 191.56/26.63 | v15) | ~ Nat$(v14) | ? [v16: A_set_list$] : ? [v17: % 191.56/26.63 | A_ltln$] : ? [v18: A_ltln_bool_fun$] : ? [v19: int] : ( % 191.56/26.63 | ~ (v19 = 0) & subsequence$(v0, all_915_0, v14) = v16 & % 191.56/26.63 | fun_app$s(v6, v16) = v17 & fun_app$e(eq$, v17) = v18 & % 191.56/26.63 | fun_app$(v18, true_ltln$) = v19 & A_ltln$(v17) & % 191.56/26.63 | A_set_list$(v16) & A_ltln_bool_fun$(v18))) & ! [v14: % 191.56/26.63 | Nat$] : ! [v15: A_set_list$] : ( ~ (subsequence$(v0, % 191.56/26.63 | all_915_0, v14) = v15) | ~ Nat$(v14) | ? [v16: int] : % 191.56/26.63 | ? [v17: A_ltln$] : ? [v18: A_ltln_bool_fun$] : ? [v19: % 191.56/26.63 | any] : (fun_app$y(of_nat$, v14) = v16 & fun_app$s(v6, % 191.56/26.63 | v15) = v17 & fun_app$e(eq$, v17) = v18 & fun_app$(v18, % 191.56/26.63 | true_ltln$) = v19 & A_ltln$(v17) & % 191.56/26.63 | A_ltln_bool_fun$(v18) & ( ~ (v19 = 0) | ~ ($lesseq(1, % 191.56/26.63 | $difference(v16, v8)))))))))) % 191.56/26.63 | % 191.56/26.63 | ALPHA: (183) implies: % 191.56/26.63 | (184) until_ltln$(true_ltln$) = all_915_1 % 191.56/26.64 | (185) af_letter_F$(eq$) = all_915_2 % 191.56/26.64 | % 191.56/26.64 | DELTA: instantiating (50) with fresh symbols all_919_0, all_919_1 gives: % 191.56/26.64 | (186) nat$(0) = all_919_0 & until_ltln$(true_ltln$) = all_919_1 & % 191.56/26.64 | Nat$(all_919_0) & A_ltln_a_ltln_fun$(all_919_1) & ? [v0: % 191.56/26.64 | Nat_a_set_fun$] : ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 191.56/26.64 | A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: % 191.56/26.64 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ! [v5: % 191.56/26.64 | A_ltln_a_set_a_ltln_fun_fun$] : ! [v6: A_ltln$] : ! [v7: % 191.56/26.64 | A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v1, v2) = 0) | % 191.56/26.64 | ~ (foldl$(v5, v6) = v7) | ~ (fun_app$c(v4, v3) = v5) | ~ % 191.56/26.64 | (af_letter_F$(v1) = v4) | ~ (fun_app$d(all_919_1, v3) = v6) | ~ % 191.56/26.64 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v0) | ~ % 191.56/26.64 | A_ltln$(v3) | ~ A_ltln_a_ltln_fun$(v2) | ? [v8: % 191.56/26.64 | A_set_list_a_ltln_fun$] : ? [v9: Nat$] : ? [v10: int] : % 191.56/26.64 | (Nat$(v9) & ((fun_app$y(of_nat$, v9) = v10 & ! [v11: Nat$] : ! % 191.56/26.64 | [v12: int] : ( ~ ($lesseq(1, $difference(v12, v10))) | ~ % 191.56/26.64 | (fun_app$y(of_nat$, v11) = v12) | ~ Nat$(v11) | ? [v13: % 191.56/26.64 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.56/26.64 | A_ltln_bool_fun$] : ? [v16: int] : ( ~ (v16 = 0) & % 191.56/26.64 | subsequence$(v0, all_919_0, v11) = v13 & fun_app$s(v7, % 191.56/26.64 | v13) = v14 & fun_app$e(v1, v14) = v15 & fun_app$(v15, % 191.56/26.64 | true_ltln$) = v16 & A_ltln$(v14) & A_set_list$(v13) & % 191.56/26.64 | A_ltln_bool_fun$(v15))) & ! [v11: Nat$] : ! [v12: % 191.56/26.64 | A_set_list$] : ( ~ (subsequence$(v0, all_919_0, v11) = v12) % 191.56/26.64 | | ~ Nat$(v11) | ? [v13: int] : ? [v14: A_ltln$] : ? % 191.56/26.64 | [v15: A_ltln_bool_fun$] : ? [v16: any] : % 191.56/26.64 | (fun_app$y(of_nat$, v11) = v13 & fun_app$s(v7, v12) = v14 & % 191.56/26.64 | fun_app$e(v1, v14) = v15 & fun_app$(v15, true_ltln$) = % 191.56/26.64 | v16 & A_ltln$(v14) & A_ltln_bool_fun$(v15) & ( ~ (v16 = % 191.56/26.64 | 0) | ~ ($lesseq(1, $difference(v13, v10))))))) | % 191.56/26.64 | (foldl$(af_letter$, v6) = v8 & A_set_list_a_ltln_fun$(v8) & ? % 191.56/26.64 | [v11: Nat$] : ( ~ Nat$(v11) | ? [v12: Nat$] : ? [v13: % 191.56/26.64 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: % 191.56/26.64 | A_ltln_bool_fun$] : (subsequence$(v0, v11, v12) = v13 & % 191.56/26.64 | fun_app$s(v8, v13) = v14 & fun_app$e(ltl_lang_equiv$, % 191.56/26.64 | v14) = v15 & fun_app$(v15, true_ltln$) = 0 & % 191.56/26.64 | A_ltln$(v14) & A_set_list$(v13) & A_ltln_bool_fun$(v15) & % 191.56/26.64 | Nat$(v12))))))) & ? [v0: Nat_a_set_fun$] : ? [v1: Nat$] % 191.56/26.64 | : ! [v2: A_ltln_a_ltln_bool_fun_fun$] : ! [v3: A_ltln_a_ltln_fun$] % 191.56/26.64 | : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 191.56/26.64 | A_set_list_a_ltln_fun$] : ( ~ (transition_functions$(v2, v3) = 0) | % 191.56/26.64 | ~ (foldl$(af_letter$, v5) = v6) | ~ (fun_app$d(all_919_1, v4) = % 191.56/26.64 | v5) | ~ A_ltln_a_ltln_bool_fun_fun$(v2) | ~ Nat_a_set_fun$(v0) % 191.56/26.64 | | ~ A_ltln$(v4) | ~ Nat$(v1) | ~ A_ltln_a_ltln_fun$(v3) | ? % 191.56/26.64 | [v7: A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$] : ? [v8: % 191.56/26.64 | A_ltln_a_set_a_ltln_fun_fun$] : ? [v9: A_set_list_a_ltln_fun$] : % 191.56/26.64 | ? [v10: Nat$] : ? [v11: int] : ? [v12: Nat$] : ? [v13: % 191.56/26.64 | A_set_list$] : ? [v14: A_ltln$] : ? [v15: A_ltln_bool_fun$] : % 191.56/26.64 | ? [v16: int] : (Nat$(v12) & Nat$(v10) & ((v16 = 0 & % 191.56/26.64 | subsequence$(v0, v1, v12) = v13 & fun_app$s(v6, v13) = v14 & % 191.56/26.64 | fun_app$e(ltl_lang_equiv$, v14) = v15 & fun_app$(v15, % 191.56/26.64 | true_ltln$) = 0 & A_ltln$(v14) & A_set_list$(v13) & % 191.56/26.64 | A_ltln_bool_fun$(v15)) | (fun_app$y(of_nat$, v10) = v11 & % 191.56/26.64 | foldl$(v8, v5) = v9 & fun_app$c(v7, v4) = v8 & % 191.56/26.64 | af_letter_F$(v2) = v7 & A_set_list_a_ltln_fun$(v9) & % 191.56/26.64 | A_ltln_a_set_a_ltln_fun_fun$(v8) & % 191.56/26.64 | A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$(v7) & ! [v17: Nat$] % 191.56/26.64 | : ! [v18: int] : ( ~ ($lesseq(1, $difference(v18, v11))) | % 191.56/26.64 | ~ (fun_app$y(of_nat$, v17) = v18) | ~ Nat$(v17) | ? [v19: % 191.56/26.64 | A_set_list$] : ? [v20: A_ltln$] : ? [v21: % 191.56/26.64 | A_ltln_bool_fun$] : ? [v22: int] : ( ~ (v22 = 0) & % 191.56/26.64 | subsequence$(v0, all_919_0, v17) = v19 & fun_app$s(v9, % 191.56/26.64 | v19) = v20 & fun_app$e(v2, v20) = v21 & fun_app$(v21, % 191.56/26.64 | true_ltln$) = v22 & A_ltln$(v20) & A_set_list$(v19) & % 191.56/26.64 | A_ltln_bool_fun$(v21))) & ! [v17: Nat$] : ! [v18: % 191.56/26.64 | A_set_list$] : ( ~ (subsequence$(v0, all_919_0, v17) = v18) % 191.56/26.64 | | ~ Nat$(v17) | ? [v19: int] : ? [v20: A_ltln$] : ? % 191.56/26.64 | [v21: A_ltln_bool_fun$] : ? [v22: any] : % 191.56/26.64 | (fun_app$y(of_nat$, v17) = v19 & fun_app$s(v9, v18) = v20 & % 191.56/26.64 | fun_app$e(v2, v20) = v21 & fun_app$(v21, true_ltln$) = % 191.56/26.64 | v22 & A_ltln$(v20) & A_ltln_bool_fun$(v21) & ( ~ (v22 = % 191.56/26.64 | 0) | ~ ($lesseq(1, $difference(v19, v11)))))))))) % 191.56/26.64 | % 191.56/26.64 | ALPHA: (186) implies: % 191.56/26.64 | (187) until_ltln$(true_ltln$) = all_919_1 % 191.56/26.64 | % 191.56/26.64 | DELTA: instantiating (36) with fresh symbol all_935_0 gives: % 191.56/26.65 | (188) nat$(0) = all_935_0 & Nat$(all_935_0) & ! [v0: % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 191.56/26.65 | [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! [v5: % 191.56/26.65 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: A_ltln_bool_fun$] : ! [v8: % 191.56/26.65 | A_ltln$] : ! [v9: A_ltln$] : ! [v10: int] : (v10 = 0 | ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (gF_advice$(v8, v4) % 191.56/26.65 | = v9) | ~ (gF_advice$(v5, v4) = v6) | ~ (fun_app$e(v0, v6) = % 191.56/26.65 | v7) | ~ (fun_app$d(v1, v3) = v8) | ~ (fun_app$d(v1, v2) = v5) | % 191.56/26.65 | ~ (fun_app$(v7, v9) = v10) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | % 191.56/26.65 | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_ltln_set$(v4) | ~ % 191.56/26.65 | A_ltln_a_ltln_fun$(v1) | ? [v11: A_ltln_bool_fun$] : ? [v12: int] % 191.56/26.65 | : ( ~ (v12 = 0) & fun_app$e(v0, v2) = v11 & fun_app$(v11, v3) = v12 % 191.56/26.65 | & A_ltln_bool_fun$(v11))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] % 191.56/26.65 | : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 191.56/26.65 | A_ltln$] : ! [v4: A_ltln_set$] : ! [v5: A_ltln_bool_fun$] : ! % 191.56/26.65 | [v6: A_ltln$] : ! [v7: A_ltln$] : ! [v8: int] : (v8 = 0 | ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (semantics_ltln$(v2) % 191.56/26.65 | = v5) | ~ (gF_advice$(v6, v4) = v7) | ~ (fun_app$d(v1, v3) = % 191.56/26.65 | v6) | ~ (fun_app$(v5, v7) = v8) | ~ % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 191.56/26.65 | A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? % 191.56/26.65 | [v9: A_ltln$] : ? [v10: int] : ( ~ (v10 = 0) & gF_advice$(v3, v4) % 191.56/26.65 | = v9 & fun_app$(v5, v9) = v10 & A_ltln$(v9))) & ! [v0: % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 191.56/26.65 | [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! % 191.56/26.65 | [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (semantics_ltln$(v2) % 191.56/26.65 | = v5) | ~ (gF_advice$(v6, v4) = v7) | ~ (fun_app$d(v1, v3) = % 191.56/26.65 | v6) | ~ (fun_app$(v5, v7) = 0) | ~ % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 191.56/26.65 | A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? % 191.56/26.65 | [v8: A_set_list_a_ltln_fun$] : ? [v9: Nat$] : ? [v10: % 191.56/26.65 | Nat_a_set_fun$] : ? [v11: A_ltln_bool_fun$] : ? [v12: % 191.56/26.65 | A_set_list$] : ? [v13: A_ltln$] : ? [v14: A_ltln$] : % 191.56/26.65 | (suffix$(v9, v2) = v10 & subsequence$(v2, all_935_0, v9) = v12 & % 191.56/26.65 | semantics_ltln$(v10) = v11 & gF_advice$(v13, v4) = v14 & % 191.56/26.65 | foldl$(af_letter$, v3) = v8 & fun_app$s(v8, v12) = v13 & % 191.56/26.65 | fun_app$(v11, v14) = 0 & A_set_list_a_ltln_fun$(v8) & % 191.56/26.65 | Nat_a_set_fun$(v10) & A_ltln$(v14) & A_ltln$(v13) & % 191.56/26.65 | A_set_list$(v12) & A_ltln_bool_fun$(v11) & Nat$(v9))) & ! [v0: % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 191.56/26.65 | [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! % 191.56/26.65 | [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ( ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (semantics_ltln$(v2) % 191.56/26.65 | = v5) | ~ (gF_advice$(v3, v4) = v6) | ~ (fun_app$(v5, v6) = 0) % 191.56/26.65 | | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 191.56/26.65 | A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? % 191.56/26.65 | [v7: A_ltln$] : ? [v8: A_ltln$] : (gF_advice$(v7, v4) = v8 & % 191.56/26.65 | fun_app$d(v1, v3) = v7 & fun_app$(v5, v8) = 0 & A_ltln$(v8) & % 191.56/26.65 | A_ltln$(v7))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 191.56/26.65 | A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] % 191.56/26.65 | : ( ~ (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$e(v0, % 191.56/26.65 | v2) = v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) % 191.56/26.65 | | ~ A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln$] : (fun_app$d(v1, v2) % 191.56/26.65 | = v4 & fun_app$(v3, v4) = 0 & A_ltln$(v4))) & ! [v0: % 191.56/26.65 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 191.56/26.65 | [v2: A_ltln$] : ! [v3: A_ltln$] : ( ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$d(v1, v2) = % 191.56/26.65 | v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) | ~ % 191.56/26.65 | A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln_bool_fun$] : (fun_app$e(v0, % 191.56/26.65 | v2) = v4 & fun_app$(v4, v3) = 0 & A_ltln_bool_fun$(v4))) & ! % 191.56/26.65 | [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 191.56/26.65 | [v2: int] : (v2 = 0 | ~ (gF_advice_congruent_axioms$(v0, v1) = v2) | % 191.56/26.65 | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? % 191.56/26.65 | [v3: A_ltln$] : ? [v4: A_ltln$] : ? [v5: A_ltln_set$] : ? [v6: % 191.56/26.65 | A_ltln_bool_fun$] : ? [v7: int] : ? [v8: A_ltln$] : ? [v9: % 191.56/26.65 | A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: A_ltln$] : ? % 191.56/26.65 | [v12: A_ltln$] : ? [v13: int] : ? [v14: Nat_a_set_fun$] : ? % 191.56/26.65 | [v15: A_ltln$] : ? [v16: A_ltln_set$] : ? [v17: A_ltln_bool_fun$] % 191.56/26.65 | : ? [v18: A_ltln$] : ? [v19: A_ltln$] : ? [v20: int] : ? [v21: % 191.56/26.65 | A_set_list_a_ltln_fun$] : ? [v22: Nat_a_set_fun$] : ? [v23: % 191.56/26.65 | A_ltln$] : ? [v24: A_ltln_set$] : ? [v25: A_ltln_bool_fun$] : % 191.56/26.65 | ? [v26: A_ltln$] : ? [v27: int] : ? [v28: A_ltln$] : ? [v29: % 191.56/26.65 | A_ltln$] : ? [v30: int] : ? [v31: A_ltln$] : ? [v32: % 191.56/26.65 | A_ltln_bool_fun$] : ? [v33: A_ltln$] : ? [v34: int] : % 191.56/26.65 | (Nat_a_set_fun$(v22) & Nat_a_set_fun$(v14) & A_ltln$(v31) & % 191.56/26.65 | A_ltln$(v23) & A_ltln$(v15) & A_ltln$(v4) & A_ltln$(v3) & % 191.56/26.65 | A_ltln_set$(v24) & A_ltln_set$(v16) & A_ltln_set$(v5) & ((v27 = 0 % 191.56/26.65 | & ~ (v30 = 0) & semantics_ltln$(v22) = v25 & gF_advice$(v28, % 191.56/26.65 | v24) = v29 & gF_advice$(v23, v24) = v26 & fun_app$d(v1, % 191.56/26.65 | v23) = v28 & fun_app$(v25, v29) = v30 & fun_app$(v25, v26) % 191.56/26.65 | = 0 & A_ltln$(v29) & A_ltln$(v28) & A_ltln$(v26) & % 191.56/26.65 | A_ltln_bool_fun$(v25)) | (v20 = 0 & semantics_ltln$(v14) = % 191.56/26.65 | v17 & gF_advice$(v18, v16) = v19 & foldl$(af_letter$, v15) = % 191.56/26.65 | v21 & fun_app$d(v1, v15) = v18 & fun_app$(v17, v19) = 0 & % 191.56/26.65 | A_set_list_a_ltln_fun$(v21) & A_ltln$(v19) & A_ltln$(v18) & % 191.56/26.65 | A_ltln_bool_fun$(v17) & ! [v35: Nat$] : ! [v36: % 191.56/26.65 | Nat_a_set_fun$] : ( ~ (suffix$(v35, v14) = v36) | ~ % 191.56/26.65 | Nat$(v35) | ? [v37: A_ltln_bool_fun$] : ? [v38: % 191.56/26.65 | A_set_list$] : ? [v39: A_ltln$] : ? [v40: A_ltln$] : ? % 191.56/26.65 | [v41: int] : ( ~ (v41 = 0) & subsequence$(v14, all_935_0, % 191.56/26.65 | v35) = v38 & semantics_ltln$(v36) = v37 & % 191.56/26.65 | gF_advice$(v39, v16) = v40 & fun_app$s(v21, v38) = v39 & % 191.56/26.65 | fun_app$(v37, v40) = v41 & A_ltln$(v40) & A_ltln$(v39) & % 191.56/26.65 | A_set_list$(v38) & A_ltln_bool_fun$(v37))) & ! [v35: % 191.56/26.65 | Nat$] : ! [v36: A_set_list$] : ( ~ (subsequence$(v14, % 191.56/26.65 | all_935_0, v35) = v36) | ~ Nat$(v35) | ? [v37: % 191.56/26.65 | Nat_a_set_fun$] : ? [v38: A_ltln_bool_fun$] : ? [v39: % 191.56/26.65 | A_ltln$] : ? [v40: A_ltln$] : ? [v41: int] : ( ~ (v41 = % 191.56/26.65 | 0) & suffix$(v35, v14) = v37 & semantics_ltln$(v37) = % 191.56/26.65 | v38 & gF_advice$(v39, v16) = v40 & fun_app$s(v21, v36) = % 191.56/26.65 | v39 & fun_app$(v38, v40) = v41 & Nat_a_set_fun$(v37) & % 191.56/26.65 | A_ltln$(v40) & A_ltln$(v39) & A_ltln_bool_fun$(v38)))) | % 191.56/26.65 | (v7 = 0 & ~ (v13 = 0) & gF_advice$(v11, v5) = v12 & % 191.56/26.65 | gF_advice$(v8, v5) = v9 & fun_app$e(v0, v9) = v10 & % 191.56/26.65 | fun_app$e(v0, v3) = v6 & fun_app$d(v1, v4) = v11 & % 191.56/26.65 | fun_app$d(v1, v3) = v8 & fun_app$(v10, v12) = v13 & % 191.56/26.65 | fun_app$(v6, v4) = 0 & A_ltln$(v12) & A_ltln$(v11) & % 191.56/26.65 | A_ltln$(v9) & A_ltln$(v8) & A_ltln_bool_fun$(v10) & % 191.56/26.65 | A_ltln_bool_fun$(v6)) | ( ~ (v34 = 0) & fun_app$e(v0, v31) = % 191.56/26.65 | v32 & fun_app$d(v1, v31) = v33 & fun_app$(v32, v33) = v34 & % 191.56/26.65 | A_ltln$(v33) & A_ltln_bool_fun$(v32))))) % 191.56/26.65 | % 191.56/26.65 | ALPHA: (188) implies: % 191.56/26.65 | (189) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.65 | ! [v2: A_ltln$] : ! [v3: A_ltln$] : ( ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$d(v1, v2) = % 191.56/26.65 | v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) | ~ % 191.56/26.65 | A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln_bool_fun$] : (fun_app$e(v0, % 191.56/26.65 | v2) = v4 & fun_app$(v4, v3) = 0 & A_ltln_bool_fun$(v4))) % 191.56/26.65 | (190) ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : % 191.56/26.65 | ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ( ~ % 191.56/26.65 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$e(v0, v2) = % 191.56/26.65 | v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) | ~ % 191.56/26.65 | A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln$] : (fun_app$d(v1, v2) = v4 % 191.56/26.65 | & fun_app$(v3, v4) = 0 & A_ltln$(v4))) % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_650_0, all_674_0, true_ltln$, % 191.56/26.65 | simplifying with (121), (125) gives: % 191.56/26.65 | (191) all_674_0 = all_650_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_674_0, all_683_0, true_ltln$, % 191.56/26.65 | simplifying with (125), (127) gives: % 191.56/26.65 | (192) all_683_0 = all_674_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_683_0, all_686_0, true_ltln$, % 191.56/26.65 | simplifying with (127), (130) gives: % 191.56/26.65 | (193) all_686_0 = all_683_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_686_0, all_704_0, true_ltln$, % 191.56/26.65 | simplifying with (130), (135) gives: % 191.56/26.65 | (194) all_704_0 = all_686_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_704_0, all_722_0, true_ltln$, % 191.56/26.65 | simplifying with (135), (139) gives: % 191.56/26.65 | (195) all_722_0 = all_704_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_722_0, all_728_0, true_ltln$, % 191.56/26.65 | simplifying with (139), (141) gives: % 191.56/26.65 | (196) all_728_0 = all_722_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_728_0, all_731_1, true_ltln$, % 191.56/26.65 | simplifying with (141), (143) gives: % 191.56/26.65 | (197) all_731_1 = all_728_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_731_1, all_773_0, true_ltln$, % 191.56/26.65 | simplifying with (143), (145) gives: % 191.56/26.65 | (198) all_773_0 = all_731_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_773_0, all_785_1, true_ltln$, % 191.56/26.65 | simplifying with (145), (148) gives: % 191.56/26.65 | (199) all_785_1 = all_773_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_785_1, all_788_1, true_ltln$, % 191.56/26.65 | simplifying with (148), (150) gives: % 191.56/26.65 | (200) all_788_1 = all_785_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_788_1, all_791_1, true_ltln$, % 191.56/26.65 | simplifying with (150), (152) gives: % 191.56/26.65 | (201) all_791_1 = all_788_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_791_1, all_794_0, true_ltln$, % 191.56/26.65 | simplifying with (152), (154) gives: % 191.56/26.65 | (202) all_794_0 = all_791_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_794_0, all_797_1, true_ltln$, % 191.56/26.65 | simplifying with (154), (156) gives: % 191.56/26.65 | (203) all_797_1 = all_794_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_797_1, all_800_0, true_ltln$, % 191.56/26.65 | simplifying with (156), (158) gives: % 191.56/26.65 | (204) all_800_0 = all_797_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_650_0, all_806_0, true_ltln$, % 191.56/26.65 | simplifying with (121), (162) gives: % 191.56/26.65 | (205) all_806_0 = all_650_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_624_3, all_806_0, true_ltln$, % 191.56/26.65 | simplifying with (113), (162) gives: % 191.56/26.65 | (206) all_806_0 = all_624_3 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_800_0, all_815_1, true_ltln$, % 191.56/26.65 | simplifying with (158), (166) gives: % 191.56/26.65 | (207) all_815_1 = all_800_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_815_1, all_824_0, true_ltln$, % 191.56/26.65 | simplifying with (166), (170) gives: % 191.56/26.65 | (208) all_824_0 = all_815_1 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_818_0, all_835_0, true_ltln$, % 191.56/26.65 | simplifying with (168), (172) gives: % 191.56/26.65 | (209) all_835_0 = all_818_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_812_0, all_835_0, true_ltln$, % 191.56/26.65 | simplifying with (164), (172) gives: % 191.56/26.65 | (210) all_835_0 = all_812_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_806_0, all_835_0, true_ltln$, % 191.56/26.65 | simplifying with (162), (172) gives: % 191.56/26.65 | (211) all_835_0 = all_806_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_824_0, all_841_0, true_ltln$, % 191.56/26.65 | simplifying with (170), (174) gives: % 191.56/26.65 | (212) all_841_0 = all_824_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_650_0, all_885_2, true_ltln$, % 191.56/26.65 | simplifying with (121), (179) gives: % 191.56/26.65 | (213) all_885_2 = all_650_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_615_0, all_885_2, true_ltln$, % 191.56/26.65 | simplifying with (104), (179) gives: % 191.56/26.65 | (214) all_885_2 = all_615_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_846_0, all_895_1, true_ltln$, % 191.56/26.65 | simplifying with (176), (182) gives: % 191.56/26.65 | (215) all_895_1 = all_846_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_818_0, all_895_1, true_ltln$, % 191.56/26.65 | simplifying with (168), (182) gives: % 191.56/26.65 | (216) all_895_1 = all_818_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_803_0, all_895_1, true_ltln$, % 191.56/26.65 | simplifying with (160), (182) gives: % 191.56/26.65 | (217) all_895_1 = all_803_0 % 191.56/26.65 | % 191.56/26.65 | GROUND_INST: instantiating (75) with all_841_0, all_915_1, true_ltln$, % 191.56/26.65 | simplifying with (174), (184) gives: % 191.56/26.65 | (218) all_915_1 = all_841_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (75) with all_915_1, all_919_1, true_ltln$, % 191.56/26.66 | simplifying with (184), (187) gives: % 191.56/26.66 | (219) all_919_1 = all_915_1 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (75) with all_527_2, all_919_1, true_ltln$, % 191.56/26.66 | simplifying with (98), (187) gives: % 191.56/26.66 | (220) all_919_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_624_8, all_668_0, eq$, simplifying % 191.56/26.66 | with (114), (123) gives: % 191.56/26.66 | (221) all_668_0 = all_624_8 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_668_0, all_683_1, eq$, simplifying % 191.56/26.66 | with (123), (128) gives: % 191.56/26.66 | (222) all_683_1 = all_668_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_683_1, all_686_1, eq$, simplifying % 191.56/26.66 | with (128), (131) gives: % 191.56/26.66 | (223) all_686_1 = all_683_1 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_686_1, all_698_0, eq$, simplifying % 191.56/26.66 | with (131), (133) gives: % 191.56/26.66 | (224) all_698_0 = all_686_1 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_698_0, all_710_0, eq$, simplifying % 191.56/26.66 | with (133), (137) gives: % 191.56/26.66 | (225) all_710_0 = all_698_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_710_0, all_773_1, eq$, simplifying % 191.56/26.66 | with (137), (146) gives: % 191.56/26.66 | (226) all_773_1 = all_710_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_773_1, all_885_1, eq$, simplifying % 191.56/26.66 | with (146), (180) gives: % 191.56/26.66 | (227) all_885_1 = all_773_1 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_885_1, all_915_2, eq$, simplifying % 191.56/26.66 | with (180), (185) gives: % 191.56/26.66 | (228) all_915_2 = all_885_1 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (76) with all_641_0, all_915_2, eq$, simplifying % 191.56/26.66 | with (119), (185) gives: % 191.56/26.66 | (229) all_915_2 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (82) with all_535_0, all_538_1, true_ltln$, % 191.56/26.66 | af_letter$, simplifying with (100), (102) gives: % 191.56/26.66 | (230) all_538_1 = all_535_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (82) with all_499_0, all_538_1, true_ltln$, % 191.56/26.66 | af_letter$, simplifying with (91), (102) gives: % 191.56/26.66 | (231) all_538_1 = all_499_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (77) with all_485_0, all_491_0, nil$, simplifying % 191.56/26.66 | with (87), (89) gives: % 191.56/26.66 | (232) all_491_0 = all_485_0 % 191.56/26.66 | % 191.56/26.66 | GROUND_INST: instantiating (77) with all_477_0, all_491_0, nil$, simplifying % 191.56/26.66 | with (85), (89) gives: % 191.56/26.66 | (233) all_491_0 = all_477_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (219), (220) imply: % 191.56/26.66 | (234) all_915_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (234) implies: % 191.56/26.66 | (235) all_915_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (218), (235) imply: % 191.56/26.66 | (236) all_841_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (236) implies: % 191.56/26.66 | (237) all_841_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (228), (229) imply: % 191.56/26.66 | (238) all_885_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (238) implies: % 191.56/26.66 | (239) all_885_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (215), (217) imply: % 191.56/26.66 | (240) all_846_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (215), (216) imply: % 191.56/26.66 | (241) all_846_0 = all_818_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (227), (239) imply: % 191.56/26.66 | (242) all_773_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (242) implies: % 191.56/26.66 | (243) all_773_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (213), (214) imply: % 191.56/26.66 | (244) all_650_0 = all_615_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (244) implies: % 191.56/26.66 | (245) all_650_0 = all_615_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (240), (241) imply: % 191.56/26.66 | (246) all_818_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (246) implies: % 191.56/26.66 | (247) all_818_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (212), (237) imply: % 191.56/26.66 | (248) all_824_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (248) implies: % 191.56/26.66 | (249) all_824_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (209), (210) imply: % 191.56/26.66 | (250) all_818_0 = all_812_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (250) implies: % 191.56/26.66 | (251) all_818_0 = all_812_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (210), (211) imply: % 191.56/26.66 | (252) all_812_0 = all_806_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (208), (249) imply: % 191.56/26.66 | (253) all_815_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (253) implies: % 191.56/26.66 | (254) all_815_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (247), (251) imply: % 191.56/26.66 | (255) all_812_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (255) implies: % 191.56/26.66 | (256) all_812_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (207), (254) imply: % 191.56/26.66 | (257) all_800_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (257) implies: % 191.56/26.66 | (258) all_800_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (252), (256) imply: % 191.56/26.66 | (259) all_806_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (259) implies: % 191.56/26.66 | (260) all_806_0 = all_803_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (206), (260) imply: % 191.56/26.66 | (261) all_803_0 = all_624_3 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (205), (260) imply: % 191.56/26.66 | (262) all_803_0 = all_650_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (261), (262) imply: % 191.56/26.66 | (263) all_650_0 = all_624_3 % 191.56/26.66 | % 191.56/26.66 | SIMP: (263) implies: % 191.56/26.66 | (264) all_650_0 = all_624_3 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (204), (258) imply: % 191.56/26.66 | (265) all_797_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (265) implies: % 191.56/26.66 | (266) all_797_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (203), (266) imply: % 191.56/26.66 | (267) all_794_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (267) implies: % 191.56/26.66 | (268) all_794_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (202), (268) imply: % 191.56/26.66 | (269) all_791_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (269) implies: % 191.56/26.66 | (270) all_791_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (201), (270) imply: % 191.56/26.66 | (271) all_788_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (271) implies: % 191.56/26.66 | (272) all_788_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (200), (272) imply: % 191.56/26.66 | (273) all_785_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (273) implies: % 191.56/26.66 | (274) all_785_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (199), (274) imply: % 191.56/26.66 | (275) all_773_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (275) implies: % 191.56/26.66 | (276) all_773_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (198), (276) imply: % 191.56/26.66 | (277) all_731_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (277) implies: % 191.56/26.66 | (278) all_731_1 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (226), (243) imply: % 191.56/26.66 | (279) all_710_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (279) implies: % 191.56/26.66 | (280) all_710_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (197), (278) imply: % 191.56/26.66 | (281) all_728_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (281) implies: % 191.56/26.66 | (282) all_728_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (196), (282) imply: % 191.56/26.66 | (283) all_722_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (283) implies: % 191.56/26.66 | (284) all_722_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (195), (284) imply: % 191.56/26.66 | (285) all_704_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (285) implies: % 191.56/26.66 | (286) all_704_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (225), (280) imply: % 191.56/26.66 | (287) all_698_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (287) implies: % 191.56/26.66 | (288) all_698_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (194), (286) imply: % 191.56/26.66 | (289) all_686_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (289) implies: % 191.56/26.66 | (290) all_686_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (224), (288) imply: % 191.56/26.66 | (291) all_686_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (291) implies: % 191.56/26.66 | (292) all_686_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (193), (290) imply: % 191.56/26.66 | (293) all_683_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (293) implies: % 191.56/26.66 | (294) all_683_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (223), (292) imply: % 191.56/26.66 | (295) all_683_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (295) implies: % 191.56/26.66 | (296) all_683_1 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (192), (294) imply: % 191.56/26.66 | (297) all_674_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (297) implies: % 191.56/26.66 | (298) all_674_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (222), (296) imply: % 191.56/26.66 | (299) all_668_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | SIMP: (299) implies: % 191.56/26.66 | (300) all_668_0 = all_641_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (191), (298) imply: % 191.56/26.66 | (301) all_650_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | SIMP: (301) implies: % 191.56/26.66 | (302) all_650_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (221), (300) imply: % 191.56/26.66 | (303) all_641_0 = all_624_8 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (245), (264) imply: % 191.56/26.66 | (304) all_624_3 = all_615_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (264), (302) imply: % 191.56/26.66 | (305) all_624_3 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (304), (305) imply: % 191.56/26.66 | (306) all_615_0 = all_527_2 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (230), (231) imply: % 191.56/26.66 | (307) all_535_0 = all_499_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (232), (233) imply: % 191.56/26.66 | (308) all_485_0 = all_477_0 % 191.56/26.66 | % 191.56/26.66 | COMBINE_EQS: (261), (305) imply: % 191.56/26.67 | (309) all_803_0 = all_527_2 % 191.56/26.67 | % 191.56/26.67 | COMBINE_EQS: (240), (309) imply: % 191.56/26.67 | (310) all_846_0 = all_527_2 % 191.56/26.67 | % 191.56/26.67 | REDUCE: (112), (305) imply: % 191.56/26.67 | (311) fun_app$d(all_527_2, phi$) = all_624_2 % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (79) with all_527_1, all_624_2, phi$, all_527_2, % 191.56/26.67 | simplifying with (97), (311) gives: % 191.56/26.67 | (312) all_624_2 = all_527_1 % 191.56/26.67 | % 191.56/26.67 | REDUCE: (111), (312) imply: % 191.56/26.67 | (313) nested_prop_atoms$(all_527_1) = all_624_1 % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (74) with all_527_0, all_624_1, all_527_1, % 191.56/26.67 | simplifying with (96), (313) gives: % 191.56/26.67 | (314) all_624_1 = all_527_0 % 191.56/26.67 | % 191.56/26.67 | REDUCE: (109), (314) imply: % 191.56/26.67 | (315) less_eq$(all_624_4, all_527_0) = all_624_0 % 191.56/26.67 | % 191.56/26.67 | REDUCE: (108), (314) imply: % 191.56/26.67 | (316) A_ltln_set$(all_527_0) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (39) with all_527_3, all_527_0, simplifying with % 191.56/26.67 | (93), (94), (316) gives: % 191.56/26.67 | (317) ? [v0: any] : ? [v1: any] : (less$(all_527_3, all_527_0) = v1 & % 191.56/26.67 | less_eq$(all_527_0, all_527_3) = v0 & (v1 = 0 | v0 = 0)) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (6) with all_527_3, all_527_0, simplifying with % 191.56/26.67 | (93), (94), (316) gives: % 191.56/26.67 | (318) ? [v0: any] : (less_eq$(all_527_0, all_527_3) = v0 & ( ~ (v0 = 0) | % 191.56/26.67 | all_527_0 = all_527_3) & ( ~ (all_527_0 = all_527_3) | v0 = 0)) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (41) with all_527_0, all_527_3, 0, simplifying with % 191.56/26.67 | (93), (94), (316) gives: % 191.56/26.67 | (319) ? [v0: int] : ? [v1: MultipleValueBool] : ( ~ (v0 = 0) & % 191.56/26.67 | less$(all_527_0, all_527_3) = v0 & less_eq$(all_527_0, all_527_3) = % 191.56/26.67 | v1) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (40) with all_527_3, all_527_0, 0, simplifying with % 191.56/26.67 | (93), (94), (316) gives: % 191.56/26.67 | (320) ? [v0: any] : ? [v1: any] : (less$(all_527_3, all_527_0) = v0 & % 191.56/26.67 | less_eq$(all_527_0, all_527_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (8) with all_527_3, all_527_0, all_624_4, % 191.56/26.67 | all_624_0, simplifying with (93), (94), (107), (315), (316) % 191.56/26.67 | gives: % 191.56/26.67 | (321) all_624_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less_eq$(all_624_4, % 191.56/26.67 | all_527_3) = v0) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (42) with all_527_0, all_624_4, all_624_0, % 191.56/26.67 | simplifying with (107), (315), (316) gives: % 191.56/26.67 | (322) all_624_0 = 0 | ? [v0: any] : ? [v1: any] : (less$(all_527_0, % 191.56/26.67 | all_624_4) = v1 & less_eq$(all_527_0, all_624_4) = v0 & ( ~ (v0 = % 191.56/26.67 | 0) | v1 = 0)) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (44) with all_624_4, all_527_0, all_624_0, % 191.56/26.67 | simplifying with (107), (315), (316) gives: % 191.56/26.67 | (323) all_624_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less$(all_624_4, % 191.56/26.67 | all_527_0) = v0) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (41) with all_527_0, all_624_4, all_624_0, % 191.56/26.67 | simplifying with (107), (315), (316) gives: % 191.56/26.67 | (324) ? [v0: any] : ? [v1: any] : (less$(all_527_0, all_624_4) = v0 & % 191.56/26.67 | less_eq$(all_527_0, all_624_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 191.56/26.67 | (all_624_0 = 0)))) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (40) with all_624_4, all_527_0, all_624_0, % 191.56/26.67 | simplifying with (107), (315), (316) gives: % 191.56/26.67 | (325) ? [v0: any] : ? [v1: any] : (less$(all_624_4, all_527_0) = v0 & % 191.56/26.67 | less_eq$(all_527_0, all_624_4) = v1 & ( ~ (v0 = 0) | (all_624_0 = 0 % 191.56/26.67 | & ~ (v1 = 0)))) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (3) with psi$, all_527_3, simplifying with (69), % 191.56/26.67 | (95) gives: % 191.56/26.67 | (326) ? [v0: A_ltln$] : ? [v1: A_ltln_set$] : (fun_app$d(normalise$, % 191.56/26.67 | psi$) = v0 & nested_prop_atoms$(v0) = v1 & less_eq$(v1, % 191.56/26.67 | all_527_3) = 0 & A_ltln$(v0) & A_ltln_set$(v1)) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (13) with eq$, normalise$, simplifying with (4), % 191.56/26.67 | (51), (72) gives: % 191.56/26.67 | (327) transition_functions_size_axioms$(normalise$) = 0 & % 191.56/26.67 | transition_functions$(eq$, normalise$) = 0 % 191.56/26.67 | % 191.56/26.67 | ALPHA: (327) implies: % 191.56/26.67 | (328) transition_functions$(eq$, normalise$) = 0 % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (24) with eq$, normalise$, simplifying with (9), % 191.56/26.67 | (51), (72) gives: % 191.56/26.67 | (329) gF_advice_congruent_axioms$(eq$, normalise$) = 0 & % 191.56/26.67 | ltl_equivalence$(eq$) = 0 % 191.56/26.67 | % 191.56/26.67 | ALPHA: (329) implies: % 191.56/26.67 | (330) gF_advice_congruent_axioms$(eq$, normalise$) = 0 % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (54) with af_letter$, true_ltln$, all_499_0, % 191.56/26.67 | simplifying with (67), (70), (91) gives: % 191.56/26.67 | (331) fun_app$s(all_499_0, nil$) = true_ltln$ % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (177) with eq$, normalise$, phi$, psi$, nu$, % 191.56/26.67 | all_624_8, all_624_7, all_624_6, all_624_5, simplifying with % 191.56/26.67 | (51), (68), (69), (71), (72), (114), (115), (116), (117), (328) % 191.56/26.67 | gives: % 191.56/26.67 | (332) ? [v0: A_ltln_bool_fun$] : ? [v1: any] : ? [v2: A_ltln$] : ? [v3: % 191.56/26.67 | A_set_a_ltln_fun$] : ? [v4: A_ltln$] : (fun_app$b(af_letter$, % 191.56/26.67 | psi$) = v3 & fun_app$a(v3, nu$) = v4 & fun_app$e(eq$, psi$) = v0 % 191.56/26.67 | & fun_app$d(all_846_0, phi$) = v2 & fun_app$(v0, true_ltln$) = v1 & % 191.56/26.67 | A_ltln$(v4) & A_ltln$(v2) & A_ltln_bool_fun$(v0) & % 191.56/26.67 | A_set_a_ltln_fun$(v3) & ( ~ (v1 = 0) | v2 = all_624_5) & (v4 = % 191.56/26.67 | all_624_5 | v1 = 0)) % 191.56/26.67 | % 191.56/26.67 | GROUND_INST: instantiating (52) with nil$, all_477_0, simplifying with (60), % 191.56/26.67 | (85) gives: % 191.56/26.67 | (333) fun_app$t(all_477_0, nil$) = nil$ % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (319) with fresh symbols all_1044_0, all_1044_1 gives: % 191.56/26.67 | (334) ~ (all_1044_1 = 0) & less$(all_527_0, all_527_3) = all_1044_1 & % 191.56/26.67 | less_eq$(all_527_0, all_527_3) = all_1044_0 % 191.56/26.67 | % 191.56/26.67 | ALPHA: (334) implies: % 191.56/26.67 | (335) less_eq$(all_527_0, all_527_3) = all_1044_0 % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (320) with fresh symbols all_1056_0, all_1056_1 gives: % 191.56/26.67 | (336) less$(all_527_3, all_527_0) = all_1056_1 & less_eq$(all_527_0, % 191.56/26.67 | all_527_3) = all_1056_0 & ( ~ (all_1056_0 = 0) | ~ (all_1056_1 = % 191.56/26.67 | 0)) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (336) implies: % 191.56/26.67 | (337) less_eq$(all_527_0, all_527_3) = all_1056_0 % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (317) with fresh symbols all_1058_0, all_1058_1 gives: % 191.56/26.67 | (338) less$(all_527_3, all_527_0) = all_1058_0 & less_eq$(all_527_0, % 191.56/26.67 | all_527_3) = all_1058_1 & (all_1058_0 = 0 | all_1058_1 = 0) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (338) implies: % 191.56/26.67 | (339) less_eq$(all_527_0, all_527_3) = all_1058_1 % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (318) with fresh symbol all_1106_0 gives: % 191.56/26.67 | (340) less_eq$(all_527_0, all_527_3) = all_1106_0 & ( ~ (all_1106_0 = 0) | % 191.56/26.67 | all_527_0 = all_527_3) & ( ~ (all_527_0 = all_527_3) | all_1106_0 = % 191.56/26.67 | 0) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (340) implies: % 191.56/26.67 | (341) less_eq$(all_527_0, all_527_3) = all_1106_0 % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (325) with fresh symbols all_1108_0, all_1108_1 gives: % 191.56/26.67 | (342) less$(all_624_4, all_527_0) = all_1108_1 & less_eq$(all_527_0, % 191.56/26.67 | all_624_4) = all_1108_0 & ( ~ (all_1108_1 = 0) | (all_624_0 = 0 & % 191.56/26.67 | ~ (all_1108_0 = 0))) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (342) implies: % 191.56/26.67 | (343) less_eq$(all_527_0, all_624_4) = all_1108_0 % 191.56/26.67 | (344) less$(all_624_4, all_527_0) = all_1108_1 % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (324) with fresh symbols all_1112_0, all_1112_1 gives: % 191.56/26.67 | (345) less$(all_527_0, all_624_4) = all_1112_1 & less_eq$(all_527_0, % 191.56/26.67 | all_624_4) = all_1112_0 & ( ~ (all_1112_1 = 0) | (all_1112_0 = 0 & % 191.56/26.67 | ~ (all_624_0 = 0))) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (345) implies: % 191.56/26.67 | (346) less_eq$(all_527_0, all_624_4) = all_1112_0 % 191.56/26.67 | (347) less$(all_527_0, all_624_4) = all_1112_1 % 191.56/26.67 | (348) ~ (all_1112_1 = 0) | (all_1112_0 = 0 & ~ (all_624_0 = 0)) % 191.56/26.67 | % 191.56/26.67 | DELTA: instantiating (326) with fresh symbols all_1134_0, all_1134_1 gives: % 191.56/26.67 | (349) fun_app$d(normalise$, psi$) = all_1134_1 & % 191.56/26.67 | nested_prop_atoms$(all_1134_1) = all_1134_0 & less_eq$(all_1134_0, % 191.56/26.67 | all_527_3) = 0 & A_ltln$(all_1134_1) & A_ltln_set$(all_1134_0) % 191.56/26.67 | % 191.56/26.67 | ALPHA: (349) implies: % 191.56/26.67 | (350) A_ltln_set$(all_1134_0) % 191.56/26.68 | (351) less_eq$(all_1134_0, all_527_3) = 0 % 191.56/26.68 | (352) fun_app$d(normalise$, psi$) = all_1134_1 % 191.56/26.68 | % 191.56/26.68 | DELTA: instantiating (332) with fresh symbols all_1136_0, all_1136_1, % 191.56/26.68 | all_1136_2, all_1136_3, all_1136_4 gives: % 191.56/26.68 | (353) fun_app$b(af_letter$, psi$) = all_1136_1 & fun_app$a(all_1136_1, nu$) % 191.56/26.68 | = all_1136_0 & fun_app$e(eq$, psi$) = all_1136_4 & % 191.56/26.68 | fun_app$d(all_846_0, phi$) = all_1136_2 & fun_app$(all_1136_4, % 191.56/26.68 | true_ltln$) = all_1136_3 & A_ltln$(all_1136_0) & % 191.56/26.68 | A_ltln$(all_1136_2) & A_ltln_bool_fun$(all_1136_4) & % 191.56/26.68 | A_set_a_ltln_fun$(all_1136_1) & ( ~ (all_1136_3 = 0) | all_1136_2 = % 191.56/26.68 | all_624_5) & (all_1136_0 = all_624_5 | all_1136_3 = 0) % 191.56/26.68 | % 191.56/26.68 | ALPHA: (353) implies: % 191.56/26.68 | (354) fun_app$(all_1136_4, true_ltln$) = all_1136_3 % 191.56/26.68 | (355) fun_app$d(all_846_0, phi$) = all_1136_2 % 191.56/26.68 | (356) fun_app$e(eq$, psi$) = all_1136_4 % 191.56/26.68 | (357) fun_app$a(all_1136_1, nu$) = all_1136_0 % 191.56/26.68 | (358) fun_app$b(af_letter$, psi$) = all_1136_1 % 191.56/26.68 | (359) all_1136_0 = all_624_5 | all_1136_3 = 0 % 191.56/26.68 | (360) ~ (all_1136_3 = 0) | all_1136_2 = all_624_5 % 191.56/26.68 | % 191.56/26.68 | REDUCE: (310), (355) imply: % 191.56/26.68 | (361) fun_app$d(all_527_2, phi$) = all_1136_2 % 191.56/26.68 | % 191.56/26.68 | BETA: splitting (323) gives: % 191.56/26.68 | % 191.56/26.68 | Case 1: % 191.56/26.68 | | % 191.56/26.68 | | (362) all_624_0 = 0 % 191.56/26.68 | | % 191.56/26.68 | | REDUCE: (106), (362) imply: % 191.56/26.68 | | (363) $false % 191.56/26.68 | | % 191.56/26.68 | | CLOSE: (363) is inconsistent. % 191.56/26.68 | | % 192.00/26.68 | Case 2: % 192.00/26.68 | | % 192.00/26.68 | | (364) ? [v0: int] : ( ~ (v0 = 0) & less$(all_624_4, all_527_0) = v0) % 192.00/26.68 | | % 192.00/26.68 | | DELTA: instantiating (364) with fresh symbol all_1142_0 gives: % 192.00/26.68 | | (365) ~ (all_1142_0 = 0) & less$(all_624_4, all_527_0) = all_1142_0 % 192.00/26.68 | | % 192.00/26.68 | | ALPHA: (365) implies: % 192.00/26.68 | | (366) ~ (all_1142_0 = 0) % 192.00/26.68 | | (367) less$(all_624_4, all_527_0) = all_1142_0 % 192.00/26.68 | | % 192.00/26.68 | | BETA: splitting (321) gives: % 192.00/26.68 | | % 192.00/26.68 | | Case 1: % 192.00/26.68 | | | % 192.00/26.68 | | | (368) all_624_0 = 0 % 192.00/26.68 | | | % 192.00/26.68 | | | REDUCE: (106), (368) imply: % 192.00/26.68 | | | (369) $false % 192.00/26.68 | | | % 192.00/26.68 | | | CLOSE: (369) is inconsistent. % 192.00/26.68 | | | % 192.00/26.68 | | Case 2: % 192.00/26.68 | | | % 192.00/26.68 | | | (370) ? [v0: int] : ( ~ (v0 = 0) & less_eq$(all_624_4, all_527_3) = % 192.00/26.68 | | | v0) % 192.00/26.68 | | | % 192.00/26.68 | | | DELTA: instantiating (370) with fresh symbol all_1156_0 gives: % 192.00/26.68 | | | (371) ~ (all_1156_0 = 0) & less_eq$(all_624_4, all_527_3) = all_1156_0 % 192.00/26.68 | | | % 192.00/26.68 | | | ALPHA: (371) implies: % 192.00/26.68 | | | (372) ~ (all_1156_0 = 0) % 192.00/26.68 | | | (373) less_eq$(all_624_4, all_527_3) = all_1156_0 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (78) with all_1056_0, all_1058_1, all_527_3, % 192.00/26.68 | | | all_527_0, simplifying with (337), (339) gives: % 192.00/26.68 | | | (374) all_1058_1 = all_1056_0 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (78) with all_1058_1, all_1106_0, all_527_3, % 192.00/26.68 | | | all_527_0, simplifying with (339), (341) gives: % 192.00/26.68 | | | (375) all_1106_0 = all_1058_1 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (78) with all_1044_0, all_1106_0, all_527_3, % 192.00/26.68 | | | all_527_0, simplifying with (335), (341) gives: % 192.00/26.68 | | | (376) all_1106_0 = all_1044_0 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (78) with all_1108_0, all_1112_0, all_624_4, % 192.00/26.68 | | | all_527_0, simplifying with (343), (346) gives: % 192.00/26.68 | | | (377) all_1112_0 = all_1108_0 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (79) with all_527_1, all_1136_2, phi$, % 192.00/26.68 | | | all_527_2, simplifying with (97), (361) gives: % 192.00/26.68 | | | (378) all_1136_2 = all_527_1 % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (83) with all_1108_1, all_1142_0, all_527_0, % 192.00/26.68 | | | all_624_4, simplifying with (344), (367) gives: % 192.00/26.68 | | | (379) all_1142_0 = all_1108_1 % 192.00/26.68 | | | % 192.00/26.68 | | | COMBINE_EQS: (375), (376) imply: % 192.00/26.68 | | | (380) all_1058_1 = all_1044_0 % 192.00/26.68 | | | % 192.00/26.68 | | | SIMP: (380) implies: % 192.00/26.68 | | | (381) all_1058_1 = all_1044_0 % 192.00/26.68 | | | % 192.00/26.68 | | | COMBINE_EQS: (374), (381) imply: % 192.00/26.68 | | | (382) all_1056_0 = all_1044_0 % 192.00/26.68 | | | % 192.00/26.68 | | | SIMP: (382) implies: % 192.00/26.68 | | | (383) all_1056_0 = all_1044_0 % 192.00/26.68 | | | % 192.00/26.68 | | | REDUCE: (366), (379) imply: % 192.00/26.68 | | | (384) ~ (all_1108_1 = 0) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (41) with all_527_3, all_527_0, all_1044_0, % 192.00/26.68 | | | simplifying with (93), (316), (335) gives: % 192.00/26.68 | | | (385) ? [v0: any] : ? [v1: any] : (less$(all_527_3, all_527_0) = v0 & % 192.00/26.68 | | | less_eq$(all_527_3, all_527_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 192.00/26.68 | | | ~ (all_1044_0 = 0)))) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (40) with all_527_0, all_624_4, all_1108_0, % 192.00/26.68 | | | simplifying with (107), (316), (343) gives: % 192.00/26.68 | | | (386) ? [v0: any] : ? [v1: any] : (less$(all_527_0, all_624_4) = v0 & % 192.00/26.68 | | | less_eq$(all_624_4, all_527_0) = v1 & ( ~ (v0 = 0) | % 192.00/26.68 | | | (all_1108_0 = 0 & ~ (v1 = 0)))) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (8) with all_1134_0, all_527_3, all_624_4, % 192.00/26.68 | | | all_1156_0, simplifying with (93), (107), (350), (351), (373) % 192.00/26.68 | | | gives: % 192.00/26.68 | | | (387) all_1156_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 192.00/26.68 | | | less_eq$(all_624_4, all_1134_0) = v0) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (11) with psi$, nu$, all_1136_1, all_1136_0, % 192.00/26.68 | | | simplifying with (68), (69), (357), (358) gives: % 192.00/26.68 | | | (388) ? [v0: A_ltln_set$] : ? [v1: A_ltln_set$] : % 192.00/26.68 | | | (nested_prop_atoms$(all_1136_0) = v0 & nested_prop_atoms$(psi$) = % 192.00/26.68 | | | v1 & less_eq$(v0, v1) = 0 & A_ltln_set$(v1) & A_ltln_set$(v0)) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (46) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.68 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.68 | | | (85), (91), (331), (333) gives: % 192.00/26.68 | | | (389) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.68 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.68 | | | nil$) = v0 & fun_app$e(ltl_lang_equiv$, v0) = v1 & % 192.00/26.68 | | | fun_app$e(ltl_lang_equiv$, true_ltln$) = v3 & fun_app$(v3, % 192.00/26.68 | | | true_ltln$) = v4 & fun_app$(v1, true_ltln$) = v2 & % 192.00/26.68 | | | A_ltln$(v0) & A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ % 192.00/26.68 | | | (v2 = 0) | v4 = 0)) % 192.00/26.68 | | | % 192.00/26.68 | | | GROUND_INST: instantiating (45) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.68 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.68 | | | (85), (91), (331), (333) gives: % 192.00/26.69 | | | (390) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.69 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.69 | | | nil$) = v0 & fun_app$e(ltl_lang_equiv$, v0) = v1 & % 192.00/26.69 | | | fun_app$e(ltl_lang_equiv$, true_ltln$) = v3 & fun_app$(v3, % 192.00/26.69 | | | false_ltln$) = v4 & fun_app$(v1, false_ltln$) = v2 & % 192.00/26.69 | | | A_ltln$(v0) & A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ % 192.00/26.69 | | | (v2 = 0) | v4 = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (19) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.69 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.69 | | | (85), (91), (331), (333) gives: % 192.00/26.69 | | | (391) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.69 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.69 | | | nil$) = v0 & fun_app$e(eq$, v0) = v1 & fun_app$e(eq$, % 192.00/26.69 | | | true_ltln$) = v3 & fun_app$(v3, true_ltln$) = v4 & % 192.00/26.69 | | | fun_app$(v1, true_ltln$) = v2 & A_ltln$(v0) & % 192.00/26.69 | | | A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ (v2 = 0) | v4 % 192.00/26.69 | | | = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (21) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.69 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.69 | | | (85), (91), (331), (333) gives: % 192.00/26.69 | | | (392) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.69 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.69 | | | nil$) = v0 & fun_app$e(eq$, v0) = v1 & fun_app$e(eq$, % 192.00/26.69 | | | true_ltln$) = v3 & fun_app$(v3, false_ltln$) = v4 & % 192.00/26.69 | | | fun_app$(v1, false_ltln$) = v2 & A_ltln$(v0) & % 192.00/26.69 | | | A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ (v2 = 0) | v4 % 192.00/26.69 | | | = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (64) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.69 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.69 | | | (85), (91), (331), (333) gives: % 192.00/26.69 | | | (393) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.69 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.69 | | | nil$) = v0 & fun_app$e(ltl_prop_equiv$, v0) = v1 & % 192.00/26.69 | | | fun_app$e(ltl_prop_equiv$, true_ltln$) = v3 & fun_app$(v3, % 192.00/26.69 | | | true_ltln$) = v4 & fun_app$(v1, true_ltln$) = v2 & % 192.00/26.69 | | | A_ltln$(v0) & A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ % 192.00/26.69 | | | (v2 = 0) | v4 = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (63) with true_ltln$, nil$, nil$, all_499_0, % 192.00/26.69 | | | all_477_0, nil$, true_ltln$, simplifying with (60), (70), % 192.00/26.69 | | | (85), (91), (331), (333) gives: % 192.00/26.69 | | | (394) ? [v0: A_ltln$] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] : ? % 192.00/26.69 | | | [v3: A_ltln_bool_fun$] : ? [v4: any] : (fun_app$s(all_499_0, % 192.00/26.69 | | | nil$) = v0 & fun_app$e(ltl_prop_equiv$, v0) = v1 & % 192.00/26.69 | | | fun_app$e(ltl_prop_equiv$, true_ltln$) = v3 & fun_app$(v3, % 192.00/26.69 | | | false_ltln$) = v4 & fun_app$(v1, false_ltln$) = v2 & % 192.00/26.69 | | | A_ltln$(v0) & A_ltln_bool_fun$(v3) & A_ltln_bool_fun$(v1) & ( ~ % 192.00/26.69 | | | (v2 = 0) | v4 = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (190) with eq$, normalise$, psi$, all_1136_4, % 192.00/26.69 | | | simplifying with (51), (69), (72), (330), (356) gives: % 192.00/26.69 | | | (395) ? [v0: A_ltln$] : (fun_app$d(normalise$, psi$) = v0 & % 192.00/26.69 | | | fun_app$(all_1136_4, v0) = 0 & A_ltln$(v0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (189) with eq$, normalise$, psi$, all_1134_1, % 192.00/26.69 | | | simplifying with (51), (69), (72), (330), (352) gives: % 192.00/26.69 | | | (396) ? [v0: A_ltln_bool_fun$] : (fun_app$e(eq$, psi$) = v0 & % 192.00/26.69 | | | fun_app$(v0, all_1134_1) = 0 & A_ltln_bool_fun$(v0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (43) with all_527_0, all_624_4, all_1112_1, % 192.00/26.69 | | | simplifying with (107), (316), (347) gives: % 192.00/26.69 | | | (397) all_1112_1 = 0 | ? [v0: any] : ? [v1: any] : % 192.00/26.69 | | | (less_eq$(all_624_4, all_527_0) = v1 & less_eq$(all_527_0, % 192.00/26.69 | | | all_624_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | GROUND_INST: instantiating (33) with all_624_4, all_527_0, all_1108_1, % 192.00/26.69 | | | simplifying with (107), (316), (344) gives: % 192.00/26.69 | | | (398) all_1108_1 = 0 | ? [v0: any] : (less_eq$(all_624_4, all_527_0) = % 192.00/26.69 | | | v0 & ( ~ (v0 = 0) | all_624_4 = all_527_0) & ( ~ (all_624_4 = % 192.00/26.69 | | | all_527_0) | v0 = 0)) % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (396) with fresh symbol all_1256_0 gives: % 192.00/26.69 | | | (399) fun_app$e(eq$, psi$) = all_1256_0 & fun_app$(all_1256_0, % 192.00/26.69 | | | all_1134_1) = 0 & A_ltln_bool_fun$(all_1256_0) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (399) implies: % 192.00/26.69 | | | (400) fun_app$e(eq$, psi$) = all_1256_0 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (395) with fresh symbol all_1260_0 gives: % 192.00/26.69 | | | (401) fun_app$d(normalise$, psi$) = all_1260_0 & fun_app$(all_1136_4, % 192.00/26.69 | | | all_1260_0) = 0 & A_ltln$(all_1260_0) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (401) implies: % 192.00/26.69 | | | (402) A_ltln$(all_1260_0) % 192.00/26.69 | | | (403) fun_app$(all_1136_4, all_1260_0) = 0 % 192.00/26.69 | | | (404) fun_app$d(normalise$, psi$) = all_1260_0 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (388) with fresh symbols all_1294_0, all_1294_1 % 192.00/26.69 | | | gives: % 192.00/26.69 | | | (405) nested_prop_atoms$(all_1136_0) = all_1294_1 & % 192.00/26.69 | | | nested_prop_atoms$(psi$) = all_1294_0 & less_eq$(all_1294_1, % 192.00/26.69 | | | all_1294_0) = 0 & A_ltln_set$(all_1294_0) & % 192.00/26.69 | | | A_ltln_set$(all_1294_1) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (405) implies: % 192.00/26.69 | | | (406) A_ltln_set$(all_1294_1) % 192.00/26.69 | | | (407) A_ltln_set$(all_1294_0) % 192.00/26.69 | | | (408) less_eq$(all_1294_1, all_1294_0) = 0 % 192.00/26.69 | | | (409) nested_prop_atoms$(psi$) = all_1294_0 % 192.00/26.69 | | | (410) nested_prop_atoms$(all_1136_0) = all_1294_1 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (386) with fresh symbols all_1314_0, all_1314_1 % 192.00/26.69 | | | gives: % 192.00/26.69 | | | (411) less$(all_527_0, all_624_4) = all_1314_1 & less_eq$(all_624_4, % 192.00/26.69 | | | all_527_0) = all_1314_0 & ( ~ (all_1314_1 = 0) | (all_1108_0 = % 192.00/26.69 | | | 0 & ~ (all_1314_0 = 0))) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (411) implies: % 192.00/26.69 | | | (412) less_eq$(all_624_4, all_527_0) = all_1314_0 % 192.00/26.69 | | | (413) less$(all_527_0, all_624_4) = all_1314_1 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (385) with fresh symbols all_1316_0, all_1316_1 % 192.00/26.69 | | | gives: % 192.00/26.69 | | | (414) less$(all_527_3, all_527_0) = all_1316_1 & less_eq$(all_527_3, % 192.00/26.69 | | | all_527_0) = all_1316_0 & ( ~ (all_1316_1 = 0) | (all_1316_0 = % 192.00/26.69 | | | 0 & ~ (all_1044_0 = 0))) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (414) implies: % 192.00/26.69 | | | (415) less_eq$(all_527_3, all_527_0) = all_1316_0 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (394) with fresh symbols all_1330_0, all_1330_1, % 192.00/26.69 | | | all_1330_2, all_1330_3, all_1330_4 gives: % 192.00/26.69 | | | (416) fun_app$s(all_499_0, nil$) = all_1330_4 & % 192.00/26.69 | | | fun_app$e(ltl_prop_equiv$, all_1330_4) = all_1330_3 & % 192.00/26.69 | | | fun_app$e(ltl_prop_equiv$, true_ltln$) = all_1330_1 & % 192.00/26.69 | | | fun_app$(all_1330_1, false_ltln$) = all_1330_0 & % 192.00/26.69 | | | fun_app$(all_1330_3, false_ltln$) = all_1330_2 & % 192.00/26.69 | | | A_ltln$(all_1330_4) & A_ltln_bool_fun$(all_1330_1) & % 192.00/26.69 | | | A_ltln_bool_fun$(all_1330_3) & ( ~ (all_1330_2 = 0) | all_1330_0 % 192.00/26.69 | | | = 0) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (416) implies: % 192.00/26.69 | | | (417) A_ltln$(all_1330_4) % 192.00/26.69 | | | (418) fun_app$s(all_499_0, nil$) = all_1330_4 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (391) with fresh symbols all_1332_0, all_1332_1, % 192.00/26.69 | | | all_1332_2, all_1332_3, all_1332_4 gives: % 192.00/26.69 | | | (419) fun_app$s(all_499_0, nil$) = all_1332_4 & fun_app$e(eq$, % 192.00/26.69 | | | all_1332_4) = all_1332_3 & fun_app$e(eq$, true_ltln$) = % 192.00/26.69 | | | all_1332_1 & fun_app$(all_1332_1, true_ltln$) = all_1332_0 & % 192.00/26.69 | | | fun_app$(all_1332_3, true_ltln$) = all_1332_2 & % 192.00/26.69 | | | A_ltln$(all_1332_4) & A_ltln_bool_fun$(all_1332_1) & % 192.00/26.69 | | | A_ltln_bool_fun$(all_1332_3) & ( ~ (all_1332_2 = 0) | all_1332_0 % 192.00/26.69 | | | = 0) % 192.00/26.69 | | | % 192.00/26.69 | | | ALPHA: (419) implies: % 192.00/26.69 | | | (420) fun_app$s(all_499_0, nil$) = all_1332_4 % 192.00/26.69 | | | % 192.00/26.69 | | | DELTA: instantiating (390) with fresh symbols all_1334_0, all_1334_1, % 192.00/26.69 | | | all_1334_2, all_1334_3, all_1334_4 gives: % 192.00/26.70 | | | (421) fun_app$s(all_499_0, nil$) = all_1334_4 & % 192.00/26.70 | | | fun_app$e(ltl_lang_equiv$, all_1334_4) = all_1334_3 & % 192.00/26.70 | | | fun_app$e(ltl_lang_equiv$, true_ltln$) = all_1334_1 & % 192.00/26.70 | | | fun_app$(all_1334_1, false_ltln$) = all_1334_0 & % 192.00/26.70 | | | fun_app$(all_1334_3, false_ltln$) = all_1334_2 & % 192.00/26.70 | | | A_ltln$(all_1334_4) & A_ltln_bool_fun$(all_1334_1) & % 192.00/26.70 | | | A_ltln_bool_fun$(all_1334_3) & ( ~ (all_1334_2 = 0) | all_1334_0 % 192.00/26.70 | | | = 0) % 192.00/26.70 | | | % 192.00/26.70 | | | ALPHA: (421) implies: % 192.00/26.70 | | | (422) fun_app$s(all_499_0, nil$) = all_1334_4 % 192.00/26.70 | | | % 192.00/26.70 | | | DELTA: instantiating (393) with fresh symbols all_1336_0, all_1336_1, % 192.00/26.70 | | | all_1336_2, all_1336_3, all_1336_4 gives: % 192.00/26.70 | | | (423) fun_app$s(all_499_0, nil$) = all_1336_4 & % 192.00/26.70 | | | fun_app$e(ltl_prop_equiv$, all_1336_4) = all_1336_3 & % 192.00/26.70 | | | fun_app$e(ltl_prop_equiv$, true_ltln$) = all_1336_1 & % 192.00/26.70 | | | fun_app$(all_1336_1, true_ltln$) = all_1336_0 & % 192.00/26.70 | | | fun_app$(all_1336_3, true_ltln$) = all_1336_2 & % 192.00/26.70 | | | A_ltln$(all_1336_4) & A_ltln_bool_fun$(all_1336_1) & % 192.00/26.70 | | | A_ltln_bool_fun$(all_1336_3) & ( ~ (all_1336_2 = 0) | all_1336_0 % 192.00/26.70 | | | = 0) % 192.00/26.70 | | | % 192.00/26.70 | | | ALPHA: (423) implies: % 192.09/26.70 | | | (424) fun_app$s(all_499_0, nil$) = all_1336_4 % 192.09/26.70 | | | % 192.09/26.70 | | | DELTA: instantiating (392) with fresh symbols all_1338_0, all_1338_1, % 192.09/26.70 | | | all_1338_2, all_1338_3, all_1338_4 gives: % 192.09/26.70 | | | (425) fun_app$s(all_499_0, nil$) = all_1338_4 & fun_app$e(eq$, % 192.09/26.70 | | | all_1338_4) = all_1338_3 & fun_app$e(eq$, true_ltln$) = % 192.09/26.70 | | | all_1338_1 & fun_app$(all_1338_1, false_ltln$) = all_1338_0 & % 192.09/26.70 | | | fun_app$(all_1338_3, false_ltln$) = all_1338_2 & % 192.09/26.70 | | | A_ltln$(all_1338_4) & A_ltln_bool_fun$(all_1338_1) & % 192.09/26.70 | | | A_ltln_bool_fun$(all_1338_3) & ( ~ (all_1338_2 = 0) | all_1338_0 % 192.09/26.70 | | | = 0) % 192.09/26.70 | | | % 192.09/26.70 | | | ALPHA: (425) implies: % 192.09/26.70 | | | (426) fun_app$s(all_499_0, nil$) = all_1338_4 % 192.09/26.70 | | | % 192.09/26.70 | | | DELTA: instantiating (389) with fresh symbols all_1342_0, all_1342_1, % 192.09/26.70 | | | all_1342_2, all_1342_3, all_1342_4 gives: % 192.09/26.70 | | | (427) fun_app$s(all_499_0, nil$) = all_1342_4 & % 192.09/26.70 | | | fun_app$e(ltl_lang_equiv$, all_1342_4) = all_1342_3 & % 192.09/26.70 | | | fun_app$e(ltl_lang_equiv$, true_ltln$) = all_1342_1 & % 192.09/26.70 | | | fun_app$(all_1342_1, true_ltln$) = all_1342_0 & % 192.09/26.70 | | | fun_app$(all_1342_3, true_ltln$) = all_1342_2 & % 192.09/26.70 | | | A_ltln$(all_1342_4) & A_ltln_bool_fun$(all_1342_1) & % 192.09/26.70 | | | A_ltln_bool_fun$(all_1342_3) & ( ~ (all_1342_2 = 0) | all_1342_0 % 192.09/26.70 | | | = 0) % 192.09/26.70 | | | % 192.09/26.70 | | | ALPHA: (427) implies: % 192.09/26.70 | | | (428) fun_app$s(all_499_0, nil$) = all_1342_4 % 192.09/26.70 | | | % 192.09/26.70 | | | BETA: splitting (387) gives: % 192.09/26.70 | | | % 192.09/26.70 | | | Case 1: % 192.09/26.70 | | | | % 192.09/26.70 | | | | (429) all_1156_0 = 0 % 192.09/26.70 | | | | % 192.09/26.70 | | | | REDUCE: (372), (429) imply: % 192.09/26.70 | | | | (430) $false % 192.09/26.70 | | | | % 192.09/26.70 | | | | CLOSE: (430) is inconsistent. % 192.09/26.70 | | | | % 192.09/26.70 | | | Case 2: % 192.09/26.70 | | | | % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (78) with 0, all_1316_0, all_527_0, % 192.09/26.70 | | | | all_527_3, simplifying with (94), (415) gives: % 192.09/26.70 | | | | (431) all_1316_0 = 0 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (78) with all_624_0, all_1314_0, all_527_0, % 192.09/26.70 | | | | all_624_4, simplifying with (315), (412) gives: % 192.09/26.70 | | | | (432) all_1314_0 = all_624_0 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (74) with all_527_3, all_1294_0, psi$, % 192.09/26.70 | | | | simplifying with (95), (409) gives: % 192.09/26.70 | | | | (433) all_1294_0 = all_527_3 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (79) with all_1134_1, all_1260_0, psi$, % 192.09/26.70 | | | | normalise$, simplifying with (352), (404) gives: % 192.09/26.70 | | | | (434) all_1260_0 = all_1134_1 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (80) with all_1136_4, all_1256_0, psi$, eq$, % 192.09/26.70 | | | | simplifying with (356), (400) gives: % 192.09/26.70 | | | | (435) all_1256_0 = all_1136_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with all_1334_4, all_1336_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (422), (424) gives: % 192.09/26.70 | | | | (436) all_1336_4 = all_1334_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with all_1332_4, all_1336_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (420), (424) gives: % 192.09/26.70 | | | | (437) all_1336_4 = all_1332_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with true_ltln$, all_1338_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (331), (426) gives: % 192.09/26.70 | | | | (438) all_1338_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with all_1336_4, all_1338_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (424), (426) gives: % 192.09/26.70 | | | | (439) all_1338_4 = all_1336_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with all_1336_4, all_1342_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (424), (428) gives: % 192.09/26.70 | | | | (440) all_1342_4 = all_1336_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (81) with all_1330_4, all_1342_4, nil$, % 192.09/26.70 | | | | all_499_0, simplifying with (418), (428) gives: % 192.09/26.70 | | | | (441) all_1342_4 = all_1330_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | GROUND_INST: instantiating (83) with all_1112_1, all_1314_1, all_624_4, % 192.09/26.70 | | | | all_527_0, simplifying with (347), (413) gives: % 192.09/26.70 | | | | (442) all_1314_1 = all_1112_1 % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (440), (441) imply: % 192.09/26.70 | | | | (443) all_1336_4 = all_1330_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | SIMP: (443) implies: % 192.09/26.70 | | | | (444) all_1336_4 = all_1330_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (438), (439) imply: % 192.09/26.70 | | | | (445) all_1336_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | SIMP: (445) implies: % 192.09/26.70 | | | | (446) all_1336_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (436), (446) imply: % 192.09/26.70 | | | | (447) all_1334_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (436), (444) imply: % 192.09/26.70 | | | | (448) all_1334_4 = all_1330_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (436), (437) imply: % 192.09/26.70 | | | | (449) all_1334_4 = all_1332_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (448), (449) imply: % 192.09/26.70 | | | | (450) all_1332_4 = all_1330_4 % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (447), (449) imply: % 192.09/26.70 | | | | (451) all_1332_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | COMBINE_EQS: (450), (451) imply: % 192.09/26.70 | | | | (452) all_1330_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | SIMP: (452) implies: % 192.09/26.70 | | | | (453) all_1330_4 = true_ltln$ % 192.09/26.70 | | | | % 192.09/26.70 | | | | REDUCE: (408), (433) imply: % 192.09/26.70 | | | | (454) less_eq$(all_1294_1, all_527_3) = 0 % 192.09/26.70 | | | | % 192.09/26.70 | | | | REDUCE: (403), (434) imply: % 192.09/26.70 | | | | (455) fun_app$(all_1136_4, all_1134_1) = 0 % 192.09/26.70 | | | | % 192.09/26.70 | | | | REDUCE: (402), (434) imply: % 192.09/26.70 | | | | (456) A_ltln$(all_1134_1) % 192.09/26.70 | | | | % 192.09/26.70 | | | | BETA: splitting (398) gives: % 192.09/26.70 | | | | % 192.09/26.70 | | | | Case 1: % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | (457) all_1108_1 = 0 % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | REDUCE: (384), (457) imply: % 192.09/26.70 | | | | | (458) $false % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | CLOSE: (458) is inconsistent. % 192.09/26.70 | | | | | % 192.09/26.70 | | | | Case 2: % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | (459) ? [v0: any] : (less_eq$(all_624_4, all_527_0) = v0 & ( ~ (v0 % 192.09/26.70 | | | | | = 0) | all_624_4 = all_527_0) & ( ~ (all_624_4 = % 192.09/26.70 | | | | | all_527_0) | v0 = 0)) % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | DELTA: instantiating (459) with fresh symbol all_1449_0 gives: % 192.09/26.70 | | | | | (460) less_eq$(all_624_4, all_527_0) = all_1449_0 & ( ~ (all_1449_0 % 192.09/26.70 | | | | | = 0) | all_624_4 = all_527_0) & ( ~ (all_624_4 = % 192.09/26.70 | | | | | all_527_0) | all_1449_0 = 0) % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | ALPHA: (460) implies: % 192.09/26.70 | | | | | (461) less_eq$(all_624_4, all_527_0) = all_1449_0 % 192.09/26.70 | | | | | (462) ~ (all_624_4 = all_527_0) | all_1449_0 = 0 % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | GROUND_INST: instantiating (78) with all_624_0, all_1449_0, all_527_0, % 192.09/26.70 | | | | | all_624_4, simplifying with (315), (461) gives: % 192.09/26.70 | | | | | (463) all_1449_0 = all_624_0 % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | BETA: splitting (462) gives: % 192.09/26.70 | | | | | % 192.09/26.70 | | | | | Case 1: % 192.09/26.70 | | | | | | % 192.09/26.70 | | | | | | (464) ~ (all_624_4 = all_527_0) % 192.09/26.70 | | | | | | % 192.09/26.70 | | | | | | BETA: splitting (322) gives: % 192.09/26.70 | | | | | | % 192.09/26.70 | | | | | | Case 1: % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | (465) all_624_0 = 0 % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | REDUCE: (106), (465) imply: % 192.09/26.70 | | | | | | | (466) $false % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | CLOSE: (466) is inconsistent. % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | Case 2: % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | (467) ? [v0: any] : ? [v1: any] : (less$(all_527_0, % 192.09/26.70 | | | | | | | all_624_4) = v1 & less_eq$(all_527_0, all_624_4) = v0 % 192.09/26.70 | | | | | | | & ( ~ (v0 = 0) | v1 = 0)) % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | DELTA: instantiating (467) with fresh symbols all_1647_0, % 192.09/26.70 | | | | | | | all_1647_1 gives: % 192.09/26.70 | | | | | | | (468) less$(all_527_0, all_624_4) = all_1647_0 & % 192.09/26.70 | | | | | | | less_eq$(all_527_0, all_624_4) = all_1647_1 & ( ~ % 192.09/26.70 | | | | | | | (all_1647_1 = 0) | all_1647_0 = 0) % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | ALPHA: (468) implies: % 192.09/26.70 | | | | | | | (469) less$(all_527_0, all_624_4) = all_1647_0 % 192.09/26.70 | | | | | | | (470) ~ (all_1647_1 = 0) | all_1647_0 = 0 % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | GROUND_INST: instantiating (83) with all_1112_1, all_1647_0, % 192.09/26.70 | | | | | | | all_624_4, all_527_0, simplifying with (347), (469) % 192.09/26.70 | | | | | | | gives: % 192.09/26.70 | | | | | | | (471) all_1647_0 = all_1112_1 % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | BETA: splitting (348) gives: % 192.09/26.70 | | | | | | | % 192.09/26.70 | | | | | | | Case 1: % 192.09/26.70 | | | | | | | | % 192.09/26.70 | | | | | | | | (472) ~ (all_1112_1 = 0) % 192.09/26.70 | | | | | | | | % 192.09/26.70 | | | | | | | | BETA: splitting (397) gives: % 192.09/26.70 | | | | | | | | % 192.09/26.70 | | | | | | | | Case 1: % 192.09/26.70 | | | | | | | | | % 192.09/26.70 | | | | | | | | | (473) all_1112_1 = 0 % 192.09/26.70 | | | | | | | | | % 192.09/26.70 | | | | | | | | | REDUCE: (472), (473) imply: % 192.09/26.70 | | | | | | | | | (474) $false % 192.09/26.70 | | | | | | | | | % 192.09/26.70 | | | | | | | | | CLOSE: (474) is inconsistent. % 192.09/26.70 | | | | | | | | | % 192.09/26.70 | | | | | | | | Case 2: % 192.09/26.70 | | | | | | | | | % 192.09/26.71 | | | | | | | | | (475) ? [v0: any] : ? [v1: any] : (less_eq$(all_624_4, % 192.09/26.71 | | | | | | | | | all_527_0) = v1 & less_eq$(all_527_0, all_624_4) % 192.09/26.71 | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 192.09/26.71 | | | | | | | | | % 192.09/26.71 | | | | | | | | | DELTA: instantiating (475) with fresh symbols all_1677_0, % 192.09/26.71 | | | | | | | | | all_1677_1 gives: % 192.09/26.71 | | | | | | | | | (476) less_eq$(all_624_4, all_527_0) = all_1677_0 & % 192.09/26.71 | | | | | | | | | less_eq$(all_527_0, all_624_4) = all_1677_1 & ( ~ % 192.09/26.71 | | | | | | | | | (all_1677_1 = 0) | all_1677_0 = 0) % 192.09/26.71 | | | | | | | | | % 192.09/26.71 | | | | | | | | | ALPHA: (476) implies: % 192.09/26.71 | | | | | | | | | (477) less_eq$(all_624_4, all_527_0) = all_1677_0 % 192.09/26.71 | | | | | | | | | % 192.09/26.71 | | | | | | | | | BETA: splitting (470) gives: % 192.09/26.71 | | | | | | | | | % 192.09/26.71 | | | | | | | | | Case 1: % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | GROUND_INST: instantiating (78) with all_624_0, all_1677_0, % 192.09/26.71 | | | | | | | | | | all_527_0, all_624_4, simplifying with (315), % 192.09/26.71 | | | | | | | | | | (477) gives: % 192.09/26.71 | | | | | | | | | | (478) all_1677_0 = all_624_0 % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | GROUND_INST: instantiating (5) with eq$, psi$, all_1134_1, % 192.09/26.71 | | | | | | | | | | true_ltln$, all_1136_4, all_1136_3, simplifying % 192.09/26.71 | | | | | | | | | | with (69), (70), (72), (354), (356), (455), (456) % 192.09/26.71 | | | | | | | | | | gives: % 192.09/26.71 | | | | | | | | | | (479) all_1136_3 = 0 | ? [v0: any] : ? [v1: % 192.09/26.71 | | | | | | | | | | A_ltln_bool_fun$] : ? [v2: any] : % 192.09/26.71 | | | | | | | | | | (ltl_equivalence$(eq$) = v0 & fun_app$e(eq$, % 192.09/26.71 | | | | | | | | | | all_1134_1) = v1 & fun_app$(v1, true_ltln$) = % 192.09/26.71 | | | | | | | | | | v2 & A_ltln_bool_fun$(v1) & ( ~ (v2 = 0) | ~ (v0 % 192.09/26.71 | | | | | | | | | | = 0))) % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | GROUND_INST: instantiating (7) with all_527_3, all_527_0, % 192.09/26.71 | | | | | | | | | | all_1294_1, simplifying with (93), (94), (316), % 192.09/26.71 | | | | | | | | | | (406), (454) gives: % 192.09/26.71 | | | | | | | | | | (480) less_eq$(all_1294_1, all_527_0) = 0 % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | REF_CLOSE: (74), (78), (96), (106), (110), (315), (359), % 192.09/26.71 | | | | | | | | | | (360), (378), (410), (464), (479), (480) are % 192.09/26.71 | | | | | | | | | | inconsistent by sub-proof #1. % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | Case 2: % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | (481) all_1647_0 = 0 % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | COMBINE_EQS: (471), (481) imply: % 192.09/26.71 | | | | | | | | | | (482) all_1112_1 = 0 % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | REDUCE: (472), (482) imply: % 192.09/26.71 | | | | | | | | | | (483) $false % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | | CLOSE: (483) is inconsistent. % 192.09/26.71 | | | | | | | | | | % 192.09/26.71 | | | | | | | | | End of split % 192.09/26.71 | | | | | | | | | % 192.09/26.71 | | | | | | | | End of split % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | Case 2: % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | | (484) all_1112_0 = 0 & ~ (all_624_0 = 0) % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | | GROUND_INST: instantiating (5) with eq$, psi$, all_1134_1, % 192.09/26.71 | | | | | | | | true_ltln$, all_1136_4, all_1136_3, simplifying % 192.09/26.71 | | | | | | | | with (69), (70), (72), (354), (356), (455), (456) % 192.09/26.71 | | | | | | | | gives: % 192.09/26.71 | | | | | | | | (485) all_1136_3 = 0 | ? [v0: any] : ? [v1: % 192.09/26.71 | | | | | | | | A_ltln_bool_fun$] : ? [v2: any] : % 192.09/26.71 | | | | | | | | (ltl_equivalence$(eq$) = v0 & fun_app$e(eq$, % 192.09/26.71 | | | | | | | | all_1134_1) = v1 & fun_app$(v1, true_ltln$) = v2 & % 192.09/26.71 | | | | | | | | A_ltln_bool_fun$(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | | GROUND_INST: instantiating (7) with all_527_3, all_527_0, % 192.09/26.71 | | | | | | | | all_1294_1, simplifying with (93), (94), (316), % 192.09/26.71 | | | | | | | | (406), (454) gives: % 192.09/26.71 | | | | | | | | (486) less_eq$(all_1294_1, all_527_0) = 0 % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | | REF_CLOSE: (74), (78), (96), (106), (110), (315), (359), (360), % 192.09/26.71 | | | | | | | | (378), (410), (464), (485), (486) are inconsistent by % 192.09/26.71 | | | | | | | | sub-proof #1. % 192.09/26.71 | | | | | | | | % 192.09/26.71 | | | | | | | End of split % 192.09/26.71 | | | | | | | % 192.09/26.71 | | | | | | End of split % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | Case 2: % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | | (487) all_1449_0 = 0 % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | | COMBINE_EQS: (463), (487) imply: % 192.09/26.71 | | | | | | (488) all_624_0 = 0 % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | | REDUCE: (106), (488) imply: % 192.09/26.71 | | | | | | (489) $false % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | | CLOSE: (489) is inconsistent. % 192.09/26.71 | | | | | | % 192.09/26.71 | | | | | End of split % 192.09/26.71 | | | | | % 192.09/26.71 | | | | End of split % 192.09/26.71 | | | | % 192.09/26.71 | | | End of split % 192.09/26.71 | | | % 192.09/26.71 | | End of split % 192.09/26.71 | | % 192.09/26.71 | End of split % 192.09/26.71 | % 192.09/26.71 End of proof % 192.09/26.71 % 192.09/26.71 Sub-proof #1 shows that the following formulas are inconsistent: % 192.09/26.71 ---------------------------------------------------------------- % 192.09/26.71 (1) less_eq$(all_1294_1, all_527_0) = 0 % 192.09/26.71 (2) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = v0 % 192.09/26.71 | ~ (nested_prop_atoms$(v2) = v1) | ~ (nested_prop_atoms$(v2) = v0)) % 192.09/26.71 (3) less_eq$(all_624_4, all_527_0) = all_624_0 % 192.09/26.71 (4) nested_prop_atoms$(all_624_5) = all_624_4 % 192.09/26.71 (5) all_1136_2 = all_527_1 % 192.09/26.71 (6) all_1136_3 = 0 | ? [v0: any] : ? [v1: A_ltln_bool_fun$] : ? [v2: any] % 192.09/26.71 : (ltl_equivalence$(eq$) = v0 & fun_app$e(eq$, all_1134_1) = v1 & % 192.09/26.71 fun_app$(v1, true_ltln$) = v2 & A_ltln_bool_fun$(v1) & ( ~ (v2 = 0) | % 192.09/26.71 ~ (v0 = 0))) % 192.09/26.71 (7) nested_prop_atoms$(all_527_1) = all_527_0 % 192.09/26.71 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.09/26.71 A_ltln_set$] : ! [v3: A_ltln_set$] : (v1 = v0 | ~ (less_eq$(v3, v2) = % 192.09/26.71 v1) | ~ (less_eq$(v3, v2) = v0)) % 192.09/26.71 (9) all_1136_0 = all_624_5 | all_1136_3 = 0 % 192.09/26.71 (10) ~ (all_1136_3 = 0) | all_1136_2 = all_624_5 % 192.09/26.71 (11) ~ (all_624_0 = 0) % 192.09/26.71 (12) nested_prop_atoms$(all_1136_0) = all_1294_1 % 192.09/26.71 (13) ~ (all_624_4 = all_527_0) % 192.09/26.71 % 192.09/26.71 Begin of proof % 192.09/26.71 | % 192.09/26.71 | BETA: splitting (10) gives: % 192.09/26.71 | % 192.09/26.71 | Case 1: % 192.09/26.71 | | % 192.09/26.71 | | (14) ~ (all_1136_3 = 0) % 192.09/26.71 | | % 192.09/26.71 | | BETA: splitting (9) gives: % 192.09/26.71 | | % 192.09/26.71 | | Case 1: % 192.09/26.71 | | | % 192.09/26.71 | | | (15) all_1136_3 = 0 % 192.09/26.71 | | | % 192.09/26.71 | | | REDUCE: (14), (15) imply: % 192.09/26.71 | | | (16) $false % 192.09/26.71 | | | % 192.09/26.71 | | | CLOSE: (16) is inconsistent. % 192.09/26.71 | | | % 192.09/26.71 | | Case 2: % 192.09/26.71 | | | % 192.09/26.71 | | | (17) all_1136_0 = all_624_5 % 192.09/26.71 | | | % 192.09/26.71 | | | REDUCE: (12), (17) imply: % 192.09/26.71 | | | (18) nested_prop_atoms$(all_624_5) = all_1294_1 % 192.09/26.71 | | | % 192.09/26.71 | | | BETA: splitting (6) gives: % 192.09/26.71 | | | % 192.09/26.71 | | | Case 1: % 192.09/26.71 | | | | % 192.09/26.71 | | | | (19) all_1136_3 = 0 % 192.09/26.71 | | | | % 192.09/26.71 | | | | REDUCE: (14), (19) imply: % 192.09/26.71 | | | | (20) $false % 192.09/26.71 | | | | % 192.09/26.71 | | | | CLOSE: (20) is inconsistent. % 192.09/26.71 | | | | % 192.09/26.71 | | | Case 2: % 192.09/26.71 | | | | % 192.09/26.71 | | | | % 192.09/26.71 | | | | GROUND_INST: instantiating (2) with all_624_4, all_1294_1, all_624_5, % 192.09/26.71 | | | | simplifying with (4), (18) gives: % 192.20/26.71 | | | | (21) all_1294_1 = all_624_4 % 192.20/26.71 | | | | % 192.20/26.71 | | | | REDUCE: (1), (21) imply: % 192.20/26.71 | | | | (22) less_eq$(all_624_4, all_527_0) = 0 % 192.20/26.71 | | | | % 192.20/26.72 | | | | GROUND_INST: instantiating (8) with all_624_0, 0, all_527_0, all_624_4, % 192.20/26.72 | | | | simplifying with (3), (22) gives: % 192.20/26.72 | | | | (23) all_624_0 = 0 % 192.20/26.72 | | | | % 192.20/26.72 | | | | REDUCE: (11), (23) imply: % 192.20/26.72 | | | | (24) $false % 192.20/26.72 | | | | % 192.20/26.72 | | | | CLOSE: (24) is inconsistent. % 192.20/26.72 | | | | % 192.20/26.72 | | | End of split % 192.20/26.72 | | | % 192.20/26.72 | | End of split % 192.20/26.72 | | % 192.20/26.72 | Case 2: % 192.20/26.72 | | % 192.20/26.72 | | (25) all_1136_2 = all_624_5 % 192.20/26.72 | | % 192.20/26.72 | | COMBINE_EQS: (5), (25) imply: % 192.20/26.72 | | (26) all_624_5 = all_527_1 % 192.20/26.72 | | % 192.20/26.72 | | SIMP: (26) implies: % 192.20/26.72 | | (27) all_624_5 = all_527_1 % 192.20/26.72 | | % 192.20/26.72 | | REDUCE: (4), (27) imply: % 192.20/26.72 | | (28) nested_prop_atoms$(all_527_1) = all_624_4 % 192.20/26.72 | | % 192.20/26.72 | | GROUND_INST: instantiating (2) with all_527_0, all_624_4, all_527_1, % 192.20/26.72 | | simplifying with (7), (28) gives: % 192.20/26.72 | | (29) all_624_4 = all_527_0 % 192.20/26.72 | | % 192.20/26.72 | | REDUCE: (13), (29) imply: % 192.20/26.72 | | (30) $false % 192.20/26.72 | | % 192.20/26.72 | | CLOSE: (30) is inconsistent. % 192.20/26.72 | | % 192.20/26.72 | End of split % 192.20/26.72 | % 192.20/26.72 End of proof % 192.20/26.72 % SZS output end Proof for theBenchmark % 192.20/26.72 % 192.20/26.72 26080ms %------------------------------------------------------------------------------