%------------------------------------------------------------------------------ % 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 : n022.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 151.06s 20.84s % Output : Proof 152.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n022.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 12:14:09 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 14.17/2.66 Prover 4: Preprocessing ... % 14.17/2.66 Prover 1: Preprocessing ... % 15.33/2.80 Prover 6: Preprocessing ... % 15.33/2.80 Prover 0: Preprocessing ... % 15.33/2.81 Prover 5: Preprocessing ... % 15.33/2.83 Prover 3: Preprocessing ... % 15.33/2.84 Prover 2: Preprocessing ... % 35.96/5.49 Prover 3: Warning: ignoring some quantifiers % 35.96/5.52 Prover 6: Proving ... % 35.96/5.56 Prover 1: Warning: ignoring some quantifiers % 35.96/5.59 Prover 3: Constructing countermodel ... % 37.92/5.76 Prover 1: Constructing countermodel ... % 41.68/6.33 Prover 0: Proving ... % 41.68/6.38 Prover 4: Warning: ignoring some quantifiers % 44.14/6.58 Prover 4: Constructing countermodel ... % 45.43/6.80 Prover 5: Proving ... % 51.90/7.66 Prover 2: Proving ... % 99.32/13.96 Prover 5: stopped % 99.32/13.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 104.45/14.58 Prover 7: Preprocessing ... % 105.47/14.81 Prover 2: stopped % 106.11/14.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 110.47/15.48 Prover 8: Preprocessing ... % 115.84/16.03 Prover 1: stopped % 115.84/16.04 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.84/16.10 Prover 7: Warning: ignoring some quantifiers % 116.59/16.18 Prover 7: Constructing countermodel ... % 117.78/16.31 Prover 8: Warning: ignoring some quantifiers % 119.07/16.46 Prover 8: Constructing countermodel ... % 120.85/16.69 Prover 9: Preprocessing ... % 129.22/17.87 Prover 6: stopped % 129.22/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.36/18.24 Prover 9: Warning: ignoring some quantifiers % 133.22/18.30 Prover 9: Constructing countermodel ... % 134.54/18.54 Prover 10: Preprocessing ... % 139.23/19.16 Prover 10: Warning: ignoring some quantifiers % 139.94/19.22 Prover 10: Constructing countermodel ... % 149.38/20.51 Prover 7: Found proof (size 296) % 149.38/20.51 Prover 7: proved (6470ms) % 149.38/20.51 Prover 9: stopped % 149.38/20.51 Prover 8: stopped % 149.38/20.51 Prover 10: stopped % 149.38/20.52 Prover 0: stopped % 149.38/20.52 Prover 4: stopped % 151.06/20.83 Prover 3: stopped % 151.06/20.83 % 151.06/20.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 151.06/20.84 % 151.28/20.94 % SZS output start Proof for theBenchmark % 151.46/20.96 Assumptions after simplification: % 151.46/20.96 --------------------------------- % 151.46/20.96 % 151.46/20.96 (axiom13) % 151.50/20.98 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.50/20.98 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.50/20.98 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 151.50/20.98 ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ % 151.50/20.98 (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 151.50/20.98 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.50/20.99 A_ltln$(v2) | ~ fun_app$(v4, v7) | ? [v8: A_ltln$] : (fun_app$a(v0, v3) % 151.50/20.99 = v8 & A_ltln$(v8) & fun_app$(v4, v8))) & ! [v1: Nat_a_set_fun$] : ! % 151.50/20.99 [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.50/20.99 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 151.50/20.99 (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, % 151.50/20.99 v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.50/20.99 A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v7) | ? [v8: A_ltln$] : % 151.50/20.99 (fun_app$a(v0, v3) = v8 & A_ltln$(v8) & ~ fun_app$(v4, v8)))) % 151.50/20.99 % 151.50/20.99 (axiom17) % 151.50/20.99 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.50/20.99 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.50/20.99 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.50/20.99 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! % 151.50/20.99 [v7: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.50/20.99 ~ (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.50/20.99 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v7) % 151.50/20.99 | ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & A_ltln$(v8) & fun_app$(v4, % 151.50/20.99 v8))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] % 151.50/20.99 : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 151.50/20.99 : ! [v7: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 151.50/20.99 v6) | ~ (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.50/20.99 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v7) | % 151.50/20.99 ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & A_ltln$(v8) & ~ fun_app$(v4, % 151.50/20.99 v8)))) % 151.50/20.99 % 151.50/20.99 (axiom208) % 151.50/21.00 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.50/21.00 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.50/21.00 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 151.50/21.00 ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 151.50/21.00 v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.50/21.00 A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? % 151.50/21.00 [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ((until_ltln$(v2) = v8 & % 151.50/21.00 fun_app$a(v8, v3) = v9 & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & % 151.50/21.00 fun_app$(v4, v9)) | (fun_app$a(v0, v3) = v7 & A_ltln$(v7) & ~ % 151.50/21.00 fun_app$(v4, v7)))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.50/21.00 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.50/21.00 [v6: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.50/21.00 ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.50/21.00 A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln_a_ltln_fun$] : ? [v8: % 151.50/21.00 A_ltln$] : ? [v9: A_ltln$] : ((weakUntil_ltln$(v2) = v7 & fun_app$a(v7, % 151.50/21.00 v3) = v8 & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, % 151.50/21.00 v8)) | (fun_app$a(v0, v3) = v9 & A_ltln$(v9) & ~ fun_app$(v4, % 151.50/21.00 v9))))) % 151.50/21.00 % 151.50/21.00 (axiom209) % 151.50/21.00 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.50/21.00 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.50/21.00 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.50/21.00 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 151.50/21.00 (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.50/21.00 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.50/21.00 A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln_a_ltln_fun$] : ? [v8: % 151.50/21.00 A_ltln$] : ? [v9: A_ltln$] : ((release_ltln$(v2) = v7 & fun_app$a(v7, % 151.50/21.00 v3) = v8 & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, % 151.50/21.00 v8)) | (fun_app$a(v0, v3) = v9 & A_ltln$(v9) & fun_app$(v4, v9)))) & % 151.50/21.00 ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.50/21.00 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 151.50/21.00 (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.50/21.00 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.50/21.00 A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.50/21.00 A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ((strongRelease_ltln$(v2) = v8 % 151.50/21.00 & fun_app$a(v8, v3) = v9 & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & % 151.50/21.00 fun_app$(v4, v9)) | (fun_app$a(v0, v3) = v7 & A_ltln$(v7) & % 151.50/21.00 fun_app$(v4, v7))))) % 151.50/21.00 % 151.50/21.00 (axiom218) % 151.61/21.01 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.61/21.01 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.61/21.01 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.61/21.01 A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] : ! % 151.61/21.01 [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] : ( ~ % 151.61/21.01 (or_ltln$(v5) = v6) | ~ (until_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = % 151.61/21.01 v8) | ~ (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v2) = v5) | ~ % 151.61/21.01 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.61/21.01 A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: A_ltln_a_ltln_fun$] : ? % 151.61/21.01 [v11: A_ltln$] : (weakUntil_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 151.61/21.01 A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & fun_app$(v4, v11))) & ! [v1: % 151.61/21.01 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.61/21.01 A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] : ! % 151.61/21.01 [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] : ( ~ % 151.61/21.01 (or_ltln$(v5) = v6) | ~ (until_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = % 151.61/21.01 v8) | ~ (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v2) = v5) | ~ % 151.61/21.01 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.61/21.01 A_ltln$(v2) | fun_app$(v4, v9) | ? [v10: A_ltln_a_ltln_fun$] : ? [v11: % 151.61/21.01 A_ltln$] : (weakUntil_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 151.61/21.01 A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ fun_app$(v4, v11))) & ! % 151.61/21.01 [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.61/21.01 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 151.61/21.01 (weakUntil_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.61/21.01 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.61/21.01 A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.61/21.01 A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : % 151.61/21.01 ? [v11: A_ltln$] : (or_ltln$(v7) = v8 & until_ltln$(v2) = v9 & % 151.61/21.01 fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v2) = % 151.61/21.01 v7 & A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) % 151.61/21.01 & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] % 151.61/21.01 : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.61/21.01 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v5) | % 151.61/21.02 ~ (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.61/21.02 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | % 151.61/21.02 ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.61/21.02 A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 151.61/21.02 (or_ltln$(v7) = v8 & until_ltln$(v2) = v9 & fun_app$a(v9, v3) = v10 & % 151.61/21.02 fun_app$a(v8, v10) = v11 & fun_app$a(v0, v2) = v7 & A_ltln$(v11) & % 151.61/21.02 A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & % 151.61/21.02 A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v11)))) % 151.61/21.02 % 151.61/21.02 (axiom219) % 151.61/21.03 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.61/21.03 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.61/21.03 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 151.61/21.03 A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! % 151.61/21.03 [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ (release_ltln$(v2) = v7) | ~ % 151.61/21.03 (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, % 151.61/21.03 v2) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.61/21.03 A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 151.61/21.03 A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (strongRelease_ltln$(v2) = v10 % 151.61/21.03 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & % 151.61/21.03 fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.61/21.03 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 151.61/21.03 A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! % 151.61/21.03 [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ (release_ltln$(v2) = v7) | ~ % 151.61/21.03 (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, % 151.61/21.03 v2) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.61/21.03 A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v9) | ? [v10: % 151.61/21.03 A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (strongRelease_ltln$(v2) = v10 % 151.61/21.03 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ % 151.61/21.03 fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.61/21.03 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.61/21.03 [v6: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 151.61/21.03 v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.61/21.03 A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? % 151.61/21.03 [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 151.61/21.03 : ? [v11: A_ltln$] : (and_ltln$(v7) = v8 & release_ltln$(v2) = v9 & % 151.61/21.03 fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v2) = % 151.61/21.03 v7 & A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) % 151.61/21.03 & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] % 151.61/21.03 : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.61/21.03 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = % 151.61/21.03 v5) | ~ (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.61/21.03 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | % 151.61/21.03 ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.61/21.03 A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 151.61/21.03 (and_ltln$(v7) = v8 & release_ltln$(v2) = v9 & fun_app$a(v9, v3) = v10 & % 151.61/21.03 fun_app$a(v8, v10) = v11 & fun_app$a(v0, v2) = v7 & A_ltln$(v11) & % 151.61/21.03 A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & % 151.61/21.03 A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v11)))) % 151.61/21.03 % 151.61/21.03 (axiom221) % 151.69/21.04 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.69/21.04 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.69/21.04 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 151.69/21.04 ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (and_ltln$(v2) = v5) | ~ % 151.69/21.04 (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 151.69/21.04 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.04 A_ltln$(v2) | ~ fun_app$(v4, v7) | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.69/21.04 A_ltln$] : ? [v10: A_ltln$] : (strongRelease_ltln$(v2) = v8 & % 151.69/21.04 fun_app$a(v8, v3) = v9 & fun_app$a(v0, v9) = v10 & A_ltln$(v10) & % 151.69/21.04 A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v10))) & ! [v1: % 151.69/21.04 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.04 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! % 151.69/21.04 [v7: A_ltln$] : ( ~ (and_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.69/21.04 (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.04 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v7) | % 151.69/21.04 ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 151.69/21.04 (strongRelease_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & fun_app$a(v0, v9) % 151.69/21.04 = v10 & A_ltln$(v10) & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & ~ % 151.69/21.04 fun_app$(v4, v10))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.04 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.69/21.04 [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v5) | ~ % 151.69/21.04 (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 151.69/21.04 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.04 A_ltln$(v2) | ~ fun_app$(v4, v7) | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.69/21.04 A_ltln$] : ? [v10: A_ltln$] : (and_ltln$(v2) = v8 & fun_app$a(v8, v3) = % 151.69/21.04 v9 & fun_app$a(v0, v9) = v10 & A_ltln$(v10) & A_ltln$(v9) & % 151.69/21.04 A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v10))) & ! [v1: Nat_a_set_fun$] : % 151.69/21.04 ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.69/21.04 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 151.69/21.04 (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.69/21.04 (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.04 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v7) | % 151.69/21.04 ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 151.69/21.04 (and_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & fun_app$a(v0, v9) = v10 & % 151.69/21.04 A_ltln$(v10) & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, % 151.69/21.04 v10)))) % 151.69/21.04 % 151.69/21.04 (axiom222) % 151.69/21.05 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.05 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v1 & % 151.69/21.05 release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.05 A_ltln_a_ltln_fun$(v0) & ? [v2: A_ltln_set$] : ? [v3: A_ltln_set$] : ! % 151.69/21.05 [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: A_ltln_set$] : ( ~ % 151.69/21.05 (g_F$(v4, v5) = v6) | ~ Nat_a_set_fun$(v5) | ~ A_ltln$(v4) | ~ % 151.69/21.05 A_ltln_set$(v3) | ~ A_ltln_set$(v2) | ? [v7: A_ltln_set$] : ? [v8: % 151.69/21.05 A_ltln_set$] : ? [v9: A_ltln_bool_fun$] : ? [v10: A_ltln_set$] : ? % 151.69/21.05 [v11: A_ltln$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? [v14: A_ltln$] % 151.69/21.05 : ? [v15: A_ltln$] : ? [v16: A_ltln$] : ? [v17: A_ltln$] : ? [v18: % 151.69/21.05 A_ltln$] : (A_ltln$(v15) & A_ltln$(v11) & ((subformulas_mu$(v4) = v7 & % 151.69/21.05 A_ltln_set$(v7) & ~ less_eq$(v2, v7)) | (subformulas_nu$(v4) = v8 & % 151.69/21.05 A_ltln_set$(v8) & ~ less_eq$(v3, v8)) | (fG_advice$(v15, v3) = v16 % 151.69/21.05 & fun_app$a(v1, v16) = v17 & fun_app$a(v0, v17) = v18 & % 151.69/21.05 semantics_ltln$(v5) = v9 & A_ltln$(v18) & A_ltln$(v17) & % 151.69/21.05 A_ltln$(v16) & A_ltln_bool_fun$(v9) & member$(v15, v2) & ~ % 151.69/21.05 fun_app$(v9, v18)) | (fun_app$a(v1, v13) = v14 & fun_app$a(v0, v12) % 151.69/21.05 = v13 & gF_advice$(v11, v2) = v12 & semantics_ltln$(v5) = v9 & % 151.69/21.05 A_ltln$(v14) & A_ltln$(v13) & A_ltln$(v12) & A_ltln_bool_fun$(v9) & % 151.69/21.05 member$(v11, v3) & ~ fun_app$(v9, v14)) | (f_G$(v4, v5) = v10 & % 151.69/21.05 A_ltln_set$(v10) & less_eq$(v3, v10) & less_eq$(v2, v6))))) & ? % 151.69/21.05 [v2: A_ltln_set$] : ? [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! [v5: % 151.69/21.05 Nat_a_set_fun$] : ! [v6: A_ltln_set$] : ( ~ (f_G$(v4, v5) = v6) | ~ % 151.69/21.05 Nat_a_set_fun$(v5) | ~ A_ltln$(v4) | ~ A_ltln_set$(v3) | ~ % 151.69/21.05 A_ltln_set$(v2) | ? [v7: A_ltln_set$] : ? [v8: A_ltln_set$] : ? [v9: % 151.69/21.05 A_ltln_bool_fun$] : ? [v10: A_ltln_set$] : ? [v11: A_ltln$] : ? [v12: % 151.69/21.05 A_ltln$] : ? [v13: A_ltln$] : ? [v14: A_ltln$] : ? [v15: A_ltln$] : % 151.69/21.05 ? [v16: A_ltln$] : ? [v17: A_ltln$] : ? [v18: A_ltln$] : (A_ltln$(v15) & % 151.69/21.05 A_ltln$(v11) & ((subformulas_mu$(v4) = v7 & A_ltln_set$(v7) & ~ % 151.69/21.05 less_eq$(v2, v7)) | (subformulas_nu$(v4) = v8 & A_ltln_set$(v8) & ~ % 151.69/21.05 less_eq$(v3, v8)) | (fG_advice$(v15, v3) = v16 & fun_app$a(v1, v16) % 151.69/21.05 = v17 & fun_app$a(v0, v17) = v18 & semantics_ltln$(v5) = v9 & % 151.69/21.05 A_ltln$(v18) & A_ltln$(v17) & A_ltln$(v16) & A_ltln_bool_fun$(v9) & % 151.69/21.05 member$(v15, v2) & ~ fun_app$(v9, v18)) | (g_F$(v4, v5) = v10 & % 151.69/21.05 A_ltln_set$(v10) & less_eq$(v3, v6) & less_eq$(v2, v10)) | % 151.69/21.05 (fun_app$a(v1, v13) = v14 & fun_app$a(v0, v12) = v13 & gF_advice$(v11, % 151.69/21.05 v2) = v12 & semantics_ltln$(v5) = v9 & A_ltln$(v14) & A_ltln$(v13) % 151.69/21.05 & A_ltln$(v12) & A_ltln_bool_fun$(v9) & member$(v11, v3) & ~ % 151.69/21.05 fun_app$(v9, v14)))))) % 151.69/21.05 % 151.69/21.05 (axiom223) % 151.69/21.05 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.69/21.05 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.69/21.05 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 151.69/21.05 A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! % 151.69/21.05 [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ (weakUntil_ltln$(v2) = v7) | % 151.69/21.05 ~ (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 151.69/21.06 (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.06 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) % 151.69/21.06 | ? [v10: A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (until_ltln$(v2) = % 151.69/21.06 v10 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) % 151.69/21.06 & fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.06 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 151.69/21.06 A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! % 151.69/21.06 [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ (weakUntil_ltln$(v2) = v7) | % 151.69/21.06 ~ (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 151.69/21.06 (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.06 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v9) | % 151.69/21.06 ? [v10: A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (until_ltln$(v2) = v10 & % 151.69/21.06 fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ % 151.69/21.06 fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.06 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.69/21.06 [v6: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.69/21.06 ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.06 A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : % 151.69/21.06 ? [v11: A_ltln$] : (and_ltln$(v7) = v8 & weakUntil_ltln$(v2) = v9 & % 151.69/21.06 fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = % 151.69/21.06 v7 & A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) % 151.69/21.06 & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] % 151.69/21.06 : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.69/21.06 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ % 151.69/21.06 (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.06 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | % 151.69/21.06 ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 151.69/21.06 (and_ltln$(v7) = v8 & weakUntil_ltln$(v2) = v9 & fun_app$a(v9, v3) = v10 & % 151.69/21.06 fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = v7 & A_ltln$(v11) & % 151.69/21.06 A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & % 151.69/21.06 A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v11)))) % 151.69/21.06 % 151.69/21.06 (axiom245) % 151.69/21.06 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.69/21.06 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.69/21.06 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.06 A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] : ! % 151.69/21.06 [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln_a_ltln_fun$] : ! [v9: A_ltln$] : % 151.69/21.06 ! [v10: A_ltln$] : ! [v11: A_ltln$] : ( ~ (and_ltln$(v2) = v8) | ~ % 151.69/21.06 (or_ltln$(v5) = v6) | ~ (until_ltln$(v3) = v7) | ~ (fun_app$a(v8, v3) = % 151.69/21.06 v9) | ~ (fun_app$a(v7, v9) = v10) | ~ (fun_app$a(v6, v10) = v11) | ~ % 151.69/21.06 (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.06 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, % 151.69/21.06 v11) | ? [v12: A_ltln_a_ltln_fun$] : ? [v13: A_ltln$] : % 151.69/21.06 (release_ltln$(v2) = v12 & fun_app$a(v12, v3) = v13 & A_ltln$(v13) & % 151.69/21.06 A_ltln_a_ltln_fun$(v12) & fun_app$(v4, v13))) & ! [v1: Nat_a_set_fun$] % 151.69/21.06 : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.69/21.06 A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! % 151.69/21.06 [v8: A_ltln_a_ltln_fun$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ! [v11: % 151.69/21.06 A_ltln$] : ( ~ (and_ltln$(v2) = v8) | ~ (or_ltln$(v5) = v6) | ~ % 151.69/21.06 (until_ltln$(v3) = v7) | ~ (fun_app$a(v8, v3) = v9) | ~ (fun_app$a(v7, % 151.69/21.06 v9) = v10) | ~ (fun_app$a(v6, v10) = v11) | ~ (fun_app$a(v0, v3) = % 151.69/21.06 v5) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.69/21.06 A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v11) | ? [v12: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v13: A_ltln$] : (release_ltln$(v2) = v12 & % 151.69/21.06 fun_app$a(v12, v3) = v13 & A_ltln$(v13) & A_ltln_a_ltln_fun$(v12) & ~ % 151.69/21.06 fun_app$(v4, v13))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.06 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.69/21.06 [v6: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.69/21.06 ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | % 151.69/21.06 ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] : ? [v13: % 151.69/21.06 A_ltln$] : (and_ltln$(v2) = v10 & or_ltln$(v7) = v8 & until_ltln$(v3) = % 151.69/21.06 v9 & fun_app$a(v10, v3) = v11 & fun_app$a(v9, v11) = v12 & fun_app$a(v8, % 151.69/21.06 v12) = v13 & fun_app$a(v0, v3) = v7 & A_ltln$(v13) & A_ltln$(v12) & % 151.69/21.06 A_ltln$(v11) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v10) & % 151.69/21.06 A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v13))) & % 151.69/21.06 ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.06 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 151.69/21.06 (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.69/21.06 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.06 A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: % 151.69/21.06 A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] : ? [v13: % 151.69/21.06 A_ltln$] : (and_ltln$(v2) = v10 & or_ltln$(v7) = v8 & until_ltln$(v3) = % 151.69/21.06 v9 & fun_app$a(v10, v3) = v11 & fun_app$a(v9, v11) = v12 & fun_app$a(v8, % 151.69/21.06 v12) = v13 & fun_app$a(v0, v3) = v7 & A_ltln$(v13) & A_ltln$(v12) & % 151.69/21.06 A_ltln$(v11) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v10) & % 151.69/21.06 A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, % 151.69/21.06 v13)))) % 151.69/21.06 % 151.69/21.06 (axiom27) % 151.69/21.06 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.69/21.06 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.69/21.06 A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.06 A_ltln_bool_fun$] : ! [v5: A_ltln$] : ( ~ (fG_advice$(v3, v1) = v5) | ~ % 151.69/21.06 (semantics_ltln$(v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v3) | ~ % 151.69/21.06 A_ltln_set$(v1) | ~ fun_app$(v4, v5) | fun_app$(v4, v3) | ? [v6: % 151.69/21.06 A_ltln$] : ? [v7: A_ltln$] : (fun_app$a(v0, v6) = v7 & A_ltln$(v7) & % 151.69/21.06 A_ltln$(v6) & member$(v6, v1) & ~ fun_app$(v4, v7)))) % 151.69/21.06 % 151.69/21.06 (axiom28) % 151.69/21.06 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.06 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v1 & % 151.69/21.06 release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.06 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 151.69/21.07 [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ( ~ % 151.69/21.07 (fG_advice$(v4, v5) = v6) | ~ (f_G$(v2, v3) = v5) | ~ Nat_a_set_fun$(v3) % 151.69/21.07 | ~ A_ltln$(v4) | ~ A_ltln$(v2) | ? [v7: A_ltln_set$] : ? [v8: % 151.69/21.07 A_ltln_bool_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : ((g_F$(v2, % 151.69/21.07 v3) = v7 & A_ltln_set$(v7) & ~ member$(v4, v7)) | (fun_app$a(v1, % 151.69/21.07 v6) = v9 & fun_app$a(v0, v9) = v10 & semantics_ltln$(v3) = v8 & % 151.69/21.07 A_ltln$(v10) & A_ltln$(v9) & A_ltln_bool_fun$(v8) & fun_app$(v8, % 151.69/21.07 v10))))) % 151.69/21.07 % 151.69/21.07 (axiom3) % 151.69/21.07 Nat_a_set_fun$(w$) & A_ltln$(phi$) & ? [v0: A_ltln_bool_fun$] : % 151.69/21.07 (semantics_ltln$(w$) = v0 & A_ltln_bool_fun$(v0) & fun_app$(v0, phi$)) % 151.69/21.07 % 151.69/21.07 (axiom316) % 151.69/21.07 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.69/21.07 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.69/21.07 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.07 A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] : ! % 151.69/21.07 [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] : ( ~ % 151.69/21.07 (or_ltln$(v5) = v6) | ~ (strongRelease_ltln$(v2) = v7) | ~ % 151.69/21.07 (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, % 151.69/21.07 v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.69/21.07 A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 151.69/21.07 A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (release_ltln$(v2) = v10 & % 151.69/21.07 fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & % 151.69/21.07 fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.07 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 151.69/21.07 A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! % 151.69/21.07 [v9: A_ltln$] : ( ~ (or_ltln$(v5) = v6) | ~ (strongRelease_ltln$(v2) = v7) % 151.69/21.07 | ~ (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 151.69/21.07 (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.07 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v9) | % 151.69/21.07 ? [v10: A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (release_ltln$(v2) = v10 % 151.69/21.07 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ % 151.69/21.07 fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.07 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.69/21.07 [v6: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.69/21.07 ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | % 151.69/21.07 ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.69/21.07 A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : % 151.69/21.07 ? [v11: A_ltln$] : (or_ltln$(v7) = v8 & strongRelease_ltln$(v2) = v9 & % 151.69/21.07 fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = % 151.69/21.07 v7 & A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) % 151.69/21.07 & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] % 151.69/21.07 : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.69/21.07 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ % 151.69/21.07 (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.07 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | % 151.69/21.07 ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 151.69/21.07 A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 151.69/21.07 (or_ltln$(v7) = v8 & strongRelease_ltln$(v2) = v9 & fun_app$a(v9, v3) = % 151.69/21.07 v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = v7 & A_ltln$(v11) & % 151.69/21.07 A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & % 151.69/21.07 A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v11)))) % 151.69/21.07 % 151.69/21.07 (axiom4) % 151.69/21.07 A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & A_ltln$(phi$) & % 151.69/21.07 A_ltln$(psi$) & ? [v0: A_ltln_set$] : (restricted_subformulas$(phi$) = v0 & % 151.69/21.07 A_ltln_set$(v0) & ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : ( ~ % 151.69/21.07 (gF_advice$(psi$, v1) = v2) | ~ A_ltln_set$(v1) | ~ member$(psi$, v0) | % 151.69/21.07 ? [v3: A_ltln_set_a_ltln_set_fun$] : ? [v4: A_ltln_set$] : % 151.69/21.07 (gF_advice$(psi$, v4) = v2 & fun_app$c(inf$, v1) = v3 & fun_app$b(v3, v0) % 151.69/21.07 = v4 & A_ltln_set_a_ltln_set_fun$(v3) & A_ltln$(v2) & A_ltln_set$(v4))) % 151.69/21.07 & ! [v1: A_ltln_set$] : ! [v2: A_ltln_set_a_ltln_set_fun$] : ( ~ % 151.69/21.07 (fun_app$c(inf$, v1) = v2) | ~ A_ltln_set$(v1) | ~ member$(psi$, v0) | % 151.69/21.07 ? [v3: A_ltln_set$] : ? [v4: A_ltln$] : (gF_advice$(psi$, v3) = v4 & % 151.69/21.07 gF_advice$(psi$, v1) = v4 & fun_app$b(v2, v0) = v3 & A_ltln$(v4) & % 151.69/21.07 A_ltln_set$(v3)))) % 151.69/21.07 % 151.69/21.07 (axiom40) % 151.69/21.07 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.07 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v1 & % 151.69/21.07 release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.07 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln_set$] : ! [v3: Nat_a_set_fun$] : ! % 151.69/21.07 [v4: A_ltln$] : ! [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ( ~ % 151.69/21.07 (gF_advice$(v4, v2) = v6) | ~ (semantics_ltln$(v3) = v5) | ~ % 151.69/21.07 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v2) | ~ fun_app$(v5, % 151.69/21.07 v6) | fun_app$(v5, v4) | ? [v7: A_ltln$] : ? [v8: A_ltln$] : ? [v9: % 151.69/21.07 A_ltln$] : (fun_app$a(v1, v7) = v8 & fun_app$a(v0, v8) = v9 & % 151.69/21.07 A_ltln$(v9) & A_ltln$(v8) & A_ltln$(v7) & member$(v7, v2) & ~ % 151.69/21.07 fun_app$(v5, v9)))) % 151.69/21.07 % 151.69/21.07 (axiom41) % 151.69/21.08 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.08 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 151.69/21.08 release_ltln$(false_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.08 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.08 Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: % 151.69/21.08 A_ltln$] : ( ~ (fun_app$a(v1, v2) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 151.69/21.08 (f_G$(v3, v4) = v5) | ~ Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | ~ % 151.69/21.08 A_ltln$(v2) | ~ member$(v2, v5) | ? [v8: A_ltln_bool_fun$] : % 151.69/21.08 (semantics_ltln$(v4) = v8 & A_ltln_bool_fun$(v8) & fun_app$(v8, v7)))) % 151.69/21.08 % 151.69/21.08 (axiom42) % 151.69/21.08 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.08 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v1 & % 151.69/21.08 release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.08 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.08 Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: % 151.69/21.08 A_ltln$] : ( ~ (g_F$(v3, v4) = v5) | ~ (fun_app$a(v1, v2) = v6) | ~ % 151.69/21.08 (fun_app$a(v0, v6) = v7) | ~ Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | ~ % 151.69/21.08 A_ltln$(v2) | ~ member$(v2, v5) | ? [v8: A_ltln_bool_fun$] : % 151.69/21.08 (semantics_ltln$(v4) = v8 & A_ltln_bool_fun$(v8) & fun_app$(v8, v7)))) % 151.69/21.08 % 151.69/21.08 (axiom5) % 151.69/21.08 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.08 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 151.69/21.08 release_ltln$(false_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.08 A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 151.69/21.08 [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ( ~ (g_F$(v2, v3) % 151.69/21.08 = v5) | ~ (gF_advice$(v4, v5) = v6) | ~ Nat_a_set_fun$(v3) | ~ % 151.69/21.08 A_ltln$(v4) | ~ A_ltln$(v2) | ? [v7: A_ltln_set$] : ? [v8: % 151.69/21.08 A_ltln_bool_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 151.69/21.08 ((fun_app$a(v1, v6) = v9 & fun_app$a(v0, v9) = v10 & semantics_ltln$(v3) = % 151.69/21.08 v8 & A_ltln$(v10) & A_ltln$(v9) & A_ltln_bool_fun$(v8) & fun_app$(v8, % 151.69/21.08 v10)) | (f_G$(v2, v3) = v7 & A_ltln_set$(v7) & ~ member$(v4, % 151.69/21.08 v7))))) % 151.69/21.08 % 151.69/21.08 (axiom589) % 151.69/21.08 A_ltln_set$(bot$) & ! [v0: A_ltln$] : ( ~ A_ltln$(v0) | ~ member$(v0, bot$)) % 151.69/21.08 & ? [v0: A_ltln_set$] : (v0 = bot$ | ~ A_ltln_set$(v0) | ? [v1: A_ltln$] : % 151.69/21.08 (A_ltln$(v1) & member$(v1, v0))) % 151.69/21.08 % 151.69/21.08 (axiom614) % 151.69/21.08 A_ltln$(true_ltln$) & A_ltln_set$(bot$) & ! [v0: Nat_a_set_fun$] : ! [v1: % 151.69/21.08 A_ltln_set$] : (v1 = bot$ | ~ (f_G$(true_ltln$, v0) = v1) | ~ % 151.69/21.08 Nat_a_set_fun$(v0)) % 151.69/21.08 % 151.69/21.08 (axiom629) % 151.69/21.08 A_ltln_set$(bot$) & ! [v0: A_ltln$] : ( ~ A_ltln$(v0) | ~ member$(v0, bot$)) % 151.69/21.08 & ? [v0: A_ltln_set$] : (v0 = bot$ | ~ A_ltln_set$(v0) | ? [v1: A_ltln$] : % 151.69/21.08 (A_ltln$(v1) & member$(v1, v0))) % 151.69/21.08 % 151.69/21.08 (axiom7) % 151.69/21.08 Nat_a_set_fun$(w$) & A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & % 151.69/21.08 A_ltln$(phi$) & A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: % 151.69/21.08 A_ltln_set$] : ? [v1: A_ltln_set_a_ltln_set_fun$] : ? [v2: A_ltln_set$] : % 151.69/21.08 ? [v3: A_ltln_set$] : ? [v4: A_ltln_bool_fun$] : ? [v5: A_ltln_a_ltln_fun$] % 151.69/21.08 : ? [v6: A_ltln_a_ltln_fun$] : ? [v7: A_ltln_set$] : ? [v8: % 151.69/21.08 A_ltln_set_a_ltln_set_fun$] : ? [v9: A_ltln_set$] : % 151.69/21.08 (until_ltln$(true_ltln$) = v6 & release_ltln$(false_ltln$) = v5 & g_F$(phi$, % 151.69/21.08 w$) = v0 & semantics_ltln$(w$) = v4 & f_G$(phi$, w$) = v7 & % 151.69/21.08 fun_app$c(inf$, v7) = v8 & fun_app$c(inf$, v0) = v1 & % 151.69/21.08 restricted_subformulas$(phi$) = v2 & fun_app$b(v8, v2) = v9 & fun_app$b(v1, % 151.69/21.08 v2) = v3 & A_ltln_set_a_ltln_set_fun$(v8) & A_ltln_set_a_ltln_set_fun$(v1) % 151.69/21.08 & A_ltln_set$(v9) & A_ltln_set$(v7) & A_ltln_set$(v3) & A_ltln_set$(v2) & % 151.69/21.08 A_ltln_set$(v0) & A_ltln_bool_fun$(v4) & A_ltln_a_ltln_fun$(v6) & % 151.69/21.08 A_ltln_a_ltln_fun$(v5) & ! [v10: A_ltln$] : ! [v11: A_ltln$] : ( ~ % 151.69/21.08 (fG_advice$(v10, v9) = v11) | ~ A_ltln$(v10) | ~ member$(v10, v3) | ? % 151.69/21.08 [v12: A_ltln$] : ? [v13: A_ltln$] : (fun_app$a(v6, v11) = v12 & % 151.69/21.08 fun_app$a(v5, v12) = v13 & A_ltln$(v13) & A_ltln$(v12) & fun_app$(v4, % 151.69/21.08 v13)))) % 151.69/21.08 % 151.69/21.08 (axiom81) % 151.69/21.08 A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & ! [v0: A_ltln$] : ! [v1: % 151.69/21.08 A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln_set_a_ltln_set_fun$] : % 151.69/21.08 ! [v4: A_ltln_set$] : ( ~ (fun_app$c(inf$, v1) = v3) | ~ (fun_app$b(v3, v2) = % 151.69/21.08 v4) | ~ A_ltln$(v0) | ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ % 151.69/21.08 member$(v0, v4) | member$(v0, v1)) % 151.69/21.08 % 151.69/21.08 (axiom82) % 151.69/21.08 A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & ! [v0: A_ltln$] : ! [v1: % 151.69/21.08 A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln_set_a_ltln_set_fun$] : % 151.69/21.08 ! [v4: A_ltln_set$] : ( ~ (fun_app$c(inf$, v1) = v3) | ~ (fun_app$b(v3, v2) = % 151.69/21.08 v4) | ~ A_ltln$(v0) | ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ % 151.69/21.08 member$(v0, v4) | member$(v0, v2)) % 151.69/21.08 % 151.69/21.08 (axiom88) % 151.69/21.09 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.09 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 151.69/21.09 release_ltln$(false_ltln$) = v1 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.09 A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 151.69/21.09 A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: Nat_a_set_fun$] : % 151.69/21.09 ! [v8: A_ltln_bool_fun$] : ( ~ (suffix$(v2, v3) = v7) | ~ (fun_app$a(v1, % 151.69/21.09 v4) = v5) | ~ (fun_app$a(v0, v5) = v6) | ~ (semantics_ltln$(v7) = % 151.69/21.09 v8) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | % 151.69/21.09 fun_app$(v8, v6) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & % 151.69/21.09 A_ltln_bool_fun$(v9) & ~ fun_app$(v9, v6))) & ! [v2: Nat$] : ! [v3: % 151.69/21.09 Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: % 151.69/21.09 A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ (suffix$(v2, % 151.69/21.09 v3) = v5) | ~ (fun_app$a(v1, v4) = v7) | ~ (fun_app$a(v0, v7) = v8) % 151.69/21.09 | ~ (semantics_ltln$(v5) = v6) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 151.69/21.09 ~ Nat$(v2) | ~ fun_app$(v6, v8) | ? [v9: A_ltln_bool_fun$] : % 151.69/21.09 (semantics_ltln$(v3) = v9 & A_ltln_bool_fun$(v9) & fun_app$(v9, v8)))) % 151.69/21.09 % 151.69/21.09 (axiom89) % 151.69/21.09 A_ltln$(true_ltln$) & A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : ? % 151.69/21.09 [v1: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v1 & % 151.69/21.09 release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v1) & % 151.69/21.09 A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 151.69/21.09 A_ltln$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: Nat_a_set_fun$] : % 151.69/21.09 ! [v8: A_ltln_bool_fun$] : ( ~ (suffix$(v2, v3) = v7) | ~ (fun_app$a(v1, % 151.69/21.09 v4) = v5) | ~ (fun_app$a(v0, v5) = v6) | ~ (semantics_ltln$(v7) = % 151.69/21.09 v8) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | % 151.69/21.09 fun_app$(v8, v6) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & % 151.69/21.09 A_ltln_bool_fun$(v9) & ~ fun_app$(v9, v6))) & ! [v2: Nat$] : ! [v3: % 151.69/21.09 Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: % 151.69/21.09 A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ (suffix$(v2, % 151.69/21.09 v3) = v5) | ~ (fun_app$a(v1, v4) = v7) | ~ (fun_app$a(v0, v7) = v8) % 151.69/21.09 | ~ (semantics_ltln$(v5) = v6) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 151.69/21.09 ~ Nat$(v2) | ~ fun_app$(v6, v8) | ? [v9: A_ltln_bool_fun$] : % 151.69/21.09 (semantics_ltln$(v3) = v9 & A_ltln_bool_fun$(v9) & fun_app$(v9, v8)))) % 151.69/21.09 % 151.69/21.09 (axiom90) % 151.69/21.09 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.69/21.09 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.69/21.09 ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : % 151.69/21.09 ! [v6: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) % 151.69/21.09 = v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 151.69/21.09 A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: % 151.69/21.09 A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 151.69/21.09 ((release_ltln$(v2) = v7 & fun_app$a(v7, v3) = v8 & A_ltln$(v8) & % 151.69/21.09 A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, v8)) | (fun_app$a(v0, v2) = % 151.69/21.09 v9 & A_ltln$(v9) & ~ fun_app$(v4, v9)))) & ! [v1: Nat_a_set_fun$] : % 151.69/21.09 ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 151.69/21.09 A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ % 151.69/21.09 (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 151.69/21.09 Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) % 151.69/21.09 | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : % 151.69/21.09 ((strongRelease_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & A_ltln$(v9) & % 151.69/21.09 A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v9)) | (fun_app$a(v0, v2) = v7 & % 151.69/21.09 A_ltln$(v7) & ~ fun_app$(v4, v7))))) % 151.69/21.09 % 151.69/21.09 (axiom91) % 151.69/21.09 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.69/21.09 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.69/21.09 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 151.69/21.09 A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 151.69/21.09 (weakUntil_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 151.69/21.09 (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.09 A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 151.69/21.09 A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ((until_ltln$(v2) = v8 & % 151.69/21.09 fun_app$a(v8, v3) = v9 & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & % 151.69/21.09 fun_app$(v4, v9)) | (fun_app$a(v0, v2) = v7 & A_ltln$(v7) & % 151.69/21.09 fun_app$(v4, v7)))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.09 [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! % 151.69/21.09 [v6: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | % 151.69/21.09 ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ % 151.69/21.09 A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln_a_ltln_fun$] : ? [v8: % 151.69/21.09 A_ltln$] : ? [v9: A_ltln$] : ((weakUntil_ltln$(v2) = v7 & fun_app$a(v7, % 151.69/21.09 v3) = v8 & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, % 151.69/21.09 v8)) | (fun_app$a(v0, v2) = v9 & A_ltln$(v9) & fun_app$(v4, v9))))) % 151.69/21.09 % 151.69/21.09 (axiom92) % 151.69/21.09 Nat_a_set_fun$(w$) & A_ltln$(phi$) & Nat$(i$) & ? [v0: A_ltln_set$] : ? [v1: % 151.69/21.09 Nat_a_set_fun$] : (suffix$(i$, w$) = v1 & g_F$(phi$, v1) = v0 & g_F$(phi$, % 151.69/21.09 w$) = v0 & Nat_a_set_fun$(v1) & A_ltln_set$(v0)) % 151.69/21.09 % 151.69/21.09 (axiom94) % 151.69/21.10 A_ltln$(true_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = % 151.69/21.10 v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 151.69/21.10 ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : % 151.69/21.10 ( ~ (strongRelease_ltln$(v2) = v4) | ~ (fun_app$a(v4, true_ltln$) = v5) | % 151.69/21.10 ~ (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ % 151.69/21.10 fun_app$(v3, v5) | ? [v6: A_ltln$] : (fun_app$a(v0, v2) = v6 & % 151.69/21.10 A_ltln$(v6) & fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: % 151.69/21.10 A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! % 151.69/21.10 [v5: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v4) | ~ (fun_app$a(v4, % 151.69/21.10 true_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 151.69/21.10 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | fun_app$(v3, v5) | ? [v6: A_ltln$] % 151.69/21.10 : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & ~ fun_app$(v3, v6))) & ! [v1: % 151.69/21.10 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 151.69/21.10 A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | ~ (semantics_ltln$(v1) = v3) | % 151.69/21.10 ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v4) | ? [v5: % 151.69/21.10 A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : (strongRelease_ltln$(v2) = v5 & % 151.69/21.10 fun_app$a(v5, true_ltln$) = v6 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & % 151.69/21.10 fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.10 [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | % 151.69/21.10 ~ (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 151.69/21.10 fun_app$(v3, v4) | ? [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : % 151.69/21.10 (strongRelease_ltln$(v2) = v5 & fun_app$a(v5, true_ltln$) = v6 & % 151.69/21.10 A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & ~ fun_app$(v3, v6)))) % 151.69/21.10 % 151.69/21.10 (axiom95) % 151.69/21.10 A_ltln$(false_ltln$) & ? [v0: A_ltln_a_ltln_fun$] : % 151.69/21.10 (release_ltln$(false_ltln$) = v0 & A_ltln_a_ltln_fun$(v0) & ! [v1: % 151.69/21.10 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 151.69/21.10 A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v4) | % 151.69/21.10 ~ (fun_app$a(v4, false_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 151.69/21.10 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v5) | ? [v6: % 151.69/21.10 A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & fun_app$(v3, v6))) & % 151.69/21.10 ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! % 151.69/21.10 [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v4) % 151.69/21.10 | ~ (fun_app$a(v4, false_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | % 151.69/21.10 ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | fun_app$(v3, v5) | ? [v6: % 151.69/21.10 A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & ~ fun_app$(v3, v6))) % 151.69/21.10 & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : % 151.69/21.10 ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | ~ (semantics_ltln$(v1) = % 151.69/21.10 v3) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v4) | ? % 151.69/21.10 [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : (weakUntil_ltln$(v2) = v5 & % 151.69/21.10 fun_app$a(v5, false_ltln$) = v6 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & % 151.69/21.10 fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 151.69/21.10 [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | % 151.69/21.10 ~ (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 151.69/21.10 fun_app$(v3, v4) | ? [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : % 151.69/21.10 (weakUntil_ltln$(v2) = v5 & fun_app$a(v5, false_ltln$) = v6 & A_ltln$(v6) % 151.69/21.10 & A_ltln_a_ltln_fun$(v5) & ~ fun_app$(v3, v6)))) % 151.69/21.10 % 151.69/21.10 (conjecture1) % 151.69/21.10 Nat_a_set_fun$(w$) & A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & % 151.69/21.10 A_ltln$(phi$) & A_ltln$(true_ltln$) & A_ltln$(psi$) & A_ltln$(false_ltln$) & % 151.69/21.10 ? [v0: A_ltln_bool_fun$] : ? [v1: A_ltln_a_ltln_fun$] : ? [v2: % 151.69/21.10 A_ltln_a_ltln_fun$] : ? [v3: A_ltln_set$] : ? [v4: % 151.69/21.10 A_ltln_set_a_ltln_set_fun$] : ? [v5: A_ltln_set$] : ? [v6: A_ltln_set$] : % 151.69/21.10 ? [v7: A_ltln$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 151.69/21.10 (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v2 & g_F$(phi$, % 151.69/21.10 w$) = v3 & fun_app$a(v2, v7) = v8 & fun_app$a(v1, v8) = v9 & % 151.69/21.10 gF_advice$(psi$, v6) = v7 & semantics_ltln$(w$) = v0 & fun_app$c(inf$, v3) = % 151.69/21.10 v4 & restricted_subformulas$(phi$) = v5 & fun_app$b(v4, v5) = v6 & % 151.69/21.10 A_ltln_set_a_ltln_set_fun$(v4) & A_ltln$(v9) & A_ltln$(v8) & A_ltln$(v7) & % 151.69/21.10 A_ltln_set$(v6) & A_ltln_set$(v5) & A_ltln_set$(v3) & A_ltln_bool_fun$(v0) & % 151.69/21.10 A_ltln_a_ltln_fun$(v2) & A_ltln_a_ltln_fun$(v1) & ~ fun_app$(v0, v9)) % 151.69/21.10 % 151.69/21.10 (hypothesis2) % 151.69/21.10 Nat_a_set_fun$(w$) & A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$(inf$) & % 151.69/21.10 A_ltln$(phi$) & A_ltln$(psi$) & ? [v0: A_ltln_set$] : ? [v1: % 151.69/21.10 A_ltln_set_a_ltln_set_fun$] : ? [v2: A_ltln_set$] : ? [v3: A_ltln_set$] : % 151.69/21.10 (f_G$(phi$, w$) = v0 & fun_app$c(inf$, v0) = v1 & % 151.69/21.10 restricted_subformulas$(phi$) = v2 & fun_app$b(v1, v2) = v3 & % 151.69/21.10 A_ltln_set_a_ltln_set_fun$(v1) & A_ltln_set$(v3) & A_ltln_set$(v2) & % 151.69/21.10 A_ltln_set$(v0) & member$(psi$, v3)) % 151.69/21.10 % 151.69/21.10 (function-axioms) % 151.69/21.11 ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : ! [v3: % 151.69/21.11 Nat_a_set_fun$] : (v1 = v0 | ~ (gF_singleton$(v3, v2) = v1) | ~ % 151.69/21.11 (gF_singleton$(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] % 151.69/21.11 : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : (v1 = v0 | ~ % 151.69/21.11 (fG_singleton$(v3, v2) = v1) | ~ (fG_singleton$(v3, v2) = v0)) & ! [v0: % 151.69/21.11 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3: % 151.69/21.11 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = v1) | ~ % 151.69/21.11 (fun_app$j(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! % 151.69/21.11 [v2: int] : ! [v3: Int_a_ltln_set_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = % 151.69/21.11 v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 151.69/21.11 A_ltln_set$] : ! [v3: A_ltln_set_int_fun$] : (v1 = v0 | ~ (fun_app$g(v3, % 151.69/21.11 v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0: A_ltln_bool_fun$] : % 151.69/21.11 ! [v1: A_ltln_bool_fun$] : ! [v2: A_ltln$] : ! [v3: % 151.69/21.11 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~ % 151.69/21.11 (fun_app$f(v3, v2) = v0)) & ! [v0: Nat_a_set_fun$] : ! [v1: % 151.69/21.11 Nat_a_set_fun$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ % 151.69/21.11 (suffix$(v3, v2) = v1) | ~ (suffix$(v3, v2) = v0)) & ! [v0: Int_int_fun$] % 151.69/21.11 : ! [v1: Int_int_fun$] : ! [v2: int] : ! [v3: Int_int_int_fun_fun$] : (v1 = % 151.69/21.11 v0 | ~ (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0: % 151.69/21.11 int] : ! [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ % 151.69/21.11 (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0: A_ltln$] : % 151.69/21.11 ! [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln$] : (v1 = v0 | ~ % 151.69/21.11 (fG_advice$(v3, v2) = v1) | ~ (fG_advice$(v3, v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 151.69/21.11 A_ltln$] : (v1 = v0 | ~ (g_F$(v3, v2) = v1) | ~ (g_F$(v3, v2) = v0)) & ! % 151.69/21.11 [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 151.69/21.11 A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ % 151.69/21.11 (fun_app$a(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: % 151.69/21.11 A_ltln_set$] : ! [v3: A_ltln$] : (v1 = v0 | ~ (gF_advice$(v3, v2) = v1) | % 151.69/21.11 ~ (gF_advice$(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : % 151.69/21.11 ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : (v1 = v0 | ~ (f_G$(v3, v2) = v1) % 151.69/21.11 | ~ (f_G$(v3, v2) = v0)) & ! [v0: A_ltln_set_a_ltln_set_fun$] : ! [v1: % 151.69/21.11 A_ltln_set_a_ltln_set_fun$] : ! [v2: A_ltln_set$] : ! [v3: % 151.69/21.11 A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$] : (v1 = v0 | ~ (fun_app$c(v3, % 151.69/21.11 v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: A_ltln_set$] : ! % 151.69/21.11 [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln_set_a_ltln_set_fun$] % 151.69/21.11 : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! % 151.69/21.11 [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ % 151.69/21.11 (nat$(v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A$] : (v1 = % 151.69/21.11 v0 | ~ (nprop_ltln$(v2) = v1) | ~ (nprop_ltln$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln$] : ! [v1: A_ltln$] : ! [v2: A$] : (v1 = v0 | ~ (prop_ltln$(v2) = % 151.69/21.11 v1) | ~ (prop_ltln$(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 151.69/21.11 Nat$] : (v1 = v0 | ~ (of_nat$(v2) = v1) | ~ (of_nat$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 151.69/21.11 (subformulas_mu$(v2) = v1) | ~ (subformulas_mu$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 151.69/21.11 (subformulas_nu$(v2) = v1) | ~ (subformulas_nu$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = % 151.69/21.11 v0 | ~ (and_ltln$(v2) = v1) | ~ (and_ltln$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = % 151.69/21.11 v0 | ~ (or_ltln$(v2) = v1) | ~ (or_ltln$(v2) = v0)) & ! [v0: % 151.69/21.11 A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : (v1 = % 151.69/21.11 v0 | ~ (weakUntil_ltln$(v2) = v1) | ~ (weakUntil_ltln$(v2) = v0)) & ! % 151.69/21.11 [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] : % 151.69/21.11 (v1 = v0 | ~ (strongRelease_ltln$(v2) = v1) | ~ (strongRelease_ltln$(v2) = % 151.69/21.11 v0)) & ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: % 151.69/21.11 A_ltln_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) = % 151.69/21.11 v0)) & ! [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 151.69/21.11 A_ltln$] : (v1 = v0 | ~ (until_ltln$(v2) = v1) | ~ (until_ltln$(v2) = v0)) % 151.69/21.11 & ! [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: A_ltln$] % 151.69/21.11 : (v1 = v0 | ~ (release_ltln$(v2) = v1) | ~ (release_ltln$(v2) = v0)) & ! % 151.69/21.11 [v0: A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: Nat_a_set_fun$] : % 151.69/21.11 (v1 = v0 | ~ (semantics_ltln$(v2) = v1) | ~ (semantics_ltln$(v2) = v0)) & ! % 151.69/21.11 [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 151.69/21.11 (restricted_subformulas$(v2) = v1) | ~ (restricted_subformulas$(v2) = v0)) % 151.69/21.11 & ! [v0: A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: A_ltln_set$] % 151.69/21.11 : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) % 151.69/21.11 % 151.69/21.11 Further assumptions not needed in the proof: % 151.69/21.11 -------------------------------------------- % 151.69/21.11 axiom0, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, axiom105, % 151.69/21.11 axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112, % 151.69/21.11 axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12, % 151.69/21.11 axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127, % 151.69/21.11 axiom128, axiom129, axiom130, axiom131, axiom132, axiom133, axiom134, axiom135, % 151.69/21.11 axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, axiom141, axiom142, % 151.69/21.11 axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, axiom149, axiom15, % 151.69/21.11 axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, axiom156, axiom157, % 151.69/21.11 axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, axiom163, axiom164, % 151.69/21.11 axiom165, axiom166, axiom167, axiom168, axiom169, axiom170, axiom171, axiom172, % 151.69/21.11 axiom173, axiom174, axiom175, axiom176, axiom177, axiom178, axiom179, axiom18, % 151.69/21.11 axiom180, axiom181, axiom182, axiom183, axiom184, axiom185, axiom186, axiom187, % 151.69/21.11 axiom188, axiom189, axiom19, axiom190, axiom191, axiom192, axiom193, axiom194, % 151.69/21.11 axiom195, axiom196, axiom197, axiom198, axiom199, axiom20, axiom200, axiom201, % 151.69/21.11 axiom202, axiom203, axiom204, axiom205, axiom206, axiom207, axiom21, axiom210, % 151.69/21.11 axiom211, axiom212, axiom213, axiom214, axiom215, axiom216, axiom217, axiom22, % 151.69/21.11 axiom220, axiom224, axiom225, axiom226, axiom227, axiom228, axiom229, axiom23, % 151.69/21.11 axiom230, axiom231, axiom232, axiom233, axiom234, axiom235, axiom236, axiom237, % 151.69/21.11 axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, % 151.69/21.11 axiom246, axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, axiom252, % 151.69/21.11 axiom253, axiom254, axiom255, axiom256, axiom257, axiom258, axiom259, axiom26, % 151.69/21.11 axiom260, axiom261, axiom262, axiom263, axiom264, axiom265, axiom266, axiom267, % 151.69/21.11 axiom268, axiom269, axiom270, axiom271, axiom272, axiom273, axiom274, axiom275, % 151.69/21.11 axiom276, axiom277, axiom278, axiom279, axiom280, axiom281, axiom282, axiom283, % 151.69/21.11 axiom284, axiom285, axiom286, axiom287, axiom288, axiom289, axiom29, axiom290, % 151.69/21.11 axiom291, axiom292, axiom293, axiom294, axiom295, axiom296, axiom297, axiom298, % 151.69/21.11 axiom299, axiom30, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, % 151.69/21.11 axiom306, axiom307, axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, % 151.69/21.11 axiom313, axiom314, axiom315, axiom317, axiom318, axiom319, axiom32, axiom320, % 151.69/21.11 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328, % 151.69/21.11 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335, % 151.69/21.11 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342, % 151.69/21.11 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35, % 151.69/21.11 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357, % 151.69/21.11 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364, % 151.69/21.11 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371, % 151.69/21.11 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, axiom379, % 151.69/21.11 axiom38, axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, % 151.69/21.11 axiom387, axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, % 151.69/21.11 axiom394, axiom395, axiom396, axiom397, axiom398, axiom399, axiom400, axiom401, % 151.69/21.11 axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, % 151.69/21.11 axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, axiom416, axiom417, % 151.69/21.11 axiom418, axiom419, axiom420, axiom421, axiom422, axiom423, axiom424, axiom425, % 151.69/21.11 axiom426, axiom427, axiom428, axiom429, axiom43, axiom430, axiom431, axiom432, % 151.69/21.11 axiom433, axiom434, axiom435, axiom436, axiom437, axiom438, axiom439, axiom44, % 151.69/21.11 axiom440, axiom441, axiom442, axiom443, axiom444, axiom445, axiom446, axiom447, % 151.69/21.11 axiom448, axiom449, axiom45, axiom450, axiom451, axiom452, axiom453, axiom454, % 151.69/21.11 axiom455, axiom456, axiom457, axiom458, axiom459, axiom46, axiom460, axiom461, % 151.69/21.11 axiom462, axiom463, axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, % 151.69/21.11 axiom47, axiom470, axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, % 151.69/21.11 axiom477, axiom478, axiom479, axiom48, axiom480, axiom481, axiom482, axiom483, % 151.69/21.11 axiom484, axiom485, axiom486, axiom487, axiom488, axiom489, axiom49, axiom490, % 151.69/21.11 axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, axiom497, axiom498, % 151.69/21.11 axiom499, axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, axiom505, % 151.69/21.11 axiom506, axiom507, axiom508, axiom509, axiom51, axiom510, axiom511, axiom512, % 151.69/21.11 axiom513, axiom514, axiom515, axiom516, axiom517, axiom518, axiom519, axiom52, % 151.69/21.11 axiom520, axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, % 151.69/21.11 axiom528, axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, % 151.69/21.11 axiom535, axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, % 151.69/21.11 axiom542, axiom543, axiom544, axiom545, axiom546, axiom547, axiom548, axiom549, % 151.69/21.11 axiom55, axiom550, axiom551, axiom552, axiom553, axiom554, axiom555, axiom556, % 151.69/21.11 axiom557, axiom558, axiom559, axiom56, axiom560, axiom561, axiom562, axiom563, % 151.69/21.11 axiom564, axiom565, axiom566, axiom567, axiom568, axiom569, axiom57, axiom570, % 151.69/21.11 axiom571, axiom572, axiom573, axiom574, axiom575, axiom576, axiom577, axiom578, % 151.69/21.11 axiom579, axiom58, axiom580, axiom581, axiom582, axiom583, axiom584, axiom585, % 151.69/21.11 axiom586, axiom587, axiom588, axiom59, axiom590, axiom591, axiom592, axiom593, % 151.69/21.11 axiom594, axiom595, axiom596, axiom597, axiom598, axiom599, axiom6, axiom60, % 151.69/21.11 axiom600, axiom601, axiom602, axiom603, axiom604, axiom605, axiom606, axiom607, % 151.69/21.11 axiom608, axiom609, axiom61, axiom610, axiom611, axiom612, axiom613, axiom615, % 151.69/21.11 axiom616, axiom617, axiom618, axiom619, axiom62, axiom620, axiom621, axiom622, % 151.69/21.11 axiom623, axiom624, axiom625, axiom626, axiom627, axiom628, axiom63, axiom630, % 151.69/21.11 axiom631, axiom632, axiom64, axiom65, axiom66, axiom67, axiom68, axiom69, % 151.69/21.11 axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, axiom76, axiom77, axiom78, % 151.69/21.11 axiom79, axiom8, axiom80, axiom83, axiom84, axiom85, axiom86, axiom87, axiom9, % 151.69/21.11 axiom93, axiom96, axiom97, axiom98, axiom99, formula_634, formula_635 % 151.69/21.11 % 151.69/21.11 Those formulas are unsatisfiable: % 151.69/21.11 --------------------------------- % 151.69/21.11 % 151.69/21.11 Begin of proof % 151.69/21.11 | % 151.69/21.12 | ALPHA: (hypothesis2) implies: % 151.69/21.12 | (1) ? [v0: A_ltln_set$] : ? [v1: A_ltln_set_a_ltln_set_fun$] : ? [v2: % 151.69/21.12 | A_ltln_set$] : ? [v3: A_ltln_set$] : (f_G$(phi$, w$) = v0 & % 151.69/21.12 | fun_app$c(inf$, v0) = v1 & restricted_subformulas$(phi$) = v2 & % 151.69/21.12 | fun_app$b(v1, v2) = v3 & A_ltln_set_a_ltln_set_fun$(v1) & % 151.69/21.12 | A_ltln_set$(v3) & A_ltln_set$(v2) & A_ltln_set$(v0) & member$(psi$, % 151.69/21.12 | v3)) % 151.69/21.12 | % 151.69/21.12 | ALPHA: (axiom3) implies: % 151.69/21.12 | (2) ? [v0: A_ltln_bool_fun$] : (semantics_ltln$(w$) = v0 & % 151.69/21.12 | A_ltln_bool_fun$(v0) & fun_app$(v0, phi$)) % 151.69/21.12 | % 151.69/21.12 | ALPHA: (axiom4) implies: % 152.10/21.12 | (3) ? [v0: A_ltln_set$] : (restricted_subformulas$(phi$) = v0 & % 152.10/21.12 | A_ltln_set$(v0) & ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : ( ~ % 152.10/21.12 | (gF_advice$(psi$, v1) = v2) | ~ A_ltln_set$(v1) | ~ member$(psi$, % 152.10/21.12 | v0) | ? [v3: A_ltln_set_a_ltln_set_fun$] : ? [v4: A_ltln_set$] % 152.10/21.12 | : (gF_advice$(psi$, v4) = v2 & fun_app$c(inf$, v1) = v3 & % 152.10/21.12 | fun_app$b(v3, v0) = v4 & A_ltln_set_a_ltln_set_fun$(v3) & % 152.10/21.12 | A_ltln$(v2) & A_ltln_set$(v4))) & ! [v1: A_ltln_set$] : ! [v2: % 152.10/21.12 | A_ltln_set_a_ltln_set_fun$] : ( ~ (fun_app$c(inf$, v1) = v2) | ~ % 152.10/21.12 | A_ltln_set$(v1) | ~ member$(psi$, v0) | ? [v3: A_ltln_set$] : ? % 152.10/21.12 | [v4: A_ltln$] : (gF_advice$(psi$, v3) = v4 & gF_advice$(psi$, v1) = % 152.10/21.12 | v4 & fun_app$b(v2, v0) = v3 & A_ltln$(v4) & A_ltln_set$(v3)))) % 152.10/21.12 | % 152.10/21.12 | ALPHA: (axiom5) implies: % 152.10/21.12 | (4) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.12 | (until_ltln$(true_ltln$) = v0 & release_ltln$(false_ltln$) = v1 & % 152.10/21.12 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 152.10/21.12 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 152.10/21.12 | [v6: A_ltln$] : ( ~ (g_F$(v2, v3) = v5) | ~ (gF_advice$(v4, v5) = % 152.10/21.12 | v6) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln$(v2) | % 152.10/21.12 | ? [v7: A_ltln_set$] : ? [v8: A_ltln_bool_fun$] : ? [v9: A_ltln$] % 152.10/21.12 | : ? [v10: A_ltln$] : ((fun_app$a(v1, v6) = v9 & fun_app$a(v0, v9) % 152.10/21.12 | = v10 & semantics_ltln$(v3) = v8 & A_ltln$(v10) & A_ltln$(v9) & % 152.10/21.12 | A_ltln_bool_fun$(v8) & fun_app$(v8, v10)) | (f_G$(v2, v3) = v7 % 152.10/21.12 | & A_ltln_set$(v7) & ~ member$(v4, v7))))) % 152.10/21.12 | % 152.10/21.12 | ALPHA: (axiom7) implies: % 152.10/21.12 | (5) ? [v0: A_ltln_set$] : ? [v1: A_ltln_set_a_ltln_set_fun$] : ? [v2: % 152.10/21.12 | A_ltln_set$] : ? [v3: A_ltln_set$] : ? [v4: A_ltln_bool_fun$] : ? % 152.10/21.12 | [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln_a_ltln_fun$] : ? [v7: % 152.10/21.12 | A_ltln_set$] : ? [v8: A_ltln_set_a_ltln_set_fun$] : ? [v9: % 152.10/21.12 | A_ltln_set$] : (until_ltln$(true_ltln$) = v6 & % 152.10/21.12 | release_ltln$(false_ltln$) = v5 & g_F$(phi$, w$) = v0 & % 152.10/21.12 | semantics_ltln$(w$) = v4 & f_G$(phi$, w$) = v7 & fun_app$c(inf$, v7) % 152.10/21.12 | = v8 & fun_app$c(inf$, v0) = v1 & restricted_subformulas$(phi$) = v2 % 152.10/21.12 | & fun_app$b(v8, v2) = v9 & fun_app$b(v1, v2) = v3 & % 152.10/21.12 | A_ltln_set_a_ltln_set_fun$(v8) & A_ltln_set_a_ltln_set_fun$(v1) & % 152.10/21.12 | A_ltln_set$(v9) & A_ltln_set$(v7) & A_ltln_set$(v3) & A_ltln_set$(v2) % 152.10/21.12 | & A_ltln_set$(v0) & A_ltln_bool_fun$(v4) & A_ltln_a_ltln_fun$(v6) & % 152.10/21.12 | A_ltln_a_ltln_fun$(v5) & ! [v10: A_ltln$] : ! [v11: A_ltln$] : ( ~ % 152.10/21.12 | (fG_advice$(v10, v9) = v11) | ~ A_ltln$(v10) | ~ member$(v10, v3) % 152.10/21.12 | | ? [v12: A_ltln$] : ? [v13: A_ltln$] : (fun_app$a(v6, v11) = v12 % 152.10/21.12 | & fun_app$a(v5, v12) = v13 & A_ltln$(v13) & A_ltln$(v12) & % 152.10/21.12 | fun_app$(v4, v13)))) % 152.10/21.12 | % 152.10/21.12 | ALPHA: (axiom13) implies: % 152.10/21.12 | (6) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.12 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 152.10/21.12 | ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.12 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.12 | (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.12 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.12 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.12 | fun_app$(v4, v7) | ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & % 152.10/21.12 | A_ltln$(v8) & fun_app$(v4, v8))) & ! [v1: Nat_a_set_fun$] : ! % 152.10/21.12 | [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! % 152.10/21.12 | [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.12 | (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.12 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.12 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, % 152.10/21.12 | v7) | ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & A_ltln$(v8) & % 152.10/21.12 | ~ fun_app$(v4, v8)))) % 152.10/21.12 | % 152.10/21.12 | ALPHA: (axiom17) implies: % 152.10/21.13 | (7) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 152.10/21.13 | ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.13 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.13 | (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.13 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.13 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.13 | fun_app$(v4, v7) | ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & % 152.10/21.13 | A_ltln$(v8) & fun_app$(v4, v8))) & ! [v1: Nat_a_set_fun$] : ! % 152.10/21.13 | [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! % 152.10/21.13 | [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.13 | (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.13 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.13 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, % 152.10/21.13 | v7) | ? [v8: A_ltln$] : (fun_app$a(v0, v3) = v8 & A_ltln$(v8) & % 152.10/21.13 | ~ fun_app$(v4, v8)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom27) implies: % 152.10/21.13 | (8) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v0) & ! [v1: A_ltln_set$] : ! [v2: % 152.10/21.13 | Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! % 152.10/21.13 | [v5: A_ltln$] : ( ~ (fG_advice$(v3, v1) = v5) | ~ % 152.10/21.13 | (semantics_ltln$(v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v3) % 152.10/21.13 | | ~ A_ltln_set$(v1) | ~ fun_app$(v4, v5) | fun_app$(v4, v3) | ? % 152.10/21.13 | [v6: A_ltln$] : ? [v7: A_ltln$] : (fun_app$a(v0, v6) = v7 & % 152.10/21.13 | A_ltln$(v7) & A_ltln$(v6) & member$(v6, v1) & ~ fun_app$(v4, % 152.10/21.13 | v7)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom28) implies: % 152.10/21.13 | (9) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 152.10/21.13 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 152.10/21.13 | [v6: A_ltln$] : ( ~ (fG_advice$(v4, v5) = v6) | ~ (f_G$(v2, v3) = % 152.10/21.13 | v5) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln$(v2) | % 152.10/21.13 | ? [v7: A_ltln_set$] : ? [v8: A_ltln_bool_fun$] : ? [v9: A_ltln$] % 152.10/21.13 | : ? [v10: A_ltln$] : ((g_F$(v2, v3) = v7 & A_ltln_set$(v7) & ~ % 152.10/21.13 | member$(v4, v7)) | (fun_app$a(v1, v6) = v9 & fun_app$a(v0, v9) % 152.10/21.13 | = v10 & semantics_ltln$(v3) = v8 & A_ltln$(v10) & A_ltln$(v9) & % 152.10/21.13 | A_ltln_bool_fun$(v8) & fun_app$(v8, v10))))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom40) implies: % 152.10/21.13 | (10) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: % 152.10/21.13 | A_ltln_set$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! % 152.10/21.13 | [v5: A_ltln_bool_fun$] : ! [v6: A_ltln$] : ( ~ (gF_advice$(v4, v2) % 152.10/21.13 | = v6) | ~ (semantics_ltln$(v3) = v5) | ~ Nat_a_set_fun$(v3) | % 152.10/21.13 | ~ A_ltln$(v4) | ~ A_ltln_set$(v2) | ~ fun_app$(v5, v6) | % 152.10/21.13 | fun_app$(v5, v4) | ? [v7: A_ltln$] : ? [v8: A_ltln$] : ? [v9: % 152.10/21.13 | A_ltln$] : (fun_app$a(v1, v7) = v8 & fun_app$a(v0, v8) = v9 & % 152.10/21.13 | A_ltln$(v9) & A_ltln$(v8) & A_ltln$(v7) & member$(v7, v2) & ~ % 152.10/21.13 | fun_app$(v5, v9)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom41) implies: % 152.10/21.13 | (11) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v0 & release_ltln$(false_ltln$) = v1 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 152.10/21.13 | ! [v3: A_ltln$] : ! [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : % 152.10/21.13 | ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (fun_app$a(v1, v2) = v6) | % 152.10/21.13 | ~ (fun_app$a(v0, v6) = v7) | ~ (f_G$(v3, v4) = v5) | ~ % 152.10/21.13 | Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.13 | member$(v2, v5) | ? [v8: A_ltln_bool_fun$] : (semantics_ltln$(v4) % 152.10/21.13 | = v8 & A_ltln_bool_fun$(v8) & fun_app$(v8, v7)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom42) implies: % 152.10/21.13 | (12) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: A_ltln$] : % 152.10/21.13 | ! [v3: A_ltln$] : ! [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : % 152.10/21.13 | ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (g_F$(v3, v4) = v5) | ~ % 152.10/21.13 | (fun_app$a(v1, v2) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 152.10/21.13 | Nat_a_set_fun$(v4) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.13 | member$(v2, v5) | ? [v8: A_ltln_bool_fun$] : (semantics_ltln$(v4) % 152.10/21.13 | = v8 & A_ltln_bool_fun$(v8) & fun_app$(v8, v7)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom81) implies: % 152.10/21.13 | (13) ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ! % 152.10/21.13 | [v3: A_ltln_set_a_ltln_set_fun$] : ! [v4: A_ltln_set$] : ( ~ % 152.10/21.13 | (fun_app$c(inf$, v1) = v3) | ~ (fun_app$b(v3, v2) = v4) | ~ % 152.10/21.13 | A_ltln$(v0) | ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ % 152.10/21.13 | member$(v0, v4) | member$(v0, v1)) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom82) implies: % 152.10/21.13 | (14) ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : ! % 152.10/21.13 | [v3: A_ltln_set_a_ltln_set_fun$] : ! [v4: A_ltln_set$] : ( ~ % 152.10/21.13 | (fun_app$c(inf$, v1) = v3) | ~ (fun_app$b(v3, v2) = v4) | ~ % 152.10/21.13 | A_ltln$(v0) | ~ A_ltln_set$(v2) | ~ A_ltln_set$(v1) | ~ % 152.10/21.13 | member$(v0, v4) | member$(v0, v2)) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom88) implies: % 152.10/21.13 | (15) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v0 & release_ltln$(false_ltln$) = v1 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! % 152.10/21.13 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 152.10/21.13 | A_ltln$] : ! [v7: Nat_a_set_fun$] : ! [v8: A_ltln_bool_fun$] : ( % 152.10/21.13 | ~ (suffix$(v2, v3) = v7) | ~ (fun_app$a(v1, v4) = v5) | ~ % 152.10/21.13 | (fun_app$a(v0, v5) = v6) | ~ (semantics_ltln$(v7) = v8) | ~ % 152.10/21.13 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | fun_app$(v8, % 152.10/21.13 | v6) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & % 152.10/21.13 | A_ltln_bool_fun$(v9) & ~ fun_app$(v9, v6))) & ! [v2: Nat$] : % 152.10/21.13 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] % 152.10/21.13 | : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : % 152.10/21.13 | ( ~ (suffix$(v2, v3) = v5) | ~ (fun_app$a(v1, v4) = v7) | ~ % 152.10/21.13 | (fun_app$a(v0, v7) = v8) | ~ (semantics_ltln$(v5) = v6) | ~ % 152.10/21.13 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ~ % 152.10/21.13 | fun_app$(v6, v8) | ? [v9: A_ltln_bool_fun$] : % 152.10/21.13 | (semantics_ltln$(v3) = v9 & A_ltln_bool_fun$(v9) & fun_app$(v9, % 152.10/21.13 | v8)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom89) implies: % 152.10/21.13 | (16) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.13 | (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v0 & % 152.10/21.13 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ! [v2: Nat$] : ! % 152.10/21.13 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ! [v6: % 152.10/21.13 | A_ltln$] : ! [v7: Nat_a_set_fun$] : ! [v8: A_ltln_bool_fun$] : ( % 152.10/21.13 | ~ (suffix$(v2, v3) = v7) | ~ (fun_app$a(v1, v4) = v5) | ~ % 152.10/21.13 | (fun_app$a(v0, v5) = v6) | ~ (semantics_ltln$(v7) = v8) | ~ % 152.10/21.13 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | fun_app$(v8, % 152.10/21.13 | v6) | ? [v9: A_ltln_bool_fun$] : (semantics_ltln$(v3) = v9 & % 152.10/21.13 | A_ltln_bool_fun$(v9) & ~ fun_app$(v9, v6))) & ! [v2: Nat$] : % 152.10/21.13 | ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: Nat_a_set_fun$] % 152.10/21.13 | : ! [v6: A_ltln_bool_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : % 152.10/21.13 | ( ~ (suffix$(v2, v3) = v5) | ~ (fun_app$a(v1, v4) = v7) | ~ % 152.10/21.13 | (fun_app$a(v0, v7) = v8) | ~ (semantics_ltln$(v5) = v6) | ~ % 152.10/21.13 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ Nat$(v2) | ~ % 152.10/21.13 | fun_app$(v6, v8) | ? [v9: A_ltln_bool_fun$] : % 152.10/21.13 | (semantics_ltln$(v3) = v9 & A_ltln_bool_fun$(v9) & fun_app$(v9, % 152.10/21.13 | v8)))) % 152.10/21.13 | % 152.10/21.13 | ALPHA: (axiom90) implies: % 152.10/21.14 | (17) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.14 | (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((release_ltln$(v2) = v7 & fun_app$a(v7, v3) = v8 & A_ltln$(v8) & % 152.10/21.14 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, v8)) | (fun_app$a(v0, % 152.10/21.14 | v2) = v9 & A_ltln$(v9) & ~ fun_app$(v4, v9)))) & ! [v1: % 152.10/21.14 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.14 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.14 | : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((strongRelease_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & % 152.10/21.14 | A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v9)) | % 152.10/21.14 | (fun_app$a(v0, v2) = v7 & A_ltln$(v7) & ~ fun_app$(v4, v7))))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom91) implies: % 152.10/21.14 | (18) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) % 152.10/21.14 | = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = % 152.10/21.14 | v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.14 | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ((until_ltln$(v2) = v8 % 152.10/21.14 | & fun_app$a(v8, v3) = v9 & A_ltln$(v9) & % 152.10/21.14 | A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v9)) | (fun_app$a(v0, % 152.10/21.14 | v2) = v7 & A_ltln$(v7) & fun_app$(v4, v7)))) & ! [v1: % 152.10/21.14 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.14 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.14 | : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((weakUntil_ltln$(v2) = v7 & fun_app$a(v7, v3) = v8 & A_ltln$(v8) % 152.10/21.14 | & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, v8)) | % 152.10/21.14 | (fun_app$a(v0, v2) = v9 & A_ltln$(v9) & fun_app$(v4, v9))))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom92) implies: % 152.10/21.14 | (19) ? [v0: A_ltln_set$] : ? [v1: Nat_a_set_fun$] : (suffix$(i$, w$) = v1 % 152.10/21.14 | & g_F$(phi$, v1) = v0 & g_F$(phi$, w$) = v0 & Nat_a_set_fun$(v1) & % 152.10/21.14 | A_ltln_set$(v0)) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom94) implies: % 152.10/21.14 | (20) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.14 | A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v4) | ~ (fun_app$a(v4, % 152.10/21.14 | true_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v5) | ? % 152.10/21.14 | [v6: A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & % 152.10/21.14 | fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.14 | A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v4) | ~ (fun_app$a(v4, % 152.10/21.14 | true_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | fun_app$(v3, v5) | ? [v6: % 152.10/21.14 | A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & ~ % 152.10/21.14 | fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, % 152.10/21.14 | v2) = v4) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v4) | ? % 152.10/21.14 | [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : % 152.10/21.14 | (strongRelease_ltln$(v2) = v5 & fun_app$a(v5, true_ltln$) = v6 & % 152.10/21.14 | A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & fun_app$(v3, v6))) & ! % 152.10/21.14 | [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] % 152.10/21.14 | : ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v2) | fun_app$(v3, v4) | ? [v5: A_ltln_a_ltln_fun$] : ? % 152.10/21.14 | [v6: A_ltln$] : (strongRelease_ltln$(v2) = v5 & fun_app$a(v5, % 152.10/21.14 | true_ltln$) = v6 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & ~ % 152.10/21.14 | fun_app$(v3, v6)))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom95) implies: % 152.10/21.14 | (21) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.14 | A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v4) | ~ (fun_app$a(v4, % 152.10/21.14 | false_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v5) | ? % 152.10/21.14 | [v6: A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & % 152.10/21.14 | fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.14 | A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v4) | ~ (fun_app$a(v4, % 152.10/21.14 | false_ltln$) = v5) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | fun_app$(v3, v5) | ? [v6: % 152.10/21.14 | A_ltln$] : (fun_app$a(v0, v2) = v6 & A_ltln$(v6) & ~ % 152.10/21.14 | fun_app$(v3, v6))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, % 152.10/21.14 | v2) = v4) | ~ (semantics_ltln$(v1) = v3) | ~ % 152.10/21.14 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ fun_app$(v3, v4) | ? % 152.10/21.14 | [v5: A_ltln_a_ltln_fun$] : ? [v6: A_ltln$] : (weakUntil_ltln$(v2) % 152.10/21.14 | = v5 & fun_app$a(v5, false_ltln$) = v6 & A_ltln$(v6) & % 152.10/21.14 | A_ltln_a_ltln_fun$(v5) & fun_app$(v3, v6))) & ! [v1: % 152.10/21.14 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : % 152.10/21.14 | ! [v4: A_ltln$] : ( ~ (fun_app$a(v0, v2) = v4) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v2) | fun_app$(v3, v4) | ? [v5: A_ltln_a_ltln_fun$] : ? % 152.10/21.14 | [v6: A_ltln$] : (weakUntil_ltln$(v2) = v5 & fun_app$a(v5, % 152.10/21.14 | false_ltln$) = v6 & A_ltln$(v6) & A_ltln_a_ltln_fun$(v5) & ~ % 152.10/21.14 | fun_app$(v3, v6)))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom208) implies: % 152.10/21.14 | (22) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) % 152.10/21.14 | = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = % 152.10/21.14 | v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.14 | ~ fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ((until_ltln$(v2) = v8 % 152.10/21.14 | & fun_app$a(v8, v3) = v9 & A_ltln$(v9) & % 152.10/21.14 | A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v9)) | (fun_app$a(v0, % 152.10/21.14 | v3) = v7 & A_ltln$(v7) & ~ fun_app$(v4, v7)))) & ! [v1: % 152.10/21.14 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.14 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.14 | : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((weakUntil_ltln$(v2) = v7 & fun_app$a(v7, v3) = v8 & A_ltln$(v8) % 152.10/21.14 | & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, v8)) | % 152.10/21.14 | (fun_app$a(v0, v3) = v9 & A_ltln$(v9) & ~ fun_app$(v4, v9))))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom209) implies: % 152.10/21.14 | (23) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.14 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.14 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.14 | (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((release_ltln$(v2) = v7 & fun_app$a(v7, v3) = v8 & A_ltln$(v8) & % 152.10/21.14 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v4, v8)) | (fun_app$a(v0, % 152.10/21.14 | v3) = v9 & A_ltln$(v9) & fun_app$(v4, v9)))) & ! [v1: % 152.10/21.14 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.14 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.14 | : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.14 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.14 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: % 152.10/21.14 | A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : % 152.10/21.14 | ((strongRelease_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & % 152.10/21.14 | A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v9)) | % 152.10/21.14 | (fun_app$a(v0, v3) = v7 & A_ltln$(v7) & fun_app$(v4, v7))))) % 152.10/21.14 | % 152.10/21.14 | ALPHA: (axiom218) implies: % 152.10/21.15 | (24) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.15 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 152.10/21.15 | ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.15 | A_ltln$] : ! [v9: A_ltln$] : ( ~ (or_ltln$(v5) = v6) | ~ % 152.10/21.15 | (until_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = v8) | ~ % 152.10/21.15 | (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v2) = v5) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (weakUntil_ltln$(v2) = % 152.10/21.15 | v10 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & % 152.10/21.15 | A_ltln_a_ltln_fun$(v10) & fun_app$(v4, v11))) & ! [v1: % 152.10/21.15 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.15 | A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] % 152.10/21.15 | : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] % 152.10/21.15 | : ( ~ (or_ltln$(v5) = v6) | ~ (until_ltln$(v2) = v7) | ~ % 152.10/21.15 | (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 152.10/21.15 | (fun_app$a(v0, v2) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.15 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.15 | fun_app$(v4, v9) | ? [v10: A_ltln_a_ltln_fun$] : ? [v11: % 152.10/21.15 | A_ltln$] : (weakUntil_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 % 152.10/21.15 | & A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ fun_app$(v4, % 152.10/21.15 | v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.15 | A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.15 | : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) = v5) | ~ % 152.10/21.15 | (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.15 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.15 | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] % 152.10/21.15 | : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 152.10/21.15 | A_ltln$] : (or_ltln$(v7) = v8 & until_ltln$(v2) = v9 & % 152.10/21.15 | fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & % 152.10/21.15 | fun_app$a(v0, v2) = v7 & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.15 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.15 | fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ (weakUntil_ltln$(v2) % 152.10/21.15 | = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = % 152.10/21.15 | v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.15 | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] % 152.10/21.15 | : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 152.10/21.15 | A_ltln$] : (or_ltln$(v7) = v8 & until_ltln$(v2) = v9 & % 152.10/21.15 | fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & % 152.10/21.15 | fun_app$a(v0, v2) = v7 & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.15 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.15 | ~ fun_app$(v4, v11)))) % 152.10/21.15 | % 152.10/21.15 | ALPHA: (axiom219) implies: % 152.10/21.15 | (25) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.15 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 152.10/21.15 | ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.15 | A_ltln$] : ! [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ % 152.10/21.15 | (release_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = v8) | ~ % 152.10/21.15 | (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v2) = v5) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : % 152.10/21.15 | (strongRelease_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 152.10/21.15 | A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & fun_app$(v4, v11))) & % 152.10/21.15 | ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.15 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.15 | A_ltln$] : ! [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ % 152.10/21.15 | (release_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = v8) | ~ % 152.10/21.15 | (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v2) = v5) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v9) | ? [v10: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : % 152.10/21.15 | (strongRelease_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 152.10/21.15 | A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ fun_app$(v4, v11))) % 152.10/21.15 | & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.15 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.15 | A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, % 152.10/21.15 | v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.15 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.15 | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] % 152.10/21.15 | : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 152.10/21.15 | A_ltln$] : (and_ltln$(v7) = v8 & release_ltln$(v2) = v9 & % 152.10/21.15 | fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & % 152.10/21.15 | fun_app$a(v0, v2) = v7 & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.15 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.15 | fun_app$(v4, v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.15 | (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln$] % 152.10/21.15 | : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? % 152.10/21.15 | [v10: A_ltln$] : ? [v11: A_ltln$] : (and_ltln$(v7) = v8 & % 152.10/21.15 | release_ltln$(v2) = v9 & fun_app$a(v9, v3) = v10 & fun_app$a(v8, % 152.10/21.15 | v10) = v11 & fun_app$a(v0, v2) = v7 & A_ltln$(v11) & % 152.10/21.15 | A_ltln$(v10) & A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & % 152.10/21.15 | A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v11)))) % 152.10/21.15 | % 152.10/21.15 | ALPHA: (axiom221) implies: % 152.10/21.15 | (26) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.15 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.15 | (and_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.15 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.15 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.15 | fun_app$(v4, v7) | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] % 152.10/21.15 | : ? [v10: A_ltln$] : (strongRelease_ltln$(v2) = v8 & % 152.10/21.15 | fun_app$a(v8, v3) = v9 & fun_app$a(v0, v9) = v10 & A_ltln$(v10) % 152.10/21.15 | & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v10))) & % 152.10/21.15 | ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.15 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.15 | A_ltln$] : ! [v7: A_ltln$] : ( ~ (and_ltln$(v2) = v5) | ~ % 152.10/21.15 | (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v7) | ? [v8: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 152.10/21.15 | (strongRelease_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & % 152.10/21.15 | fun_app$a(v0, v9) = v10 & A_ltln$(v10) & A_ltln$(v9) & % 152.10/21.15 | A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v10))) & ! [v1: % 152.10/21.15 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.15 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.15 | : ! [v7: A_ltln$] : ( ~ (strongRelease_ltln$(v2) = v5) | ~ % 152.10/21.15 | (fun_app$a(v5, v3) = v6) | ~ (fun_app$a(v0, v6) = v7) | ~ % 152.10/21.15 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.15 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v7) | ? [v8: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 152.10/21.15 | (and_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 & fun_app$a(v0, v9) = % 152.10/21.15 | v10 & A_ltln$(v10) & A_ltln$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.15 | fun_app$(v4, v10))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.15 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: % 152.10/21.15 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 152.10/21.15 | (strongRelease_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.15 | (fun_app$a(v0, v6) = v7) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.15 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.15 | fun_app$(v4, v7) | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] % 152.10/21.15 | : ? [v10: A_ltln$] : (and_ltln$(v2) = v8 & fun_app$a(v8, v3) = v9 % 152.10/21.15 | & fun_app$a(v0, v9) = v10 & A_ltln$(v10) & A_ltln$(v9) & % 152.10/21.15 | A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v10)))) % 152.10/21.15 | % 152.10/21.15 | ALPHA: (axiom222) implies: % 152.10/21.15 | (27) ? [v0: A_ltln_a_ltln_fun$] : ? [v1: A_ltln_a_ltln_fun$] : % 152.10/21.15 | (until_ltln$(true_ltln$) = v1 & release_ltln$(false_ltln$) = v0 & % 152.10/21.15 | A_ltln_a_ltln_fun$(v1) & A_ltln_a_ltln_fun$(v0) & ? [v2: % 152.10/21.15 | A_ltln_set$] : ? [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! [v5: % 152.10/21.15 | Nat_a_set_fun$] : ! [v6: A_ltln_set$] : ( ~ (g_F$(v4, v5) = v6) | % 152.10/21.15 | ~ Nat_a_set_fun$(v5) | ~ A_ltln$(v4) | ~ A_ltln_set$(v3) | ~ % 152.10/21.15 | A_ltln_set$(v2) | ? [v7: A_ltln_set$] : ? [v8: A_ltln_set$] : ? % 152.10/21.15 | [v9: A_ltln_bool_fun$] : ? [v10: A_ltln_set$] : ? [v11: A_ltln$] % 152.10/21.15 | : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? [v14: A_ltln$] : ? % 152.10/21.15 | [v15: A_ltln$] : ? [v16: A_ltln$] : ? [v17: A_ltln$] : ? [v18: % 152.10/21.15 | A_ltln$] : (A_ltln$(v15) & A_ltln$(v11) & ((subformulas_mu$(v4) % 152.10/21.15 | = v7 & A_ltln_set$(v7) & ~ less_eq$(v2, v7)) | % 152.10/21.15 | (subformulas_nu$(v4) = v8 & A_ltln_set$(v8) & ~ less_eq$(v3, % 152.10/21.15 | v8)) | (fG_advice$(v15, v3) = v16 & fun_app$a(v1, v16) = % 152.10/21.15 | v17 & fun_app$a(v0, v17) = v18 & semantics_ltln$(v5) = v9 & % 152.10/21.15 | A_ltln$(v18) & A_ltln$(v17) & A_ltln$(v16) & % 152.10/21.15 | A_ltln_bool_fun$(v9) & member$(v15, v2) & ~ fun_app$(v9, % 152.10/21.15 | v18)) | (fun_app$a(v1, v13) = v14 & fun_app$a(v0, v12) = % 152.10/21.15 | v13 & gF_advice$(v11, v2) = v12 & semantics_ltln$(v5) = v9 & % 152.10/21.15 | A_ltln$(v14) & A_ltln$(v13) & A_ltln$(v12) & % 152.10/21.15 | A_ltln_bool_fun$(v9) & member$(v11, v3) & ~ fun_app$(v9, % 152.10/21.15 | v14)) | (f_G$(v4, v5) = v10 & A_ltln_set$(v10) & % 152.10/21.15 | less_eq$(v3, v10) & less_eq$(v2, v6))))) & ? [v2: % 152.10/21.15 | A_ltln_set$] : ? [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! [v5: % 152.10/21.15 | Nat_a_set_fun$] : ! [v6: A_ltln_set$] : ( ~ (f_G$(v4, v5) = v6) | % 152.10/21.15 | ~ Nat_a_set_fun$(v5) | ~ A_ltln$(v4) | ~ A_ltln_set$(v3) | ~ % 152.10/21.15 | A_ltln_set$(v2) | ? [v7: A_ltln_set$] : ? [v8: A_ltln_set$] : ? % 152.10/21.15 | [v9: A_ltln_bool_fun$] : ? [v10: A_ltln_set$] : ? [v11: A_ltln$] % 152.10/21.15 | : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? [v14: A_ltln$] : ? % 152.10/21.15 | [v15: A_ltln$] : ? [v16: A_ltln$] : ? [v17: A_ltln$] : ? [v18: % 152.10/21.15 | A_ltln$] : (A_ltln$(v15) & A_ltln$(v11) & ((subformulas_mu$(v4) % 152.10/21.15 | = v7 & A_ltln_set$(v7) & ~ less_eq$(v2, v7)) | % 152.10/21.15 | (subformulas_nu$(v4) = v8 & A_ltln_set$(v8) & ~ less_eq$(v3, % 152.10/21.15 | v8)) | (fG_advice$(v15, v3) = v16 & fun_app$a(v1, v16) = % 152.10/21.15 | v17 & fun_app$a(v0, v17) = v18 & semantics_ltln$(v5) = v9 & % 152.10/21.15 | A_ltln$(v18) & A_ltln$(v17) & A_ltln$(v16) & % 152.10/21.15 | A_ltln_bool_fun$(v9) & member$(v15, v2) & ~ fun_app$(v9, % 152.10/21.15 | v18)) | (g_F$(v4, v5) = v10 & A_ltln_set$(v10) & % 152.10/21.15 | less_eq$(v3, v6) & less_eq$(v2, v10)) | (fun_app$a(v1, v13) % 152.10/21.15 | = v14 & fun_app$a(v0, v12) = v13 & gF_advice$(v11, v2) = v12 % 152.10/21.15 | & semantics_ltln$(v5) = v9 & A_ltln$(v14) & A_ltln$(v13) & % 152.10/21.15 | A_ltln$(v12) & A_ltln_bool_fun$(v9) & member$(v11, v3) & ~ % 152.10/21.15 | fun_app$(v9, v14)))))) % 152.10/21.15 | % 152.10/21.15 | ALPHA: (axiom223) implies: % 152.10/21.16 | (28) ? [v0: A_ltln_a_ltln_fun$] : (until_ltln$(true_ltln$) = v0 & % 152.10/21.16 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.16 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 152.10/21.16 | ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.16 | A_ltln$] : ! [v9: A_ltln$] : ( ~ (and_ltln$(v5) = v6) | ~ % 152.10/21.16 | (weakUntil_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = v8) | ~ % 152.10/21.16 | (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v3) = v5) | ~ % 152.10/21.16 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (until_ltln$(v2) = v10 % 152.10/21.16 | & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v10) & fun_app$(v4, v11))) & ! [v1: % 152.10/21.16 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.16 | A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] % 152.10/21.16 | : ( ~ (and_ltln$(v5) = v6) | ~ (weakUntil_ltln$(v2) = v7) | ~ % 152.10/21.16 | (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 152.10/21.16 | (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.16 | fun_app$(v4, v9) | ? [v10: A_ltln_a_ltln_fun$] : ? [v11: % 152.10/21.16 | A_ltln$] : (until_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 152.10/21.16 | A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ fun_app$(v4, v11))) % 152.10/21.16 | & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.16 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.16 | A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 152.10/21.16 | v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: % 152.10/21.16 | A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 152.10/21.16 | (and_ltln$(v7) = v8 & weakUntil_ltln$(v2) = v9 & fun_app$a(v9, v3) % 152.10/21.16 | = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = v7 & % 152.10/21.16 | A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, % 152.10/21.16 | v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.16 | A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ! [v6: A_ltln$] : ( ~ (until_ltln$(v2) = v5) | ~ (fun_app$a(v5, % 152.10/21.16 | v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.16 | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 152.10/21.16 | A_ltln$] : (and_ltln$(v7) = v8 & weakUntil_ltln$(v2) = v9 & % 152.10/21.16 | fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & % 152.10/21.16 | fun_app$a(v0, v3) = v7 & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.16 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.16 | ~ fun_app$(v4, v11)))) % 152.10/21.16 | % 152.10/21.16 | ALPHA: (axiom245) implies: % 152.10/21.16 | (29) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.16 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.16 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 152.10/21.16 | ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ! % 152.10/21.16 | [v11: A_ltln$] : ( ~ (and_ltln$(v2) = v8) | ~ (or_ltln$(v5) = v6) | % 152.10/21.16 | ~ (until_ltln$(v3) = v7) | ~ (fun_app$a(v8, v3) = v9) | ~ % 152.10/21.16 | (fun_app$a(v7, v9) = v10) | ~ (fun_app$a(v6, v10) = v11) | ~ % 152.10/21.16 | (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | ~ % 152.10/21.16 | fun_app$(v4, v11) | ? [v12: A_ltln_a_ltln_fun$] : ? [v13: % 152.10/21.16 | A_ltln$] : (release_ltln$(v2) = v12 & fun_app$a(v12, v3) = v13 & % 152.10/21.16 | A_ltln$(v13) & A_ltln_a_ltln_fun$(v12) & fun_app$(v4, v13))) & % 152.10/21.16 | ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.16 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ! % 152.10/21.16 | [v11: A_ltln$] : ( ~ (and_ltln$(v2) = v8) | ~ (or_ltln$(v5) = v6) | % 152.10/21.16 | ~ (until_ltln$(v3) = v7) | ~ (fun_app$a(v8, v3) = v9) | ~ % 152.10/21.16 | (fun_app$a(v7, v9) = v10) | ~ (fun_app$a(v6, v10) = v11) | ~ % 152.10/21.16 | (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.16 | fun_app$(v4, v11) | ? [v12: A_ltln_a_ltln_fun$] : ? [v13: % 152.10/21.16 | A_ltln$] : (release_ltln$(v2) = v12 & fun_app$a(v12, v3) = v13 & % 152.10/21.16 | A_ltln$(v13) & A_ltln_a_ltln_fun$(v12) & ~ fun_app$(v4, v13))) % 152.10/21.16 | & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.16 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.16 | A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 152.10/21.16 | v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: % 152.10/21.16 | A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln_a_ltln_fun$] : ? [v11: % 152.10/21.16 | A_ltln$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : % 152.10/21.16 | (and_ltln$(v2) = v10 & or_ltln$(v7) = v8 & until_ltln$(v3) = v9 & % 152.10/21.16 | fun_app$a(v10, v3) = v11 & fun_app$a(v9, v11) = v12 & % 152.10/21.16 | fun_app$a(v8, v12) = v13 & fun_app$a(v0, v3) = v7 & A_ltln$(v13) % 152.10/21.16 | & A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v7) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v10) & A_ltln_a_ltln_fun$(v9) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v8) & fun_app$(v4, v13))) & ! [v1: % 152.10/21.16 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.16 | A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln$] % 152.10/21.16 | : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = v6) | ~ % 152.10/21.16 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | fun_app$(v4, v6) | ? [v7: A_ltln$] % 152.10/21.16 | : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln_a_ltln_fun$] : ? % 152.10/21.16 | [v10: A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] % 152.10/21.16 | : ? [v13: A_ltln$] : (and_ltln$(v2) = v10 & or_ltln$(v7) = v8 & % 152.10/21.16 | until_ltln$(v3) = v9 & fun_app$a(v10, v3) = v11 & fun_app$a(v9, % 152.10/21.16 | v11) = v12 & fun_app$a(v8, v12) = v13 & fun_app$a(v0, v3) = v7 % 152.10/21.16 | & A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v7) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v10) & A_ltln_a_ltln_fun$(v9) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v8) & ~ fun_app$(v4, v13)))) % 152.10/21.16 | % 152.10/21.16 | ALPHA: (axiom316) implies: % 152.10/21.16 | (30) ? [v0: A_ltln_a_ltln_fun$] : (release_ltln$(false_ltln$) = v0 & % 152.10/21.16 | A_ltln_a_ltln_fun$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 152.10/21.16 | : ! [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : % 152.10/21.16 | ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.16 | A_ltln$] : ! [v9: A_ltln$] : ( ~ (or_ltln$(v5) = v6) | ~ % 152.10/21.16 | (strongRelease_ltln$(v2) = v7) | ~ (fun_app$a(v7, v3) = v8) | ~ % 152.10/21.16 | (fun_app$a(v6, v8) = v9) | ~ (fun_app$a(v0, v3) = v5) | ~ % 152.10/21.16 | (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v9) | ? [v10: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ? [v11: A_ltln$] : (release_ltln$(v2) = % 152.10/21.16 | v10 & fun_app$a(v10, v3) = v11 & A_ltln$(v11) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v10) & fun_app$(v4, v11))) & ! [v1: % 152.10/21.16 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.16 | A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: A_ltln$] : ! [v9: A_ltln$] % 152.10/21.16 | : ( ~ (or_ltln$(v5) = v6) | ~ (strongRelease_ltln$(v2) = v7) | ~ % 152.10/21.16 | (fun_app$a(v7, v3) = v8) | ~ (fun_app$a(v6, v8) = v9) | ~ % 152.10/21.16 | (fun_app$a(v0, v3) = v5) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.16 | fun_app$(v4, v9) | ? [v10: A_ltln_a_ltln_fun$] : ? [v11: % 152.10/21.16 | A_ltln$] : (release_ltln$(v2) = v10 & fun_app$a(v10, v3) = v11 & % 152.10/21.16 | A_ltln$(v11) & A_ltln_a_ltln_fun$(v10) & ~ fun_app$(v4, v11))) % 152.10/21.16 | & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! % 152.10/21.16 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.16 | A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ (fun_app$a(v5, v3) = % 152.10/21.16 | v6) | ~ (semantics_ltln$(v1) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.16 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ fun_app$(v4, v6) | ? [v7: % 152.10/21.16 | A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.16 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 152.10/21.16 | (or_ltln$(v7) = v8 & strongRelease_ltln$(v2) = v9 & fun_app$a(v9, % 152.10/21.16 | v3) = v10 & fun_app$a(v8, v10) = v11 & fun_app$a(v0, v3) = v7 % 152.10/21.16 | & A_ltln$(v11) & A_ltln$(v10) & A_ltln$(v7) & % 152.10/21.16 | A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & fun_app$(v4, % 152.10/21.16 | v11))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.16 | A_ltln$] : ! [v4: A_ltln_bool_fun$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ! [v6: A_ltln$] : ( ~ (release_ltln$(v2) = v5) | ~ % 152.10/21.16 | (fun_app$a(v5, v3) = v6) | ~ (semantics_ltln$(v1) = v4) | ~ % 152.10/21.16 | Nat_a_set_fun$(v1) | ~ A_ltln$(v3) | ~ A_ltln$(v2) | % 152.10/21.16 | fun_app$(v4, v6) | ? [v7: A_ltln$] : ? [v8: A_ltln_a_ltln_fun$] % 152.10/21.16 | : ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: % 152.10/21.16 | A_ltln$] : (or_ltln$(v7) = v8 & strongRelease_ltln$(v2) = v9 & % 152.10/21.16 | fun_app$a(v9, v3) = v10 & fun_app$a(v8, v10) = v11 & % 152.10/21.16 | fun_app$a(v0, v3) = v7 & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.16 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.16 | ~ fun_app$(v4, v11)))) % 152.10/21.16 | % 152.10/21.16 | ALPHA: (axiom614) implies: % 152.10/21.16 | (31) ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln_set$] : (v1 = bot$ | ~ % 152.10/21.16 | (f_G$(true_ltln$, v0) = v1) | ~ Nat_a_set_fun$(v0)) % 152.10/21.16 | % 152.10/21.16 | ALPHA: (axiom629) implies: % 152.10/21.16 | (32) ! [v0: A_ltln$] : ( ~ A_ltln$(v0) | ~ member$(v0, bot$)) % 152.10/21.16 | % 152.10/21.16 | ALPHA: (conjecture1) implies: % 152.10/21.16 | (33) A_ltln$(psi$) % 152.10/21.16 | (34) A_ltln$(true_ltln$) % 152.10/21.16 | (35) A_ltln$(phi$) % 152.10/21.16 | (36) Nat_a_set_fun$(w$) % 152.10/21.17 | (37) ? [v0: A_ltln_bool_fun$] : ? [v1: A_ltln_a_ltln_fun$] : ? [v2: % 152.10/21.17 | A_ltln_a_ltln_fun$] : ? [v3: A_ltln_set$] : ? [v4: % 152.10/21.17 | A_ltln_set_a_ltln_set_fun$] : ? [v5: A_ltln_set$] : ? [v6: % 152.10/21.17 | A_ltln_set$] : ? [v7: A_ltln$] : ? [v8: A_ltln$] : ? [v9: % 152.10/21.17 | A_ltln$] : (until_ltln$(true_ltln$) = v1 & % 152.10/21.17 | release_ltln$(false_ltln$) = v2 & g_F$(phi$, w$) = v3 & % 152.10/21.17 | fun_app$a(v2, v7) = v8 & fun_app$a(v1, v8) = v9 & gF_advice$(psi$, % 152.10/21.17 | v6) = v7 & semantics_ltln$(w$) = v0 & fun_app$c(inf$, v3) = v4 & % 152.10/21.17 | restricted_subformulas$(phi$) = v5 & fun_app$b(v4, v5) = v6 & % 152.10/21.17 | A_ltln_set_a_ltln_set_fun$(v4) & A_ltln$(v9) & A_ltln$(v8) & % 152.10/21.17 | A_ltln$(v7) & A_ltln_set$(v6) & A_ltln_set$(v5) & A_ltln_set$(v3) & % 152.10/21.17 | A_ltln_bool_fun$(v0) & A_ltln_a_ltln_fun$(v2) & % 152.10/21.17 | A_ltln_a_ltln_fun$(v1) & ~ fun_app$(v0, v9)) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (function-axioms) implies: % 152.10/21.17 | (38) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : (v1 = % 152.10/21.17 | v0 | ~ (restricted_subformulas$(v2) = v1) | ~ % 152.10/21.17 | (restricted_subformulas$(v2) = v0)) % 152.10/21.17 | (39) ! [v0: A_ltln_bool_fun$] : ! [v1: A_ltln_bool_fun$] : ! [v2: % 152.10/21.17 | Nat_a_set_fun$] : (v1 = v0 | ~ (semantics_ltln$(v2) = v1) | ~ % 152.10/21.17 | (semantics_ltln$(v2) = v0)) % 152.10/21.17 | (40) ! [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 152.10/21.17 | A_ltln$] : (v1 = v0 | ~ (release_ltln$(v2) = v1) | ~ % 152.10/21.17 | (release_ltln$(v2) = v0)) % 152.10/21.17 | (41) ! [v0: A_ltln_a_ltln_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 152.10/21.17 | A_ltln$] : (v1 = v0 | ~ (until_ltln$(v2) = v1) | ~ % 152.10/21.17 | (until_ltln$(v2) = v0)) % 152.10/21.17 | (42) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln_set$] : % 152.10/21.17 | ! [v3: A_ltln_set_a_ltln_set_fun$] : (v1 = v0 | ~ (fun_app$b(v3, v2) % 152.10/21.17 | = v1) | ~ (fun_app$b(v3, v2) = v0)) % 152.10/21.17 | (43) ! [v0: A_ltln_set_a_ltln_set_fun$] : ! [v1: % 152.10/21.17 | A_ltln_set_a_ltln_set_fun$] : ! [v2: A_ltln_set$] : ! [v3: % 152.10/21.17 | A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$] : (v1 = v0 | ~ % 152.10/21.17 | (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) % 152.10/21.17 | (44) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] % 152.10/21.17 | : ! [v3: A_ltln$] : (v1 = v0 | ~ (f_G$(v3, v2) = v1) | ~ (f_G$(v3, % 152.10/21.17 | v2) = v0)) % 152.10/21.17 | (45) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: % 152.10/21.17 | A_ltln$] : (v1 = v0 | ~ (gF_advice$(v3, v2) = v1) | ~ % 152.10/21.17 | (gF_advice$(v3, v2) = v0)) % 152.10/21.17 | (46) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.17 | A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ % 152.10/21.17 | (fun_app$a(v3, v2) = v0)) % 152.10/21.17 | (47) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] % 152.10/21.17 | : ! [v3: A_ltln$] : (v1 = v0 | ~ (g_F$(v3, v2) = v1) | ~ (g_F$(v3, % 152.10/21.17 | v2) = v0)) % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (2) with fresh symbol all_587_0 gives: % 152.10/21.17 | (48) semantics_ltln$(w$) = all_587_0 & A_ltln_bool_fun$(all_587_0) & % 152.10/21.17 | fun_app$(all_587_0, phi$) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (48) implies: % 152.10/21.17 | (49) semantics_ltln$(w$) = all_587_0 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (19) with fresh symbols all_614_0, all_614_1 gives: % 152.10/21.17 | (50) suffix$(i$, w$) = all_614_0 & g_F$(phi$, all_614_0) = all_614_1 & % 152.10/21.17 | g_F$(phi$, w$) = all_614_1 & Nat_a_set_fun$(all_614_0) & % 152.10/21.17 | A_ltln_set$(all_614_1) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (50) implies: % 152.10/21.17 | (51) g_F$(phi$, w$) = all_614_1 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (1) with fresh symbols all_637_0, all_637_1, all_637_2, % 152.10/21.17 | all_637_3 gives: % 152.10/21.17 | (52) f_G$(phi$, w$) = all_637_3 & fun_app$c(inf$, all_637_3) = all_637_2 & % 152.10/21.17 | restricted_subformulas$(phi$) = all_637_1 & fun_app$b(all_637_2, % 152.10/21.17 | all_637_1) = all_637_0 & A_ltln_set_a_ltln_set_fun$(all_637_2) & % 152.10/21.17 | A_ltln_set$(all_637_0) & A_ltln_set$(all_637_1) & % 152.10/21.17 | A_ltln_set$(all_637_3) & member$(psi$, all_637_0) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (52) implies: % 152.10/21.17 | (53) member$(psi$, all_637_0) % 152.10/21.17 | (54) fun_app$b(all_637_2, all_637_1) = all_637_0 % 152.10/21.17 | (55) restricted_subformulas$(phi$) = all_637_1 % 152.10/21.17 | (56) fun_app$c(inf$, all_637_3) = all_637_2 % 152.10/21.17 | (57) f_G$(phi$, w$) = all_637_3 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (8) with fresh symbol all_659_0 gives: % 152.10/21.17 | (58) release_ltln$(false_ltln$) = all_659_0 & A_ltln_a_ltln_fun$(all_659_0) % 152.10/21.17 | & ! [v0: A_ltln_set$] : ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 152.10/21.17 | ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ( ~ (fG_advice$(v2, v0) % 152.10/21.17 | = v4) | ~ (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ % 152.10/21.17 | A_ltln$(v2) | ~ A_ltln_set$(v0) | ~ fun_app$(v3, v4) | % 152.10/21.17 | fun_app$(v3, v2) | ? [v5: A_ltln$] : ? [v6: A_ltln$] : % 152.10/21.17 | (fun_app$a(all_659_0, v5) = v6 & A_ltln$(v6) & A_ltln$(v5) & % 152.10/21.17 | member$(v5, v0) & ~ fun_app$(v3, v6))) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (58) implies: % 152.10/21.17 | (59) release_ltln$(false_ltln$) = all_659_0 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (11) with fresh symbols all_662_0, all_662_1 gives: % 152.10/21.17 | (60) until_ltln$(true_ltln$) = all_662_1 & release_ltln$(false_ltln$) = % 152.10/21.17 | all_662_0 & A_ltln_a_ltln_fun$(all_662_0) & % 152.10/21.17 | A_ltln_a_ltln_fun$(all_662_1) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : % 152.10/21.17 | ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! % 152.10/21.17 | [v5: A_ltln$] : ( ~ (fun_app$a(all_662_0, v0) = v4) | ~ % 152.10/21.17 | (fun_app$a(all_662_1, v4) = v5) | ~ (f_G$(v1, v2) = v3) | ~ % 152.10/21.17 | Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ A_ltln$(v0) | ~ % 152.10/21.17 | member$(v0, v3) | ? [v6: A_ltln_bool_fun$] : (semantics_ltln$(v2) = % 152.10/21.17 | v6 & A_ltln_bool_fun$(v6) & fun_app$(v6, v5))) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (60) implies: % 152.10/21.17 | (61) until_ltln$(true_ltln$) = all_662_1 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (12) with fresh symbols all_665_0, all_665_1 gives: % 152.10/21.17 | (62) until_ltln$(true_ltln$) = all_665_0 & release_ltln$(false_ltln$) = % 152.10/21.17 | all_665_1 & A_ltln_a_ltln_fun$(all_665_0) & % 152.10/21.17 | A_ltln_a_ltln_fun$(all_665_1) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : % 152.10/21.17 | ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! % 152.10/21.17 | [v5: A_ltln$] : ( ~ (g_F$(v1, v2) = v3) | ~ (fun_app$a(all_665_0, v0) % 152.10/21.17 | = v4) | ~ (fun_app$a(all_665_1, v4) = v5) | ~ Nat_a_set_fun$(v2) % 152.10/21.17 | | ~ A_ltln$(v1) | ~ A_ltln$(v0) | ~ member$(v0, v3) | ? [v6: % 152.10/21.17 | A_ltln_bool_fun$] : (semantics_ltln$(v2) = v6 & % 152.10/21.17 | A_ltln_bool_fun$(v6) & fun_app$(v6, v5))) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (62) implies: % 152.10/21.17 | (63) until_ltln$(true_ltln$) = all_665_0 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (10) with fresh symbols all_668_0, all_668_1 gives: % 152.10/21.17 | (64) until_ltln$(true_ltln$) = all_668_0 & release_ltln$(false_ltln$) = % 152.10/21.17 | all_668_1 & A_ltln_a_ltln_fun$(all_668_0) & % 152.10/21.17 | A_ltln_a_ltln_fun$(all_668_1) & ! [v0: A_ltln_set$] : ! [v1: % 152.10/21.17 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! % 152.10/21.17 | [v4: A_ltln$] : ( ~ (gF_advice$(v2, v0) = v4) | ~ % 152.10/21.17 | (semantics_ltln$(v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) % 152.10/21.17 | | ~ A_ltln_set$(v0) | ~ fun_app$(v3, v4) | fun_app$(v3, v2) | ? % 152.10/21.17 | [v5: A_ltln$] : ? [v6: A_ltln$] : ? [v7: A_ltln$] : % 152.10/21.17 | (fun_app$a(all_668_0, v5) = v6 & fun_app$a(all_668_1, v6) = v7 & % 152.10/21.17 | A_ltln$(v7) & A_ltln$(v6) & A_ltln$(v5) & member$(v5, v0) & ~ % 152.10/21.17 | fun_app$(v3, v7))) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (64) implies: % 152.10/21.17 | (65) until_ltln$(true_ltln$) = all_668_0 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (9) with fresh symbols all_671_0, all_671_1 gives: % 152.10/21.17 | (66) until_ltln$(true_ltln$) = all_671_0 & release_ltln$(false_ltln$) = % 152.10/21.17 | all_671_1 & A_ltln_a_ltln_fun$(all_671_0) & % 152.10/21.17 | A_ltln_a_ltln_fun$(all_671_1) & ! [v0: A_ltln$] : ! [v1: % 152.10/21.17 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: % 152.10/21.17 | A_ltln$] : ( ~ (fG_advice$(v2, v3) = v4) | ~ (f_G$(v0, v1) = v3) | % 152.10/21.17 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ A_ltln$(v0) | ? [v5: % 152.10/21.17 | A_ltln_set$] : ? [v6: A_ltln_bool_fun$] : ? [v7: A_ltln$] : ? % 152.10/21.17 | [v8: A_ltln$] : ((g_F$(v0, v1) = v5 & A_ltln_set$(v5) & ~ % 152.10/21.17 | member$(v2, v5)) | (fun_app$a(all_671_0, v4) = v7 & % 152.10/21.17 | fun_app$a(all_671_1, v7) = v8 & semantics_ltln$(v1) = v6 & % 152.10/21.17 | A_ltln$(v8) & A_ltln$(v7) & A_ltln_bool_fun$(v6) & fun_app$(v6, % 152.10/21.17 | v8)))) % 152.10/21.17 | % 152.10/21.17 | ALPHA: (66) implies: % 152.10/21.17 | (67) until_ltln$(true_ltln$) = all_671_0 % 152.10/21.17 | % 152.10/21.17 | DELTA: instantiating (3) with fresh symbol all_674_0 gives: % 152.10/21.18 | (68) restricted_subformulas$(phi$) = all_674_0 & A_ltln_set$(all_674_0) & % 152.10/21.18 | ! [v0: A_ltln_set$] : ! [v1: A_ltln$] : ( ~ (gF_advice$(psi$, v0) = % 152.10/21.18 | v1) | ~ A_ltln_set$(v0) | ~ member$(psi$, all_674_0) | ? [v2: % 152.10/21.18 | A_ltln_set_a_ltln_set_fun$] : ? [v3: A_ltln_set$] : % 152.10/21.18 | (gF_advice$(psi$, v3) = v1 & fun_app$c(inf$, v0) = v2 & % 152.10/21.18 | fun_app$b(v2, all_674_0) = v3 & A_ltln_set_a_ltln_set_fun$(v2) & % 152.10/21.18 | A_ltln$(v1) & A_ltln_set$(v3))) & ! [v0: A_ltln_set$] : ! [v1: % 152.10/21.18 | A_ltln_set_a_ltln_set_fun$] : ( ~ (fun_app$c(inf$, v0) = v1) | ~ % 152.10/21.18 | A_ltln_set$(v0) | ~ member$(psi$, all_674_0) | ? [v2: A_ltln_set$] % 152.10/21.18 | : ? [v3: A_ltln$] : (gF_advice$(psi$, v2) = v3 & gF_advice$(psi$, % 152.10/21.18 | v0) = v3 & fun_app$b(v1, all_674_0) = v2 & A_ltln$(v3) & % 152.10/21.18 | A_ltln_set$(v2))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (68) implies: % 152.10/21.18 | (69) A_ltln_set$(all_674_0) % 152.10/21.18 | (70) restricted_subformulas$(phi$) = all_674_0 % 152.10/21.18 | (71) ! [v0: A_ltln_set$] : ! [v1: A_ltln_set_a_ltln_set_fun$] : ( ~ % 152.10/21.18 | (fun_app$c(inf$, v0) = v1) | ~ A_ltln_set$(v0) | ~ member$(psi$, % 152.10/21.18 | all_674_0) | ? [v2: A_ltln_set$] : ? [v3: A_ltln$] : % 152.10/21.18 | (gF_advice$(psi$, v2) = v3 & gF_advice$(psi$, v0) = v3 & % 152.10/21.18 | fun_app$b(v1, all_674_0) = v2 & A_ltln$(v3) & A_ltln_set$(v2))) % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (4) with fresh symbols all_677_0, all_677_1 gives: % 152.10/21.18 | (72) until_ltln$(true_ltln$) = all_677_1 & release_ltln$(false_ltln$) = % 152.10/21.18 | all_677_0 & A_ltln_a_ltln_fun$(all_677_0) & % 152.10/21.18 | A_ltln_a_ltln_fun$(all_677_1) & ! [v0: A_ltln$] : ! [v1: % 152.10/21.18 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: % 152.10/21.18 | A_ltln$] : ( ~ (g_F$(v0, v1) = v3) | ~ (gF_advice$(v2, v3) = v4) | % 152.10/21.18 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ A_ltln$(v0) | ? [v5: % 152.10/21.18 | A_ltln_set$] : ? [v6: A_ltln_bool_fun$] : ? [v7: A_ltln$] : ? % 152.10/21.18 | [v8: A_ltln$] : ((fun_app$a(all_677_0, v4) = v7 & % 152.10/21.18 | fun_app$a(all_677_1, v7) = v8 & semantics_ltln$(v1) = v6 & % 152.10/21.18 | A_ltln$(v8) & A_ltln$(v7) & A_ltln_bool_fun$(v6) & fun_app$(v6, % 152.10/21.18 | v8)) | (f_G$(v0, v1) = v5 & A_ltln_set$(v5) & ~ member$(v2, % 152.10/21.18 | v5)))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (72) implies: % 152.10/21.18 | (73) release_ltln$(false_ltln$) = all_677_0 % 152.10/21.18 | (74) until_ltln$(true_ltln$) = all_677_1 % 152.10/21.18 | (75) ! [v0: A_ltln$] : ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! % 152.10/21.18 | [v3: A_ltln_set$] : ! [v4: A_ltln$] : ( ~ (g_F$(v0, v1) = v3) | ~ % 152.10/21.18 | (gF_advice$(v2, v3) = v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 152.10/21.18 | ~ A_ltln$(v0) | ? [v5: A_ltln_set$] : ? [v6: A_ltln_bool_fun$] : % 152.10/21.18 | ? [v7: A_ltln$] : ? [v8: A_ltln$] : ((fun_app$a(all_677_0, v4) = v7 % 152.10/21.18 | & fun_app$a(all_677_1, v7) = v8 & semantics_ltln$(v1) = v6 & % 152.10/21.18 | A_ltln$(v8) & A_ltln$(v7) & A_ltln_bool_fun$(v6) & fun_app$(v6, % 152.10/21.18 | v8)) | (f_G$(v0, v1) = v5 & A_ltln_set$(v5) & ~ member$(v2, % 152.10/21.18 | v5)))) % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (37) with fresh symbols all_680_0, all_680_1, all_680_2, % 152.10/21.18 | all_680_3, all_680_4, all_680_5, all_680_6, all_680_7, all_680_8, % 152.10/21.18 | all_680_9 gives: % 152.10/21.18 | (76) until_ltln$(true_ltln$) = all_680_8 & release_ltln$(false_ltln$) = % 152.10/21.18 | all_680_7 & g_F$(phi$, w$) = all_680_6 & fun_app$a(all_680_7, % 152.10/21.18 | all_680_2) = all_680_1 & fun_app$a(all_680_8, all_680_1) = all_680_0 % 152.10/21.18 | & gF_advice$(psi$, all_680_3) = all_680_2 & semantics_ltln$(w$) = % 152.10/21.18 | all_680_9 & fun_app$c(inf$, all_680_6) = all_680_5 & % 152.10/21.18 | restricted_subformulas$(phi$) = all_680_4 & fun_app$b(all_680_5, % 152.10/21.18 | all_680_4) = all_680_3 & A_ltln_set_a_ltln_set_fun$(all_680_5) & % 152.10/21.18 | A_ltln$(all_680_0) & A_ltln$(all_680_1) & A_ltln$(all_680_2) & % 152.10/21.18 | A_ltln_set$(all_680_3) & A_ltln_set$(all_680_4) & % 152.10/21.18 | A_ltln_set$(all_680_6) & A_ltln_bool_fun$(all_680_9) & % 152.10/21.18 | A_ltln_a_ltln_fun$(all_680_7) & A_ltln_a_ltln_fun$(all_680_8) & ~ % 152.10/21.18 | fun_app$(all_680_9, all_680_0) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (76) implies: % 152.10/21.18 | (77) ~ fun_app$(all_680_9, all_680_0) % 152.10/21.18 | (78) A_ltln_set$(all_680_6) % 152.10/21.18 | (79) A_ltln$(all_680_1) % 152.10/21.18 | (80) fun_app$b(all_680_5, all_680_4) = all_680_3 % 152.10/21.18 | (81) restricted_subformulas$(phi$) = all_680_4 % 152.10/21.18 | (82) fun_app$c(inf$, all_680_6) = all_680_5 % 152.10/21.18 | (83) semantics_ltln$(w$) = all_680_9 % 152.10/21.18 | (84) gF_advice$(psi$, all_680_3) = all_680_2 % 152.10/21.18 | (85) fun_app$a(all_680_8, all_680_1) = all_680_0 % 152.10/21.18 | (86) fun_app$a(all_680_7, all_680_2) = all_680_1 % 152.10/21.18 | (87) g_F$(phi$, w$) = all_680_6 % 152.10/21.18 | (88) release_ltln$(false_ltln$) = all_680_7 % 152.10/21.18 | (89) until_ltln$(true_ltln$) = all_680_8 % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (7) with fresh symbol all_682_0 gives: % 152.10/21.18 | (90) release_ltln$(false_ltln$) = all_682_0 & A_ltln_a_ltln_fun$(all_682_0) % 152.10/21.18 | & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.18 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.18 | A_ltln$] : ! [v6: A_ltln$] : ( ~ (release_ltln$(v1) = v4) | ~ % 152.10/21.18 | (fun_app$a(v4, v2) = v5) | ~ (fun_app$a(all_682_0, v5) = v6) | ~ % 152.10/21.18 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.18 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v6) | ? [v7: A_ltln$] : % 152.10/21.18 | (fun_app$a(all_682_0, v2) = v7 & A_ltln$(v7) & fun_app$(v3, v7))) & % 152.10/21.18 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.18 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : % 152.10/21.18 | ! [v6: A_ltln$] : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.18 | v2) = v5) | ~ (fun_app$a(all_682_0, v5) = v6) | ~ % 152.10/21.18 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.18 | | ~ A_ltln$(v1) | fun_app$(v3, v6) | ? [v7: A_ltln$] : % 152.10/21.18 | (fun_app$a(all_682_0, v2) = v7 & A_ltln$(v7) & ~ fun_app$(v3, v7))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (90) implies: % 152.10/21.18 | (91) release_ltln$(false_ltln$) = all_682_0 % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (6) with fresh symbol all_685_0 gives: % 152.10/21.18 | (92) until_ltln$(true_ltln$) = all_685_0 & A_ltln_a_ltln_fun$(all_685_0) & % 152.10/21.18 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.18 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : % 152.10/21.18 | ! [v6: A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) % 152.10/21.18 | = v5) | ~ (fun_app$a(all_685_0, v5) = v6) | ~ % 152.10/21.18 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.18 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v6) | ? [v7: A_ltln$] : % 152.10/21.18 | (fun_app$a(all_685_0, v2) = v7 & A_ltln$(v7) & fun_app$(v3, v7))) & % 152.10/21.18 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.18 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : % 152.10/21.18 | ! [v6: A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) % 152.10/21.18 | = v5) | ~ (fun_app$a(all_685_0, v5) = v6) | ~ % 152.10/21.18 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.18 | | ~ A_ltln$(v1) | fun_app$(v3, v6) | ? [v7: A_ltln$] : % 152.10/21.18 | (fun_app$a(all_685_0, v2) = v7 & A_ltln$(v7) & ~ fun_app$(v3, v7))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (92) implies: % 152.10/21.18 | (93) until_ltln$(true_ltln$) = all_685_0 % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (15) with fresh symbols all_688_0, all_688_1 gives: % 152.10/21.18 | (94) until_ltln$(true_ltln$) = all_688_1 & release_ltln$(false_ltln$) = % 152.10/21.18 | all_688_0 & A_ltln_a_ltln_fun$(all_688_0) & % 152.10/21.18 | A_ltln_a_ltln_fun$(all_688_1) & ! [v0: Nat$] : ! [v1: % 152.10/21.18 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.18 | A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ( ~ % 152.10/21.18 | (suffix$(v0, v1) = v5) | ~ (fun_app$a(all_688_0, v2) = v3) | ~ % 152.10/21.18 | (fun_app$a(all_688_1, v3) = v4) | ~ (semantics_ltln$(v5) = v6) | ~ % 152.10/21.18 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | fun_app$(v6, v4) % 152.10/21.18 | | ? [v7: A_ltln_bool_fun$] : (semantics_ltln$(v1) = v7 & % 152.10/21.18 | A_ltln_bool_fun$(v7) & ~ fun_app$(v7, v4))) & ! [v0: Nat$] : ! % 152.10/21.18 | [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 152.10/21.18 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.18 | (suffix$(v0, v1) = v3) | ~ (fun_app$a(all_688_0, v2) = v5) | ~ % 152.10/21.18 | (fun_app$a(all_688_1, v5) = v6) | ~ (semantics_ltln$(v3) = v4) | ~ % 152.10/21.18 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | ~ fun_app$(v4, % 152.10/21.18 | v6) | ? [v7: A_ltln_bool_fun$] : (semantics_ltln$(v1) = v7 & % 152.10/21.18 | A_ltln_bool_fun$(v7) & fun_app$(v7, v6))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (94) implies: % 152.10/21.18 | (95) release_ltln$(false_ltln$) = all_688_0 % 152.10/21.18 | (96) until_ltln$(true_ltln$) = all_688_1 % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (16) with fresh symbols all_691_0, all_691_1 gives: % 152.10/21.18 | (97) until_ltln$(true_ltln$) = all_691_0 & release_ltln$(false_ltln$) = % 152.10/21.18 | all_691_1 & A_ltln_a_ltln_fun$(all_691_0) & % 152.10/21.18 | A_ltln_a_ltln_fun$(all_691_1) & ! [v0: Nat$] : ! [v1: % 152.10/21.18 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 152.10/21.18 | A_ltln$] : ! [v5: Nat_a_set_fun$] : ! [v6: A_ltln_bool_fun$] : ( ~ % 152.10/21.18 | (suffix$(v0, v1) = v5) | ~ (fun_app$a(all_691_0, v2) = v3) | ~ % 152.10/21.18 | (fun_app$a(all_691_1, v3) = v4) | ~ (semantics_ltln$(v5) = v6) | ~ % 152.10/21.18 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | fun_app$(v6, v4) % 152.10/21.18 | | ? [v7: A_ltln_bool_fun$] : (semantics_ltln$(v1) = v7 & % 152.10/21.18 | A_ltln_bool_fun$(v7) & ~ fun_app$(v7, v4))) & ! [v0: Nat$] : ! % 152.10/21.18 | [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! % 152.10/21.18 | [v4: A_ltln_bool_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.18 | (suffix$(v0, v1) = v3) | ~ (fun_app$a(all_691_0, v2) = v5) | ~ % 152.10/21.18 | (fun_app$a(all_691_1, v5) = v6) | ~ (semantics_ltln$(v3) = v4) | ~ % 152.10/21.18 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ Nat$(v0) | ~ fun_app$(v4, % 152.10/21.18 | v6) | ? [v7: A_ltln_bool_fun$] : (semantics_ltln$(v1) = v7 & % 152.10/21.18 | A_ltln_bool_fun$(v7) & fun_app$(v7, v6))) % 152.10/21.18 | % 152.10/21.18 | ALPHA: (97) implies: % 152.10/21.18 | (98) release_ltln$(false_ltln$) = all_691_1 % 152.10/21.18 | (99) until_ltln$(true_ltln$) = all_691_0 % 152.10/21.18 | % 152.10/21.18 | DELTA: instantiating (5) with fresh symbols all_694_0, all_694_1, all_694_2, % 152.10/21.18 | all_694_3, all_694_4, all_694_5, all_694_6, all_694_7, all_694_8, % 152.10/21.18 | all_694_9 gives: % 152.10/21.19 | (100) until_ltln$(true_ltln$) = all_694_3 & release_ltln$(false_ltln$) = % 152.10/21.19 | all_694_4 & g_F$(phi$, w$) = all_694_9 & semantics_ltln$(w$) = % 152.10/21.19 | all_694_5 & f_G$(phi$, w$) = all_694_2 & fun_app$c(inf$, all_694_2) = % 152.10/21.19 | all_694_1 & fun_app$c(inf$, all_694_9) = all_694_8 & % 152.10/21.19 | restricted_subformulas$(phi$) = all_694_7 & fun_app$b(all_694_1, % 152.10/21.19 | all_694_7) = all_694_0 & fun_app$b(all_694_8, all_694_7) = % 152.10/21.19 | all_694_6 & A_ltln_set_a_ltln_set_fun$(all_694_1) & % 152.10/21.19 | A_ltln_set_a_ltln_set_fun$(all_694_8) & A_ltln_set$(all_694_0) & % 152.10/21.19 | A_ltln_set$(all_694_2) & A_ltln_set$(all_694_6) & % 152.10/21.19 | A_ltln_set$(all_694_7) & A_ltln_set$(all_694_9) & % 152.10/21.19 | A_ltln_bool_fun$(all_694_5) & A_ltln_a_ltln_fun$(all_694_3) & % 152.10/21.19 | A_ltln_a_ltln_fun$(all_694_4) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : % 152.10/21.19 | ( ~ (fG_advice$(v0, all_694_0) = v1) | ~ A_ltln$(v0) | ~ % 152.10/21.19 | member$(v0, all_694_6) | ? [v2: A_ltln$] : ? [v3: A_ltln$] : % 152.10/21.19 | (fun_app$a(all_694_3, v1) = v2 & fun_app$a(all_694_4, v2) = v3 & % 152.10/21.19 | A_ltln$(v3) & A_ltln$(v2) & fun_app$(all_694_5, v3))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (100) implies: % 152.10/21.19 | (101) A_ltln_set$(all_694_2) % 152.10/21.19 | (102) fun_app$b(all_694_8, all_694_7) = all_694_6 % 152.10/21.19 | (103) fun_app$b(all_694_1, all_694_7) = all_694_0 % 152.10/21.19 | (104) restricted_subformulas$(phi$) = all_694_7 % 152.10/21.19 | (105) fun_app$c(inf$, all_694_9) = all_694_8 % 152.10/21.19 | (106) fun_app$c(inf$, all_694_2) = all_694_1 % 152.10/21.19 | (107) f_G$(phi$, w$) = all_694_2 % 152.10/21.19 | (108) semantics_ltln$(w$) = all_694_5 % 152.10/21.19 | (109) g_F$(phi$, w$) = all_694_9 % 152.10/21.19 | (110) until_ltln$(true_ltln$) = all_694_3 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (18) with fresh symbol all_697_0 gives: % 152.10/21.19 | (111) release_ltln$(false_ltln$) = all_697_0 & % 152.10/21.19 | A_ltln_a_ltln_fun$(all_697_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.19 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.19 | A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (weakUntil_ltln$(v1) = % 152.10/21.19 | v4) | ~ (fun_app$a(v4, v2) = v5) | ~ (semantics_ltln$(v0) = v3) % 152.10/21.19 | | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.19 | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : % 152.10/21.19 | ? [v8: A_ltln$] : ((until_ltln$(v1) = v7 & fun_app$a(v7, v2) = v8 % 152.10/21.19 | & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v8)) | % 152.10/21.19 | (fun_app$a(all_697_0, v1) = v6 & A_ltln$(v6) & fun_app$(v3, % 152.10/21.19 | v6)))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] % 152.10/21.19 | : ! [v5: A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.19 | v2) = v5) | ~ (semantics_ltln$(v0) = v3) | ~ % 152.10/21.19 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, % 152.10/21.19 | v5) | ? [v6: A_ltln_a_ltln_fun$] : ? [v7: A_ltln$] : ? [v8: % 152.10/21.19 | A_ltln$] : ((weakUntil_ltln$(v1) = v6 & fun_app$a(v6, v2) = v7 & % 152.10/21.19 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v6) & ~ fun_app$(v3, v7)) | % 152.10/21.19 | (fun_app$a(all_697_0, v1) = v8 & A_ltln$(v8) & fun_app$(v3, % 152.10/21.19 | v8)))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (111) implies: % 152.10/21.19 | (112) release_ltln$(false_ltln$) = all_697_0 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (23) with fresh symbol all_700_0 gives: % 152.10/21.19 | (113) release_ltln$(false_ltln$) = all_700_0 & % 152.10/21.19 | A_ltln_a_ltln_fun$(all_700_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.19 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.19 | A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ % 152.10/21.19 | (strongRelease_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.19 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.19 | | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln_a_ltln_fun$] : % 152.10/21.19 | ? [v7: A_ltln$] : ? [v8: A_ltln$] : ((release_ltln$(v1) = v6 & % 152.10/21.19 | fun_app$a(v6, v2) = v7 & A_ltln$(v7) & A_ltln_a_ltln_fun$(v6) & % 152.10/21.19 | ~ fun_app$(v3, v7)) | (fun_app$a(all_700_0, v2) = v8 & % 152.10/21.19 | A_ltln$(v8) & fun_app$(v3, v8)))) & ! [v0: Nat_a_set_fun$] : % 152.10/21.19 | ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! % 152.10/21.19 | [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ( ~ (release_ltln$(v1) % 152.10/21.19 | = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ (semantics_ltln$(v0) = % 152.10/21.19 | v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | % 152.10/21.19 | ~ fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] % 152.10/21.19 | : ? [v8: A_ltln$] : ((strongRelease_ltln$(v1) = v7 & fun_app$a(v7, % 152.10/21.19 | v2) = v8 & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & % 152.10/21.19 | fun_app$(v3, v8)) | (fun_app$a(all_700_0, v2) = v6 & % 152.10/21.19 | A_ltln$(v6) & fun_app$(v3, v6)))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (113) implies: % 152.10/21.19 | (114) release_ltln$(false_ltln$) = all_700_0 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (17) with fresh symbol all_703_0 gives: % 152.10/21.19 | (115) until_ltln$(true_ltln$) = all_703_0 & A_ltln_a_ltln_fun$(all_703_0) & % 152.10/21.19 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.19 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.19 | A_ltln$] : ( ~ (strongRelease_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.19 | v2) = v5) | ~ (semantics_ltln$(v0) = v3) | ~ % 152.10/21.19 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, % 152.10/21.19 | v5) | ? [v6: A_ltln_a_ltln_fun$] : ? [v7: A_ltln$] : ? [v8: % 152.10/21.19 | A_ltln$] : ((release_ltln$(v1) = v6 & fun_app$a(v6, v2) = v7 & % 152.10/21.19 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v6) & ~ fun_app$(v3, v7)) | % 152.10/21.19 | (fun_app$a(all_703_0, v1) = v8 & A_ltln$(v8) & ~ fun_app$(v3, % 152.10/21.19 | v8)))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] % 152.10/21.19 | : ! [v5: A_ltln$] : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.19 | v2) = v5) | ~ (semantics_ltln$(v0) = v3) | ~ % 152.10/21.19 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.19 | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : % 152.10/21.19 | ? [v8: A_ltln$] : ((strongRelease_ltln$(v1) = v7 & fun_app$a(v7, % 152.10/21.19 | v2) = v8 & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & % 152.10/21.19 | fun_app$(v3, v8)) | (fun_app$a(all_703_0, v1) = v6 & % 152.10/21.19 | A_ltln$(v6) & ~ fun_app$(v3, v6)))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (115) implies: % 152.10/21.19 | (116) until_ltln$(true_ltln$) = all_703_0 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (22) with fresh symbol all_706_0 gives: % 152.10/21.19 | (117) until_ltln$(true_ltln$) = all_706_0 & A_ltln_a_ltln_fun$(all_706_0) & % 152.10/21.19 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.19 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.19 | A_ltln$] : ( ~ (weakUntil_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = % 152.10/21.19 | v5) | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.19 | A_ltln$(v2) | ~ A_ltln$(v1) | ~ fun_app$(v3, v5) | ? [v6: % 152.10/21.19 | A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : % 152.10/21.19 | ((until_ltln$(v1) = v7 & fun_app$a(v7, v2) = v8 & A_ltln$(v8) & % 152.10/21.19 | A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v8)) | % 152.10/21.19 | (fun_app$a(all_706_0, v2) = v6 & A_ltln$(v6) & ~ fun_app$(v3, % 152.10/21.19 | v6)))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] % 152.10/21.19 | : ! [v5: A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.19 | v2) = v5) | ~ (semantics_ltln$(v0) = v3) | ~ % 152.10/21.19 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, % 152.10/21.19 | v5) | ? [v6: A_ltln_a_ltln_fun$] : ? [v7: A_ltln$] : ? [v8: % 152.10/21.19 | A_ltln$] : ((weakUntil_ltln$(v1) = v6 & fun_app$a(v6, v2) = v7 & % 152.10/21.19 | A_ltln$(v7) & A_ltln_a_ltln_fun$(v6) & ~ fun_app$(v3, v7)) | % 152.10/21.19 | (fun_app$a(all_706_0, v2) = v8 & A_ltln$(v8) & ~ fun_app$(v3, % 152.10/21.19 | v8)))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (117) implies: % 152.10/21.19 | (118) until_ltln$(true_ltln$) = all_706_0 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (20) with fresh symbol all_709_0 gives: % 152.10/21.19 | (119) until_ltln$(true_ltln$) = all_709_0 & A_ltln_a_ltln_fun$(all_709_0) & % 152.10/21.19 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] : ! [v4: A_ltln$] % 152.10/21.19 | : ( ~ (strongRelease_ltln$(v1) = v3) | ~ (fun_app$a(v3, true_ltln$) % 152.10/21.19 | = v4) | ~ (semantics_ltln$(v0) = v2) | ~ Nat_a_set_fun$(v0) | % 152.10/21.19 | ~ A_ltln$(v1) | ~ fun_app$(v2, v4) | ? [v5: A_ltln$] : % 152.10/21.19 | (fun_app$a(all_709_0, v1) = v5 & A_ltln$(v5) & fun_app$(v2, v5))) & % 152.10/21.19 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] : ! [v4: A_ltln$] % 152.10/21.19 | : ( ~ (strongRelease_ltln$(v1) = v3) | ~ (fun_app$a(v3, true_ltln$) % 152.10/21.19 | = v4) | ~ (semantics_ltln$(v0) = v2) | ~ Nat_a_set_fun$(v0) | % 152.10/21.19 | ~ A_ltln$(v1) | fun_app$(v2, v4) | ? [v5: A_ltln$] : % 152.10/21.19 | (fun_app$a(all_709_0, v1) = v5 & A_ltln$(v5) & ~ fun_app$(v2, % 152.10/21.19 | v5))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: % 152.10/21.19 | A_ltln_bool_fun$] : ! [v3: A_ltln$] : ( ~ (fun_app$a(all_709_0, % 152.10/21.19 | v1) = v3) | ~ (semantics_ltln$(v0) = v2) | ~ % 152.10/21.19 | Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ~ fun_app$(v2, v3) | ? [v4: % 152.10/21.19 | A_ltln_a_ltln_fun$] : ? [v5: A_ltln$] : (strongRelease_ltln$(v1) % 152.10/21.19 | = v4 & fun_app$a(v4, true_ltln$) = v5 & A_ltln$(v5) & % 152.10/21.19 | A_ltln_a_ltln_fun$(v4) & fun_app$(v2, v5))) & ! [v0: % 152.10/21.19 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln_bool_fun$] : ! % 152.10/21.19 | [v3: A_ltln$] : ( ~ (fun_app$a(all_709_0, v1) = v3) | ~ % 152.10/21.19 | (semantics_ltln$(v0) = v2) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) % 152.10/21.19 | | fun_app$(v2, v3) | ? [v4: A_ltln_a_ltln_fun$] : ? [v5: A_ltln$] % 152.10/21.19 | : (strongRelease_ltln$(v1) = v4 & fun_app$a(v4, true_ltln$) = v5 & % 152.10/21.19 | A_ltln$(v5) & A_ltln_a_ltln_fun$(v4) & ~ fun_app$(v2, v5))) % 152.10/21.19 | % 152.10/21.19 | ALPHA: (119) implies: % 152.10/21.19 | (120) until_ltln$(true_ltln$) = all_709_0 % 152.10/21.19 | % 152.10/21.19 | DELTA: instantiating (21) with fresh symbol all_712_0 gives: % 152.10/21.20 | (121) release_ltln$(false_ltln$) = all_712_0 & % 152.10/21.20 | A_ltln_a_ltln_fun$(all_712_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.20 | A_ltln$] : ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] % 152.10/21.20 | : ! [v4: A_ltln$] : ( ~ (weakUntil_ltln$(v1) = v3) | ~ % 152.10/21.20 | (fun_app$a(v3, false_ltln$) = v4) | ~ (semantics_ltln$(v0) = v2) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ~ fun_app$(v2, v4) | ? % 152.10/21.20 | [v5: A_ltln$] : (fun_app$a(all_712_0, v1) = v5 & A_ltln$(v5) & % 152.10/21.20 | fun_app$(v2, v5))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : % 152.10/21.20 | ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln_a_ltln_fun$] : ! [v4: % 152.10/21.20 | A_ltln$] : ( ~ (weakUntil_ltln$(v1) = v3) | ~ (fun_app$a(v3, % 152.10/21.20 | false_ltln$) = v4) | ~ (semantics_ltln$(v0) = v2) | ~ % 152.10/21.20 | Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | fun_app$(v2, v4) | ? [v5: % 152.10/21.20 | A_ltln$] : (fun_app$a(all_712_0, v1) = v5 & A_ltln$(v5) & ~ % 152.10/21.20 | fun_app$(v2, v5))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : % 152.10/21.20 | ! [v2: A_ltln_bool_fun$] : ! [v3: A_ltln$] : ( ~ % 152.10/21.20 | (fun_app$a(all_712_0, v1) = v3) | ~ (semantics_ltln$(v0) = v2) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ~ fun_app$(v2, v3) | ? % 152.10/21.20 | [v4: A_ltln_a_ltln_fun$] : ? [v5: A_ltln$] : (weakUntil_ltln$(v1) % 152.10/21.20 | = v4 & fun_app$a(v4, false_ltln$) = v5 & A_ltln$(v5) & % 152.10/21.20 | A_ltln_a_ltln_fun$(v4) & fun_app$(v2, v5))) & ! [v0: % 152.10/21.20 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln_bool_fun$] : ! % 152.10/21.20 | [v3: A_ltln$] : ( ~ (fun_app$a(all_712_0, v1) = v3) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v2) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) % 152.10/21.20 | | fun_app$(v2, v3) | ? [v4: A_ltln_a_ltln_fun$] : ? [v5: A_ltln$] % 152.10/21.20 | : (weakUntil_ltln$(v1) = v4 & fun_app$a(v4, false_ltln$) = v5 & % 152.10/21.20 | A_ltln$(v5) & A_ltln_a_ltln_fun$(v4) & ~ fun_app$(v2, v5))) % 152.10/21.20 | % 152.10/21.20 | ALPHA: (121) implies: % 152.10/21.20 | (122) release_ltln$(false_ltln$) = all_712_0 % 152.10/21.20 | % 152.10/21.20 | DELTA: instantiating (26) with fresh symbol all_735_0 gives: % 152.10/21.20 | (123) until_ltln$(true_ltln$) = all_735_0 & A_ltln_a_ltln_fun$(all_735_0) & % 152.10/21.20 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.20 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.20 | A_ltln$] : ! [v6: A_ltln$] : ( ~ (and_ltln$(v1) = v4) | ~ % 152.10/21.20 | (fun_app$a(v4, v2) = v5) | ~ (fun_app$a(all_735_0, v5) = v6) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.20 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v6) | ? [v7: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : % 152.10/21.20 | (strongRelease_ltln$(v1) = v7 & fun_app$a(v7, v2) = v8 & % 152.10/21.20 | fun_app$a(all_735_0, v8) = v9 & A_ltln$(v9) & A_ltln$(v8) & % 152.10/21.20 | A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v9))) & ! [v0: % 152.10/21.20 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.20 | : ! [v6: A_ltln$] : ( ~ (and_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) % 152.10/21.20 | = v5) | ~ (fun_app$a(all_735_0, v5) = v6) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.20 | | ~ A_ltln$(v1) | fun_app$(v3, v6) | ? [v7: A_ltln_a_ltln_fun$] : % 152.10/21.20 | ? [v8: A_ltln$] : ? [v9: A_ltln$] : (strongRelease_ltln$(v1) = v7 % 152.10/21.20 | & fun_app$a(v7, v2) = v8 & fun_app$a(all_735_0, v8) = v9 & % 152.10/21.20 | A_ltln$(v9) & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & ~ % 152.10/21.20 | fun_app$(v3, v9))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : % 152.10/21.20 | ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 152.10/21.20 | (strongRelease_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.20 | (fun_app$a(all_735_0, v5) = v6) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.20 | fun_app$(v3, v6) | ? [v7: A_ltln_a_ltln_fun$] : ? [v8: A_ltln$] : % 152.10/21.20 | ? [v9: A_ltln$] : (and_ltln$(v1) = v7 & fun_app$a(v7, v2) = v8 & % 152.10/21.20 | fun_app$a(all_735_0, v8) = v9 & A_ltln$(v9) & A_ltln$(v8) & % 152.10/21.20 | A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v9))) & ! [v0: % 152.10/21.20 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.20 | : ! [v6: A_ltln$] : ( ~ (strongRelease_ltln$(v1) = v4) | ~ % 152.10/21.20 | (fun_app$a(v4, v2) = v5) | ~ (fun_app$a(all_735_0, v5) = v6) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.20 | | ~ A_ltln$(v1) | fun_app$(v3, v6) | ? [v7: A_ltln_a_ltln_fun$] : % 152.10/21.20 | ? [v8: A_ltln$] : ? [v9: A_ltln$] : (and_ltln$(v1) = v7 & % 152.10/21.20 | fun_app$a(v7, v2) = v8 & fun_app$a(all_735_0, v8) = v9 & % 152.10/21.20 | A_ltln$(v9) & A_ltln$(v8) & A_ltln_a_ltln_fun$(v7) & ~ % 152.10/21.20 | fun_app$(v3, v9))) % 152.10/21.20 | % 152.10/21.20 | ALPHA: (123) implies: % 152.10/21.20 | (124) until_ltln$(true_ltln$) = all_735_0 % 152.10/21.20 | % 152.10/21.20 | DELTA: instantiating (24) with fresh symbol all_738_0 gives: % 152.10/21.20 | (125) release_ltln$(false_ltln$) = all_738_0 & % 152.10/21.20 | A_ltln_a_ltln_fun$(all_738_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.20 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.20 | A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ % 152.10/21.20 | (or_ltln$(v4) = v5) | ~ (until_ltln$(v1) = v6) | ~ (fun_app$a(v6, % 152.10/21.20 | v2) = v7) | ~ (fun_app$a(v5, v7) = v8) | ~ % 152.10/21.20 | (fun_app$a(all_738_0, v1) = v4) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.20 | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 152.10/21.20 | : (weakUntil_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & % 152.10/21.20 | A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & fun_app$(v3, v10))) & ! % 152.10/21.20 | [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.20 | : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : % 152.10/21.20 | ( ~ (or_ltln$(v4) = v5) | ~ (until_ltln$(v1) = v6) | ~ % 152.10/21.20 | (fun_app$a(v6, v2) = v7) | ~ (fun_app$a(v5, v7) = v8) | ~ % 152.10/21.20 | (fun_app$a(all_738_0, v1) = v4) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | % 152.10/21.20 | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 152.10/21.20 | : (weakUntil_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & % 152.10/21.20 | A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & ~ fun_app$(v3, v10))) & % 152.10/21.20 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.20 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.20 | A_ltln$] : ( ~ (weakUntil_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = % 152.10/21.20 | v5) | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.20 | A_ltln$(v2) | ~ A_ltln$(v1) | ~ fun_app$(v3, v5) | ? [v6: % 152.10/21.20 | A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : ? [v8: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 152.10/21.20 | (or_ltln$(v6) = v7 & until_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 % 152.10/21.20 | & fun_app$a(v7, v9) = v10 & fun_app$a(all_738_0, v1) = v6 & % 152.10/21.20 | A_ltln$(v10) & A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) % 152.10/21.20 | & A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v10))) & ! [v0: % 152.10/21.20 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.20 | : ( ~ (weakUntil_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.20 | | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.20 | A_ltln$] : ? [v10: A_ltln$] : (or_ltln$(v6) = v7 & % 152.10/21.20 | until_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & fun_app$a(v7, v9) % 152.10/21.20 | = v10 & fun_app$a(all_738_0, v1) = v6 & A_ltln$(v10) & % 152.10/21.20 | A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.20 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v10))) % 152.10/21.20 | % 152.10/21.20 | ALPHA: (125) implies: % 152.10/21.20 | (126) release_ltln$(false_ltln$) = all_738_0 % 152.10/21.20 | % 152.10/21.20 | DELTA: instantiating (25) with fresh symbol all_741_0 gives: % 152.10/21.20 | (127) until_ltln$(true_ltln$) = all_741_0 & A_ltln_a_ltln_fun$(all_741_0) & % 152.10/21.20 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.20 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: % 152.10/21.20 | A_ltln$] : ! [v8: A_ltln$] : ( ~ (and_ltln$(v4) = v5) | ~ % 152.10/21.20 | (release_ltln$(v1) = v6) | ~ (fun_app$a(v6, v2) = v7) | ~ % 152.10/21.20 | (fun_app$a(v5, v7) = v8) | ~ (fun_app$a(all_741_0, v1) = v4) | ~ % 152.10/21.20 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.20 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v8) | ? [v9: % 152.10/21.20 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : % 152.10/21.20 | (strongRelease_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & % 152.10/21.20 | A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & fun_app$(v3, v10))) & ! % 152.10/21.20 | [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.20 | : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : % 152.10/21.20 | ( ~ (and_ltln$(v4) = v5) | ~ (release_ltln$(v1) = v6) | ~ % 152.10/21.20 | (fun_app$a(v6, v2) = v7) | ~ (fun_app$a(v5, v7) = v8) | ~ % 152.10/21.20 | (fun_app$a(all_741_0, v1) = v4) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.20 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | % 152.10/21.20 | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 152.10/21.20 | : (strongRelease_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & % 152.10/21.20 | A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & ~ fun_app$(v3, v10))) & % 152.10/21.20 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.20 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.20 | A_ltln$] : ( ~ (strongRelease_ltln$(v1) = v4) | ~ (fun_app$a(v4, % 152.10/21.20 | v2) = v5) | ~ (semantics_ltln$(v0) = v3) | ~ % 152.10/21.20 | Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.20 | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : % 152.10/21.20 | ? [v8: A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] % 152.10/21.20 | : (and_ltln$(v6) = v7 & release_ltln$(v1) = v8 & fun_app$a(v8, v2) % 152.10/21.20 | = v9 & fun_app$a(v7, v9) = v10 & fun_app$a(all_741_0, v1) = v6 & % 152.10/21.20 | A_ltln$(v10) & A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) % 152.10/21.20 | & A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v10))) & ! [v0: % 152.10/21.20 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.20 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.20 | : ( ~ (strongRelease_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | % 152.10/21.20 | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.20 | A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] % 152.10/21.20 | : ? [v7: A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? % 152.10/21.20 | [v9: A_ltln$] : ? [v10: A_ltln$] : (and_ltln$(v6) = v7 & % 152.10/21.20 | release_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & fun_app$a(v7, % 152.10/21.20 | v9) = v10 & fun_app$a(all_741_0, v1) = v6 & A_ltln$(v10) & % 152.10/21.20 | A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.20 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v10))) % 152.10/21.20 | % 152.10/21.20 | ALPHA: (127) implies: % 152.10/21.20 | (128) until_ltln$(true_ltln$) = all_741_0 % 152.10/21.20 | % 152.10/21.20 | DELTA: instantiating (28) with fresh symbol all_744_0 gives: % 152.10/21.21 | (129) until_ltln$(true_ltln$) = all_744_0 & A_ltln_a_ltln_fun$(all_744_0) & % 152.10/21.21 | ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.21 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: % 152.10/21.21 | A_ltln$] : ! [v8: A_ltln$] : ( ~ (and_ltln$(v4) = v5) | ~ % 152.10/21.21 | (weakUntil_ltln$(v1) = v6) | ~ (fun_app$a(v6, v2) = v7) | ~ % 152.10/21.21 | (fun_app$a(v5, v7) = v8) | ~ (fun_app$a(all_744_0, v2) = v4) | ~ % 152.10/21.21 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.21 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v8) | ? [v9: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : (until_ltln$(v1) = v9 & % 152.10/21.21 | fun_app$a(v9, v2) = v10 & A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & % 152.10/21.21 | fun_app$(v3, v10))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] % 152.10/21.21 | : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: A_ltln$] : % 152.10/21.21 | ! [v5: A_ltln_a_ltln_fun$] : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: % 152.10/21.21 | A_ltln$] : ! [v8: A_ltln$] : ( ~ (and_ltln$(v4) = v5) | ~ % 152.10/21.21 | (weakUntil_ltln$(v1) = v6) | ~ (fun_app$a(v6, v2) = v7) | ~ % 152.10/21.21 | (fun_app$a(v5, v7) = v8) | ~ (fun_app$a(all_744_0, v2) = v4) | ~ % 152.10/21.21 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.21 | | ~ A_ltln$(v1) | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : % 152.10/21.21 | ? [v10: A_ltln$] : (until_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 % 152.10/21.21 | & A_ltln$(v10) & A_ltln_a_ltln_fun$(v9) & ~ fun_app$(v3, v10))) % 152.10/21.21 | & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.21 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.21 | A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) % 152.10/21.21 | | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.21 | A_ltln$(v2) | ~ A_ltln$(v1) | ~ fun_app$(v3, v5) | ? [v6: % 152.10/21.21 | A_ltln$] : ? [v7: A_ltln_a_ltln_fun$] : ? [v8: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : % 152.10/21.21 | (and_ltln$(v6) = v7 & weakUntil_ltln$(v1) = v8 & fun_app$a(v8, v2) % 152.10/21.21 | = v9 & fun_app$a(v7, v9) = v10 & fun_app$a(all_744_0, v2) = v6 & % 152.10/21.21 | A_ltln$(v10) & A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) % 152.10/21.21 | & A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v10))) & ! [v0: % 152.10/21.21 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.21 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.21 | : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.21 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.21 | | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.21 | A_ltln$] : ? [v10: A_ltln$] : (and_ltln$(v6) = v7 & % 152.10/21.21 | weakUntil_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & fun_app$a(v7, % 152.10/21.21 | v9) = v10 & fun_app$a(all_744_0, v2) = v6 & A_ltln$(v10) & % 152.10/21.21 | A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.21 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v10))) % 152.10/21.21 | % 152.10/21.21 | ALPHA: (129) implies: % 152.10/21.21 | (130) until_ltln$(true_ltln$) = all_744_0 % 152.10/21.21 | (131) ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! % 152.10/21.21 | [v3: A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: % 152.10/21.21 | A_ltln$] : ( ~ (until_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) % 152.10/21.21 | | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.21 | A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] % 152.10/21.21 | : ? [v7: A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? % 152.10/21.21 | [v9: A_ltln$] : ? [v10: A_ltln$] : (and_ltln$(v6) = v7 & % 152.10/21.21 | weakUntil_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & fun_app$a(v7, % 152.10/21.21 | v9) = v10 & fun_app$a(all_744_0, v2) = v6 & A_ltln$(v10) & % 152.10/21.21 | A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.21 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v10))) % 152.10/21.21 | % 152.10/21.21 | DELTA: instantiating (30) with fresh symbol all_747_0 gives: % 152.10/21.21 | (132) release_ltln$(false_ltln$) = all_747_0 & % 152.10/21.21 | A_ltln_a_ltln_fun$(all_747_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.21 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.21 | A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : ( ~ % 152.10/21.21 | (or_ltln$(v4) = v5) | ~ (strongRelease_ltln$(v1) = v6) | ~ % 152.10/21.21 | (fun_app$a(v6, v2) = v7) | ~ (fun_app$a(v5, v7) = v8) | ~ % 152.10/21.21 | (fun_app$a(all_747_0, v2) = v4) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.21 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | ~ % 152.10/21.21 | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 152.10/21.21 | : (release_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & A_ltln$(v10) % 152.10/21.21 | & A_ltln_a_ltln_fun$(v9) & fun_app$(v3, v10))) & ! [v0: % 152.10/21.21 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.21 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.21 | : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln$] : ! [v8: A_ltln$] : % 152.10/21.21 | ( ~ (or_ltln$(v4) = v5) | ~ (strongRelease_ltln$(v1) = v6) | ~ % 152.10/21.21 | (fun_app$a(v6, v2) = v7) | ~ (fun_app$a(v5, v7) = v8) | ~ % 152.10/21.21 | (fun_app$a(all_747_0, v2) = v4) | ~ (semantics_ltln$(v0) = v3) | % 152.10/21.21 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) | ~ A_ltln$(v1) | % 152.10/21.21 | fun_app$(v3, v8) | ? [v9: A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] % 152.10/21.21 | : (release_ltln$(v1) = v9 & fun_app$a(v9, v2) = v10 & A_ltln$(v10) % 152.10/21.21 | & A_ltln_a_ltln_fun$(v9) & ~ fun_app$(v3, v10))) & ! [v0: % 152.10/21.21 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.21 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.21 | : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.21 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.21 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.21 | A_ltln$] : ? [v10: A_ltln$] : (or_ltln$(v6) = v7 & % 152.10/21.21 | strongRelease_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & % 152.10/21.21 | fun_app$a(v7, v9) = v10 & fun_app$a(all_747_0, v2) = v6 & % 152.10/21.21 | A_ltln$(v10) & A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) % 152.10/21.21 | & A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v10))) & ! [v0: % 152.10/21.21 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.21 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.21 | : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.21 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.21 | | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.21 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.21 | A_ltln$] : ? [v10: A_ltln$] : (or_ltln$(v6) = v7 & % 152.10/21.21 | strongRelease_ltln$(v1) = v8 & fun_app$a(v8, v2) = v9 & % 152.10/21.21 | fun_app$a(v7, v9) = v10 & fun_app$a(all_747_0, v2) = v6 & % 152.10/21.21 | A_ltln$(v10) & A_ltln$(v9) & A_ltln$(v6) & A_ltln_a_ltln_fun$(v8) % 152.10/21.21 | & A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v10))) % 152.10/21.21 | % 152.10/21.21 | ALPHA: (132) implies: % 152.10/21.21 | (133) release_ltln$(false_ltln$) = all_747_0 % 152.10/21.21 | % 152.10/21.21 | DELTA: instantiating (27) with fresh symbols all_750_0, all_750_1 gives: % 152.10/21.21 | (134) until_ltln$(true_ltln$) = all_750_0 & release_ltln$(false_ltln$) = % 152.10/21.21 | all_750_1 & A_ltln_a_ltln_fun$(all_750_0) & % 152.10/21.21 | A_ltln_a_ltln_fun$(all_750_1) & ? [v0: A_ltln_set$] : ? [v1: % 152.10/21.21 | A_ltln_set$] : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 152.10/21.21 | A_ltln_set$] : ( ~ (g_F$(v2, v3) = v4) | ~ Nat_a_set_fun$(v3) | ~ % 152.10/21.21 | A_ltln$(v2) | ~ A_ltln_set$(v1) | ~ A_ltln_set$(v0) | ? [v5: % 152.10/21.21 | A_ltln_set$] : ? [v6: A_ltln_set$] : ? [v7: A_ltln_bool_fun$] : % 152.10/21.21 | ? [v8: A_ltln_set$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : ? % 152.10/21.21 | [v11: A_ltln$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? [v14: % 152.10/21.21 | A_ltln$] : ? [v15: A_ltln$] : ? [v16: A_ltln$] : (A_ltln$(v13) % 152.10/21.21 | & A_ltln$(v9) & ((subformulas_mu$(v2) = v5 & A_ltln_set$(v5) & ~ % 152.10/21.21 | less_eq$(v0, v5)) | (subformulas_nu$(v2) = v6 & % 152.10/21.21 | A_ltln_set$(v6) & ~ less_eq$(v1, v6)) | (fG_advice$(v13, v1) % 152.10/21.21 | = v14 & fun_app$a(all_750_0, v14) = v15 & % 152.10/21.21 | fun_app$a(all_750_1, v15) = v16 & semantics_ltln$(v3) = v7 & % 152.10/21.21 | A_ltln$(v16) & A_ltln$(v15) & A_ltln$(v14) & % 152.10/21.21 | A_ltln_bool_fun$(v7) & member$(v13, v0) & ~ fun_app$(v7, % 152.10/21.21 | v16)) | (fun_app$a(all_750_0, v11) = v12 & % 152.10/21.21 | fun_app$a(all_750_1, v10) = v11 & gF_advice$(v9, v0) = v10 & % 152.10/21.21 | semantics_ltln$(v3) = v7 & A_ltln$(v12) & A_ltln$(v11) & % 152.10/21.21 | A_ltln$(v10) & A_ltln_bool_fun$(v7) & member$(v9, v1) & ~ % 152.10/21.21 | fun_app$(v7, v12)) | (f_G$(v2, v3) = v8 & A_ltln_set$(v8) & % 152.10/21.21 | less_eq$(v1, v8) & less_eq$(v0, v4))))) & ? [v0: % 152.10/21.21 | A_ltln_set$] : ? [v1: A_ltln_set$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.21 | Nat_a_set_fun$] : ! [v4: A_ltln_set$] : ( ~ (f_G$(v2, v3) = v4) | % 152.10/21.21 | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v2) | ~ A_ltln_set$(v1) | ~ % 152.10/21.21 | A_ltln_set$(v0) | ? [v5: A_ltln_set$] : ? [v6: A_ltln_set$] : ? % 152.10/21.21 | [v7: A_ltln_bool_fun$] : ? [v8: A_ltln_set$] : ? [v9: A_ltln$] : % 152.10/21.21 | ? [v10: A_ltln$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] : ? [v13: % 152.10/21.21 | A_ltln$] : ? [v14: A_ltln$] : ? [v15: A_ltln$] : ? [v16: % 152.10/21.21 | A_ltln$] : (A_ltln$(v13) & A_ltln$(v9) & ((subformulas_mu$(v2) = % 152.10/21.21 | v5 & A_ltln_set$(v5) & ~ less_eq$(v0, v5)) | % 152.10/21.21 | (subformulas_nu$(v2) = v6 & A_ltln_set$(v6) & ~ less_eq$(v1, % 152.10/21.21 | v6)) | (fG_advice$(v13, v1) = v14 & fun_app$a(all_750_0, % 152.10/21.21 | v14) = v15 & fun_app$a(all_750_1, v15) = v16 & % 152.10/21.21 | semantics_ltln$(v3) = v7 & A_ltln$(v16) & A_ltln$(v15) & % 152.10/21.21 | A_ltln$(v14) & A_ltln_bool_fun$(v7) & member$(v13, v0) & ~ % 152.10/21.21 | fun_app$(v7, v16)) | (g_F$(v2, v3) = v8 & A_ltln_set$(v8) & % 152.10/21.21 | less_eq$(v1, v4) & less_eq$(v0, v8)) | (fun_app$a(all_750_0, % 152.10/21.21 | v11) = v12 & fun_app$a(all_750_1, v10) = v11 & % 152.10/21.21 | gF_advice$(v9, v0) = v10 & semantics_ltln$(v3) = v7 & % 152.10/21.21 | A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.21 | A_ltln_bool_fun$(v7) & member$(v9, v1) & ~ fun_app$(v7, % 152.10/21.21 | v12))))) % 152.10/21.21 | % 152.10/21.21 | ALPHA: (134) implies: % 152.10/21.21 | (135) release_ltln$(false_ltln$) = all_750_1 % 152.10/21.21 | (136) until_ltln$(true_ltln$) = all_750_0 % 152.10/21.21 | % 152.10/21.21 | DELTA: instantiating (29) with fresh symbol all_752_0 gives: % 152.10/21.22 | (137) release_ltln$(false_ltln$) = all_752_0 & % 152.10/21.22 | A_ltln_a_ltln_fun$(all_752_0) & ! [v0: Nat_a_set_fun$] : ! [v1: % 152.10/21.22 | A_ltln$] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ! [v4: % 152.10/21.22 | A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] : ! [v6: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.22 | A_ltln$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ( ~ % 152.10/21.22 | (and_ltln$(v1) = v7) | ~ (or_ltln$(v4) = v5) | ~ (until_ltln$(v2) % 152.10/21.22 | = v6) | ~ (fun_app$a(v7, v2) = v8) | ~ (fun_app$a(v6, v8) = v9) % 152.10/21.22 | | ~ (fun_app$a(v5, v9) = v10) | ~ (fun_app$a(all_752_0, v2) = v4) % 152.10/21.22 | | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.22 | A_ltln$(v2) | ~ A_ltln$(v1) | ~ fun_app$(v3, v10) | ? [v11: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v12: A_ltln$] : (release_ltln$(v1) = % 152.10/21.22 | v11 & fun_app$a(v11, v2) = v12 & A_ltln$(v12) & % 152.10/21.22 | A_ltln_a_ltln_fun$(v11) & fun_app$(v3, v12))) & ! [v0: % 152.10/21.22 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.22 | A_ltln_bool_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_a_ltln_fun$] % 152.10/21.22 | : ! [v6: A_ltln_a_ltln_fun$] : ! [v7: A_ltln_a_ltln_fun$] : ! [v8: % 152.10/21.22 | A_ltln$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ( ~ % 152.10/21.22 | (and_ltln$(v1) = v7) | ~ (or_ltln$(v4) = v5) | ~ (until_ltln$(v2) % 152.10/21.22 | = v6) | ~ (fun_app$a(v7, v2) = v8) | ~ (fun_app$a(v6, v8) = v9) % 152.10/21.22 | | ~ (fun_app$a(v5, v9) = v10) | ~ (fun_app$a(all_752_0, v2) = v4) % 152.10/21.22 | | ~ (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 152.10/21.22 | A_ltln$(v2) | ~ A_ltln$(v1) | fun_app$(v3, v10) | ? [v11: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v12: A_ltln$] : (release_ltln$(v1) = % 152.10/21.22 | v11 & fun_app$a(v11, v2) = v12 & A_ltln$(v12) & % 152.10/21.22 | A_ltln_a_ltln_fun$(v11) & ~ fun_app$(v3, v12))) & ! [v0: % 152.10/21.22 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.22 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.22 | : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.22 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.22 | | ~ A_ltln$(v1) | ~ fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : ? % 152.10/21.22 | [v12: A_ltln$] : (and_ltln$(v1) = v9 & or_ltln$(v6) = v7 & % 152.10/21.22 | until_ltln$(v2) = v8 & fun_app$a(v9, v2) = v10 & fun_app$a(v8, % 152.10/21.22 | v10) = v11 & fun_app$a(v7, v11) = v12 & fun_app$a(all_752_0, % 152.10/21.22 | v2) = v6 & A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.22 | A_ltln$(v6) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.22 | A_ltln_a_ltln_fun$(v7) & fun_app$(v3, v12))) & ! [v0: % 152.10/21.22 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 152.10/21.22 | A_ltln_bool_fun$] : ! [v4: A_ltln_a_ltln_fun$] : ! [v5: A_ltln$] % 152.10/21.22 | : ( ~ (release_ltln$(v1) = v4) | ~ (fun_app$a(v4, v2) = v5) | ~ % 152.10/21.22 | (semantics_ltln$(v0) = v3) | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v2) % 152.10/21.22 | | ~ A_ltln$(v1) | fun_app$(v3, v5) | ? [v6: A_ltln$] : ? [v7: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v8: A_ltln_a_ltln_fun$] : ? [v9: % 152.10/21.22 | A_ltln_a_ltln_fun$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : ? % 152.10/21.22 | [v12: A_ltln$] : (and_ltln$(v1) = v9 & or_ltln$(v6) = v7 & % 152.10/21.22 | until_ltln$(v2) = v8 & fun_app$a(v9, v2) = v10 & fun_app$a(v8, % 152.10/21.22 | v10) = v11 & fun_app$a(v7, v11) = v12 & fun_app$a(all_752_0, % 152.10/21.22 | v2) = v6 & A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v10) & % 152.10/21.22 | A_ltln$(v6) & A_ltln_a_ltln_fun$(v9) & A_ltln_a_ltln_fun$(v8) & % 152.10/21.22 | A_ltln_a_ltln_fun$(v7) & ~ fun_app$(v3, v12))) % 152.10/21.22 | % 152.10/21.22 | ALPHA: (137) implies: % 152.10/21.22 | (138) release_ltln$(false_ltln$) = all_752_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (38) with all_674_0, all_680_4, phi$, simplifying % 152.10/21.22 | with (70), (81) gives: % 152.10/21.22 | (139) all_680_4 = all_674_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (38) with all_680_4, all_694_7, phi$, simplifying % 152.10/21.22 | with (81), (104) gives: % 152.10/21.22 | (140) all_694_7 = all_680_4 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (38) with all_637_1, all_694_7, phi$, simplifying % 152.10/21.22 | with (55), (104) gives: % 152.10/21.22 | (141) all_694_7 = all_637_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (43) with all_680_5, all_694_8, all_680_6, inf$, % 152.10/21.22 | simplifying with (82) gives: % 152.10/21.22 | (142) all_694_8 = all_680_5 | ~ (fun_app$c(inf$, all_680_6) = all_694_8) % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (43) with all_637_2, all_694_1, all_637_3, inf$, % 152.10/21.22 | simplifying with (56) gives: % 152.10/21.22 | (143) all_694_1 = all_637_2 | ~ (fun_app$c(inf$, all_637_3) = all_694_1) % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (44) with all_637_3, all_694_2, w$, phi$, % 152.10/21.22 | simplifying with (57), (107) gives: % 152.10/21.22 | (144) all_694_2 = all_637_3 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (39) with all_680_9, all_694_5, w$, simplifying % 152.10/21.22 | with (83), (108) gives: % 152.10/21.22 | (145) all_694_5 = all_680_9 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (39) with all_587_0, all_694_5, w$, simplifying % 152.10/21.22 | with (49), (108) gives: % 152.10/21.22 | (146) all_694_5 = all_587_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (47) with all_680_6, all_694_9, w$, phi$, % 152.10/21.22 | simplifying with (87), (109) gives: % 152.10/21.22 | (147) all_694_9 = all_680_6 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (47) with all_614_1, all_694_9, w$, phi$, % 152.10/21.22 | simplifying with (51), (109) gives: % 152.10/21.22 | (148) all_694_9 = all_614_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_677_0, all_680_7, false_ltln$, % 152.10/21.22 | simplifying with (73), (88) gives: % 152.10/21.22 | (149) all_680_7 = all_677_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_680_7, all_682_0, false_ltln$, % 152.10/21.22 | simplifying with (88), (91) gives: % 152.10/21.22 | (150) all_682_0 = all_680_7 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_682_0, all_688_0, false_ltln$, % 152.10/21.22 | simplifying with (91), (95) gives: % 152.10/21.22 | (151) all_688_0 = all_682_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_688_0, all_691_1, false_ltln$, % 152.10/21.22 | simplifying with (95), (98) gives: % 152.10/21.22 | (152) all_691_1 = all_688_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_691_1, all_697_0, false_ltln$, % 152.10/21.22 | simplifying with (98), (112) gives: % 152.10/21.22 | (153) all_697_0 = all_691_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_697_0, all_700_0, false_ltln$, % 152.10/21.22 | simplifying with (112), (114) gives: % 152.10/21.22 | (154) all_700_0 = all_697_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_738_0, all_747_0, false_ltln$, % 152.10/21.22 | simplifying with (126), (133) gives: % 152.10/21.22 | (155) all_747_0 = all_738_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_747_0, all_750_1, false_ltln$, % 152.10/21.22 | simplifying with (133), (135) gives: % 152.10/21.22 | (156) all_750_1 = all_747_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_659_0, all_750_1, false_ltln$, % 152.10/21.22 | simplifying with (59), (135) gives: % 152.10/21.22 | (157) all_750_1 = all_659_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_738_0, all_752_0, false_ltln$, % 152.10/21.22 | simplifying with (126), (138) gives: % 152.10/21.22 | (158) all_752_0 = all_738_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_712_0, all_752_0, false_ltln$, % 152.10/21.22 | simplifying with (122), (138) gives: % 152.10/21.22 | (159) all_752_0 = all_712_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (40) with all_700_0, all_752_0, false_ltln$, % 152.10/21.22 | simplifying with (114), (138) gives: % 152.10/21.22 | (160) all_752_0 = all_700_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_677_1, all_685_0, true_ltln$, % 152.10/21.22 | simplifying with (74), (93) gives: % 152.10/21.22 | (161) all_685_0 = all_677_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_691_0, all_703_0, true_ltln$, % 152.10/21.22 | simplifying with (99), (116) gives: % 152.10/21.22 | (162) all_703_0 = all_691_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_680_8, all_703_0, true_ltln$, % 152.10/21.22 | simplifying with (89), (116) gives: % 152.10/21.22 | (163) all_703_0 = all_680_8 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_662_1, all_703_0, true_ltln$, % 152.10/21.22 | simplifying with (61), (116) gives: % 152.10/21.22 | (164) all_703_0 = all_662_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_703_0, all_706_0, true_ltln$, % 152.10/21.22 | simplifying with (116), (118) gives: % 152.10/21.22 | (165) all_706_0 = all_703_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_677_1, all_706_0, true_ltln$, % 152.10/21.22 | simplifying with (74), (118) gives: % 152.10/21.22 | (166) all_706_0 = all_677_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_671_0, all_706_0, true_ltln$, % 152.10/21.22 | simplifying with (67), (118) gives: % 152.10/21.22 | (167) all_706_0 = all_671_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_665_0, all_706_0, true_ltln$, % 152.10/21.22 | simplifying with (63), (118) gives: % 152.10/21.22 | (168) all_706_0 = all_665_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_668_0, all_709_0, true_ltln$, % 152.10/21.22 | simplifying with (65), (120) gives: % 152.10/21.22 | (169) all_709_0 = all_668_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_709_0, all_735_0, true_ltln$, % 152.10/21.22 | simplifying with (120), (124) gives: % 152.10/21.22 | (170) all_735_0 = all_709_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_709_0, all_741_0, true_ltln$, % 152.10/21.22 | simplifying with (120), (128) gives: % 152.10/21.22 | (171) all_741_0 = all_709_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_688_1, all_741_0, true_ltln$, % 152.10/21.22 | simplifying with (96), (128) gives: % 152.10/21.22 | (172) all_741_0 = all_688_1 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_685_0, all_741_0, true_ltln$, % 152.10/21.22 | simplifying with (93), (128) gives: % 152.10/21.22 | (173) all_741_0 = all_685_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_744_0, all_750_0, true_ltln$, % 152.10/21.22 | simplifying with (130), (136) gives: % 152.10/21.22 | (174) all_750_0 = all_744_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_735_0, all_750_0, true_ltln$, % 152.10/21.22 | simplifying with (124), (136) gives: % 152.10/21.22 | (175) all_750_0 = all_735_0 % 152.10/21.22 | % 152.10/21.22 | GROUND_INST: instantiating (41) with all_694_3, all_750_0, true_ltln$, % 152.10/21.22 | simplifying with (110), (136) gives: % 152.10/21.23 | (176) all_750_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (159), (160) imply: % 152.10/21.23 | (177) all_712_0 = all_700_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (158), (159) imply: % 152.10/21.23 | (178) all_738_0 = all_712_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (178) implies: % 152.10/21.23 | (179) all_738_0 = all_712_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (174), (176) imply: % 152.10/21.23 | (180) all_744_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (174), (175) imply: % 152.10/21.23 | (181) all_744_0 = all_735_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (156), (157) imply: % 152.10/21.23 | (182) all_747_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (182) implies: % 152.10/21.23 | (183) all_747_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (155), (183) imply: % 152.10/21.23 | (184) all_738_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (184) implies: % 152.10/21.23 | (185) all_738_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (180), (181) imply: % 152.10/21.23 | (186) all_735_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | SIMP: (186) implies: % 152.10/21.23 | (187) all_735_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (172), (173) imply: % 152.10/21.23 | (188) all_688_1 = all_685_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (171), (172) imply: % 152.10/21.23 | (189) all_709_0 = all_688_1 % 152.10/21.23 | % 152.10/21.23 | SIMP: (189) implies: % 152.10/21.23 | (190) all_709_0 = all_688_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (179), (185) imply: % 152.10/21.23 | (191) all_712_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (191) implies: % 152.10/21.23 | (192) all_712_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (170), (187) imply: % 152.10/21.23 | (193) all_709_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | SIMP: (193) implies: % 152.10/21.23 | (194) all_709_0 = all_694_3 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (177), (192) imply: % 152.10/21.23 | (195) all_700_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (195) implies: % 152.10/21.23 | (196) all_700_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (169), (194) imply: % 152.10/21.23 | (197) all_694_3 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (190), (194) imply: % 152.10/21.23 | (198) all_694_3 = all_688_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (166), (167) imply: % 152.10/21.23 | (199) all_677_1 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (199) implies: % 152.10/21.23 | (200) all_677_1 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (167), (168) imply: % 152.10/21.23 | (201) all_671_0 = all_665_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (165), (167) imply: % 152.10/21.23 | (202) all_703_0 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (202) implies: % 152.10/21.23 | (203) all_703_0 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (162), (163) imply: % 152.10/21.23 | (204) all_691_0 = all_680_8 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (162), (164) imply: % 152.10/21.23 | (205) all_691_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (162), (203) imply: % 152.10/21.23 | (206) all_691_0 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (154), (196) imply: % 152.10/21.23 | (207) all_697_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (207) implies: % 152.10/21.23 | (208) all_697_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (153), (208) imply: % 152.10/21.23 | (209) all_691_1 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (209) implies: % 152.10/21.23 | (210) all_691_1 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (197), (198) imply: % 152.10/21.23 | (211) all_688_1 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (211) implies: % 152.10/21.23 | (212) all_688_1 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (145), (146) imply: % 152.10/21.23 | (213) all_680_9 = all_587_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (213) implies: % 152.10/21.23 | (214) all_680_9 = all_587_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (140), (141) imply: % 152.10/21.23 | (215) all_680_4 = all_637_1 % 152.10/21.23 | % 152.10/21.23 | SIMP: (215) implies: % 152.10/21.23 | (216) all_680_4 = all_637_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (147), (148) imply: % 152.10/21.23 | (217) all_680_6 = all_614_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (204), (206) imply: % 152.10/21.23 | (218) all_680_8 = all_671_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (204), (205) imply: % 152.10/21.23 | (219) all_680_8 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (152), (210) imply: % 152.10/21.23 | (220) all_688_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (220) implies: % 152.10/21.23 | (221) all_688_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (151), (221) imply: % 152.10/21.23 | (222) all_682_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (222) implies: % 152.10/21.23 | (223) all_682_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (188), (212) imply: % 152.10/21.23 | (224) all_685_0 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (224) implies: % 152.10/21.23 | (225) all_685_0 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (161), (225) imply: % 152.10/21.23 | (226) all_677_1 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (226) implies: % 152.10/21.23 | (227) all_677_1 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (150), (223) imply: % 152.10/21.23 | (228) all_680_7 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (228) implies: % 152.10/21.23 | (229) all_680_7 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (139), (216) imply: % 152.10/21.23 | (230) all_674_0 = all_637_1 % 152.10/21.23 | % 152.10/21.23 | SIMP: (230) implies: % 152.10/21.23 | (231) all_674_0 = all_637_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (149), (229) imply: % 152.10/21.23 | (232) all_677_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (232) implies: % 152.10/21.23 | (233) all_677_0 = all_659_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (218), (219) imply: % 152.10/21.23 | (234) all_671_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | SIMP: (234) implies: % 152.10/21.23 | (235) all_671_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (200), (227) imply: % 152.10/21.23 | (236) all_671_0 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | SIMP: (236) implies: % 152.10/21.23 | (237) all_671_0 = all_668_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (201), (237) imply: % 152.10/21.23 | (238) all_668_0 = all_665_0 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (235), (237) imply: % 152.10/21.23 | (239) all_668_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (238), (239) imply: % 152.10/21.23 | (240) all_665_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | SIMP: (240) implies: % 152.10/21.23 | (241) all_665_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (227), (239) imply: % 152.10/21.23 | (242) all_677_1 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (197), (239) imply: % 152.10/21.23 | (243) all_694_3 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | COMBINE_EQS: (180), (243) imply: % 152.10/21.23 | (244) all_744_0 = all_662_1 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (86), (229) imply: % 152.10/21.23 | (245) fun_app$a(all_659_0, all_680_2) = all_680_1 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (85), (219) imply: % 152.10/21.23 | (246) fun_app$a(all_662_1, all_680_1) = all_680_0 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (106), (144) imply: % 152.10/21.23 | (247) fun_app$c(inf$, all_637_3) = all_694_1 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (105), (148) imply: % 152.10/21.23 | (248) fun_app$c(inf$, all_614_1) = all_694_8 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (103), (141) imply: % 152.10/21.23 | (249) fun_app$b(all_694_1, all_637_1) = all_694_0 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (102), (141) imply: % 152.10/21.23 | (250) fun_app$b(all_694_8, all_637_1) = all_694_6 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (80), (216) imply: % 152.10/21.23 | (251) fun_app$b(all_680_5, all_637_1) = all_680_3 % 152.10/21.23 | % 152.10/21.23 | REDUCE: (101), (144) imply: % 152.10/21.23 | (252) A_ltln_set$(all_637_3) % 152.10/21.23 | % 152.10/21.23 | REDUCE: (78), (217) imply: % 152.10/21.23 | (253) A_ltln_set$(all_614_1) % 152.10/21.23 | % 152.10/21.23 | REDUCE: (69), (231) imply: % 152.10/21.23 | (254) A_ltln_set$(all_637_1) % 152.10/21.23 | % 152.10/21.23 | REDUCE: (77), (214) imply: % 152.10/21.23 | (255) ~ fun_app$(all_587_0, all_680_0) % 152.10/21.23 | % 152.10/21.23 | BETA: splitting (143) gives: % 152.10/21.23 | % 152.10/21.23 | Case 1: % 152.10/21.23 | | % 152.10/21.23 | | (256) ~ (fun_app$c(inf$, all_637_3) = all_694_1) % 152.10/21.23 | | % 152.10/21.23 | | PRED_UNIFY: (247), (256) imply: % 152.10/21.23 | | (257) $false % 152.10/21.24 | | % 152.10/21.24 | | CLOSE: (257) is inconsistent. % 152.10/21.24 | | % 152.10/21.24 | Case 2: % 152.10/21.24 | | % 152.10/21.24 | | (258) all_694_1 = all_637_2 % 152.10/21.24 | | % 152.10/21.24 | | REDUCE: (249), (258) imply: % 152.10/21.24 | | (259) fun_app$b(all_637_2, all_637_1) = all_694_0 % 152.10/21.24 | | % 152.10/21.24 | | BETA: splitting (142) gives: % 152.10/21.24 | | % 152.10/21.24 | | Case 1: % 152.10/21.24 | | | % 152.10/21.24 | | | (260) ~ (fun_app$c(inf$, all_680_6) = all_694_8) % 152.10/21.24 | | | % 152.10/21.24 | | | REDUCE: (217), (260) imply: % 152.10/21.24 | | | (261) ~ (fun_app$c(inf$, all_614_1) = all_694_8) % 152.10/21.24 | | | % 152.10/21.24 | | | PRED_UNIFY: (248), (261) imply: % 152.10/21.24 | | | (262) $false % 152.10/21.24 | | | % 152.10/21.24 | | | CLOSE: (262) is inconsistent. % 152.10/21.24 | | | % 152.10/21.24 | | Case 2: % 152.10/21.24 | | | % 152.10/21.24 | | | (263) all_694_8 = all_680_5 % 152.10/21.24 | | | % 152.10/21.24 | | | REDUCE: (248), (263) imply: % 152.10/21.24 | | | (264) fun_app$c(inf$, all_614_1) = all_680_5 % 152.10/21.24 | | | % 152.10/21.24 | | | REDUCE: (250), (263) imply: % 152.10/21.24 | | | (265) fun_app$b(all_680_5, all_637_1) = all_694_6 % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (42) with all_637_0, all_694_0, all_637_1, % 152.10/21.24 | | | all_637_2, simplifying with (54), (259) gives: % 152.10/21.24 | | | (266) all_694_0 = all_637_0 % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (42) with all_680_3, all_694_6, all_637_1, % 152.10/21.24 | | | all_680_5, simplifying with (251), (265) gives: % 152.10/21.24 | | | (267) all_694_6 = all_680_3 % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (32) with psi$, simplifying with (33) gives: % 152.10/21.24 | | | (268) ~ member$(psi$, bot$) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (71) with all_614_1, all_680_5, simplifying % 152.10/21.24 | | | with (253), (264) gives: % 152.10/21.24 | | | (269) ~ member$(psi$, all_674_0) | ? [v0: A_ltln_set$] : ? [v1: % 152.10/21.24 | | | A_ltln$] : (gF_advice$(psi$, v0) = v1 & gF_advice$(psi$, % 152.10/21.24 | | | all_614_1) = v1 & fun_app$b(all_680_5, all_674_0) = v0 & % 152.10/21.24 | | | A_ltln$(v1) & A_ltln_set$(v0)) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (14) with psi$, all_637_3, all_637_1, % 152.10/21.24 | | | all_637_2, all_637_0, simplifying with (33), (53), (54), % 152.10/21.24 | | | (56), (252), (254) gives: % 152.10/21.24 | | | (270) member$(psi$, all_637_1) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (13) with psi$, all_637_3, all_637_1, % 152.10/21.24 | | | all_637_2, all_637_0, simplifying with (33), (53), (54), % 152.10/21.24 | | | (56), (252), (254) gives: % 152.10/21.24 | | | (271) member$(psi$, all_637_3) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (71) with all_637_3, all_637_2, simplifying % 152.10/21.24 | | | with (56), (252) gives: % 152.10/21.24 | | | (272) ~ member$(psi$, all_674_0) | ? [v0: A_ltln_set$] : ? [v1: % 152.10/21.24 | | | A_ltln$] : (gF_advice$(psi$, v0) = v1 & gF_advice$(psi$, % 152.10/21.24 | | | all_637_3) = v1 & fun_app$b(all_637_2, all_674_0) = v0 & % 152.10/21.24 | | | A_ltln$(v1) & A_ltln_set$(v0)) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (31) with w$, all_637_3, simplifying with (36) % 152.10/21.24 | | | gives: % 152.10/21.24 | | | (273) all_637_3 = bot$ | ~ (f_G$(true_ltln$, w$) = all_637_3) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (75) with phi$, w$, psi$, all_614_1, all_680_2, % 152.10/21.24 | | | simplifying with (33), (35), (36), (51) gives: % 152.10/21.24 | | | (274) ~ (gF_advice$(psi$, all_614_1) = all_680_2) | ? [v0: % 152.10/21.24 | | | A_ltln_set$] : ? [v1: A_ltln_bool_fun$] : ? [v2: A_ltln$] : % 152.10/21.24 | | | ? [v3: A_ltln$] : ((fun_app$a(all_677_0, all_680_2) = v2 & % 152.10/21.24 | | | fun_app$a(all_677_1, v2) = v3 & semantics_ltln$(w$) = v1 & % 152.10/21.24 | | | A_ltln$(v3) & A_ltln$(v2) & A_ltln_bool_fun$(v1) & % 152.10/21.24 | | | fun_app$(v1, v3)) | (f_G$(phi$, w$) = v0 & A_ltln_set$(v0) & % 152.10/21.24 | | | ~ member$(psi$, v0))) % 152.10/21.24 | | | % 152.10/21.24 | | | GROUND_INST: instantiating (131) with w$, true_ltln$, all_680_1, % 152.10/21.24 | | | all_587_0, all_662_1, all_680_0, simplifying with (34), (36), % 152.10/21.24 | | | (49), (61), (79), (246), (255) gives: % 152.10/21.24 | | | (275) ? [v0: A_ltln$] : ? [v1: A_ltln_a_ltln_fun$] : ? [v2: % 152.10/21.24 | | | A_ltln_a_ltln_fun$] : ? [v3: A_ltln$] : ? [v4: A_ltln$] : % 152.10/21.24 | | | (and_ltln$(v0) = v1 & weakUntil_ltln$(true_ltln$) = v2 & % 152.10/21.24 | | | fun_app$a(v2, all_680_1) = v3 & fun_app$a(v1, v3) = v4 & % 152.10/21.24 | | | fun_app$a(all_744_0, all_680_1) = v0 & A_ltln$(v4) & % 152.10/21.24 | | | A_ltln$(v3) & A_ltln$(v0) & A_ltln_a_ltln_fun$(v2) & % 152.10/21.24 | | | A_ltln_a_ltln_fun$(v1) & ~ fun_app$(all_587_0, v4)) % 152.10/21.24 | | | % 152.10/21.24 | | | DELTA: instantiating (275) with fresh symbols all_860_0, all_860_1, % 152.10/21.24 | | | all_860_2, all_860_3, all_860_4 gives: % 152.10/21.24 | | | (276) and_ltln$(all_860_4) = all_860_3 & weakUntil_ltln$(true_ltln$) = % 152.10/21.24 | | | all_860_2 & fun_app$a(all_860_2, all_680_1) = all_860_1 & % 152.10/21.24 | | | fun_app$a(all_860_3, all_860_1) = all_860_0 & % 152.10/21.24 | | | fun_app$a(all_744_0, all_680_1) = all_860_4 & A_ltln$(all_860_0) % 152.10/21.24 | | | & A_ltln$(all_860_1) & A_ltln$(all_860_4) & % 152.10/21.24 | | | A_ltln_a_ltln_fun$(all_860_2) & A_ltln_a_ltln_fun$(all_860_3) & % 152.10/21.24 | | | ~ fun_app$(all_587_0, all_860_0) % 152.10/21.24 | | | % 152.10/21.24 | | | ALPHA: (276) implies: % 152.10/21.24 | | | (277) fun_app$a(all_744_0, all_680_1) = all_860_4 % 152.10/21.24 | | | % 152.10/21.24 | | | REDUCE: (244), (277) imply: % 152.10/21.24 | | | (278) fun_app$a(all_662_1, all_680_1) = all_860_4 % 152.10/21.24 | | | % 152.10/21.24 | | | BETA: splitting (269) gives: % 152.10/21.24 | | | % 152.10/21.24 | | | Case 1: % 152.10/21.24 | | | | % 152.10/21.24 | | | | (279) ~ member$(psi$, all_674_0) % 152.10/21.24 | | | | % 152.10/21.24 | | | | REDUCE: (231), (279) imply: % 152.10/21.24 | | | | (280) ~ member$(psi$, all_637_1) % 152.10/21.24 | | | | % 152.10/21.24 | | | | PRED_UNIFY: (270), (280) imply: % 152.10/21.24 | | | | (281) $false % 152.10/21.24 | | | | % 152.10/21.24 | | | | CLOSE: (281) is inconsistent. % 152.10/21.24 | | | | % 152.10/21.24 | | | Case 2: % 152.10/21.24 | | | | % 152.10/21.24 | | | | (282) member$(psi$, all_674_0) % 152.10/21.24 | | | | (283) ? [v0: A_ltln_set$] : ? [v1: A_ltln$] : (gF_advice$(psi$, v0) % 152.10/21.24 | | | | = v1 & gF_advice$(psi$, all_614_1) = v1 & % 152.10/21.24 | | | | fun_app$b(all_680_5, all_674_0) = v0 & A_ltln$(v1) & % 152.10/21.24 | | | | A_ltln_set$(v0)) % 152.10/21.24 | | | | % 152.10/21.24 | | | | DELTA: instantiating (283) with fresh symbols all_898_0, all_898_1 % 152.10/21.24 | | | | gives: % 152.10/21.24 | | | | (284) gF_advice$(psi$, all_898_1) = all_898_0 & gF_advice$(psi$, % 152.10/21.24 | | | | all_614_1) = all_898_0 & fun_app$b(all_680_5, all_674_0) = % 152.10/21.24 | | | | all_898_1 & A_ltln$(all_898_0) & A_ltln_set$(all_898_1) % 152.10/21.24 | | | | % 152.10/21.24 | | | | ALPHA: (284) implies: % 152.10/21.24 | | | | (285) fun_app$b(all_680_5, all_674_0) = all_898_1 % 152.10/21.24 | | | | (286) gF_advice$(psi$, all_614_1) = all_898_0 % 152.10/21.24 | | | | (287) gF_advice$(psi$, all_898_1) = all_898_0 % 152.10/21.24 | | | | % 152.10/21.24 | | | | REDUCE: (231), (285) imply: % 152.10/21.24 | | | | (288) fun_app$b(all_680_5, all_637_1) = all_898_1 % 152.10/21.24 | | | | % 152.10/21.24 | | | | BETA: splitting (272) gives: % 152.10/21.24 | | | | % 152.10/21.24 | | | | Case 1: % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | (289) ~ member$(psi$, all_674_0) % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | REDUCE: (231), (289) imply: % 152.10/21.24 | | | | | (290) ~ member$(psi$, all_637_1) % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | PRED_UNIFY: (270), (290) imply: % 152.10/21.24 | | | | | (291) $false % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | CLOSE: (291) is inconsistent. % 152.10/21.24 | | | | | % 152.10/21.24 | | | | Case 2: % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | GROUND_INST: instantiating (42) with all_680_3, all_898_1, all_637_1, % 152.10/21.24 | | | | | all_680_5, simplifying with (251), (288) gives: % 152.10/21.24 | | | | | (292) all_898_1 = all_680_3 % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | GROUND_INST: instantiating (45) with all_680_2, all_898_0, all_680_3, % 152.10/21.24 | | | | | psi$, simplifying with (84) gives: % 152.10/21.24 | | | | | (293) all_898_0 = all_680_2 | ~ (gF_advice$(psi$, all_680_3) = % 152.10/21.24 | | | | | all_898_0) % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | GROUND_INST: instantiating (46) with all_680_0, all_860_4, all_680_1, % 152.10/21.24 | | | | | all_662_1, simplifying with (246), (278) gives: % 152.10/21.24 | | | | | (294) all_860_4 = all_680_0 % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | PRED_UNIFY: (268), (271) imply: % 152.10/21.24 | | | | | (295) ~ (all_637_3 = bot$) % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | REDUCE: (287), (292) imply: % 152.10/21.24 | | | | | (296) gF_advice$(psi$, all_680_3) = all_898_0 % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | BETA: splitting (274) gives: % 152.10/21.24 | | | | | % 152.10/21.24 | | | | | Case 1: % 152.10/21.24 | | | | | | % 152.10/21.24 | | | | | | (297) ~ (gF_advice$(psi$, all_614_1) = all_680_2) % 152.10/21.24 | | | | | | % 152.10/21.24 | | | | | | BETA: splitting (293) gives: % 152.10/21.24 | | | | | | % 152.10/21.24 | | | | | | Case 1: % 152.10/21.24 | | | | | | | % 152.10/21.24 | | | | | | | (298) ~ (gF_advice$(psi$, all_680_3) = all_898_0) % 152.10/21.24 | | | | | | | % 152.10/21.24 | | | | | | | PRED_UNIFY: (296), (298) imply: % 152.10/21.24 | | | | | | | (299) $false % 152.10/21.24 | | | | | | | % 152.10/21.24 | | | | | | | CLOSE: (299) is inconsistent. % 152.10/21.24 | | | | | | | % 152.10/21.24 | | | | | | Case 2: % 152.10/21.24 | | | | | | | % 152.10/21.25 | | | | | | | (300) all_898_0 = all_680_2 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | REDUCE: (286), (300) imply: % 152.10/21.25 | | | | | | | (301) gF_advice$(psi$, all_614_1) = all_680_2 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | PRED_UNIFY: (297), (301) imply: % 152.10/21.25 | | | | | | | (302) $false % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | CLOSE: (302) is inconsistent. % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | End of split % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | Case 2: % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | | (303) ? [v0: A_ltln_set$] : ? [v1: A_ltln_bool_fun$] : ? [v2: % 152.10/21.25 | | | | | | A_ltln$] : ? [v3: A_ltln$] : ((fun_app$a(all_677_0, % 152.10/21.25 | | | | | | all_680_2) = v2 & fun_app$a(all_677_1, v2) = v3 & % 152.10/21.25 | | | | | | semantics_ltln$(w$) = v1 & A_ltln$(v3) & A_ltln$(v2) & % 152.10/21.25 | | | | | | A_ltln_bool_fun$(v1) & fun_app$(v1, v3)) | (f_G$(phi$, % 152.10/21.25 | | | | | | w$) = v0 & A_ltln_set$(v0) & ~ member$(psi$, v0))) % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | | DELTA: instantiating (303) with fresh symbols all_955_0, all_955_1, % 152.10/21.25 | | | | | | all_955_2, all_955_3 gives: % 152.10/21.25 | | | | | | (304) (fun_app$a(all_677_0, all_680_2) = all_955_1 & % 152.10/21.25 | | | | | | fun_app$a(all_677_1, all_955_1) = all_955_0 & % 152.10/21.25 | | | | | | semantics_ltln$(w$) = all_955_2 & A_ltln$(all_955_0) & % 152.10/21.25 | | | | | | A_ltln$(all_955_1) & A_ltln_bool_fun$(all_955_2) & % 152.10/21.25 | | | | | | fun_app$(all_955_2, all_955_0)) | (f_G$(phi$, w$) = % 152.10/21.25 | | | | | | all_955_3 & A_ltln_set$(all_955_3) & ~ member$(psi$, % 152.10/21.25 | | | | | | all_955_3)) % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | | BETA: splitting (304) gives: % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | | Case 1: % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | (305) fun_app$a(all_677_0, all_680_2) = all_955_1 & % 152.10/21.25 | | | | | | | fun_app$a(all_677_1, all_955_1) = all_955_0 & % 152.10/21.25 | | | | | | | semantics_ltln$(w$) = all_955_2 & A_ltln$(all_955_0) & % 152.10/21.25 | | | | | | | A_ltln$(all_955_1) & A_ltln_bool_fun$(all_955_2) & % 152.10/21.25 | | | | | | | fun_app$(all_955_2, all_955_0) % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | ALPHA: (305) implies: % 152.10/21.25 | | | | | | | (306) fun_app$(all_955_2, all_955_0) % 152.10/21.25 | | | | | | | (307) semantics_ltln$(w$) = all_955_2 % 152.10/21.25 | | | | | | | (308) fun_app$a(all_677_1, all_955_1) = all_955_0 % 152.10/21.25 | | | | | | | (309) fun_app$a(all_677_0, all_680_2) = all_955_1 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | REDUCE: (233), (309) imply: % 152.10/21.25 | | | | | | | (310) fun_app$a(all_659_0, all_680_2) = all_955_1 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | REDUCE: (242), (308) imply: % 152.10/21.25 | | | | | | | (311) fun_app$a(all_662_1, all_955_1) = all_955_0 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | BETA: splitting (273) gives: % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | Case 1: % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | GROUND_INST: instantiating (39) with all_587_0, all_955_2, w$, % 152.10/21.25 | | | | | | | | simplifying with (49), (307) gives: % 152.10/21.25 | | | | | | | | (312) all_955_2 = all_587_0 % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | GROUND_INST: instantiating (46) with all_680_1, all_955_1, % 152.10/21.25 | | | | | | | | all_680_2, all_659_0, simplifying with (245), (310) % 152.10/21.25 | | | | | | | | gives: % 152.10/21.25 | | | | | | | | (313) all_955_1 = all_680_1 % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | GROUND_INST: instantiating (46) with all_680_0, all_955_0, % 152.10/21.25 | | | | | | | | all_680_1, all_662_1, simplifying with (246) gives: % 152.10/21.25 | | | | | | | | (314) all_955_0 = all_680_0 | ~ (fun_app$a(all_662_1, % 152.10/21.25 | | | | | | | | all_680_1) = all_955_0) % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | REDUCE: (311), (313) imply: % 152.10/21.25 | | | | | | | | (315) fun_app$a(all_662_1, all_680_1) = all_955_0 % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | REDUCE: (306), (312) imply: % 152.10/21.25 | | | | | | | | (316) fun_app$(all_587_0, all_955_0) % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | BETA: splitting (314) gives: % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | Case 1: % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | (317) ~ (fun_app$a(all_662_1, all_680_1) = all_955_0) % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | PRED_UNIFY: (315), (317) imply: % 152.10/21.25 | | | | | | | | | (318) $false % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | CLOSE: (318) is inconsistent. % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | Case 2: % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | (319) all_955_0 = all_680_0 % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | REDUCE: (316), (319) imply: % 152.10/21.25 | | | | | | | | | (320) fun_app$(all_587_0, all_680_0) % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | PRED_UNIFY: (255), (320) imply: % 152.10/21.25 | | | | | | | | | (321) $false % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | | CLOSE: (321) is inconsistent. % 152.10/21.25 | | | | | | | | | % 152.10/21.25 | | | | | | | | End of split % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | Case 2: % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | (322) all_637_3 = bot$ % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | REDUCE: (295), (322) imply: % 152.10/21.25 | | | | | | | | (323) $false % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | | CLOSE: (323) is inconsistent. % 152.10/21.25 | | | | | | | | % 152.10/21.25 | | | | | | | End of split % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | Case 2: % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | (324) f_G$(phi$, w$) = all_955_3 & A_ltln_set$(all_955_3) & ~ % 152.10/21.25 | | | | | | | member$(psi$, all_955_3) % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | ALPHA: (324) implies: % 152.10/21.25 | | | | | | | (325) ~ member$(psi$, all_955_3) % 152.10/21.25 | | | | | | | (326) f_G$(phi$, w$) = all_955_3 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | GROUND_INST: instantiating (44) with all_637_3, all_955_3, w$, % 152.10/21.25 | | | | | | | phi$, simplifying with (57), (326) gives: % 152.10/21.25 | | | | | | | (327) all_955_3 = all_637_3 % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | PRED_UNIFY: (271), (325) imply: % 152.10/21.25 | | | | | | | (328) ~ (all_955_3 = all_637_3) % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | REDUCE: (327), (328) imply: % 152.10/21.25 | | | | | | | (329) $false % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | | CLOSE: (329) is inconsistent. % 152.10/21.25 | | | | | | | % 152.10/21.25 | | | | | | End of split % 152.10/21.25 | | | | | | % 152.10/21.25 | | | | | End of split % 152.10/21.25 | | | | | % 152.10/21.25 | | | | End of split % 152.10/21.25 | | | | % 152.10/21.25 | | | End of split % 152.10/21.25 | | | % 152.10/21.25 | | End of split % 152.10/21.25 | | % 152.10/21.25 | End of split % 152.10/21.25 | % 152.10/21.25 End of proof % 152.10/21.25 % SZS output end Proof for theBenchmark % 152.10/21.25 % 152.10/21.25 20648ms %------------------------------------------------------------------------------