%------------------------------------------------------------------------------ % 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 : n004.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 04:11:53 EDT 2023 % Result : Theorem 38.64s 6.00s % Output : Proof 55.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % 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 % 0.13/0.35 % Computer : n004.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 10:33:22 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 12.17/2.41 Prover 1: Preprocessing ... % 12.89/2.52 Prover 5: Preprocessing ... % 12.89/2.52 Prover 2: Preprocessing ... % 12.89/2.52 Prover 0: Preprocessing ... % 13.40/2.56 Prover 4: Preprocessing ... % 13.40/2.57 Prover 6: Preprocessing ... % 13.40/2.57 Prover 3: Preprocessing ... % 31.70/5.02 Prover 1: Warning: ignoring some quantifiers % 31.70/5.03 Prover 3: Warning: ignoring some quantifiers % 31.70/5.04 Prover 6: Proving ... % 32.35/5.07 Prover 3: Constructing countermodel ... % 32.67/5.16 Prover 1: Constructing countermodel ... % 34.36/5.40 Prover 0: Proving ... % 34.75/5.42 Prover 4: Warning: ignoring some quantifiers % 35.80/5.55 Prover 4: Constructing countermodel ... % 35.80/5.58 Prover 5: Proving ... % 38.05/5.99 Prover 0: proved (5357ms) % 38.05/5.99 % 38.64/6.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.64/6.00 % 38.64/6.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 38.64/6.02 Prover 3: stopped % 38.64/6.03 Prover 5: stopped % 38.64/6.05 Prover 6: stopped % 39.61/6.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.61/6.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.61/6.06 Prover 2: Proving ... % 39.61/6.06 Prover 2: stopped % 39.61/6.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.61/6.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 47.39/7.07 Prover 8: Preprocessing ... % 47.39/7.09 Prover 7: Preprocessing ... % 47.73/7.21 Prover 11: Preprocessing ... % 47.73/7.21 Prover 13: Preprocessing ... % 48.23/7.23 Prover 10: Preprocessing ... % 50.38/7.46 Prover 4: Found proof (size 232) % 50.38/7.46 Prover 4: proved (6832ms) % 50.38/7.47 Prover 1: stopped % 52.15/7.71 Prover 7: stopped % 52.66/7.76 Prover 11: stopped % 52.77/7.83 Prover 10: stopped % 53.59/7.98 Prover 8: Warning: ignoring some quantifiers % 54.02/8.02 Prover 13: stopped % 54.02/8.02 Prover 8: Constructing countermodel ... % 54.02/8.04 Prover 8: stopped % 54.02/8.04 % 54.02/8.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 54.02/8.04 % 54.37/8.11 % SZS output start Proof for theBenchmark % 54.37/8.12 Assumptions after simplification: % 54.37/8.12 --------------------------------- % 54.37/8.12 % 54.37/8.12 (axiom117) % 54.37/8.15 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.37/8.15 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: MultipleValueBool] % 54.37/8.15 : ! [v5: Nat$] : ! [v6: int] : ( ~ ($lesseq(1, $difference(v3, v6))) | ~ % 54.37/8.15 (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v1) = v3) | ~ % 54.37/8.15 (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v5) | ~ % 54.37/8.15 Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : % 54.37/8.15 ? [v11: int] : (Nat$(v9) & ((v8 = 0 & nat$($sum(v6, 1)) = v7 & % 54.37/8.15 fun_app$c(v2, v7) = 0 & Nat$(v7)) | ( ~ (v11 = 0) & $lesseq(v10, v3) % 54.37/8.15 & fun_app$k(of_nat$, v9) = v10 & fun_app$c(v2, v9) = v11)))) & ! % 54.37/8.15 [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: % 54.37/8.15 int] : (v5 = 0 | ~ (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v4) % 54.37/8.15 = v5) | ~ (fun_app$c(v2, v0) = 0) | ~ Nat_bool_fun$(v2) | ~ Nat$(v4) % 54.37/8.15 | ~ Nat$(v1) | ? [v6: int] : ? [v7: Nat$] : ? [v8: int] : ? [v9: % 54.37/8.15 Nat$] : ? [v10: int] : (Nat$(v7) & (( ~ (v10 = 0) & $lesseq(1, % 54.37/8.15 $difference(v3, v8)) & fun_app$k(of_nat$, v7) = v8 & nat$($sum(v8, % 54.37/8.15 1)) = v9 & fun_app$c(v2, v9) = v10 & Nat$(v9)) | ($lesseq(1, % 54.37/8.15 $difference(v6, v3)) & fun_app$k(of_nat$, v4) = v6)))) & ! [v1: % 54.37/8.15 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: % 54.37/8.15 int] : ( ~ ($lesseq(v5, v3)) | ~ (fun_app$k(of_nat$, v4) = v5) | ~ % 54.37/8.15 (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v0) = 0) | ~ % 54.37/8.15 Nat_bool_fun$(v2) | ~ Nat$(v4) | ~ Nat$(v1) | ? [v6: int] : ? [v7: % 54.37/8.15 Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : (Nat$(v7) & ((v6 % 54.37/8.15 = 0 & fun_app$c(v2, v4) = 0) | ( ~ (v10 = 0) & $lesseq(1, % 54.37/8.15 $difference(v3, v8)) & fun_app$k(of_nat$, v7) = v8 & nat$($sum(v8, % 54.37/8.15 1)) = v9 & fun_app$c(v2, v9) = v10 & Nat$(v9))))) & ! [v1: % 54.37/8.15 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : (v4 = 0 | % 54.37/8.15 ~ (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v0) = v4) | ~ % 54.37/8.15 Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v5: Nat$] : ? [v6: int] : ? [v7: % 54.37/8.15 int] : ( ~ (v7 = 0) & $lesseq(v6, v3) & fun_app$k(of_nat$, v5) = v6 & % 54.37/8.15 fun_app$c(v2, v5) = v7 & Nat$(v5)))) % 54.37/8.15 % 54.37/8.15 (axiom119) % 54.37/8.16 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.37/8.16 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : ! [v5: % 54.37/8.16 Nat$] : ! [v6: int] : (v4 = 0 | ~ ($lesseq(v6, v3)) | ~ % 54.37/8.16 (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v1) = v3) | ~ % 54.37/8.16 (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v5) | ~ % 54.37/8.16 Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : % 54.37/8.16 ? [v11: int] : (Nat$(v7) & ((v10 = 0 & $lesseq(1, $difference(v3, v8)) & % 54.37/8.16 fun_app$k(of_nat$, v7) = v8 & nat$($sum(v8, 1)) = v9 & fun_app$c(v2, % 54.37/8.16 v9) = 0 & Nat$(v9)) | ( ~ (v11 = 0) & fun_app$c(v2, v5) = v11)))) % 54.37/8.16 & ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: MultipleValueBool] : ! % 54.37/8.16 [v4: int] : ! [v5: Nat$] : ! [v6: int] : ( ~ ($lesseq(1, $difference(v4, % 54.37/8.16 v6))) | ~ (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, % 54.37/8.16 v1) = v4) | ~ (fun_app$c(v2, v0) = v3) | ~ Nat_bool_fun$(v2) | ~ % 54.37/8.16 Nat$(v5) | ~ Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: int] : ? % 54.37/8.16 [v10: Nat$] : ? [v11: int] : (Nat$(v7) & ((v9 = 0 & $lesseq(v8, v4) & % 54.37/8.16 fun_app$k(of_nat$, v7) = v8 & fun_app$c(v2, v7) = 0) | ( ~ (v11 = 0) % 54.37/8.16 & nat$($sum(v6, 1)) = v10 & fun_app$c(v2, v10) = v11 & Nat$(v10))))) % 54.37/8.16 & ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : ! % 54.37/8.16 [v5: Nat$] : (v4 = 0 | ~ (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, % 54.37/8.16 v5) = 0) | ~ (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ % 54.37/8.16 Nat$(v5) | ~ Nat$(v1) | ? [v6: Nat$] : ? [v7: int] : ? [v8: Nat$] : ? % 54.37/8.16 [v9: int] : ? [v10: int] : (Nat$(v6) & ((v9 = 0 & $lesseq(1, % 54.37/8.16 $difference(v3, v7)) & fun_app$k(of_nat$, v6) = v7 & nat$($sum(v7, % 54.37/8.16 1)) = v8 & fun_app$c(v2, v8) = 0 & Nat$(v8)) | ($lesseq(1, % 54.37/8.16 $difference(v10, v3)) & fun_app$k(of_nat$, v5) = v10)))) & ! [v1: % 54.37/8.16 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ( ~ (fun_app$k(of_nat$, % 54.37/8.16 v1) = v3) | ~ (fun_app$c(v2, v0) = 0) | ~ Nat_bool_fun$(v2) | ~ % 54.37/8.16 Nat$(v1) | ? [v4: Nat$] : ? [v5: int] : ($lesseq(v5, v3) & % 54.37/8.16 fun_app$k(of_nat$, v4) = v5 & fun_app$c(v2, v4) = 0 & Nat$(v4)))) % 54.37/8.16 % 54.37/8.16 (axiom12) % 54.37/8.17 Nat_a_set_fun$(w$) & A_ltln$(phi$) & A_ltln_set$(x$) & % 54.37/8.17 A_ltln_a_ltln_fun$(unf$) & A_ltln_a_ltln_fun$(next_ltln$) & ? [v0: A_ltln$] : % 54.37/8.17 ? [v1: A_ltln$] : ? [v2: A_ltln$] : (fun_app$i(unf$, v0) = v1 & % 54.37/8.17 fun_app$i(next_ltln$, phi$) = v0 & gF_advice$(v1, x$) = v2 & % 54.37/8.17 semantics_ltln$(w$, v2) = 0 & A_ltln$(v2) & A_ltln$(v1) & A_ltln$(v0)) % 54.37/8.17 % 54.37/8.17 (axiom122) % 54.37/8.17 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(1) = v0 & Nat$(v0) & ! [v1: % 54.37/8.17 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : (v3 = 0 | ~ % 54.37/8.17 (fun_app$c(v2, v1) = v3) | ~ Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v4: % 54.37/8.17 int] : ? [v5: any] : ? [v6: Nat$] : ? [v7: int] : ? [v8: int] : ? % 54.37/8.17 [v9: Nat$] : ? [v10: int] : (Nat$(v6) & ((v8 = 0 & ~ (v10 = 0) & % 54.37/8.17 $lesseq(1, v7) & fun_app$k(of_nat$, v6) = v7 & nat$($sum(v7, 1)) = % 54.37/8.17 v9 & fun_app$c(v2, v9) = v10 & fun_app$c(v2, v6) = 0 & Nat$(v9)) | % 54.37/8.17 (fun_app$k(of_nat$, v1) = v4 & fun_app$c(v2, v0) = v5 & ( ~ (v5 = 0) | % 54.37/8.17 ~ ($lesseq(1, v4)))))))) % 54.37/8.17 % 54.37/8.17 (axiom126) % 54.78/8.17 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 54.78/8.17 Nat$(v0) & ! [v1: Nat$] : ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! % 54.78/8.17 [v4: A_ltln_set$] : ! [v5: A_set_list$] : ! [v6: A_ltln$] : ! [v7: % 54.78/8.17 A_ltln$] : ( ~ (subsequence$(v2, v0, v1) = v5) | ~ (foldl$(af_letter$, % 54.78/8.17 v3, v5) = v6) | ~ (fG_advice$(v6, v4) = v7) | ~ Nat_a_set_fun$(v2) | % 54.78/8.17 ~ A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ Nat$(v1) | ? [v8: % 54.78/8.17 Nat_a_set_fun$] : ? [v9: any] : ? [v10: A_ltln$] : ? [v11: any] : % 54.78/8.17 (fG_advice$(v3, v4) = v10 & suffix$(v1, v2) = v8 & semantics_ltln$(v8, v7) % 54.78/8.17 = v9 & semantics_ltln$(v2, v10) = v11 & Nat_a_set_fun$(v8) & % 54.78/8.17 A_ltln$(v10) & ( ~ (v9 = 0) | v11 = 0)))) % 54.78/8.17 % 54.78/8.17 (axiom13) % 54.78/8.18 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & Nat_a_set_fun$(w$) & A_ltln$(phi$) % 54.78/8.18 & A_ltln_set$(x$) & A_ltln_a_ltln_fun$(unf$) & ? [v0: A_ltln$] : ? [v1: % 54.78/8.18 A_ltln$] : ? [v2: any] : ? [v3: Nat$] : ? [v4: Nat_a_set_fun$] : ? [v5: % 54.78/8.18 A_set_a_ltln_fun$] : ? [v6: Nat$] : ? [v7: A_set$] : ? [v8: A_ltln$] : ? % 54.78/8.18 [v9: A_ltln$] : ? [v10: any] : (suffix$(v3, w$) = v4 & fun_app$h(af_letter$, % 54.78/8.18 phi$) = v5 & nat$(1) = v3 & nat$(0) = v6 & fun_app$j(w$, v6) = v7 & % 54.78/8.18 fun_app$g(v5, v7) = v8 & fun_app$i(unf$, phi$) = v0 & gF_advice$(v8, x$) = % 54.78/8.18 v9 & gF_advice$(v0, x$) = v1 & semantics_ltln$(v4, v9) = v10 & % 54.78/8.18 semantics_ltln$(w$, v1) = v2 & Nat_a_set_fun$(v4) & A_ltln$(v9) & % 54.78/8.18 A_ltln$(v8) & A_ltln$(v1) & A_ltln$(v0) & A_set$(v7) & A_set_a_ltln_fun$(v5) % 54.78/8.18 & Nat$(v6) & Nat$(v3) & ( ~ (v2 = 0) | v10 = 0)) % 54.78/8.18 % 54.78/8.18 (axiom132) % 54.78/8.18 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.78/8.18 Nat_bool_fun$] : ! [v2: Nat$] : ( ~ (fun_app$c(v1, v2) = 0) | ~ % 54.78/8.18 Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v3: int] : ? [v4: Nat$] : ? [v5: % 54.78/8.18 int] : ? [v6: Nat$] : ? [v7: int] : ? [v8: int] : (Nat$(v4) & ((v7 = % 54.78/8.18 0 & ~ (v8 = 0) & fun_app$k(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = % 54.78/8.18 v6 & fun_app$c(v1, v6) = 0 & fun_app$c(v1, v4) = v8 & Nat$(v6)) | % 54.78/8.18 (v3 = 0 & fun_app$c(v1, v0) = 0))))) % 54.78/8.18 % 54.78/8.18 (axiom133) % 54.78/8.19 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.78/8.19 Nat_nat_bool_fun_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: % 54.78/8.19 Nat_bool_fun$] : ! [v5: int] : (v5 = 0 | ~ (fun_app$n(v1, v2) = v4) | ~ % 54.78/8.19 (fun_app$c(v4, v3) = v5) | ~ Nat$(v3) | ~ Nat$(v2) | ~ % 54.78/8.19 Nat_nat_bool_fun_fun$(v1) | ? [v6: Nat_bool_fun$] : ? [v7: Nat$] : ? % 54.78/8.19 [v8: int] : ? [v9: Nat$] : ? [v10: int] : ? [v11: Nat$] : ? [v12: % 54.78/8.19 Nat$] : ? [v13: Nat_bool_fun$] : ? [v14: int] : ? [v15: int] : ? % 54.78/8.19 [v16: Nat$] : ? [v17: Nat_bool_fun$] : ? [v18: int] : ? [v19: Nat$] : % 54.78/8.19 ? [v20: int] : ? [v21: Nat$] : ? [v22: Nat_bool_fun$] : ? [v23: int] : % 54.78/8.19 (Nat$(v21) & Nat$(v12) & Nat$(v11) & Nat$(v7) & ((v14 = 0 & ~ (v20 = 0) & % 54.78/8.19 fun_app$n(v1, v16) = v17 & fun_app$n(v1, v11) = v13 & % 54.78/8.19 fun_app$k(of_nat$, v12) = v18 & fun_app$k(of_nat$, v11) = v15 & % 54.78/8.19 nat$($sum(v18, 1)) = v19 & nat$($sum(v15, 1)) = v16 & fun_app$c(v17, % 54.78/8.19 v19) = v20 & fun_app$c(v13, v12) = 0 & Nat_bool_fun$(v17) & % 54.78/8.19 Nat_bool_fun$(v13) & Nat$(v19) & Nat$(v16)) | ( ~ (v23 = 0) & % 54.78/8.19 fun_app$n(v1, v21) = v22 & fun_app$c(v22, v0) = v23 & % 54.78/8.19 Nat_bool_fun$(v22)) | ( ~ (v10 = 0) & fun_app$n(v1, v0) = v6 & % 54.78/8.19 fun_app$k(of_nat$, v7) = v8 & nat$($sum(v8, 1)) = v9 & fun_app$c(v6, % 54.78/8.19 v9) = v10 & Nat_bool_fun$(v6) & Nat$(v9)))))) % 54.78/8.19 % 54.78/8.19 (axiom134) % 54.85/8.19 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.85/8.19 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ % 54.85/8.19 (fun_app$c(v1, v2) = v3) | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: % 54.85/8.19 int] : ? [v5: Nat$] : ? [v6: int] : ? [v7: int] : ? [v8: Nat$] : ? % 54.85/8.19 [v9: int] : (Nat$(v5) & ((v6 = 0 & ~ (v9 = 0) & fun_app$k(of_nat$, v5) = % 54.85/8.19 v7 & nat$($sum(v7, 1)) = v8 & fun_app$c(v1, v8) = v9 & fun_app$c(v1, % 54.85/8.19 v5) = 0 & Nat$(v8)) | ( ~ (v4 = 0) & fun_app$c(v1, v0) = v4))))) % 54.85/8.19 % 54.85/8.19 (axiom140) % 54.85/8.19 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 54.85/8.19 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ % 54.85/8.19 (fun_app$c(v1, v2) = v3) | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: % 54.85/8.19 int] : ? [v5: Nat$] : ? [v6: int] : ? [v7: int] : (Nat$(v5) & (( ~ % 54.85/8.19 (v7 = 0) & $lesseq(1, v6) & fun_app$k(of_nat$, v5) = v6 & % 54.85/8.19 fun_app$c(v1, v5) = v7 & ! [v8: Nat$] : ! [v9: int] : (v9 = 0 | ~ % 54.85/8.19 (fun_app$c(v1, v8) = v9) | ~ Nat$(v8) | ? [v10: int] : % 54.85/8.19 ($lesseq(v6, v10) & fun_app$k(of_nat$, v8) = v10)) & ! [v8: Nat$] % 54.85/8.19 : ! [v9: int] : ( ~ ($lesseq(1, $difference(v6, v9))) | ~ % 54.85/8.19 (fun_app$k(of_nat$, v8) = v9) | ~ Nat$(v8) | fun_app$c(v1, v8) = % 54.85/8.19 0)) | ( ~ (v4 = 0) & fun_app$c(v1, v0) = v4))))) % 54.85/8.19 % 54.85/8.19 (axiom148) % 54.85/8.21 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 54.85/8.21 Nat$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 54.85/8.21 A_ltln_a_ltln_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: % 54.85/8.21 A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! [v8: % 54.85/8.21 A_ltln_bool_fun$] : ! [v9: A_ltln$] : ! [v10: A_ltln$] : ! [v11: int] : % 54.85/8.21 (v11 = 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$m(v1, % 54.96/8.21 v7) = v8) | ~ (fun_app$l(v8, v10) = v11) | ~ (fun_app$i(v2, v4) = % 54.96/8.21 v9) | ~ (fun_app$i(v2, v3) = v6) | ~ (gF_advice$(v9, v5) = v10) | ~ % 54.96/8.21 (gF_advice$(v6, v5) = v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 54.96/8.21 A_ltln$(v4) | ~ A_ltln$(v3) | ~ A_ltln_set$(v5) | ~ % 54.96/8.21 A_ltln_a_ltln_fun$(v2) | ? [v12: A_ltln_bool_fun$] : ? [v13: int] : ( ~ % 54.96/8.21 (v13 = 0) & fun_app$m(v1, v3) = v12 & fun_app$l(v12, v4) = v13 & % 54.96/8.21 A_ltln_bool_fun$(v12))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 54.96/8.21 A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 54.96/8.21 A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ! [v8: int] : (v8 = % 54.96/8.21 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$i(v2, v4) = % 54.96/8.21 v6) | ~ (gF_advice$(v6, v5) = v7) | ~ (semantics_ltln$(v3, v7) = v8) | % 54.96/8.21 ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 54.96/8.21 A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v9: % 54.96/8.21 A_ltln$] : ? [v10: int] : ( ~ (v10 = 0) & gF_advice$(v4, v5) = v9 & % 54.96/8.21 semantics_ltln$(v3, v9) = v10 & A_ltln$(v9))) & ! [v1: % 54.96/8.21 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 54.96/8.21 Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: % 54.96/8.21 A_ltln$] : ! [v7: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = % 54.96/8.21 0) | ~ (fun_app$i(v2, v4) = v6) | ~ (gF_advice$(v6, v5) = v7) | ~ % 54.96/8.21 (semantics_ltln$(v3, v7) = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 54.96/8.21 Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ % 54.96/8.21 A_ltln_a_ltln_fun$(v2) | ? [v8: Nat$] : ? [v9: Nat_a_set_fun$] : ? % 54.96/8.21 [v10: A_set_list$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] : % 54.96/8.21 (subsequence$(v3, v0, v8) = v10 & foldl$(af_letter$, v4, v10) = v11 & % 54.96/8.21 suffix$(v8, v3) = v9 & gF_advice$(v11, v5) = v12 & semantics_ltln$(v9, % 54.96/8.21 v12) = 0 & Nat_a_set_fun$(v9) & A_ltln$(v12) & A_ltln$(v11) & % 54.96/8.21 A_set_list$(v10) & Nat$(v8))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : % 54.96/8.21 ! [v2: A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! % 54.96/8.21 [v5: A_ltln_set$] : ! [v6: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, % 54.96/8.21 v2) = 0) | ~ (gF_advice$(v4, v5) = v6) | ~ (semantics_ltln$(v3, v6) % 54.96/8.21 = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 54.96/8.21 A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v7: % 54.96/8.21 A_ltln$] : ? [v8: A_ltln$] : (fun_app$i(v2, v4) = v7 & gF_advice$(v7, % 54.96/8.21 v5) = v8 & semantics_ltln$(v3, v8) = 0 & A_ltln$(v8) & A_ltln$(v7))) & % 54.96/8.21 ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 54.96/8.21 A_ltln$] : ! [v4: A_ltln_bool_fun$] : ( ~ % 54.96/8.21 (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$m(v1, v3) = v4) | % 54.96/8.21 ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 54.96/8.21 A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln$] : (fun_app$l(v4, v5) = 0 & % 54.96/8.21 fun_app$i(v2, v3) = v5 & A_ltln$(v5))) & ! [v1: % 54.96/8.21 A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 54.96/8.21 A_ltln$] : ! [v4: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = % 54.96/8.21 0) | ~ (fun_app$i(v2, v3) = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | % 54.96/8.21 ~ A_ltln$(v3) | ~ A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln_bool_fun$] : % 54.96/8.21 (fun_app$m(v1, v3) = v5 & fun_app$l(v5, v4) = 0 & A_ltln_bool_fun$(v5))) & % 54.96/8.21 ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 54.96/8.21 int] : (v3 = 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = v3) | ~ % 54.96/8.21 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | ? [v4: % 54.96/8.21 A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? [v7: % 54.96/8.21 A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? [v10: A_ltln$] % 54.96/8.21 : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? % 54.96/8.21 [v14: int] : ? [v15: Nat_a_set_fun$] : ? [v16: A_ltln$] : ? [v17: % 54.96/8.21 A_ltln_set$] : ? [v18: A_ltln$] : ? [v19: A_ltln$] : ? [v20: int] : % 54.96/8.21 ? [v21: Nat_a_set_fun$] : ? [v22: A_ltln$] : ? [v23: A_ltln_set$] : ? % 54.96/8.21 [v24: A_ltln$] : ? [v25: int] : ? [v26: A_ltln$] : ? [v27: A_ltln$] : % 54.96/8.21 ? [v28: int] : ? [v29: A_ltln$] : ? [v30: A_ltln_bool_fun$] : ? [v31: % 54.96/8.21 A_ltln$] : ? [v32: int] : (Nat_a_set_fun$(v21) & Nat_a_set_fun$(v15) & % 54.96/8.21 A_ltln$(v29) & A_ltln$(v22) & A_ltln$(v16) & A_ltln$(v5) & A_ltln$(v4) & % 54.96/8.21 A_ltln_set$(v23) & A_ltln_set$(v17) & A_ltln_set$(v6) & ((v25 = 0 & ~ % 54.96/8.21 (v28 = 0) & fun_app$i(v2, v22) = v26 & gF_advice$(v26, v23) = v27 & % 54.96/8.21 gF_advice$(v22, v23) = v24 & semantics_ltln$(v21, v27) = v28 & % 54.96/8.21 semantics_ltln$(v21, v24) = 0 & A_ltln$(v27) & A_ltln$(v26) & % 54.96/8.21 A_ltln$(v24)) | (v20 = 0 & fun_app$i(v2, v16) = v18 & % 54.96/8.21 gF_advice$(v18, v17) = v19 & semantics_ltln$(v15, v19) = 0 & % 54.96/8.21 A_ltln$(v19) & A_ltln$(v18) & ! [v33: Nat$] : ! [v34: A_set_list$] % 54.96/8.21 : ( ~ (subsequence$(v15, v0, v33) = v34) | ~ Nat$(v33) | ? [v35: % 54.96/8.21 Nat_a_set_fun$] : ? [v36: A_ltln$] : ? [v37: A_ltln$] : ? % 54.96/8.21 [v38: int] : ( ~ (v38 = 0) & foldl$(af_letter$, v16, v34) = v36 & % 54.96/8.21 suffix$(v33, v15) = v35 & gF_advice$(v36, v17) = v37 & % 54.96/8.21 semantics_ltln$(v35, v37) = v38 & Nat_a_set_fun$(v35) & % 54.96/8.21 A_ltln$(v37) & A_ltln$(v36))) & ! [v33: Nat$] : ! [v34: % 54.96/8.21 Nat_a_set_fun$] : ( ~ (suffix$(v33, v15) = v34) | ~ Nat$(v33) | % 54.96/8.21 ? [v35: A_set_list$] : ? [v36: A_ltln$] : ? [v37: A_ltln$] : ? % 54.96/8.21 [v38: int] : ( ~ (v38 = 0) & subsequence$(v15, v0, v33) = v35 & % 54.96/8.21 foldl$(af_letter$, v16, v35) = v36 & gF_advice$(v36, v17) = v37 % 54.96/8.21 & semantics_ltln$(v34, v37) = v38 & A_ltln$(v37) & A_ltln$(v36) % 54.96/8.21 & A_set_list$(v35)))) | (v8 = 0 & ~ (v14 = 0) & fun_app$m(v1, % 54.96/8.21 v10) = v11 & fun_app$m(v1, v4) = v7 & fun_app$l(v11, v13) = v14 & % 54.96/8.21 fun_app$l(v7, v5) = 0 & fun_app$i(v2, v5) = v12 & fun_app$i(v2, v4) % 54.96/8.21 = v9 & gF_advice$(v12, v6) = v13 & gF_advice$(v9, v6) = v10 & % 54.96/8.21 A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v10) & A_ltln$(v9) & % 54.96/8.21 A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7)) | ( ~ (v32 = 0) & % 54.96/8.21 fun_app$m(v1, v29) = v30 & fun_app$l(v30, v31) = v32 & fun_app$i(v2, % 54.96/8.22 v29) = v31 & A_ltln$(v31) & A_ltln_bool_fun$(v30)))))) % 54.96/8.22 % 54.96/8.22 (axiom149) % 55.00/8.22 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.22 Nat$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 55.00/8.22 A_ltln_a_ltln_fun$] : ! [v3: int] : (v3 = 0 | ~ % 55.00/8.22 (gF_advice_congruent_axioms$(v1, v2) = v3) | ~ % 55.00/8.22 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | ? [v4: % 55.00/8.22 A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? [v7: % 55.00/8.22 A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? [v10: A_ltln$] % 55.00/8.22 : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : ? [v13: A_ltln$] : ? % 55.00/8.22 [v14: int] : ? [v15: Nat_a_set_fun$] : ? [v16: A_ltln$] : ? [v17: % 55.00/8.22 A_ltln_set$] : ? [v18: A_ltln$] : ? [v19: A_ltln$] : ? [v20: int] : % 55.00/8.22 ? [v21: Nat_a_set_fun$] : ? [v22: A_ltln$] : ? [v23: A_ltln_set$] : ? % 55.00/8.22 [v24: A_ltln$] : ? [v25: int] : ? [v26: A_ltln$] : ? [v27: A_ltln$] : % 55.00/8.22 ? [v28: int] : ? [v29: A_ltln$] : ? [v30: A_ltln_bool_fun$] : ? [v31: % 55.00/8.22 A_ltln$] : ? [v32: int] : (Nat_a_set_fun$(v21) & Nat_a_set_fun$(v15) & % 55.00/8.22 A_ltln$(v29) & A_ltln$(v22) & A_ltln$(v16) & A_ltln$(v5) & A_ltln$(v4) & % 55.00/8.22 A_ltln_set$(v23) & A_ltln_set$(v17) & A_ltln_set$(v6) & ((v25 = 0 & ~ % 55.00/8.22 (v28 = 0) & fun_app$i(v2, v22) = v26 & gF_advice$(v26, v23) = v27 & % 55.00/8.22 gF_advice$(v22, v23) = v24 & semantics_ltln$(v21, v27) = v28 & % 55.00/8.22 semantics_ltln$(v21, v24) = 0 & A_ltln$(v27) & A_ltln$(v26) & % 55.00/8.22 A_ltln$(v24)) | (v20 = 0 & fun_app$i(v2, v16) = v18 & % 55.00/8.22 gF_advice$(v18, v17) = v19 & semantics_ltln$(v15, v19) = 0 & % 55.00/8.22 A_ltln$(v19) & A_ltln$(v18) & ! [v33: Nat$] : ! [v34: A_set_list$] % 55.00/8.22 : ( ~ (subsequence$(v15, v0, v33) = v34) | ~ Nat$(v33) | ? [v35: % 55.00/8.22 Nat_a_set_fun$] : ? [v36: A_ltln$] : ? [v37: A_ltln$] : ? % 55.00/8.22 [v38: int] : ( ~ (v38 = 0) & foldl$(af_letter$, v16, v34) = v36 & % 55.00/8.22 suffix$(v33, v15) = v35 & gF_advice$(v36, v17) = v37 & % 55.00/8.22 semantics_ltln$(v35, v37) = v38 & Nat_a_set_fun$(v35) & % 55.00/8.22 A_ltln$(v37) & A_ltln$(v36))) & ! [v33: Nat$] : ! [v34: % 55.00/8.22 Nat_a_set_fun$] : ( ~ (suffix$(v33, v15) = v34) | ~ Nat$(v33) | % 55.00/8.22 ? [v35: A_set_list$] : ? [v36: A_ltln$] : ? [v37: A_ltln$] : ? % 55.00/8.22 [v38: int] : ( ~ (v38 = 0) & subsequence$(v15, v0, v33) = v35 & % 55.00/8.22 foldl$(af_letter$, v16, v35) = v36 & gF_advice$(v36, v17) = v37 % 55.00/8.22 & semantics_ltln$(v34, v37) = v38 & A_ltln$(v37) & A_ltln$(v36) % 55.00/8.22 & A_set_list$(v35)))) | (v8 = 0 & ~ (v14 = 0) & fun_app$m(v1, % 55.00/8.22 v10) = v11 & fun_app$m(v1, v4) = v7 & fun_app$l(v11, v13) = v14 & % 55.00/8.22 fun_app$l(v7, v5) = 0 & fun_app$i(v2, v5) = v12 & fun_app$i(v2, v4) % 55.00/8.22 = v9 & gF_advice$(v12, v6) = v13 & gF_advice$(v9, v6) = v10 & % 55.00/8.22 A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v10) & A_ltln$(v9) & % 55.00/8.22 A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7)) | ( ~ (v32 = 0) & % 55.00/8.22 fun_app$m(v1, v29) = v30 & fun_app$l(v30, v31) = v32 & fun_app$i(v2, % 55.00/8.22 v29) = v31 & A_ltln$(v31) & A_ltln_bool_fun$(v30)))))) % 55.00/8.22 % 55.00/8.22 (axiom15) % 55.00/8.23 A_ltln_a_ltln_fun$(next_ltln$) & ? [v0: Nat$] : (nat$(1) = v0 & Nat$(v0) & ! % 55.00/8.23 [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.00/8.23 int] : (v4 = 0 | ~ (suffix$(v0, v1) = v3) | ~ (semantics_ltln$(v3, v2) = % 55.00/8.23 v4) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v5: A_ltln$] : ? % 55.00/8.23 [v6: int] : ( ~ (v6 = 0) & fun_app$i(next_ltln$, v2) = v5 & % 55.00/8.23 semantics_ltln$(v1, v5) = v6 & A_ltln$(v5))) & ! [v1: Nat_a_set_fun$] : % 55.00/8.23 ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: int] : (v4 = 0 | ~ % 55.00/8.23 (fun_app$i(next_ltln$, v2) = v3) | ~ (semantics_ltln$(v1, v3) = v4) | ~ % 55.00/8.23 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v5: Nat_a_set_fun$] : ? [v6: % 55.00/8.23 int] : ( ~ (v6 = 0) & suffix$(v0, v1) = v5 & semantics_ltln$(v5, v2) = % 55.00/8.23 v6 & Nat_a_set_fun$(v5))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 55.00/8.23 ! [v3: Nat_a_set_fun$] : ( ~ (suffix$(v0, v1) = v3) | ~ % 55.00/8.23 (semantics_ltln$(v3, v2) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 55.00/8.23 ? [v4: A_ltln$] : (fun_app$i(next_ltln$, v2) = v4 & semantics_ltln$(v1, % 55.00/8.23 v4) = 0 & A_ltln$(v4))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : % 55.00/8.23 ! [v3: A_ltln$] : ( ~ (fun_app$i(next_ltln$, v2) = v3) | ~ % 55.00/8.23 (semantics_ltln$(v1, v3) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 55.00/8.23 ? [v4: Nat_a_set_fun$] : (suffix$(v0, v1) = v4 & semantics_ltln$(v4, v2) = % 55.00/8.23 0 & Nat_a_set_fun$(v4)))) % 55.00/8.23 % 55.00/8.23 (axiom156) % 55.00/8.23 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.23 Nat$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] % 55.00/8.23 : ! [v4: Nat$] : ! [v5: A_set_list$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] % 55.00/8.23 : ( ~ (subsequence$(v1, v0, v4) = v5) | ~ (foldl$(af_letter$, v2, v5) = v6) % 55.00/8.23 | ~ (gF_advice$(v6, v3) = v7) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 55.00/8.23 ~ A_ltln_set$(v3) | ~ Nat$(v4) | ? [v8: A_ltln$] : ? [v9: any] : ? % 55.00/8.23 [v10: Nat_a_set_fun$] : ? [v11: any] : (suffix$(v4, v1) = v10 & % 55.00/8.23 gF_advice$(v2, v3) = v8 & semantics_ltln$(v10, v7) = v11 & % 55.00/8.23 semantics_ltln$(v1, v8) = v9 & Nat_a_set_fun$(v10) & A_ltln$(v8) & ( ~ % 55.00/8.23 (v9 = 0) | v11 = 0)))) % 55.00/8.23 % 55.00/8.23 (axiom158) % 55.00/8.23 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln_a_ltln_fun$(id$) & ? [v0: % 55.00/8.23 Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: % 55.00/8.23 A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! [v5: A_ltln$] : ( % 55.00/8.23 ~ (fun_app$i(id$, v2) = v4) | ~ (gF_advice$(v4, v3) = v5) | ~ % 55.00/8.23 (semantics_ltln$(v1, v5) = 0) | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | % 55.00/8.23 ~ A_ltln_set$(v3) | ? [v6: Nat$] : ? [v7: Nat_a_set_fun$] : ? [v8: % 55.00/8.23 A_set_list$] : ? [v9: A_ltln$] : ? [v10: A_ltln$] : (subsequence$(v1, % 55.00/8.23 v0, v6) = v8 & foldl$(af_letter$, v2, v8) = v9 & suffix$(v6, v1) = v7 % 55.00/8.23 & gF_advice$(v9, v3) = v10 & semantics_ltln$(v7, v10) = 0 & % 55.00/8.23 Nat_a_set_fun$(v7) & A_ltln$(v10) & A_ltln$(v9) & A_set_list$(v8) & % 55.00/8.23 Nat$(v6)))) % 55.00/8.23 % 55.00/8.23 (axiom166) % 55.00/8.24 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.00/8.24 Nat_nat_fun$] : ! [v2: Nat$] : ! [v3: int] : ( ~ (idx_sequence$(v1) = 0) % 55.00/8.24 | ~ (fun_app$k(of_nat$, v2) = v3) | ~ Nat$(v2) | ~ Nat_nat_fun$(v1) | % 55.00/8.24 ? [v4: Nat$] : ? [v5: Nat$] : ? [v6: int] : ? [v7: Nat$] : ? [v8: int] % 55.00/8.24 : ($lesseq(1, $difference(v6, v8)) & fun_app$k(of_nat$, v7) = v8 & % 55.00/8.24 fun_app$k(of_nat$, v5) = v6 & nat$($sum(v3, 1)) = v4 & fun_app$e(v1, v4) % 55.00/8.24 = v5 & fun_app$e(v1, v2) = v7 & Nat$(v7) & Nat$(v5) & Nat$(v4))) & ! % 55.00/8.24 [v1: Nat_nat_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ( ~ (idx_sequence$(v1) % 55.00/8.24 = 0) | ~ (fun_app$e(v1, v2) = v3) | ~ Nat$(v2) | ~ Nat_nat_fun$(v1) | % 55.00/8.24 ? [v4: int] : ? [v5: Nat$] : ? [v6: Nat$] : ? [v7: int] : ? [v8: int] % 55.00/8.24 : ($lesseq(1, $difference(v7, v8)) & fun_app$k(of_nat$, v6) = v7 & % 55.00/8.24 fun_app$k(of_nat$, v3) = v8 & fun_app$k(of_nat$, v2) = v4 & % 55.00/8.24 nat$($sum(v4, 1)) = v5 & fun_app$e(v1, v5) = v6 & Nat$(v6) & Nat$(v5))) % 55.00/8.24 & ! [v1: Nat_nat_fun$] : ! [v2: int] : (v2 = 0 | ~ (idx_sequence$(v1) = % 55.00/8.24 v2) | ~ Nat_nat_fun$(v1) | ? [v3: Nat$] : ? [v4: int] : ? [v5: Nat$] % 55.00/8.24 : ? [v6: int] : ? [v7: Nat$] : ? [v8: Nat$] : ? [v9: int] : ? [v10: % 55.00/8.24 Nat$] : ? [v11: int] : (Nat$(v5) & (( ~ (v4 = 0) & fun_app$k(of_nat$, % 55.00/8.24 v3) = v4 & fun_app$e(v1, v0) = v3 & Nat$(v3)) | ($lesseq(v9, v11) % 55.00/8.24 & fun_app$k(of_nat$, v10) = v11 & fun_app$k(of_nat$, v8) = v9 & % 55.00/8.24 fun_app$k(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7 & fun_app$e(v1, % 55.00/8.24 v7) = v8 & fun_app$e(v1, v5) = v10 & Nat$(v10) & Nat$(v8) & % 55.00/8.24 Nat$(v7))))) & ! [v1: Nat_nat_fun$] : ! [v2: Nat$] : ( ~ % 55.00/8.24 (fun_app$e(v1, v0) = v2) | ~ Nat_nat_fun$(v1) | ? [v3: int] : ? [v4: % 55.00/8.24 any] : ? [v5: Nat$] : ? [v6: int] : ? [v7: Nat$] : ? [v8: Nat$] : ? % 55.00/8.24 [v9: int] : ? [v10: Nat$] : ? [v11: int] : (Nat$(v5) & (($lesseq(v9, % 55.00/8.24 v11) & fun_app$k(of_nat$, v10) = v11 & fun_app$k(of_nat$, v8) = v9 % 55.00/8.24 & fun_app$k(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7 & % 55.00/8.24 fun_app$e(v1, v7) = v8 & fun_app$e(v1, v5) = v10 & Nat$(v10) & % 55.00/8.24 Nat$(v8) & Nat$(v7)) | (idx_sequence$(v1) = v4 & fun_app$k(of_nat$, % 55.00/8.24 v2) = v3 & ( ~ (v3 = 0) | v4 = 0))))) & ! [v1: Nat_nat_fun$] : ! % 55.00/8.24 [v2: Nat$] : ( ~ (fun_app$e(v1, v0) = v2) | ~ Nat_nat_fun$(v1) | ? [v3: % 55.00/8.24 any] : ? [v4: int] : (idx_sequence$(v1) = v3 & fun_app$k(of_nat$, v2) = % 55.00/8.24 v4 & ( ~ (v3 = 0) | (v4 = 0 & ! [v5: Nat$] : ! [v6: int] : ( ~ % 55.00/8.24 (fun_app$k(of_nat$, v5) = v6) | ~ Nat$(v5) | ? [v7: Nat$] : ? % 55.00/8.24 [v8: Nat$] : ? [v9: int] : ? [v10: Nat$] : ? [v11: int] : % 55.00/8.24 ($lesseq(1, $difference(v9, v11)) & fun_app$k(of_nat$, v10) = v11 % 55.00/8.24 & fun_app$k(of_nat$, v8) = v9 & nat$($sum(v6, 1)) = v7 & % 55.00/8.24 fun_app$e(v1, v7) = v8 & fun_app$e(v1, v5) = v10 & Nat$(v10) & % 55.00/8.24 Nat$(v8) & Nat$(v7))) & ! [v5: Nat$] : ! [v6: Nat$] : ( ~ % 55.00/8.24 (fun_app$e(v1, v5) = v6) | ~ Nat$(v5) | ? [v7: int] : ? [v8: % 55.00/8.24 Nat$] : ? [v9: Nat$] : ? [v10: int] : ? [v11: int] : % 55.00/8.24 ($lesseq(1, $difference(v10, v11)) & fun_app$k(of_nat$, v9) = v10 % 55.00/8.24 & fun_app$k(of_nat$, v6) = v11 & fun_app$k(of_nat$, v5) = v7 & % 55.00/8.24 nat$($sum(v7, 1)) = v8 & fun_app$e(v1, v8) = v9 & Nat$(v9) & % 55.00/8.24 Nat$(v8))))))) & ! [v1: Nat_nat_fun$] : ( ~ (idx_sequence$(v1) % 55.00/8.24 = 0) | ~ Nat_nat_fun$(v1) | ? [v2: Nat$] : (fun_app$k(of_nat$, v2) = 0 % 55.00/8.24 & fun_app$e(v1, v0) = v2 & Nat$(v2)))) % 55.00/8.24 % 55.00/8.24 (axiom168) % 55.00/8.24 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.24 Nat$(v0) & ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! % 55.00/8.24 [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ( ~ (f$(v1, v4) = v5) | ~ % 55.00/8.24 (suffix$(v3, v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ % 55.00/8.25 Nat$(v3) | ? [v6: A_set_list$] : ? [v7: A_ltln$] : (f$(v7, v4) = v5 & % 55.00/8.25 subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 & % 55.00/8.25 A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: A_ltln$] : % 55.00/8.25 ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ! [v5: % 55.00/8.25 A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = v4) | ~ (foldl$(af_letter$, % 55.00/8.25 v1, v4) = v5) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | % 55.00/8.25 ? [v6: Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (f$(v5, v6) = v7 & f$(v1, % 55.00/8.25 v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.00/8.25 A_ltln_set$(v7)))) % 55.00/8.25 % 55.00/8.25 (axiom169) % 55.00/8.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.25 Nat$(v0) & ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! % 55.00/8.25 [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ( ~ (g$(v1, v4) = v5) | ~ % 55.00/8.25 (suffix$(v3, v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ % 55.00/8.25 Nat$(v3) | ? [v6: A_set_list$] : ? [v7: A_ltln$] : (g$(v7, v4) = v5 & % 55.00/8.25 subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 & % 55.00/8.25 A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: A_ltln$] : % 55.00/8.25 ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ! [v5: % 55.00/8.25 A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = v4) | ~ (foldl$(af_letter$, % 55.00/8.25 v1, v4) = v5) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | % 55.00/8.25 ? [v6: Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (g$(v5, v6) = v7 & g$(v1, % 55.00/8.25 v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.00/8.25 A_ltln_set$(v7)))) % 55.00/8.25 % 55.00/8.25 (axiom170) % 55.00/8.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.25 Nat$(v0) & ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! % 55.00/8.25 [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ( ~ (f_G$(v1, v4) = v5) | ~ % 55.00/8.25 (suffix$(v3, v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ % 55.00/8.25 Nat$(v3) | ? [v6: A_set_list$] : ? [v7: A_ltln$] : (f_G$(v7, v4) = v5 & % 55.00/8.25 subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 & % 55.00/8.25 A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: A_ltln$] : % 55.00/8.25 ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ! [v5: % 55.00/8.25 A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = v4) | ~ (foldl$(af_letter$, % 55.00/8.25 v1, v4) = v5) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | % 55.00/8.25 ? [v6: Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (f_G$(v5, v6) = v7 & % 55.00/8.25 f_G$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.00/8.25 A_ltln_set$(v7)))) % 55.00/8.25 % 55.00/8.25 (axiom18) % 55.00/8.25 A_ltln_a_ltln_fun$(next_ltln$) & ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ! % 55.00/8.25 [v2: A_ltln$] : ! [v3: A_ltln$] : ( ~ (fun_app$i(next_ltln$, v0) = v2) | ~ % 55.00/8.25 (gF_advice$(v2, v1) = v3) | ~ A_ltln$(v0) | ~ A_ltln_set$(v1) | ? [v4: % 55.00/8.25 A_ltln$] : (fun_app$i(next_ltln$, v4) = v3 & gF_advice$(v0, v1) = v4 & % 55.00/8.25 A_ltln$(v4) & A_ltln$(v3))) & ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ! % 55.00/8.25 [v2: A_ltln$] : ( ~ (gF_advice$(v0, v1) = v2) | ~ A_ltln$(v0) | ~ % 55.00/8.25 A_ltln_set$(v1) | ? [v3: A_ltln$] : ? [v4: A_ltln$] : % 55.00/8.25 (fun_app$i(next_ltln$, v2) = v4 & fun_app$i(next_ltln$, v0) = v3 & % 55.00/8.25 gF_advice$(v3, v1) = v4 & A_ltln$(v4) & A_ltln$(v3))) % 55.00/8.25 % 55.00/8.25 (axiom19) % 55.00/8.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & A_ltln_a_ltln_fun$(next_ltln$) & ! % 55.00/8.25 [v0: A_ltln$] : ! [v1: A_set$] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.25 A_set_a_ltln_fun$] : ! [v4: A_ltln$] : (v4 = v0 | ~ (fun_app$h(af_letter$, % 55.00/8.25 v2) = v3) | ~ (fun_app$g(v3, v1) = v4) | ~ (fun_app$i(next_ltln$, v0) % 55.00/8.25 = v2) | ~ A_ltln$(v0) | ~ A_set$(v1)) % 55.00/8.25 % 55.00/8.25 (axiom193) % 55.00/8.25 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.25 Nat$(v0) & ! [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! % 55.00/8.25 [v4: Nat_a_set_fun$] : ! [v5: A_ltln_set$] : ( ~ (g_F$(v1, v4) = v5) | ~ % 55.00/8.25 (suffix$(v3, v2) = v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ % 55.00/8.26 Nat$(v3) | ? [v6: A_set_list$] : ? [v7: A_ltln$] : (g_F$(v7, v4) = v5 & % 55.00/8.26 subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 & % 55.00/8.26 A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: A_ltln$] : % 55.00/8.26 ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ! [v5: % 55.00/8.26 A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = v4) | ~ (foldl$(af_letter$, % 55.00/8.26 v1, v4) = v5) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | % 55.00/8.26 ? [v6: Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (g_F$(v5, v6) = v7 & % 55.00/8.26 g_F$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.00/8.26 A_ltln_set$(v7)))) % 55.00/8.26 % 55.00/8.26 (axiom21) % 55.00/8.26 A_ltln_a_ltln_fun$(unf$) & A_ltln_a_ltln_fun$(next_ltln$) & ! [v0: A_ltln$] : % 55.00/8.26 ! [v1: A_ltln$] : ( ~ (fun_app$i(next_ltln$, v0) = v1) | ~ A_ltln$(v0) | % 55.00/8.26 (fun_app$i(unf$, v1) = v1 & A_ltln$(v1))) % 55.00/8.26 % 55.00/8.26 (axiom233) % 55.00/8.26 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.00/8.26 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: int] : ! [v5: % 55.00/8.26 int] : ! [v6: Nat$] : ! [v7: any] : ( ~ (fun_app$k(of_nat$, v3) = v4) | % 55.00/8.26 ~ (fun_app$k(of_nat$, v2) = v5) | ~ (nat$($difference(v5, v4)) = v6) | ~ % 55.00/8.26 (fun_app$c(v1, v6) = v7) | ~ Nat_bool_fun$(v1) | ~ Nat$(v3) | ~ % 55.00/8.26 Nat$(v2) | ? [v8: any] : ? [v9: any] : ? [v10: Nat$] : ? [v11: int] : % 55.00/8.26 ? [v12: Nat$] : ? [v13: int] : ? [v14: int] : (Nat$(v10) & ((v13 = 0 & % 55.00/8.26 ~ (v14 = 0) & fun_app$k(of_nat$, v10) = v11 & nat$($sum(v11, 1)) = % 55.00/8.26 v12 & fun_app$c(v1, v12) = 0 & fun_app$c(v1, v10) = v14 & Nat$(v12)) % 55.00/8.26 | (fun_app$c(v1, v2) = v8 & fun_app$c(v1, v0) = v9 & ( ~ (v8 = 0) | % 55.00/8.26 ((v9 = 0 | ~ ($lesseq(1, $difference(v4, v5)))) & (v7 = 0 | ~ % 55.00/8.26 ($lesseq(v4, v5)))))))))) % 55.00/8.26 % 55.00/8.26 (axiom26) % 55.00/8.26 ? [v0: Nat$] : ? [v1: Nat$] : (nat$(1) = v1 & nat$(0) = v0 & Nat$(v1) & % 55.00/8.26 Nat$(v0) & ! [v2: Nat_a_set_fun$] : ! [v3: Nat_a_set_fun$] : ( ~ % 55.00/8.26 (suffix$(v1, v2) = v3) | ~ Nat_a_set_fun$(v2) | ? [v4: A_set$] : % 55.00/8.26 (build$(v4, v3) = v2 & fun_app$j(v2, v0) = v4 & A_set$(v4))) & ! [v2: % 55.00/8.26 Nat_a_set_fun$] : ! [v3: A_set$] : ( ~ (fun_app$j(v2, v0) = v3) | ~ % 55.00/8.26 Nat_a_set_fun$(v2) | ? [v4: Nat_a_set_fun$] : (build$(v3, v4) = v2 & % 55.00/8.26 suffix$(v1, v2) = v4 & Nat_a_set_fun$(v4)))) % 55.00/8.26 % 55.00/8.26 (axiom264) % 55.00/8.26 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.00/8.26 Nat$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: int] : ! [v5: % 55.00/8.26 int] : ! [v6: Nat_a_set_fun$] : ! [v7: Nat$] : ! [v8: A_set_list$] : ( % 55.00/8.26 ~ ($lesseq(v4, v5)) | ~ (subsequence$(v6, v0, v7) = v8) | ~ % 55.00/8.26 (fun_app$k(of_nat$, v3) = v5) | ~ (fun_app$k(of_nat$, v1) = v4) | ~ % 55.00/8.26 (suffix$(v1, v2) = v6) | ~ (nat$($difference(v5, v4)) = v7) | ~ % 55.00/8.26 Nat_a_set_fun$(v2) | ~ Nat$(v3) | ~ Nat$(v1) | (subsequence$(v2, v1, v3) % 55.00/8.26 = v8 & A_set_list$(v8))) & ! [v1: Nat$] : ! [v2: Nat_a_set_fun$] : ! % 55.00/8.26 [v3: Nat$] : ! [v4: A_set_list$] : ( ~ (subsequence$(v2, v1, v3) = v4) | ~ % 55.00/8.26 Nat_a_set_fun$(v2) | ~ Nat$(v3) | ~ Nat$(v1) | ? [v5: int] : ? [v6: % 55.00/8.26 int] : ? [v7: Nat_a_set_fun$] : ? [v8: Nat$] : ? [v9: A_set_list$] : % 55.00/8.26 (subsequence$(v7, v0, v8) = v9 & fun_app$k(of_nat$, v3) = v6 & % 55.00/8.26 fun_app$k(of_nat$, v1) = v5 & suffix$(v1, v2) = v7 & % 55.00/8.26 nat$($difference(v6, v5)) = v8 & Nat_a_set_fun$(v7) & A_set_list$(v9) & % 55.00/8.26 Nat$(v8) & (v9 = v4 | ~ ($lesseq(v5, v6))))) & ! [v1: Nat$] : ! [v2: % 55.00/8.26 Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ( ~ % 55.00/8.26 (subsequence$(v2, v1, v3) = v4) | ~ Nat_a_set_fun$(v2) | ~ Nat$(v3) | ~ % 55.00/8.26 Nat$(v1) | ? [v5: int] : ? [v6: int] : ? [v7: Nat_a_set_fun$] : ? [v8: % 55.00/8.26 A_set_list$] : (subsequence$(v7, v0, v0) = v8 & fun_app$k(of_nat$, v3) = % 55.00/8.26 v6 & fun_app$k(of_nat$, v1) = v5 & suffix$(v1, v2) = v7 & % 55.00/8.26 Nat_a_set_fun$(v7) & A_set_list$(v8) & (v8 = v4 | ~ ($lesseq(1, % 55.00/8.26 $difference(v5, v6))))))) % 55.00/8.26 % 55.00/8.26 (axiom27) % 55.00/8.26 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ! [v0: A_set$] : ! [v1: % 55.00/8.26 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: % 55.00/8.26 A_set_a_ltln_fun$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: int] : % 55.00/8.26 (v7 = 0 | ~ (fun_app$h(af_letter$, v2) = v4) | ~ (fun_app$g(v4, v0) = v5) | % 55.00/8.26 ~ (gF_advice$(v5, v3) = v6) | ~ (semantics_ltln$(v1, v6) = v7) | ~ % 55.00/8.26 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ A_ltln_set$(v3) | ~ A_set$(v0) | % 55.00/8.26 ? [v8: Nat_a_set_fun$] : ? [v9: A_ltln$] : ? [v10: int] : ( ~ (v10 = 0) & % 55.00/8.26 build$(v0, v1) = v8 & gF_advice$(v2, v3) = v9 & semantics_ltln$(v8, v9) = % 55.00/8.26 v10 & Nat_a_set_fun$(v8) & A_ltln$(v9))) & ! [v0: A_set$] : ! [v1: % 55.00/8.26 Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: % 55.00/8.26 Nat_a_set_fun$] : ! [v5: A_ltln$] : ( ~ (build$(v0, v1) = v4) | ~ % 55.00/8.26 (gF_advice$(v2, v3) = v5) | ~ (semantics_ltln$(v4, v5) = 0) | ~ % 55.00/8.26 Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ~ A_ltln_set$(v3) | ~ A_set$(v0) | % 55.00/8.26 ? [v6: A_set_a_ltln_fun$] : ? [v7: A_ltln$] : ? [v8: A_ltln$] : % 55.00/8.26 (fun_app$h(af_letter$, v2) = v6 & fun_app$g(v6, v0) = v7 & gF_advice$(v7, % 55.00/8.26 v3) = v8 & semantics_ltln$(v1, v8) = 0 & A_ltln$(v8) & A_ltln$(v7) & % 55.00/8.26 A_set_a_ltln_fun$(v6))) % 55.00/8.26 % 55.00/8.26 (axiom270) % 55.00/8.26 Nat_int_fun$(of_nat$) & Nat_nat_fun$(uud$) & ? [v0: Nat$] : ? [v1: % 55.00/8.26 Nat_nat_fun$] : ? [v2: Nat$] : ? [v3: int] : (case_nat$(v0, uud$) = v1 & % 55.00/8.26 fun_app$k(of_nat$, v2) = v3 & nat$(0) = v0 & fun_app$e(v1, v0) = v2 & % 55.00/8.26 Nat$(v2) & Nat$(v0) & Nat_nat_fun$(v1) & ! [v4: Nat$] : ! [v5: Nat$] : ! % 55.00/8.26 [v6: int] : ! [v7: int] : ! [v8: Nat$] : (v3 = 0 | ~ ($lesseq(1, % 55.00/8.26 $difference(v6, v7))) | ~ (fun_app$k(of_nat$, v5) = v6) | ~ % 55.00/8.26 (fun_app$k(of_nat$, v4) = v7) | ~ (nat$($difference(v7, v6)) = v8) | ~ % 55.00/8.26 Nat$(v5) | ~ Nat$(v4)) & ! [v4: Nat$] : ! [v5: Nat$] : ! [v6: int] : % 55.00/8.26 ! [v7: int] : ! [v8: Nat$] : ( ~ ($lesseq(1, $difference(v7, v6))) | ~ % 55.00/8.26 (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v4) = v7) | ~ % 55.00/8.26 (nat$($difference(v7, v6)) = v8) | ~ Nat$(v5) | ~ Nat$(v4) | ? [v9: % 55.00/8.26 Nat$] : (fun_app$k(of_nat$, v9) = $sum($difference(v7, v6), -1) & % 55.00/8.26 fun_app$e(v1, v8) = v9 & Nat$(v9))) & ! [v4: Nat$] : ! [v5: Nat$] : ! % 55.00/8.26 [v6: int] : (v3 = 0 | ~ (fun_app$k(of_nat$, v5) = v6) | ~ % 55.00/8.26 (fun_app$k(of_nat$, v4) = v6) | ~ Nat$(v5) | ~ Nat$(v4))) % 55.00/8.26 % 55.00/8.26 (axiom292) % 55.00/8.27 ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_a_set_fun$] : ! [v2: % 55.00/8.27 Nat$] : ! [v3: A_set_list$] : ( ~ (subsequence$(v1, v0, v2) = v3) | ~ % 55.00/8.27 Nat_a_set_fun$(v1) | ~ Nat$(v2) | ? [v4: Nat_a_set_fun$] : (conc$(v3, % 55.00/8.27 v4) = v1 & suffix$(v2, v1) = v4 & Nat_a_set_fun$(v4))) & ! [v1: % 55.00/8.27 Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ( ~ % 55.00/8.27 (suffix$(v2, v1) = v3) | ~ Nat_a_set_fun$(v1) | ~ Nat$(v2) | ? [v4: % 55.00/8.27 A_set_list$] : (conc$(v4, v3) = v1 & subsequence$(v1, v0, v2) = v4 & % 55.00/8.27 A_set_list$(v4)))) % 55.00/8.27 % 55.00/8.27 (axiom294) % 55.00/8.27 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.00/8.27 Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : ! [v4: Nat_nat_fun$] : ! % 55.00/8.27 [v5: Nat$] : (v5 = v1 | ~ (case_nat$(v1, v2) = v4) | ~ (fun_app$e(v4, v3) % 55.00/8.27 = v5) | ~ Nat$(v3) | ~ Nat$(v1) | ~ Nat_nat_fun$(v2) | ? [v6: int] : % 55.00/8.27 ( ~ (v6 = 0) & fun_app$k(of_nat$, v3) = v6)) & ! [v1: Nat$] : ! [v2: % 55.00/8.27 Nat_nat_fun$] : ! [v3: Nat$] : ! [v4: Nat_nat_fun$] : ! [v5: Nat$] : ( % 55.00/8.27 ~ (case_nat$(v1, v2) = v4) | ~ (fun_app$e(v4, v3) = v5) | ~ Nat$(v3) | % 55.00/8.27 ~ Nat$(v1) | ~ Nat_nat_fun$(v2) | ? [v6: int] : ? [v7: Nat$] : ? [v8: % 55.00/8.27 Nat$] : ? [v9: Nat$] : (fun_app$k(of_nat$, v3) = v6 & nat$($sum(v6, % 55.00/8.27 -1)) = v8 & fun_app$e(v2, v8) = v9 & fun_app$e(v2, v0) = v7 & % 55.00/8.27 Nat$(v9) & Nat$(v8) & Nat$(v7) & (v6 = 0 | ((v9 = v5 | ~ ($lesseq(1, % 55.00/8.27 v6))) & (v7 = v5 | ~ ($lesseq(v6, -1)))))))) % 55.00/8.27 % 55.00/8.27 (axiom314) % 55.00/8.27 Nat_num_fun$(num_of_nat$) & Num$(one$) & ? [v0: Nat$] : % 55.00/8.27 (fun_app$p(num_of_nat$, v0) = one$ & nat$(0) = v0 & Nat$(v0)) % 55.00/8.27 % 55.00/8.27 (axiom41) % 55.00/8.27 ? [v0: Nat$] : ? [v1: Nat$] : (nat$(1) = v1 & nat$(0) = v0 & Nat$(v1) & % 55.00/8.27 Nat$(v0) & ! [v2: Nat_a_set_fun$] : ! [v3: Nat_a_set_fun$] : ( ~ % 55.00/8.27 (suffix$(v1, v2) = v3) | ~ Nat_a_set_fun$(v2) | ? [v4: A_set$] : % 55.00/8.27 (build$(v4, v3) = v2 & fun_app$j(v2, v0) = v4 & A_set$(v4))) & ! [v2: % 55.00/8.27 Nat_a_set_fun$] : ! [v3: A_set$] : ( ~ (fun_app$j(v2, v0) = v3) | ~ % 55.00/8.27 Nat_a_set_fun$(v2) | ? [v4: Nat_a_set_fun$] : (build$(v3, v4) = v2 & % 55.00/8.27 suffix$(v1, v2) = v4 & Nat_a_set_fun$(v4)))) % 55.00/8.27 % 55.00/8.27 (axiom49) % 55.00/8.27 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & ? [v0: Nat$] : (nat$(0) = v0 & % 55.00/8.27 Nat$(v0) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! [v2: % 55.00/8.27 A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: % 55.00/8.27 A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 55.00/8.27 (gF_advice_congruent$(v1, v2) = 0) | ~ (fun_app$i(v2, v4) = v6) | ~ % 55.00/8.27 (gF_advice$(v6, v5) = v7) | ~ (semantics_ltln$(v3, v7) = 0) | ~ % 55.00/8.27 A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | % 55.00/8.27 ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v8: Nat$] : ? [v9: % 55.00/8.27 Nat_a_set_fun$] : ? [v10: A_set_list$] : ? [v11: A_ltln$] : ? [v12: % 55.00/8.27 A_ltln$] : (subsequence$(v3, v0, v8) = v10 & foldl$(af_letter$, v4, v10) % 55.00/8.27 = v11 & suffix$(v8, v3) = v9 & gF_advice$(v11, v5) = v12 & % 55.00/8.27 semantics_ltln$(v9, v12) = 0 & Nat_a_set_fun$(v9) & A_ltln$(v12) & % 55.00/8.27 A_ltln$(v11) & A_set_list$(v10) & Nat$(v8)))) % 55.00/8.27 % 55.00/8.27 (conjecture11) % 55.00/8.27 A_ltln_a_set_a_ltln_fun_fun$(af_letter$) & Nat_a_set_fun$(w$) & A_ltln$(phi$) % 55.00/8.27 & A_ltln_set$(x$) & A_ltln_a_ltln_fun$(next_ltln$) & ? [v0: Nat$] : ? [v1: % 55.00/8.27 Nat_a_set_fun$] : ? [v2: A_ltln$] : ? [v3: A_set_a_ltln_fun$] : ? [v4: % 55.00/8.27 Nat$] : ? [v5: A_set$] : ? [v6: A_ltln$] : ? [v7: A_ltln$] : ? [v8: int] % 55.00/8.27 : ( ~ (v8 = 0) & suffix$(v0, w$) = v1 & fun_app$h(af_letter$, v2) = v3 & % 55.00/8.27 nat$(1) = v0 & nat$(0) = v4 & fun_app$j(w$, v4) = v5 & fun_app$g(v3, v5) = % 55.00/8.27 v6 & fun_app$i(next_ltln$, phi$) = v2 & gF_advice$(v6, x$) = v7 & % 55.00/8.27 semantics_ltln$(v1, v7) = v8 & Nat_a_set_fun$(v1) & A_ltln$(v7) & % 55.00/8.27 A_ltln$(v6) & A_ltln$(v2) & A_set$(v5) & A_set_a_ltln_fun$(v3) & Nat$(v4) & % 55.00/8.27 Nat$(v0)) % 55.00/8.27 % 55.00/8.27 (function-axioms) % 55.00/8.28 ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : % 55.00/8.28 ! [v4: tlbool] : (v1 = v0 | ~ (def_9(v4, v3, v2) = v1) | ~ (def_9(v4, v3, % 55.00/8.28 v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 55.00/8.28 Nat_bool_fun$] : ! [v4: tlbool] : (v1 = v0 | ~ (def_7(v4, v3, v2) = v1) | % 55.00/8.28 ~ (def_7(v4, v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: % 55.00/8.28 Nat$] : ! [v3: Nat_bool_fun$] : ! [v4: tlbool] : (v1 = v0 | ~ (def_5(v4, % 55.00/8.28 v3, v2) = v1) | ~ (def_5(v4, v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: % 55.00/8.28 tlbool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : ! [v4: tlbool] : (v1 = % 55.00/8.28 v0 | ~ (def_4(v4, v3, v2) = v1) | ~ (def_4(v4, v3, v2) = v0)) & ! [v0: % 55.00/8.28 A_set_list$] : ! [v1: A_set_list$] : ! [v2: Nat$] : ! [v3: Nat$] : ! % 55.00/8.28 [v4: Nat_a_set_fun$] : (v1 = v0 | ~ (subsequence$(v4, v3, v2) = v1) | ~ % 55.00/8.28 (subsequence$(v4, v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! % 55.00/8.28 [v2: A_set_list$] : ! [v3: A_ltln$] : ! [v4: A_ltln_a_set_a_ltln_fun_fun$] : % 55.00/8.28 (v1 = v0 | ~ (foldl$(v4, v3, v2) = v1) | ~ (foldl$(v4, v3, v2) = v0)) & ! % 55.00/8.28 [v0: Num$] : ! [v1: Num$] : ! [v2: Num$] : ! [v3: Num$] : (v1 = v0 | ~ % 55.00/8.28 (plus$(v3, v2) = v1) | ~ (plus$(v3, v2) = v0)) & ! [v0: int] : ! [v1: % 55.00/8.28 int] : ! [v2: Num$] : ! [v3: Num$] : (v1 = v0 | ~ (sub$(v3, v2) = v1) | % 55.00/8.28 ~ (sub$(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : % 55.00/8.28 ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (def_10(v3, v2) = v1) | ~ (def_10(v3, % 55.00/8.28 v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 55.00/8.28 Nat_bool_fun$] : (v1 = v0 | ~ (def_8(v3, v2) = v1) | ~ (def_8(v3, v2) = % 55.00/8.28 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: tlbool] : ! [v3: % 55.00/8.28 Bool_bool_fun$] : (v1 = v0 | ~ (def_6(v3, v2) = v1) | ~ (def_6(v3, v2) = % 55.00/8.28 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 55.00/8.28 Nat_bool_fun$] : (v1 = v0 | ~ (def_3(v3, v2) = v1) | ~ (def_3(v3, v2) = % 55.00/8.28 v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 55.00/8.28 Nat_bool_fun$] : ! [v3: tlbool] : (v1 = v0 | ~ (case_nat$a(v3, v2) = v1) | % 55.00/8.28 ~ (case_nat$a(v3, v2) = v0)) & ! [v0: Nat_a_set_fun$] : ! [v1: % 55.00/8.28 Nat_a_set_fun$] : ! [v2: Nat_a_set_fun$] : ! [v3: A_set_list$] : (v1 = v0 % 55.00/8.28 | ~ (conc$(v3, v2) = v1) | ~ (conc$(v3, v2) = v0)) & ! [v0: Nat_nat_fun$] % 55.00/8.28 : ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : (v1 = v0 | % 55.00/8.28 ~ (case_nat$(v3, v2) = v1) | ~ (case_nat$(v3, v2) = v0)) & ! [v0: % 55.00/8.28 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 55.00/8.28 A_ltln$] : (v1 = v0 | ~ (g_F$(v3, v2) = v1) | ~ (g_F$(v3, v2) = v0)) & ! % 55.00/8.28 [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 55.00/8.28 A_ltln$] : (v1 = v0 | ~ (f_G$(v3, v2) = v1) | ~ (f_G$(v3, v2) = v0)) & ! % 55.00/8.28 [v0: A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 55.00/8.28 A_ltln$] : (v1 = v0 | ~ (g$(v3, v2) = v1) | ~ (g$(v3, v2) = v0)) & ! [v0: % 55.00/8.28 A_ltln_set$] : ! [v1: A_ltln_set$] : ! [v2: Nat_a_set_fun$] : ! [v3: % 55.00/8.28 A_ltln$] : (v1 = v0 | ~ (f$(v3, v2) = v1) | ~ (f$(v3, v2) = v0)) & ! [v0: % 55.00/8.28 Num$] : ! [v1: Num$] : ! [v2: Nat$] : ! [v3: Nat_num_fun$] : (v1 = v0 | % 55.00/8.28 ~ (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: % 55.00/8.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Num$] : ! [v3: % 55.00/8.28 Num_bool_fun$] : (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, % 55.00/8.28 v2) = v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 55.00/8.28 Nat$] : ! [v3: Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$n(v3, v2) = % 55.00/8.28 v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : % 55.00/8.28 ! [v2: A_ltln_set$] : ! [v3: A_ltln$] : (v1 = v0 | ~ (fG_advice$(v3, v2) = % 55.00/8.28 v1) | ~ (fG_advice$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.28 MultipleValueBool] : ! [v2: A_ltln_a_ltln_fun$] : ! [v3: % 55.00/8.28 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 55.00/8.28 (gF_advice_congruent_axioms$(v3, v2) = v1) | ~ % 55.00/8.28 (gF_advice_congruent_axioms$(v3, v2) = v0)) & ! [v0: A_ltln_bool_fun$] : ! % 55.00/8.28 [v1: A_ltln_bool_fun$] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.28 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$m(v3, v2) = v1) | ~ % 55.00/8.28 (fun_app$m(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.28 MultipleValueBool] : ! [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : (v1 = v0 % 55.00/8.28 | ~ (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: int] % 55.00/8.28 : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ % 55.00/8.28 (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0: % 55.00/8.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 55.00/8.28 A_ltln_a_ltln_fun$] : ! [v3: A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ % 55.00/8.28 (gF_advice_congruent$(v3, v2) = v1) | ~ (gF_advice_congruent$(v3, v2) = % 55.00/8.28 v0)) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : ! [v2: % 55.00/8.28 Nat_a_set_fun$] : ! [v3: A_set$] : (v1 = v0 | ~ (build$(v3, v2) = v1) | ~ % 55.00/8.28 (build$(v3, v2) = v0)) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : % 55.00/8.28 ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (suffix$(v3, v2) = v1) % 55.00/8.28 | ~ (suffix$(v3, v2) = v0)) & ! [v0: A_set_a_ltln_fun$] : ! [v1: % 55.00/8.28 A_set_a_ltln_fun$] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.28 A_ltln_a_set_a_ltln_fun_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~ % 55.00/8.28 (fun_app$h(v3, v2) = v0)) & ! [v0: A_set$] : ! [v1: A_set$] : ! [v2: % 55.00/8.28 Nat$] : ! [v3: Nat_a_set_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = v1) | % 55.00/8.28 ~ (fun_app$j(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: % 55.00/8.28 A_set$] : ! [v3: A_set_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$g(v3, v2) = % 55.00/8.28 v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: A_ltln$] : % 55.00/8.28 ! [v2: A_ltln$] : ! [v3: A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$i(v3, % 55.00/8.28 v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0: A_ltln$] : ! [v1: % 55.00/8.28 A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln$] : (v1 = v0 | ~ % 55.00/8.28 (gF_advice$(v3, v2) = v1) | ~ (gF_advice$(v3, v2) = v0)) & ! [v0: % 55.00/8.28 Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3: % 55.00/8.28 Nat_nat_fun$] : (v1 = v0 | ~ (uue$(v3, v2) = v1) | ~ (uue$(v3, v2) = v0)) % 55.00/8.28 & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat_nat_fun$] : ! % 55.00/8.28 [v3: Nat_bool_fun$] : (v1 = v0 | ~ (uuf$(v3, v2) = v1) | ~ (uuf$(v3, v2) = % 55.00/8.28 v0)) & ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: % 55.00/8.28 Nat_bool_fun$] : ! [v3: Bool_nat_fun$] : (v1 = v0 | ~ (uug$(v3, v2) = v1) % 55.00/8.28 | ~ (uug$(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : % 55.00/8.28 ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~ % 55.00/8.28 (fun_app$e(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: % 55.00/8.29 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (def_2(v3, v2) = v1) | ~ % 55.00/8.29 (def_2(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: tlbool] : ! % 55.00/8.29 [v3: Bool_nat_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~ % 55.00/8.29 (fun_app$f(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: % 55.00/8.29 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (def_1(v3, v2) = v1) | ~ % 55.00/8.29 (def_1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.29 MultipleValueBool] : ! [v2: tlbool] : ! [v3: Bool_bool_fun$] : (v1 = v0 | % 55.00/8.29 ~ (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0: % 55.00/8.29 Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat_bool_fun$] : ! [v3: % 55.00/8.29 Bool_bool_fun$] : (v1 = v0 | ~ (uuh$(v3, v2) = v1) | ~ (uuh$(v3, v2) = % 55.00/8.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 55.00/8.29 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (fun_app$c(v3, v2) = v1) | ~ % 55.00/8.29 (fun_app$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.29 MultipleValueBool] : ! [v2: Nat_a_set_fun_set$] : ! [v3: Nat_a_set_fun$] : % 55.00/8.29 (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) = v0)) & ! [v0: % 55.00/8.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.29 Nat_a_set_fun$] : (v1 = v0 | ~ (semantics_ltln$(v3, v2) = v1) | ~ % 55.00/8.29 (semantics_ltln$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.29 MultipleValueBool] : ! [v2: Nat_a_set_fun$] : ! [v3: % 55.00/8.29 Nat_a_set_fun_bool_fun$] : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ % 55.00/8.29 (fun_app$b(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 55.00/8.29 [v3: Int_int_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ % 55.00/8.29 (fun_app$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.00/8.29 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~ % 55.00/8.29 (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0: Num$] : ! % 55.00/8.29 [v1: Num$] : ! [v2: Num$] : (v1 = v0 | ~ (bit1$(v2) = v1) | ~ (bit1$(v2) = % 55.00/8.29 v0)) & ! [v0: Num$] : ! [v1: Num$] : ! [v2: Num$] : (v1 = v0 | ~ % 55.00/8.29 (bit0$(v2) = v1) | ~ (bit0$(v2) = v0)) & ! [v0: Num$] : ! [v1: Num$] : ! % 55.00/8.29 [v2: Num$] : (v1 = v0 | ~ (inc$(v2) = v1) | ~ (inc$(v2) = v0)) & ! [v0: % 55.00/8.29 int] : ! [v1: int] : ! [v2: Num$] : (v1 = v0 | ~ (numeral$(v2) = v1) | ~ % 55.00/8.29 (numeral$(v2) = v0)) & ! [v0: Nat_a_set_fun_bool_fun$] : ! [v1: % 55.00/8.29 Nat_a_set_fun_bool_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ (nu_stable$(v2) % 55.00/8.29 = v1) | ~ (nu_stable$(v2) = v0)) & ! [v0: Nat_a_set_fun_bool_fun$] : ! % 55.00/8.29 [v1: Nat_a_set_fun_bool_fun$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 55.00/8.29 (mu_stable$(v2) = v1) | ~ (mu_stable$(v2) = v0)) & ! [v0: int] : ! [v1: % 55.00/8.29 int] : ! [v2: int] : (v1 = v0 | ~ (sgn$(v2) = v1) | ~ (sgn$(v2) = v0)) & % 55.00/8.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_nat_fun$] % 55.00/8.29 : (v1 = v0 | ~ (idx_sequence$(v2) = v1) | ~ (idx_sequence$(v2) = v0)) & ! % 55.00/8.29 [v0: Num_bool_fun$] : ! [v1: Num_bool_fun$] : ! [v2: Num$] : (v1 = v0 | ~ % 55.00/8.29 (less$(v2) = v1) | ~ (less$(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 55.00/8.29 [v2: int] : (v1 = v0 | ~ (dbl$(v2) = v1) | ~ (dbl$(v2) = v0)) & ! [v0: int] % 55.00/8.29 : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (dbl_dec$(v2) = v1) | ~ % 55.00/8.29 (dbl_dec$(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 % 55.00/8.29 | ~ (dbl_inc$(v2) = v1) | ~ (dbl_inc$(v2) = v0)) & ! [v0: % 55.00/8.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 55.00/8.29 A_ltln_a_ltln_bool_fun_fun$] : (v1 = v0 | ~ (af_congruent_axioms$(v2) = v1) % 55.00/8.29 | ~ (af_congruent_axioms$(v2) = v0)) & ! [v0: Nat_a_set_fun_set$] : ! % 55.00/8.29 [v1: Nat_a_set_fun_set$] : ! [v2: A_ltln$] : (v1 = v0 | ~ % 55.00/8.29 (language_ltln$(v2) = v1) | ~ (language_ltln$(v2) = v0)) & ! [v0: % 55.00/8.29 Nat_a_set_fun_set$] : ! [v1: Nat_a_set_fun_set$] : ! [v2: % 55.00/8.29 Nat_a_set_fun_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ % 55.00/8.29 (collect$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = % 55.00/8.29 v0 | ~ (nat$(v2) = v1) | ~ (nat$(v2) = v0)) & ! [v0: % 55.00/8.29 Nat_a_set_fun_bool_fun$] : ! [v1: Nat_a_set_fun_bool_fun$] : ! [v2: % 55.00/8.29 Nat_a_set_fun_set$] : (v1 = v0 | ~ (uua$(v2) = v1) | ~ (uua$(v2) = v0)) & % 55.00/8.29 ! [v0: Nat_a_set_fun_bool_fun$] : ! [v1: Nat_a_set_fun_bool_fun$] : ! [v2: % 55.00/8.29 A_ltln$] : (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) & ! [v0: % 55.00/8.29 Int_int_fun$] : ! [v1: Int_int_fun$] : ! [v2: int] : (v1 = v0 | ~ % 55.00/8.29 (uuc$(v2) = v1) | ~ (uuc$(v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: % 55.00/8.29 Int_bool_fun$] : ! [v2: int] : (v1 = v0 | ~ (uub$(v2) = v1) | ~ (uub$(v2) % 55.00/8.29 = v0)) % 55.00/8.29 % 55.00/8.29 Further assumptions not needed in the proof: % 55.00/8.29 -------------------------------------------- % 55.00/8.29 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, % 55.00/8.29 axiom105, axiom106, axiom107, axiom108, axiom109, axiom110, axiom111, axiom112, % 55.00/8.29 axiom113, axiom114, axiom115, axiom116, axiom118, axiom120, axiom121, axiom123, % 55.00/8.29 axiom124, axiom125, axiom127, axiom128, axiom129, axiom130, axiom131, axiom135, % 55.00/8.29 axiom136, axiom137, axiom138, axiom139, axiom14, axiom141, axiom142, axiom143, % 55.00/8.29 axiom144, axiom145, axiom146, axiom147, axiom150, axiom151, axiom152, axiom153, % 55.00/8.29 axiom154, axiom155, axiom157, axiom159, axiom16, axiom160, axiom161, axiom162, % 55.00/8.29 axiom163, axiom164, axiom165, axiom167, axiom17, axiom171, axiom172, axiom173, % 55.00/8.29 axiom174, axiom175, axiom176, axiom177, axiom178, axiom179, axiom180, axiom181, % 55.00/8.29 axiom182, axiom183, axiom184, axiom185, axiom186, axiom187, axiom188, axiom189, % 55.00/8.29 axiom190, axiom191, axiom192, axiom194, axiom195, axiom196, axiom197, axiom198, % 55.00/8.29 axiom199, axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, % 55.00/8.29 axiom205, axiom206, axiom207, axiom208, axiom209, axiom210, axiom211, axiom212, % 55.00/8.29 axiom213, axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22, % 55.00/8.29 axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227, % 55.00/8.29 axiom228, axiom229, axiom23, axiom230, axiom231, axiom232, axiom234, axiom235, % 55.00/8.29 axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, % 55.00/8.29 axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249, axiom25, % 55.00/8.29 axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256, axiom257, % 55.00/8.29 axiom258, axiom259, axiom260, axiom261, axiom262, axiom263, axiom265, axiom266, % 55.00/8.29 axiom267, axiom268, axiom269, axiom271, axiom272, axiom273, axiom274, axiom275, % 55.00/8.29 axiom276, axiom277, axiom278, axiom279, axiom28, axiom280, axiom281, axiom282, % 55.00/8.29 axiom283, axiom284, axiom285, axiom286, axiom287, axiom288, axiom289, axiom29, % 55.00/8.29 axiom290, axiom291, axiom293, axiom295, axiom296, axiom297, axiom298, axiom299, % 55.00/8.29 axiom3, axiom30, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, % 55.00/8.29 axiom306, axiom307, axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, % 55.00/8.29 axiom313, axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320, % 55.00/8.29 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328, % 55.00/8.29 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335, % 55.00/8.29 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342, % 55.00/8.29 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35, % 55.00/8.29 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357, % 55.00/8.29 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364, % 55.00/8.29 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371, % 55.00/8.29 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, axiom379, % 55.00/8.29 axiom38, axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, % 55.00/8.29 axiom387, axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, % 55.00/8.29 axiom394, axiom395, axiom396, axiom397, axiom398, axiom399, axiom4, axiom40, % 55.00/8.29 axiom400, axiom401, axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, % 55.00/8.29 axiom408, axiom409, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415, % 55.00/8.29 axiom416, axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422, % 55.00/8.29 axiom423, axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, axiom43, % 55.00/8.29 axiom430, axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, axiom437, % 55.00/8.29 axiom438, axiom439, axiom44, axiom440, axiom441, axiom442, axiom443, axiom444, % 55.00/8.29 axiom445, axiom446, axiom447, axiom448, axiom449, axiom45, axiom450, axiom451, % 55.00/8.29 axiom452, axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, axiom459, % 55.00/8.29 axiom46, axiom460, axiom461, axiom462, axiom463, axiom464, axiom465, axiom466, % 55.00/8.29 axiom467, axiom468, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473, % 55.00/8.29 axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, axiom48, axiom480, % 55.00/8.29 axiom481, axiom482, axiom483, axiom484, axiom485, axiom486, axiom487, axiom488, % 55.00/8.29 axiom489, axiom490, axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, % 55.00/8.29 axiom497, axiom498, axiom499, axiom5, axiom50, axiom500, axiom501, axiom502, % 55.00/8.29 axiom503, axiom51, axiom52, axiom53, axiom54, axiom55, axiom56, axiom57, % 55.00/8.29 axiom58, axiom59, axiom6, axiom60, axiom61, axiom62, axiom63, axiom64, axiom65, % 55.00/8.29 axiom66, axiom67, axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, % 55.00/8.29 axiom74, axiom75, axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81, % 55.00/8.29 axiom82, axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, % 55.00/8.29 axiom90, axiom91, axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, % 55.00/8.29 axiom99, formula_505, formula_506, formula_507, formula_508, formula_509, % 55.00/8.29 formula_510, formula_511, formula_512, formula_513, formula_514, formula_515, % 55.00/8.29 formula_516 % 55.00/8.29 % 55.00/8.29 Those formulas are unsatisfiable: % 55.00/8.29 --------------------------------- % 55.00/8.29 % 55.00/8.29 Begin of proof % 55.00/8.29 | % 55.00/8.29 | ALPHA: (axiom12) implies: % 55.00/8.29 | (1) ? [v0: A_ltln$] : ? [v1: A_ltln$] : ? [v2: A_ltln$] : % 55.00/8.29 | (fun_app$i(unf$, v0) = v1 & fun_app$i(next_ltln$, phi$) = v0 & % 55.00/8.29 | gF_advice$(v1, x$) = v2 & semantics_ltln$(w$, v2) = 0 & A_ltln$(v2) & % 55.00/8.29 | A_ltln$(v1) & A_ltln$(v0)) % 55.00/8.29 | % 55.00/8.29 | ALPHA: (axiom13) implies: % 55.00/8.29 | (2) ? [v0: A_ltln$] : ? [v1: A_ltln$] : ? [v2: any] : ? [v3: Nat$] : ? % 55.00/8.29 | [v4: Nat_a_set_fun$] : ? [v5: A_set_a_ltln_fun$] : ? [v6: Nat$] : ? % 55.00/8.29 | [v7: A_set$] : ? [v8: A_ltln$] : ? [v9: A_ltln$] : ? [v10: any] : % 55.00/8.29 | (suffix$(v3, w$) = v4 & fun_app$h(af_letter$, phi$) = v5 & nat$(1) = v3 % 55.00/8.29 | & nat$(0) = v6 & fun_app$j(w$, v6) = v7 & fun_app$g(v5, v7) = v8 & % 55.00/8.29 | fun_app$i(unf$, phi$) = v0 & gF_advice$(v8, x$) = v9 & gF_advice$(v0, % 55.00/8.29 | x$) = v1 & semantics_ltln$(v4, v9) = v10 & semantics_ltln$(w$, v1) % 55.00/8.29 | = v2 & Nat_a_set_fun$(v4) & A_ltln$(v9) & A_ltln$(v8) & A_ltln$(v1) & % 55.00/8.29 | A_ltln$(v0) & A_set$(v7) & A_set_a_ltln_fun$(v5) & Nat$(v6) & % 55.00/8.29 | Nat$(v3) & ( ~ (v2 = 0) | v10 = 0)) % 55.00/8.29 | % 55.00/8.29 | ALPHA: (axiom15) implies: % 55.00/8.29 | (3) ? [v0: Nat$] : (nat$(1) = v0 & Nat$(v0) & ! [v1: Nat_a_set_fun$] : ! % 55.00/8.29 | [v2: A_ltln$] : ! [v3: Nat_a_set_fun$] : ! [v4: int] : (v4 = 0 | ~ % 55.00/8.29 | (suffix$(v0, v1) = v3) | ~ (semantics_ltln$(v3, v2) = v4) | ~ % 55.00/8.29 | Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v5: A_ltln$] : ? [v6: % 55.00/8.29 | int] : ( ~ (v6 = 0) & fun_app$i(next_ltln$, v2) = v5 & % 55.00/8.29 | semantics_ltln$(v1, v5) = v6 & A_ltln$(v5))) & ! [v1: % 55.00/8.29 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: % 55.00/8.29 | int] : (v4 = 0 | ~ (fun_app$i(next_ltln$, v2) = v3) | ~ % 55.00/8.29 | (semantics_ltln$(v1, v3) = v4) | ~ Nat_a_set_fun$(v1) | ~ % 55.00/8.29 | A_ltln$(v2) | ? [v5: Nat_a_set_fun$] : ? [v6: int] : ( ~ (v6 = 0) % 55.00/8.29 | & suffix$(v0, v1) = v5 & semantics_ltln$(v5, v2) = v6 & % 55.00/8.29 | Nat_a_set_fun$(v5))) & ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] % 55.00/8.29 | : ! [v3: Nat_a_set_fun$] : ( ~ (suffix$(v0, v1) = v3) | ~ % 55.00/8.29 | (semantics_ltln$(v3, v2) = 0) | ~ Nat_a_set_fun$(v1) | ~ % 55.00/8.29 | A_ltln$(v2) | ? [v4: A_ltln$] : (fun_app$i(next_ltln$, v2) = v4 & % 55.00/8.29 | semantics_ltln$(v1, v4) = 0 & A_ltln$(v4))) & ! [v1: % 55.00/8.29 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln$] : ( ~ % 55.00/8.29 | (fun_app$i(next_ltln$, v2) = v3) | ~ (semantics_ltln$(v1, v3) = 0) % 55.00/8.29 | | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v2) | ? [v4: Nat_a_set_fun$] % 55.00/8.29 | : (suffix$(v0, v1) = v4 & semantics_ltln$(v4, v2) = 0 & % 55.00/8.29 | Nat_a_set_fun$(v4)))) % 55.00/8.29 | % 55.00/8.29 | ALPHA: (axiom18) implies: % 55.00/8.29 | (4) ! [v0: A_ltln$] : ! [v1: A_ltln_set$] : ! [v2: A_ltln$] : ( ~ % 55.00/8.29 | (gF_advice$(v0, v1) = v2) | ~ A_ltln$(v0) | ~ A_ltln_set$(v1) | ? % 55.00/8.29 | [v3: A_ltln$] : ? [v4: A_ltln$] : (fun_app$i(next_ltln$, v2) = v4 & % 55.00/8.29 | fun_app$i(next_ltln$, v0) = v3 & gF_advice$(v3, v1) = v4 & % 55.00/8.29 | A_ltln$(v4) & A_ltln$(v3))) % 55.00/8.29 | % 55.00/8.29 | ALPHA: (axiom19) implies: % 55.00/8.29 | (5) ! [v0: A_ltln$] : ! [v1: A_set$] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.30 | A_set_a_ltln_fun$] : ! [v4: A_ltln$] : (v4 = v0 | ~ % 55.00/8.30 | (fun_app$h(af_letter$, v2) = v3) | ~ (fun_app$g(v3, v1) = v4) | ~ % 55.00/8.30 | (fun_app$i(next_ltln$, v0) = v2) | ~ A_ltln$(v0) | ~ A_set$(v1)) % 55.00/8.30 | % 55.00/8.30 | ALPHA: (axiom21) implies: % 55.00/8.30 | (6) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ( ~ (fun_app$i(next_ltln$, v0) = % 55.00/8.30 | v1) | ~ A_ltln$(v0) | (fun_app$i(unf$, v1) = v1 & A_ltln$(v1))) % 55.00/8.30 | % 55.00/8.30 | ALPHA: (axiom27) implies: % 55.00/8.30 | (7) ! [v0: A_set$] : ! [v1: Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: % 55.00/8.30 | A_ltln_set$] : ! [v4: A_set_a_ltln_fun$] : ! [v5: A_ltln$] : ! % 55.00/8.30 | [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | ~ (fun_app$h(af_letter$, v2) % 55.00/8.30 | = v4) | ~ (fun_app$g(v4, v0) = v5) | ~ (gF_advice$(v5, v3) = v6) % 55.00/8.30 | | ~ (semantics_ltln$(v1, v6) = v7) | ~ Nat_a_set_fun$(v1) | ~ % 55.00/8.30 | A_ltln$(v2) | ~ A_ltln_set$(v3) | ~ A_set$(v0) | ? [v8: % 55.00/8.30 | Nat_a_set_fun$] : ? [v9: A_ltln$] : ? [v10: int] : ( ~ (v10 = 0) % 55.00/8.30 | & build$(v0, v1) = v8 & gF_advice$(v2, v3) = v9 & % 55.00/8.30 | semantics_ltln$(v8, v9) = v10 & Nat_a_set_fun$(v8) & A_ltln$(v9))) % 55.00/8.30 | % 55.00/8.30 | ALPHA: (axiom49) implies: % 55.00/8.30 | (8) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.00/8.30 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.00/8.30 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 55.00/8.30 | [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ (gF_advice_congruent$(v1, v2) % 55.00/8.30 | = 0) | ~ (fun_app$i(v2, v4) = v6) | ~ (gF_advice$(v6, v5) = v7) % 55.00/8.30 | | ~ (semantics_ltln$(v3, v7) = 0) | ~ % 55.00/8.30 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 55.00/8.30 | A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? % 55.00/8.30 | [v8: Nat$] : ? [v9: Nat_a_set_fun$] : ? [v10: A_set_list$] : ? % 55.00/8.30 | [v11: A_ltln$] : ? [v12: A_ltln$] : (subsequence$(v3, v0, v8) = % 55.00/8.30 | v10 & foldl$(af_letter$, v4, v10) = v11 & suffix$(v8, v3) = v9 & % 55.00/8.30 | gF_advice$(v11, v5) = v12 & semantics_ltln$(v9, v12) = 0 & % 55.00/8.30 | Nat_a_set_fun$(v9) & A_ltln$(v12) & A_ltln$(v11) & % 55.00/8.30 | A_set_list$(v10) & Nat$(v8)))) % 55.00/8.30 | % 55.00/8.30 | ALPHA: (axiom117) implies: % 55.00/8.30 | (9) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.00/8.30 | Nat_bool_fun$] : ! [v3: int] : ! [v4: MultipleValueBool] : ! % 55.00/8.30 | [v5: Nat$] : ! [v6: int] : ( ~ ($lesseq(1, $difference(v3, v6))) | % 55.00/8.30 | ~ (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v1) = v3) % 55.00/8.30 | | ~ (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v5) % 55.00/8.30 | | ~ Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? % 55.00/8.30 | [v10: int] : ? [v11: int] : (Nat$(v9) & ((v8 = 0 & nat$($sum(v6, % 55.00/8.30 | 1)) = v7 & fun_app$c(v2, v7) = 0 & Nat$(v7)) | ( ~ (v11 = % 55.00/8.30 | 0) & $lesseq(v10, v3) & fun_app$k(of_nat$, v9) = v10 & % 55.00/8.30 | fun_app$c(v2, v9) = v11)))) & ! [v1: Nat$] : ! [v2: % 55.00/8.30 | Nat_bool_fun$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: int] : (v5 % 55.00/8.30 | = 0 | ~ (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v4) = % 55.00/8.30 | v5) | ~ (fun_app$c(v2, v0) = 0) | ~ Nat_bool_fun$(v2) | ~ % 55.00/8.30 | Nat$(v4) | ~ Nat$(v1) | ? [v6: int] : ? [v7: Nat$] : ? [v8: % 55.00/8.30 | int] : ? [v9: Nat$] : ? [v10: int] : (Nat$(v7) & (( ~ (v10 = 0) % 55.00/8.30 | & $lesseq(1, $difference(v3, v8)) & fun_app$k(of_nat$, v7) = % 55.00/8.30 | v8 & nat$($sum(v8, 1)) = v9 & fun_app$c(v2, v9) = v10 & % 55.00/8.30 | Nat$(v9)) | ($lesseq(1, $difference(v6, v3)) & % 55.00/8.30 | fun_app$k(of_nat$, v4) = v6)))) & ! [v1: Nat$] : ! [v2: % 55.00/8.30 | Nat_bool_fun$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: int] : ( ~ % 55.00/8.30 | ($lesseq(v5, v3)) | ~ (fun_app$k(of_nat$, v4) = v5) | ~ % 55.00/8.30 | (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v0) = 0) | ~ % 55.00/8.30 | Nat_bool_fun$(v2) | ~ Nat$(v4) | ~ Nat$(v1) | ? [v6: int] : ? % 55.00/8.30 | [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : % 55.00/8.30 | (Nat$(v7) & ((v6 = 0 & fun_app$c(v2, v4) = 0) | ( ~ (v10 = 0) & % 55.00/8.30 | $lesseq(1, $difference(v3, v8)) & fun_app$k(of_nat$, v7) = v8 % 55.00/8.30 | & nat$($sum(v8, 1)) = v9 & fun_app$c(v2, v9) = v10 & % 55.00/8.30 | Nat$(v9))))) & ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! % 55.00/8.30 | [v3: int] : ! [v4: int] : (v4 = 0 | ~ (fun_app$k(of_nat$, v1) = v3) % 55.00/8.30 | | ~ (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v1) % 55.00/8.30 | | ? [v5: Nat$] : ? [v6: int] : ? [v7: int] : ( ~ (v7 = 0) & % 55.00/8.30 | $lesseq(v6, v3) & fun_app$k(of_nat$, v5) = v6 & fun_app$c(v2, v5) % 55.00/8.30 | = v7 & Nat$(v5)))) % 55.00/8.30 | % 55.00/8.30 | ALPHA: (axiom119) implies: % 55.35/8.30 | (10) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.35/8.30 | Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : ! [v5: Nat$] : ! % 55.35/8.30 | [v6: int] : (v4 = 0 | ~ ($lesseq(v6, v3)) | ~ (fun_app$k(of_nat$, % 55.35/8.30 | v5) = v6) | ~ (fun_app$k(of_nat$, v1) = v3) | ~ % 55.35/8.30 | (fun_app$c(v2, v0) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v5) | ~ % 55.35/8.30 | Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: % 55.35/8.30 | int] : ? [v11: int] : (Nat$(v7) & ((v10 = 0 & $lesseq(1, % 55.35/8.31 | $difference(v3, v8)) & fun_app$k(of_nat$, v7) = v8 & % 55.35/8.31 | nat$($sum(v8, 1)) = v9 & fun_app$c(v2, v9) = 0 & Nat$(v9)) | % 55.35/8.31 | ( ~ (v11 = 0) & fun_app$c(v2, v5) = v11)))) & ! [v1: Nat$] : % 55.35/8.31 | ! [v2: Nat_bool_fun$] : ! [v3: MultipleValueBool] : ! [v4: int] : % 55.35/8.31 | ! [v5: Nat$] : ! [v6: int] : ( ~ ($lesseq(1, $difference(v4, v6))) % 55.35/8.31 | | ~ (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v1) = % 55.35/8.31 | v4) | ~ (fun_app$c(v2, v0) = v3) | ~ Nat_bool_fun$(v2) | ~ % 55.35/8.31 | Nat$(v5) | ~ Nat$(v1) | ? [v7: Nat$] : ? [v8: int] : ? [v9: % 55.35/8.31 | int] : ? [v10: Nat$] : ? [v11: int] : (Nat$(v7) & ((v9 = 0 & % 55.35/8.31 | $lesseq(v8, v4) & fun_app$k(of_nat$, v7) = v8 & % 55.35/8.31 | fun_app$c(v2, v7) = 0) | ( ~ (v11 = 0) & nat$($sum(v6, 1)) = % 55.35/8.31 | v10 & fun_app$c(v2, v10) = v11 & Nat$(v10))))) & ! [v1: % 55.35/8.31 | Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : ! % 55.35/8.31 | [v5: Nat$] : (v4 = 0 | ~ (fun_app$k(of_nat$, v1) = v3) | ~ % 55.35/8.31 | (fun_app$c(v2, v5) = 0) | ~ (fun_app$c(v2, v0) = v4) | ~ % 55.35/8.31 | Nat_bool_fun$(v2) | ~ Nat$(v5) | ~ Nat$(v1) | ? [v6: Nat$] : ? % 55.35/8.31 | [v7: int] : ? [v8: Nat$] : ? [v9: int] : ? [v10: int] : % 55.35/8.31 | (Nat$(v6) & ((v9 = 0 & $lesseq(1, $difference(v3, v7)) & % 55.35/8.31 | fun_app$k(of_nat$, v6) = v7 & nat$($sum(v7, 1)) = v8 & % 55.35/8.31 | fun_app$c(v2, v8) = 0 & Nat$(v8)) | ($lesseq(1, % 55.35/8.31 | $difference(v10, v3)) & fun_app$k(of_nat$, v5) = v10)))) & % 55.35/8.31 | ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ( ~ % 55.35/8.31 | (fun_app$k(of_nat$, v1) = v3) | ~ (fun_app$c(v2, v0) = 0) | ~ % 55.35/8.31 | Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v4: Nat$] : ? [v5: int] : % 55.35/8.31 | ($lesseq(v5, v3) & fun_app$k(of_nat$, v4) = v5 & fun_app$c(v2, v4) % 55.35/8.31 | = 0 & Nat$(v4)))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom122) implies: % 55.35/8.31 | (11) ? [v0: Nat$] : (nat$(1) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.35/8.31 | Nat_bool_fun$] : ! [v3: int] : (v3 = 0 | ~ (fun_app$c(v2, v1) = % 55.35/8.31 | v3) | ~ Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v4: int] : ? % 55.35/8.31 | [v5: any] : ? [v6: Nat$] : ? [v7: int] : ? [v8: int] : ? [v9: % 55.35/8.31 | Nat$] : ? [v10: int] : (Nat$(v6) & ((v8 = 0 & ~ (v10 = 0) & % 55.35/8.31 | $lesseq(1, v7) & fun_app$k(of_nat$, v6) = v7 & nat$($sum(v7, % 55.35/8.31 | 1)) = v9 & fun_app$c(v2, v9) = v10 & fun_app$c(v2, v6) = % 55.35/8.31 | 0 & Nat$(v9)) | (fun_app$k(of_nat$, v1) = v4 & fun_app$c(v2, % 55.35/8.31 | v0) = v5 & ( ~ (v5 = 0) | ~ ($lesseq(1, v4)))))))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom126) implies: % 55.35/8.31 | (12) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.35/8.31 | Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! % 55.35/8.31 | [v5: A_set_list$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 55.35/8.31 | (subsequence$(v2, v0, v1) = v5) | ~ (foldl$(af_letter$, v3, v5) = % 55.35/8.31 | v6) | ~ (fG_advice$(v6, v4) = v7) | ~ Nat_a_set_fun$(v2) | ~ % 55.35/8.31 | A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ Nat$(v1) | ? [v8: % 55.35/8.31 | Nat_a_set_fun$] : ? [v9: any] : ? [v10: A_ltln$] : ? [v11: % 55.35/8.31 | any] : (fG_advice$(v3, v4) = v10 & suffix$(v1, v2) = v8 & % 55.35/8.31 | semantics_ltln$(v8, v7) = v9 & semantics_ltln$(v2, v10) = v11 & % 55.35/8.31 | Nat_a_set_fun$(v8) & A_ltln$(v10) & ( ~ (v9 = 0) | v11 = 0)))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom132) implies: % 55.35/8.31 | (13) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : ! % 55.35/8.31 | [v2: Nat$] : ( ~ (fun_app$c(v1, v2) = 0) | ~ Nat_bool_fun$(v1) | ~ % 55.35/8.31 | Nat$(v2) | ? [v3: int] : ? [v4: Nat$] : ? [v5: int] : ? [v6: % 55.35/8.31 | Nat$] : ? [v7: int] : ? [v8: int] : (Nat$(v4) & ((v7 = 0 & ~ % 55.35/8.31 | (v8 = 0) & fun_app$k(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = % 55.35/8.31 | v6 & fun_app$c(v1, v6) = 0 & fun_app$c(v1, v4) = v8 & % 55.35/8.31 | Nat$(v6)) | (v3 = 0 & fun_app$c(v1, v0) = 0))))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom133) implies: % 55.35/8.31 | (14) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.35/8.31 | Nat_nat_bool_fun_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: % 55.35/8.31 | Nat_bool_fun$] : ! [v5: int] : (v5 = 0 | ~ (fun_app$n(v1, v2) = % 55.35/8.31 | v4) | ~ (fun_app$c(v4, v3) = v5) | ~ Nat$(v3) | ~ Nat$(v2) | % 55.35/8.31 | ~ Nat_nat_bool_fun_fun$(v1) | ? [v6: Nat_bool_fun$] : ? [v7: % 55.35/8.31 | Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : ? [v11: % 55.35/8.31 | Nat$] : ? [v12: Nat$] : ? [v13: Nat_bool_fun$] : ? [v14: int] % 55.35/8.31 | : ? [v15: int] : ? [v16: Nat$] : ? [v17: Nat_bool_fun$] : ? % 55.35/8.31 | [v18: int] : ? [v19: Nat$] : ? [v20: int] : ? [v21: Nat$] : ? % 55.35/8.31 | [v22: Nat_bool_fun$] : ? [v23: int] : (Nat$(v21) & Nat$(v12) & % 55.35/8.31 | Nat$(v11) & Nat$(v7) & ((v14 = 0 & ~ (v20 = 0) & fun_app$n(v1, % 55.35/8.31 | v16) = v17 & fun_app$n(v1, v11) = v13 & fun_app$k(of_nat$, % 55.35/8.31 | v12) = v18 & fun_app$k(of_nat$, v11) = v15 & % 55.35/8.31 | nat$($sum(v18, 1)) = v19 & nat$($sum(v15, 1)) = v16 & % 55.35/8.31 | fun_app$c(v17, v19) = v20 & fun_app$c(v13, v12) = 0 & % 55.35/8.31 | Nat_bool_fun$(v17) & Nat_bool_fun$(v13) & Nat$(v19) & % 55.35/8.31 | Nat$(v16)) | ( ~ (v23 = 0) & fun_app$n(v1, v21) = v22 & % 55.35/8.31 | fun_app$c(v22, v0) = v23 & Nat_bool_fun$(v22)) | ( ~ (v10 = % 55.35/8.31 | 0) & fun_app$n(v1, v0) = v6 & fun_app$k(of_nat$, v7) = v8 % 55.35/8.31 | & nat$($sum(v8, 1)) = v9 & fun_app$c(v6, v9) = v10 & % 55.35/8.31 | Nat_bool_fun$(v6) & Nat$(v9)))))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom134) implies: % 55.35/8.31 | (15) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : ! % 55.35/8.31 | [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ (fun_app$c(v1, v2) = v3) | % 55.35/8.31 | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: int] : ? [v5: Nat$] : % 55.35/8.31 | ? [v6: int] : ? [v7: int] : ? [v8: Nat$] : ? [v9: int] : % 55.35/8.31 | (Nat$(v5) & ((v6 = 0 & ~ (v9 = 0) & fun_app$k(of_nat$, v5) = v7 & % 55.35/8.31 | nat$($sum(v7, 1)) = v8 & fun_app$c(v1, v8) = v9 & % 55.35/8.31 | fun_app$c(v1, v5) = 0 & Nat$(v8)) | ( ~ (v4 = 0) & % 55.35/8.31 | fun_app$c(v1, v0) = v4))))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom140) implies: % 55.35/8.31 | (16) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : ! % 55.35/8.31 | [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ (fun_app$c(v1, v2) = v3) | % 55.35/8.31 | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: int] : ? [v5: Nat$] : % 55.35/8.31 | ? [v6: int] : ? [v7: int] : (Nat$(v5) & (( ~ (v7 = 0) & % 55.35/8.31 | $lesseq(1, v6) & fun_app$k(of_nat$, v5) = v6 & fun_app$c(v1, % 55.35/8.31 | v5) = v7 & ! [v8: Nat$] : ! [v9: int] : (v9 = 0 | ~ % 55.35/8.31 | (fun_app$c(v1, v8) = v9) | ~ Nat$(v8) | ? [v10: int] : % 55.35/8.31 | ($lesseq(v6, v10) & fun_app$k(of_nat$, v8) = v10)) & ! % 55.35/8.31 | [v8: Nat$] : ! [v9: int] : ( ~ ($lesseq(1, $difference(v6, % 55.35/8.31 | v9))) | ~ (fun_app$k(of_nat$, v8) = v9) | ~ % 55.35/8.31 | Nat$(v8) | fun_app$c(v1, v8) = 0)) | ( ~ (v4 = 0) & % 55.35/8.31 | fun_app$c(v1, v0) = v4))))) % 55.35/8.31 | % 55.35/8.31 | ALPHA: (axiom148) implies: % 55.35/8.32 | (17) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.35/8.32 | [v3: A_ltln$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: % 55.35/8.32 | A_ltln$] : ! [v7: A_ltln$] : ! [v8: A_ltln_bool_fun$] : ! [v9: % 55.35/8.32 | A_ltln$] : ! [v10: A_ltln$] : ! [v11: int] : (v11 = 0 | ~ % 55.35/8.32 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$m(v1, v7) % 55.35/8.32 | = v8) | ~ (fun_app$l(v8, v10) = v11) | ~ (fun_app$i(v2, v4) = % 55.35/8.32 | v9) | ~ (fun_app$i(v2, v3) = v6) | ~ (gF_advice$(v9, v5) = % 55.35/8.32 | v10) | ~ (gF_advice$(v6, v5) = v7) | ~ % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v4) | ~ A_ltln$(v3) % 55.35/8.32 | | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? [v12: % 55.35/8.32 | A_ltln_bool_fun$] : ? [v13: int] : ( ~ (v13 = 0) & % 55.35/8.32 | fun_app$m(v1, v3) = v12 & fun_app$l(v12, v4) = v13 & % 55.35/8.32 | A_ltln_bool_fun$(v12))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : % 55.35/8.32 | ! [v2: A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.32 | A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: % 55.35/8.32 | A_ltln$] : ! [v8: int] : (v8 = 0 | ~ % 55.35/8.32 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$i(v2, v4) % 55.35/8.32 | = v6) | ~ (gF_advice$(v6, v5) = v7) | ~ (semantics_ltln$(v3, % 55.35/8.32 | v7) = v8) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ % 55.35/8.32 | Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ % 55.35/8.32 | A_ltln_a_ltln_fun$(v2) | ? [v9: A_ltln$] : ? [v10: int] : ( ~ % 55.35/8.32 | (v10 = 0) & gF_advice$(v4, v5) = v9 & semantics_ltln$(v3, v9) = % 55.35/8.32 | v10 & A_ltln$(v9))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : ! % 55.35/8.32 | [v2: A_ltln_a_ltln_fun$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.32 | A_ltln$] : ! [v5: A_ltln_set$] : ! [v6: A_ltln$] : ! [v7: % 55.35/8.32 | A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 55.35/8.32 | (fun_app$i(v2, v4) = v6) | ~ (gF_advice$(v6, v5) = v7) | ~ % 55.35/8.32 | (semantics_ltln$(v3, v7) = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) % 55.35/8.32 | | ~ Nat_a_set_fun$(v3) | ~ A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ % 55.35/8.32 | A_ltln_a_ltln_fun$(v2) | ? [v8: Nat$] : ? [v9: Nat_a_set_fun$] : % 55.35/8.32 | ? [v10: A_set_list$] : ? [v11: A_ltln$] : ? [v12: A_ltln$] : % 55.35/8.32 | (subsequence$(v3, v0, v8) = v10 & foldl$(af_letter$, v4, v10) = % 55.35/8.32 | v11 & suffix$(v8, v3) = v9 & gF_advice$(v11, v5) = v12 & % 55.35/8.32 | semantics_ltln$(v9, v12) = 0 & Nat_a_set_fun$(v9) & A_ltln$(v12) % 55.35/8.32 | & A_ltln$(v11) & A_set_list$(v10) & Nat$(v8))) & ! [v1: % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.35/8.32 | [v3: Nat_a_set_fun$] : ! [v4: A_ltln$] : ! [v5: A_ltln_set$] : ! % 55.35/8.32 | [v6: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ % 55.35/8.32 | (gF_advice$(v4, v5) = v6) | ~ (semantics_ltln$(v3, v6) = 0) | ~ % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ Nat_a_set_fun$(v3) | ~ % 55.35/8.32 | A_ltln$(v4) | ~ A_ltln_set$(v5) | ~ A_ltln_a_ltln_fun$(v2) | ? % 55.35/8.32 | [v7: A_ltln$] : ? [v8: A_ltln$] : (fun_app$i(v2, v4) = v7 & % 55.35/8.32 | gF_advice$(v7, v5) = v8 & semantics_ltln$(v3, v8) = 0 & % 55.35/8.32 | A_ltln$(v8) & A_ltln$(v7))) & ! [v1: % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.35/8.32 | [v3: A_ltln$] : ! [v4: A_ltln_bool_fun$] : ( ~ % 55.35/8.32 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$m(v1, v3) % 55.35/8.32 | = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 55.35/8.32 | A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln$] : (fun_app$l(v4, v5) = 0 % 55.35/8.32 | & fun_app$i(v2, v3) = v5 & A_ltln$(v5))) & ! [v1: % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.35/8.32 | [v3: A_ltln$] : ! [v4: A_ltln$] : ( ~ % 55.35/8.32 | (gF_advice_congruent_axioms$(v1, v2) = 0) | ~ (fun_app$i(v2, v3) % 55.35/8.32 | = v4) | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln$(v3) | ~ % 55.35/8.32 | A_ltln_a_ltln_fun$(v2) | ? [v5: A_ltln_bool_fun$] : % 55.35/8.32 | (fun_app$m(v1, v3) = v5 & fun_app$l(v5, v4) = 0 & % 55.35/8.32 | A_ltln_bool_fun$(v5))) & ! [v1: A_ltln_a_ltln_bool_fun_fun$] : % 55.35/8.32 | ! [v2: A_ltln_a_ltln_fun$] : ! [v3: int] : (v3 = 0 | ~ % 55.35/8.32 | (gF_advice_congruent_axioms$(v1, v2) = v3) | ~ % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | ? % 55.35/8.32 | [v4: A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? [v7: % 55.35/8.32 | A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? [v10: % 55.35/8.32 | A_ltln$] : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : ? % 55.35/8.32 | [v13: A_ltln$] : ? [v14: int] : ? [v15: Nat_a_set_fun$] : ? % 55.35/8.32 | [v16: A_ltln$] : ? [v17: A_ltln_set$] : ? [v18: A_ltln$] : ? % 55.35/8.32 | [v19: A_ltln$] : ? [v20: int] : ? [v21: Nat_a_set_fun$] : ? % 55.35/8.32 | [v22: A_ltln$] : ? [v23: A_ltln_set$] : ? [v24: A_ltln$] : ? % 55.35/8.32 | [v25: int] : ? [v26: A_ltln$] : ? [v27: A_ltln$] : ? [v28: int] % 55.35/8.32 | : ? [v29: A_ltln$] : ? [v30: A_ltln_bool_fun$] : ? [v31: % 55.35/8.32 | A_ltln$] : ? [v32: int] : (Nat_a_set_fun$(v21) & % 55.35/8.32 | Nat_a_set_fun$(v15) & A_ltln$(v29) & A_ltln$(v22) & A_ltln$(v16) % 55.35/8.32 | & A_ltln$(v5) & A_ltln$(v4) & A_ltln_set$(v23) & % 55.35/8.32 | A_ltln_set$(v17) & A_ltln_set$(v6) & ((v25 = 0 & ~ (v28 = 0) & % 55.35/8.32 | fun_app$i(v2, v22) = v26 & gF_advice$(v26, v23) = v27 & % 55.35/8.32 | gF_advice$(v22, v23) = v24 & semantics_ltln$(v21, v27) = v28 % 55.35/8.32 | & semantics_ltln$(v21, v24) = 0 & A_ltln$(v27) & % 55.35/8.32 | A_ltln$(v26) & A_ltln$(v24)) | (v20 = 0 & fun_app$i(v2, v16) % 55.35/8.32 | = v18 & gF_advice$(v18, v17) = v19 & semantics_ltln$(v15, % 55.35/8.32 | v19) = 0 & A_ltln$(v19) & A_ltln$(v18) & ! [v33: Nat$] : % 55.35/8.32 | ! [v34: A_set_list$] : ( ~ (subsequence$(v15, v0, v33) = % 55.35/8.32 | v34) | ~ Nat$(v33) | ? [v35: Nat_a_set_fun$] : ? % 55.35/8.32 | [v36: A_ltln$] : ? [v37: A_ltln$] : ? [v38: int] : ( ~ % 55.35/8.32 | (v38 = 0) & foldl$(af_letter$, v16, v34) = v36 & % 55.35/8.32 | suffix$(v33, v15) = v35 & gF_advice$(v36, v17) = v37 & % 55.35/8.32 | semantics_ltln$(v35, v37) = v38 & Nat_a_set_fun$(v35) & % 55.35/8.32 | A_ltln$(v37) & A_ltln$(v36))) & ! [v33: Nat$] : ! % 55.35/8.32 | [v34: Nat_a_set_fun$] : ( ~ (suffix$(v33, v15) = v34) | ~ % 55.35/8.32 | Nat$(v33) | ? [v35: A_set_list$] : ? [v36: A_ltln$] : ? % 55.35/8.32 | [v37: A_ltln$] : ? [v38: int] : ( ~ (v38 = 0) & % 55.35/8.32 | subsequence$(v15, v0, v33) = v35 & foldl$(af_letter$, % 55.35/8.32 | v16, v35) = v36 & gF_advice$(v36, v17) = v37 & % 55.35/8.32 | semantics_ltln$(v34, v37) = v38 & A_ltln$(v37) & % 55.35/8.32 | A_ltln$(v36) & A_set_list$(v35)))) | (v8 = 0 & ~ (v14 = % 55.35/8.32 | 0) & fun_app$m(v1, v10) = v11 & fun_app$m(v1, v4) = v7 & % 55.35/8.32 | fun_app$l(v11, v13) = v14 & fun_app$l(v7, v5) = 0 & % 55.35/8.32 | fun_app$i(v2, v5) = v12 & fun_app$i(v2, v4) = v9 & % 55.35/8.32 | gF_advice$(v12, v6) = v13 & gF_advice$(v9, v6) = v10 & % 55.35/8.32 | A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v10) & A_ltln$(v9) & % 55.35/8.32 | A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7)) | ( ~ (v32 = % 55.35/8.32 | 0) & fun_app$m(v1, v29) = v30 & fun_app$l(v30, v31) = v32 % 55.35/8.32 | & fun_app$i(v2, v29) = v31 & A_ltln$(v31) & % 55.35/8.32 | A_ltln_bool_fun$(v30)))))) % 55.35/8.32 | % 55.35/8.32 | ALPHA: (axiom149) implies: % 55.35/8.32 | (18) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: % 55.35/8.32 | A_ltln_a_ltln_bool_fun_fun$] : ! [v2: A_ltln_a_ltln_fun$] : ! % 55.35/8.32 | [v3: int] : (v3 = 0 | ~ (gF_advice_congruent_axioms$(v1, v2) = v3) % 55.35/8.32 | | ~ A_ltln_a_ltln_bool_fun_fun$(v1) | ~ A_ltln_a_ltln_fun$(v2) | % 55.35/8.32 | ? [v4: A_ltln$] : ? [v5: A_ltln$] : ? [v6: A_ltln_set$] : ? % 55.35/8.32 | [v7: A_ltln_bool_fun$] : ? [v8: int] : ? [v9: A_ltln$] : ? % 55.35/8.32 | [v10: A_ltln$] : ? [v11: A_ltln_bool_fun$] : ? [v12: A_ltln$] : % 55.35/8.32 | ? [v13: A_ltln$] : ? [v14: int] : ? [v15: Nat_a_set_fun$] : ? % 55.35/8.32 | [v16: A_ltln$] : ? [v17: A_ltln_set$] : ? [v18: A_ltln$] : ? % 55.35/8.32 | [v19: A_ltln$] : ? [v20: int] : ? [v21: Nat_a_set_fun$] : ? % 55.35/8.32 | [v22: A_ltln$] : ? [v23: A_ltln_set$] : ? [v24: A_ltln$] : ? % 55.35/8.32 | [v25: int] : ? [v26: A_ltln$] : ? [v27: A_ltln$] : ? [v28: int] % 55.35/8.32 | : ? [v29: A_ltln$] : ? [v30: A_ltln_bool_fun$] : ? [v31: % 55.35/8.32 | A_ltln$] : ? [v32: int] : (Nat_a_set_fun$(v21) & % 55.35/8.32 | Nat_a_set_fun$(v15) & A_ltln$(v29) & A_ltln$(v22) & A_ltln$(v16) % 55.35/8.32 | & A_ltln$(v5) & A_ltln$(v4) & A_ltln_set$(v23) & % 55.35/8.32 | A_ltln_set$(v17) & A_ltln_set$(v6) & ((v25 = 0 & ~ (v28 = 0) & % 55.35/8.32 | fun_app$i(v2, v22) = v26 & gF_advice$(v26, v23) = v27 & % 55.35/8.32 | gF_advice$(v22, v23) = v24 & semantics_ltln$(v21, v27) = v28 % 55.35/8.32 | & semantics_ltln$(v21, v24) = 0 & A_ltln$(v27) & % 55.35/8.32 | A_ltln$(v26) & A_ltln$(v24)) | (v20 = 0 & fun_app$i(v2, v16) % 55.35/8.32 | = v18 & gF_advice$(v18, v17) = v19 & semantics_ltln$(v15, % 55.35/8.32 | v19) = 0 & A_ltln$(v19) & A_ltln$(v18) & ! [v33: Nat$] : % 55.35/8.32 | ! [v34: A_set_list$] : ( ~ (subsequence$(v15, v0, v33) = % 55.35/8.32 | v34) | ~ Nat$(v33) | ? [v35: Nat_a_set_fun$] : ? % 55.35/8.32 | [v36: A_ltln$] : ? [v37: A_ltln$] : ? [v38: int] : ( ~ % 55.35/8.32 | (v38 = 0) & foldl$(af_letter$, v16, v34) = v36 & % 55.35/8.32 | suffix$(v33, v15) = v35 & gF_advice$(v36, v17) = v37 & % 55.35/8.32 | semantics_ltln$(v35, v37) = v38 & Nat_a_set_fun$(v35) & % 55.35/8.32 | A_ltln$(v37) & A_ltln$(v36))) & ! [v33: Nat$] : ! % 55.35/8.32 | [v34: Nat_a_set_fun$] : ( ~ (suffix$(v33, v15) = v34) | ~ % 55.35/8.32 | Nat$(v33) | ? [v35: A_set_list$] : ? [v36: A_ltln$] : ? % 55.35/8.32 | [v37: A_ltln$] : ? [v38: int] : ( ~ (v38 = 0) & % 55.35/8.32 | subsequence$(v15, v0, v33) = v35 & foldl$(af_letter$, % 55.35/8.32 | v16, v35) = v36 & gF_advice$(v36, v17) = v37 & % 55.35/8.32 | semantics_ltln$(v34, v37) = v38 & A_ltln$(v37) & % 55.35/8.32 | A_ltln$(v36) & A_set_list$(v35)))) | (v8 = 0 & ~ (v14 = % 55.35/8.32 | 0) & fun_app$m(v1, v10) = v11 & fun_app$m(v1, v4) = v7 & % 55.35/8.32 | fun_app$l(v11, v13) = v14 & fun_app$l(v7, v5) = 0 & % 55.35/8.32 | fun_app$i(v2, v5) = v12 & fun_app$i(v2, v4) = v9 & % 55.35/8.32 | gF_advice$(v12, v6) = v13 & gF_advice$(v9, v6) = v10 & % 55.35/8.32 | A_ltln$(v13) & A_ltln$(v12) & A_ltln$(v10) & A_ltln$(v9) & % 55.35/8.32 | A_ltln_bool_fun$(v11) & A_ltln_bool_fun$(v7)) | ( ~ (v32 = % 55.35/8.32 | 0) & fun_app$m(v1, v29) = v30 & fun_app$l(v30, v31) = v32 % 55.35/8.32 | & fun_app$i(v2, v29) = v31 & A_ltln$(v31) & % 55.35/8.32 | A_ltln_bool_fun$(v30)))))) % 55.35/8.32 | % 55.35/8.32 | ALPHA: (axiom156) implies: % 55.35/8.33 | (19) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_a_set_fun$] : % 55.35/8.33 | ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: Nat$] : ! [v5: % 55.35/8.33 | A_set_list$] : ! [v6: A_ltln$] : ! [v7: A_ltln$] : ( ~ % 55.35/8.33 | (subsequence$(v1, v0, v4) = v5) | ~ (foldl$(af_letter$, v2, v5) = % 55.35/8.33 | v6) | ~ (gF_advice$(v6, v3) = v7) | ~ Nat_a_set_fun$(v1) | ~ % 55.35/8.33 | A_ltln$(v2) | ~ A_ltln_set$(v3) | ~ Nat$(v4) | ? [v8: A_ltln$] % 55.35/8.33 | : ? [v9: any] : ? [v10: Nat_a_set_fun$] : ? [v11: any] : % 55.35/8.33 | (suffix$(v4, v1) = v10 & gF_advice$(v2, v3) = v8 & % 55.35/8.33 | semantics_ltln$(v10, v7) = v11 & semantics_ltln$(v1, v8) = v9 & % 55.35/8.33 | Nat_a_set_fun$(v10) & A_ltln$(v8) & ( ~ (v9 = 0) | v11 = 0)))) % 55.35/8.33 | % 55.35/8.33 | ALPHA: (axiom158) implies: % 55.35/8.33 | (20) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_a_set_fun$] : % 55.35/8.33 | ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: A_ltln$] : ! [v5: % 55.35/8.33 | A_ltln$] : ( ~ (fun_app$i(id$, v2) = v4) | ~ (gF_advice$(v4, v3) % 55.35/8.33 | = v5) | ~ (semantics_ltln$(v1, v5) = 0) | ~ Nat_a_set_fun$(v1) % 55.35/8.33 | | ~ A_ltln$(v2) | ~ A_ltln_set$(v3) | ? [v6: Nat$] : ? [v7: % 55.35/8.33 | Nat_a_set_fun$] : ? [v8: A_set_list$] : ? [v9: A_ltln$] : ? % 55.35/8.33 | [v10: A_ltln$] : (subsequence$(v1, v0, v6) = v8 & % 55.35/8.33 | foldl$(af_letter$, v2, v8) = v9 & suffix$(v6, v1) = v7 & % 55.35/8.33 | gF_advice$(v9, v3) = v10 & semantics_ltln$(v7, v10) = 0 & % 55.35/8.33 | Nat_a_set_fun$(v7) & A_ltln$(v10) & A_ltln$(v9) & % 55.35/8.33 | A_set_list$(v8) & Nat$(v6)))) % 55.35/8.33 | % 55.35/8.33 | ALPHA: (axiom166) implies: % 55.35/8.33 | (21) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_nat_fun$] : ! % 55.35/8.33 | [v2: Nat$] : ! [v3: int] : ( ~ (idx_sequence$(v1) = 0) | ~ % 55.35/8.33 | (fun_app$k(of_nat$, v2) = v3) | ~ Nat$(v2) | ~ Nat_nat_fun$(v1) % 55.35/8.33 | | ? [v4: Nat$] : ? [v5: Nat$] : ? [v6: int] : ? [v7: Nat$] : % 55.35/8.33 | ? [v8: int] : ($lesseq(1, $difference(v6, v8)) & % 55.35/8.33 | fun_app$k(of_nat$, v7) = v8 & fun_app$k(of_nat$, v5) = v6 & % 55.35/8.33 | nat$($sum(v3, 1)) = v4 & fun_app$e(v1, v4) = v5 & fun_app$e(v1, % 55.35/8.33 | v2) = v7 & Nat$(v7) & Nat$(v5) & Nat$(v4))) & ! [v1: % 55.35/8.33 | Nat_nat_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ( ~ % 55.35/8.33 | (idx_sequence$(v1) = 0) | ~ (fun_app$e(v1, v2) = v3) | ~ % 55.35/8.33 | Nat$(v2) | ~ Nat_nat_fun$(v1) | ? [v4: int] : ? [v5: Nat$] : ? % 55.35/8.33 | [v6: Nat$] : ? [v7: int] : ? [v8: int] : ($lesseq(1, % 55.35/8.33 | $difference(v7, v8)) & fun_app$k(of_nat$, v6) = v7 & % 55.35/8.33 | fun_app$k(of_nat$, v3) = v8 & fun_app$k(of_nat$, v2) = v4 & % 55.35/8.33 | nat$($sum(v4, 1)) = v5 & fun_app$e(v1, v5) = v6 & Nat$(v6) & % 55.35/8.33 | Nat$(v5))) & ! [v1: Nat_nat_fun$] : ! [v2: int] : (v2 = 0 | ~ % 55.35/8.33 | (idx_sequence$(v1) = v2) | ~ Nat_nat_fun$(v1) | ? [v3: Nat$] : % 55.35/8.33 | ? [v4: int] : ? [v5: Nat$] : ? [v6: int] : ? [v7: Nat$] : ? % 55.35/8.33 | [v8: Nat$] : ? [v9: int] : ? [v10: Nat$] : ? [v11: int] : % 55.35/8.33 | (Nat$(v5) & (( ~ (v4 = 0) & fun_app$k(of_nat$, v3) = v4 & % 55.35/8.33 | fun_app$e(v1, v0) = v3 & Nat$(v3)) | ($lesseq(v9, v11) & % 55.35/8.33 | fun_app$k(of_nat$, v10) = v11 & fun_app$k(of_nat$, v8) = v9 % 55.35/8.33 | & fun_app$k(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7 & % 55.35/8.33 | fun_app$e(v1, v7) = v8 & fun_app$e(v1, v5) = v10 & Nat$(v10) % 55.35/8.33 | & Nat$(v8) & Nat$(v7))))) & ! [v1: Nat_nat_fun$] : ! [v2: % 55.35/8.33 | Nat$] : ( ~ (fun_app$e(v1, v0) = v2) | ~ Nat_nat_fun$(v1) | ? % 55.35/8.33 | [v3: int] : ? [v4: any] : ? [v5: Nat$] : ? [v6: int] : ? [v7: % 55.35/8.33 | Nat$] : ? [v8: Nat$] : ? [v9: int] : ? [v10: Nat$] : ? [v11: % 55.35/8.33 | int] : (Nat$(v5) & (($lesseq(v9, v11) & fun_app$k(of_nat$, v10) % 55.35/8.33 | = v11 & fun_app$k(of_nat$, v8) = v9 & fun_app$k(of_nat$, v5) % 55.35/8.33 | = v6 & nat$($sum(v6, 1)) = v7 & fun_app$e(v1, v7) = v8 & % 55.35/8.33 | fun_app$e(v1, v5) = v10 & Nat$(v10) & Nat$(v8) & Nat$(v7)) | % 55.35/8.33 | (idx_sequence$(v1) = v4 & fun_app$k(of_nat$, v2) = v3 & ( ~ % 55.35/8.33 | (v3 = 0) | v4 = 0))))) & ! [v1: Nat_nat_fun$] : ! [v2: % 55.35/8.33 | Nat$] : ( ~ (fun_app$e(v1, v0) = v2) | ~ Nat_nat_fun$(v1) | ? % 55.35/8.33 | [v3: any] : ? [v4: int] : (idx_sequence$(v1) = v3 & % 55.35/8.33 | fun_app$k(of_nat$, v2) = v4 & ( ~ (v3 = 0) | (v4 = 0 & ! [v5: % 55.35/8.33 | Nat$] : ! [v6: int] : ( ~ (fun_app$k(of_nat$, v5) = v6) | % 55.35/8.33 | ~ Nat$(v5) | ? [v7: Nat$] : ? [v8: Nat$] : ? [v9: int] % 55.35/8.33 | : ? [v10: Nat$] : ? [v11: int] : ($lesseq(1, % 55.35/8.33 | $difference(v9, v11)) & fun_app$k(of_nat$, v10) = v11 % 55.35/8.33 | & fun_app$k(of_nat$, v8) = v9 & nat$($sum(v6, 1)) = v7 & % 55.35/8.33 | fun_app$e(v1, v7) = v8 & fun_app$e(v1, v5) = v10 & % 55.35/8.33 | Nat$(v10) & Nat$(v8) & Nat$(v7))) & ! [v5: Nat$] : ! % 55.35/8.33 | [v6: Nat$] : ( ~ (fun_app$e(v1, v5) = v6) | ~ Nat$(v5) | ? % 55.35/8.33 | [v7: int] : ? [v8: Nat$] : ? [v9: Nat$] : ? [v10: int] % 55.35/8.33 | : ? [v11: int] : ($lesseq(1, $difference(v10, v11)) & % 55.35/8.33 | fun_app$k(of_nat$, v9) = v10 & fun_app$k(of_nat$, v6) = % 55.35/8.33 | v11 & fun_app$k(of_nat$, v5) = v7 & nat$($sum(v7, 1)) = % 55.35/8.33 | v8 & fun_app$e(v1, v8) = v9 & Nat$(v9) & Nat$(v8))))))) % 55.35/8.33 | & ! [v1: Nat_nat_fun$] : ( ~ (idx_sequence$(v1) = 0) | ~ % 55.35/8.33 | Nat_nat_fun$(v1) | ? [v2: Nat$] : (fun_app$k(of_nat$, v2) = 0 & % 55.35/8.33 | fun_app$e(v1, v0) = v2 & Nat$(v2)))) % 55.35/8.33 | % 55.35/8.33 | ALPHA: (axiom168) implies: % 55.35/8.33 | (22) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_ltln$] : ! [v2: % 55.35/8.33 | Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: Nat_a_set_fun$] : ! % 55.35/8.33 | [v5: A_ltln_set$] : ( ~ (f$(v1, v4) = v5) | ~ (suffix$(v3, v2) = % 55.35/8.33 | v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? % 55.35/8.33 | [v6: A_set_list$] : ? [v7: A_ltln$] : (f$(v7, v4) = v5 & % 55.35/8.33 | subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 % 55.35/8.33 | & A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: % 55.35/8.33 | A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.33 | A_set_list$] : ! [v5: A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = % 55.35/8.33 | v4) | ~ (foldl$(af_letter$, v1, v4) = v5) | ~ % 55.35/8.33 | Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? [v6: % 55.35/8.33 | Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (f$(v5, v6) = v7 & % 55.35/8.33 | f$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.35/8.33 | A_ltln_set$(v7)))) % 55.35/8.33 | % 55.35/8.33 | ALPHA: (axiom169) implies: % 55.35/8.33 | (23) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_ltln$] : ! [v2: % 55.35/8.33 | Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: Nat_a_set_fun$] : ! % 55.35/8.33 | [v5: A_ltln_set$] : ( ~ (g$(v1, v4) = v5) | ~ (suffix$(v3, v2) = % 55.35/8.33 | v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? % 55.35/8.33 | [v6: A_set_list$] : ? [v7: A_ltln$] : (g$(v7, v4) = v5 & % 55.35/8.33 | subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 % 55.35/8.33 | & A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: % 55.35/8.33 | A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.33 | A_set_list$] : ! [v5: A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = % 55.35/8.33 | v4) | ~ (foldl$(af_letter$, v1, v4) = v5) | ~ % 55.35/8.33 | Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? [v6: % 55.35/8.33 | Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (g$(v5, v6) = v7 & % 55.35/8.33 | g$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.35/8.33 | A_ltln_set$(v7)))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom170) implies: % 55.35/8.34 | (24) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_ltln$] : ! [v2: % 55.35/8.34 | Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: Nat_a_set_fun$] : ! % 55.35/8.34 | [v5: A_ltln_set$] : ( ~ (f_G$(v1, v4) = v5) | ~ (suffix$(v3, v2) = % 55.35/8.34 | v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? % 55.35/8.34 | [v6: A_set_list$] : ? [v7: A_ltln$] : (f_G$(v7, v4) = v5 & % 55.35/8.34 | subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 % 55.35/8.34 | & A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: % 55.35/8.34 | A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.34 | A_set_list$] : ! [v5: A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = % 55.35/8.34 | v4) | ~ (foldl$(af_letter$, v1, v4) = v5) | ~ % 55.35/8.34 | Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? [v6: % 55.35/8.34 | Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (f_G$(v5, v6) = v7 & % 55.35/8.34 | f_G$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.35/8.34 | A_ltln_set$(v7)))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom193) implies: % 55.35/8.34 | (25) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_ltln$] : ! [v2: % 55.35/8.34 | Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: Nat_a_set_fun$] : ! % 55.35/8.34 | [v5: A_ltln_set$] : ( ~ (g_F$(v1, v4) = v5) | ~ (suffix$(v3, v2) = % 55.35/8.34 | v4) | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? % 55.35/8.34 | [v6: A_set_list$] : ? [v7: A_ltln$] : (g_F$(v7, v4) = v5 & % 55.35/8.34 | subsequence$(v2, v0, v3) = v6 & foldl$(af_letter$, v1, v6) = v7 % 55.35/8.34 | & A_ltln$(v7) & A_set_list$(v6) & A_ltln_set$(v5))) & ! [v1: % 55.35/8.34 | A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.34 | A_set_list$] : ! [v5: A_ltln$] : ( ~ (subsequence$(v2, v0, v3) = % 55.35/8.34 | v4) | ~ (foldl$(af_letter$, v1, v4) = v5) | ~ % 55.35/8.34 | Nat_a_set_fun$(v2) | ~ A_ltln$(v1) | ~ Nat$(v3) | ? [v6: % 55.35/8.34 | Nat_a_set_fun$] : ? [v7: A_ltln_set$] : (g_F$(v5, v6) = v7 & % 55.35/8.34 | g_F$(v1, v6) = v7 & suffix$(v3, v2) = v6 & Nat_a_set_fun$(v6) & % 55.35/8.34 | A_ltln_set$(v7)))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom233) implies: % 55.35/8.34 | (26) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : ! % 55.35/8.34 | [v2: Nat$] : ! [v3: Nat$] : ! [v4: int] : ! [v5: int] : ! [v6: % 55.35/8.34 | Nat$] : ! [v7: any] : ( ~ (fun_app$k(of_nat$, v3) = v4) | ~ % 55.35/8.34 | (fun_app$k(of_nat$, v2) = v5) | ~ (nat$($difference(v5, v4)) = % 55.35/8.34 | v6) | ~ (fun_app$c(v1, v6) = v7) | ~ Nat_bool_fun$(v1) | ~ % 55.35/8.34 | Nat$(v3) | ~ Nat$(v2) | ? [v8: any] : ? [v9: any] : ? [v10: % 55.35/8.34 | Nat$] : ? [v11: int] : ? [v12: Nat$] : ? [v13: int] : ? % 55.35/8.34 | [v14: int] : (Nat$(v10) & ((v13 = 0 & ~ (v14 = 0) & % 55.35/8.34 | fun_app$k(of_nat$, v10) = v11 & nat$($sum(v11, 1)) = v12 & % 55.35/8.34 | fun_app$c(v1, v12) = 0 & fun_app$c(v1, v10) = v14 & % 55.35/8.34 | Nat$(v12)) | (fun_app$c(v1, v2) = v8 & fun_app$c(v1, v0) = % 55.35/8.34 | v9 & ( ~ (v8 = 0) | ((v9 = 0 | ~ ($lesseq(1, % 55.35/8.34 | $difference(v4, v5)))) & (v7 = 0 | ~ ($lesseq(v4, % 55.35/8.34 | v5)))))))))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom264) implies: % 55.35/8.34 | (27) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.35/8.34 | Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: int] : ! [v5: int] : ! % 55.35/8.34 | [v6: Nat_a_set_fun$] : ! [v7: Nat$] : ! [v8: A_set_list$] : ( ~ % 55.35/8.34 | ($lesseq(v4, v5)) | ~ (subsequence$(v6, v0, v7) = v8) | ~ % 55.35/8.34 | (fun_app$k(of_nat$, v3) = v5) | ~ (fun_app$k(of_nat$, v1) = v4) | % 55.35/8.34 | ~ (suffix$(v1, v2) = v6) | ~ (nat$($difference(v5, v4)) = v7) | % 55.35/8.34 | ~ Nat_a_set_fun$(v2) | ~ Nat$(v3) | ~ Nat$(v1) | % 55.35/8.34 | (subsequence$(v2, v1, v3) = v8 & A_set_list$(v8))) & ! [v1: Nat$] % 55.35/8.34 | : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: A_set_list$] : ( % 55.35/8.34 | ~ (subsequence$(v2, v1, v3) = v4) | ~ Nat_a_set_fun$(v2) | ~ % 55.35/8.34 | Nat$(v3) | ~ Nat$(v1) | ? [v5: int] : ? [v6: int] : ? [v7: % 55.35/8.34 | Nat_a_set_fun$] : ? [v8: Nat$] : ? [v9: A_set_list$] : % 55.35/8.34 | (subsequence$(v7, v0, v8) = v9 & fun_app$k(of_nat$, v3) = v6 & % 55.35/8.34 | fun_app$k(of_nat$, v1) = v5 & suffix$(v1, v2) = v7 & % 55.35/8.34 | nat$($difference(v6, v5)) = v8 & Nat_a_set_fun$(v7) & % 55.35/8.34 | A_set_list$(v9) & Nat$(v8) & (v9 = v4 | ~ ($lesseq(v5, v6))))) % 55.35/8.34 | & ! [v1: Nat$] : ! [v2: Nat_a_set_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.34 | A_set_list$] : ( ~ (subsequence$(v2, v1, v3) = v4) | ~ % 55.35/8.34 | Nat_a_set_fun$(v2) | ~ Nat$(v3) | ~ Nat$(v1) | ? [v5: int] : ? % 55.35/8.34 | [v6: int] : ? [v7: Nat_a_set_fun$] : ? [v8: A_set_list$] : % 55.35/8.34 | (subsequence$(v7, v0, v0) = v8 & fun_app$k(of_nat$, v3) = v6 & % 55.35/8.34 | fun_app$k(of_nat$, v1) = v5 & suffix$(v1, v2) = v7 & % 55.35/8.34 | Nat_a_set_fun$(v7) & A_set_list$(v8) & (v8 = v4 | ~ ($lesseq(1, % 55.35/8.34 | $difference(v5, v6))))))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom270) implies: % 55.35/8.34 | (28) ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : ? [v2: Nat$] : ? [v3: int] : % 55.35/8.34 | (case_nat$(v0, uud$) = v1 & fun_app$k(of_nat$, v2) = v3 & nat$(0) = v0 % 55.35/8.34 | & fun_app$e(v1, v0) = v2 & Nat$(v2) & Nat$(v0) & Nat_nat_fun$(v1) & % 55.35/8.34 | ! [v4: Nat$] : ! [v5: Nat$] : ! [v6: int] : ! [v7: int] : ! [v8: % 55.35/8.34 | Nat$] : (v3 = 0 | ~ ($lesseq(1, $difference(v6, v7))) | ~ % 55.35/8.34 | (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v4) = v7) | % 55.35/8.34 | ~ (nat$($difference(v7, v6)) = v8) | ~ Nat$(v5) | ~ Nat$(v4)) & % 55.35/8.34 | ! [v4: Nat$] : ! [v5: Nat$] : ! [v6: int] : ! [v7: int] : ! % 55.35/8.34 | [v8: Nat$] : ( ~ ($lesseq(1, $difference(v7, v6))) | ~ % 55.35/8.34 | (fun_app$k(of_nat$, v5) = v6) | ~ (fun_app$k(of_nat$, v4) = v7) | % 55.35/8.34 | ~ (nat$($difference(v7, v6)) = v8) | ~ Nat$(v5) | ~ Nat$(v4) | % 55.35/8.34 | ? [v9: Nat$] : (fun_app$k(of_nat$, v9) = $sum($difference(v7, v6), % 55.35/8.34 | -1) & fun_app$e(v1, v8) = v9 & Nat$(v9))) & ! [v4: Nat$] : ! % 55.35/8.34 | [v5: Nat$] : ! [v6: int] : (v3 = 0 | ~ (fun_app$k(of_nat$, v5) = % 55.35/8.34 | v6) | ~ (fun_app$k(of_nat$, v4) = v6) | ~ Nat$(v5) | ~ % 55.35/8.34 | Nat$(v4))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom294) implies: % 55.35/8.34 | (29) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2: % 55.35/8.34 | Nat_nat_fun$] : ! [v3: Nat$] : ! [v4: Nat_nat_fun$] : ! [v5: % 55.35/8.34 | Nat$] : (v5 = v1 | ~ (case_nat$(v1, v2) = v4) | ~ (fun_app$e(v4, % 55.35/8.34 | v3) = v5) | ~ Nat$(v3) | ~ Nat$(v1) | ~ Nat_nat_fun$(v2) | % 55.35/8.34 | ? [v6: int] : ( ~ (v6 = 0) & fun_app$k(of_nat$, v3) = v6)) & ! % 55.35/8.34 | [v1: Nat$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat$] : ! [v4: % 55.35/8.34 | Nat_nat_fun$] : ! [v5: Nat$] : ( ~ (case_nat$(v1, v2) = v4) | ~ % 55.35/8.34 | (fun_app$e(v4, v3) = v5) | ~ Nat$(v3) | ~ Nat$(v1) | ~ % 55.35/8.34 | Nat_nat_fun$(v2) | ? [v6: int] : ? [v7: Nat$] : ? [v8: Nat$] : % 55.35/8.34 | ? [v9: Nat$] : (fun_app$k(of_nat$, v3) = v6 & nat$($sum(v6, -1)) = % 55.35/8.34 | v8 & fun_app$e(v2, v8) = v9 & fun_app$e(v2, v0) = v7 & Nat$(v9) % 55.35/8.34 | & Nat$(v8) & Nat$(v7) & (v6 = 0 | ((v9 = v5 | ~ ($lesseq(1, % 55.35/8.34 | v6))) & (v7 = v5 | ~ ($lesseq(v6, -1)))))))) % 55.35/8.34 | % 55.35/8.34 | ALPHA: (axiom314) implies: % 55.35/8.34 | (30) ? [v0: Nat$] : (fun_app$p(num_of_nat$, v0) = one$ & nat$(0) = v0 & % 55.35/8.34 | Nat$(v0)) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (conjecture11) implies: % 55.35/8.35 | (31) A_ltln_set$(x$) % 55.35/8.35 | (32) A_ltln$(phi$) % 55.35/8.35 | (33) Nat_a_set_fun$(w$) % 55.35/8.35 | (34) ? [v0: Nat$] : ? [v1: Nat_a_set_fun$] : ? [v2: A_ltln$] : ? [v3: % 55.35/8.35 | A_set_a_ltln_fun$] : ? [v4: Nat$] : ? [v5: A_set$] : ? [v6: % 55.35/8.35 | A_ltln$] : ? [v7: A_ltln$] : ? [v8: int] : ( ~ (v8 = 0) & % 55.35/8.35 | suffix$(v0, w$) = v1 & fun_app$h(af_letter$, v2) = v3 & nat$(1) = v0 % 55.35/8.35 | & nat$(0) = v4 & fun_app$j(w$, v4) = v5 & fun_app$g(v3, v5) = v6 & % 55.35/8.35 | fun_app$i(next_ltln$, phi$) = v2 & gF_advice$(v6, x$) = v7 & % 55.35/8.35 | semantics_ltln$(v1, v7) = v8 & Nat_a_set_fun$(v1) & A_ltln$(v7) & % 55.35/8.35 | A_ltln$(v6) & A_ltln$(v2) & A_set$(v5) & A_set_a_ltln_fun$(v3) & % 55.35/8.35 | Nat$(v4) & Nat$(v0)) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (function-axioms) implies: % 55.35/8.35 | (35) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) % 55.35/8.35 | = v1) | ~ (nat$(v2) = v0)) % 55.35/8.35 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 55.35/8.35 | A_ltln$] : ! [v3: Nat_a_set_fun$] : (v1 = v0 | ~ % 55.35/8.35 | (semantics_ltln$(v3, v2) = v1) | ~ (semantics_ltln$(v3, v2) = v0)) % 55.35/8.35 | (37) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: % 55.35/8.35 | A_ltln$] : (v1 = v0 | ~ (gF_advice$(v3, v2) = v1) | ~ % 55.35/8.35 | (gF_advice$(v3, v2) = v0)) % 55.35/8.35 | (38) ! [v0: A_ltln$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 55.35/8.35 | A_ltln_a_ltln_fun$] : (v1 = v0 | ~ (fun_app$i(v3, v2) = v1) | ~ % 55.35/8.35 | (fun_app$i(v3, v2) = v0)) % 55.35/8.35 | (39) ! [v0: A_set$] : ! [v1: A_set$] : ! [v2: Nat$] : ! [v3: % 55.35/8.35 | Nat_a_set_fun$] : (v1 = v0 | ~ (fun_app$j(v3, v2) = v1) | ~ % 55.35/8.35 | (fun_app$j(v3, v2) = v0)) % 55.35/8.35 | (40) ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : ! [v2: % 55.35/8.35 | Nat_a_set_fun$] : ! [v3: Nat$] : (v1 = v0 | ~ (suffix$(v3, v2) = % 55.35/8.35 | v1) | ~ (suffix$(v3, v2) = v0)) % 55.35/8.35 | (41) ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : ! [v2: % 55.35/8.35 | Nat_a_set_fun$] : ! [v3: A_set$] : (v1 = v0 | ~ (build$(v3, v2) = % 55.35/8.35 | v1) | ~ (build$(v3, v2) = v0)) % 55.35/8.35 | % 55.35/8.35 | DELTA: instantiating (30) with fresh symbol all_308_0 gives: % 55.35/8.35 | (42) fun_app$p(num_of_nat$, all_308_0) = one$ & nat$(0) = all_308_0 & % 55.35/8.35 | Nat$(all_308_0) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (42) implies: % 55.35/8.35 | (43) nat$(0) = all_308_0 % 55.35/8.35 | % 55.35/8.35 | DELTA: instantiating (1) with fresh symbols all_322_0, all_322_1, all_322_2 % 55.35/8.35 | gives: % 55.35/8.35 | (44) fun_app$i(unf$, all_322_2) = all_322_1 & fun_app$i(next_ltln$, phi$) = % 55.35/8.35 | all_322_2 & gF_advice$(all_322_1, x$) = all_322_0 & % 55.35/8.35 | semantics_ltln$(w$, all_322_0) = 0 & A_ltln$(all_322_0) & % 55.35/8.35 | A_ltln$(all_322_1) & A_ltln$(all_322_2) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (44) implies: % 55.35/8.35 | (45) semantics_ltln$(w$, all_322_0) = 0 % 55.35/8.35 | (46) gF_advice$(all_322_1, x$) = all_322_0 % 55.35/8.35 | (47) fun_app$i(next_ltln$, phi$) = all_322_2 % 55.35/8.35 | (48) fun_app$i(unf$, all_322_2) = all_322_1 % 55.35/8.35 | % 55.35/8.35 | DELTA: instantiating (axiom41) with fresh symbols all_328_0, all_328_1 gives: % 55.35/8.35 | (49) nat$(1) = all_328_0 & nat$(0) = all_328_1 & Nat$(all_328_0) & % 55.35/8.35 | Nat$(all_328_1) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : % 55.35/8.35 | ( ~ (suffix$(all_328_0, v0) = v1) | ~ Nat_a_set_fun$(v0) | ? [v2: % 55.35/8.35 | A_set$] : (build$(v2, v1) = v0 & fun_app$j(v0, all_328_1) = v2 & % 55.35/8.35 | A_set$(v2))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_set$] : ( ~ % 55.35/8.35 | (fun_app$j(v0, all_328_1) = v1) | ~ Nat_a_set_fun$(v0) | ? [v2: % 55.35/8.35 | Nat_a_set_fun$] : (build$(v1, v2) = v0 & suffix$(all_328_0, v0) = % 55.35/8.35 | v2 & Nat_a_set_fun$(v2))) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (49) implies: % 55.35/8.35 | (50) nat$(0) = all_328_1 % 55.35/8.35 | (51) nat$(1) = all_328_0 % 55.35/8.35 | (52) ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : ( ~ % 55.35/8.35 | (suffix$(all_328_0, v0) = v1) | ~ Nat_a_set_fun$(v0) | ? [v2: % 55.35/8.35 | A_set$] : (build$(v2, v1) = v0 & fun_app$j(v0, all_328_1) = v2 & % 55.35/8.35 | A_set$(v2))) % 55.35/8.35 | % 55.35/8.35 | DELTA: instantiating (axiom41) with fresh symbols all_331_0, all_331_1 gives: % 55.35/8.35 | (53) nat$(1) = all_331_0 & nat$(0) = all_331_1 & Nat$(all_331_0) & % 55.35/8.35 | Nat$(all_331_1) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat_a_set_fun$] : % 55.35/8.35 | ( ~ (suffix$(all_331_0, v0) = v1) | ~ Nat_a_set_fun$(v0) | ? [v2: % 55.35/8.35 | A_set$] : (build$(v2, v1) = v0 & fun_app$j(v0, all_331_1) = v2 & % 55.35/8.35 | A_set$(v2))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_set$] : ( ~ % 55.35/8.35 | (fun_app$j(v0, all_331_1) = v1) | ~ Nat_a_set_fun$(v0) | ? [v2: % 55.35/8.35 | Nat_a_set_fun$] : (build$(v1, v2) = v0 & suffix$(all_331_0, v0) = % 55.35/8.35 | v2 & Nat_a_set_fun$(v2))) % 55.35/8.35 | % 55.35/8.35 | ALPHA: (53) implies: % 55.35/8.35 | (54) nat$(1) = all_331_0 % 55.35/8.35 | % 55.35/8.35 | DELTA: instantiating (axiom292) with fresh symbol all_334_0 gives: % 55.35/8.36 | (55) nat$(0) = all_334_0 & Nat$(all_334_0) & ! [v0: Nat_a_set_fun$] : ! % 55.35/8.36 | [v1: Nat$] : ! [v2: A_set_list$] : ( ~ (subsequence$(v0, all_334_0, % 55.35/8.36 | v1) = v2) | ~ Nat_a_set_fun$(v0) | ~ Nat$(v1) | ? [v3: % 55.35/8.36 | Nat_a_set_fun$] : (conc$(v2, v3) = v0 & suffix$(v1, v0) = v3 & % 55.35/8.36 | Nat_a_set_fun$(v3))) & ! [v0: Nat_a_set_fun$] : ! [v1: Nat$] : % 55.35/8.36 | ! [v2: Nat_a_set_fun$] : ( ~ (suffix$(v1, v0) = v2) | ~ % 55.35/8.36 | Nat_a_set_fun$(v0) | ~ Nat$(v1) | ? [v3: A_set_list$] : (conc$(v3, % 55.35/8.36 | v2) = v0 & subsequence$(v0, all_334_0, v1) = v3 & % 55.35/8.36 | A_set_list$(v3))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (55) implies: % 55.35/8.36 | (56) nat$(0) = all_334_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (13) with fresh symbol all_337_0 gives: % 55.35/8.36 | (57) nat$(0) = all_337_0 & Nat$(all_337_0) & ! [v0: Nat_bool_fun$] : ! % 55.35/8.36 | [v1: Nat$] : ( ~ (fun_app$c(v0, v1) = 0) | ~ Nat_bool_fun$(v0) | ~ % 55.35/8.36 | Nat$(v1) | ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : ? [v5: % 55.35/8.36 | Nat$] : ? [v6: int] : ? [v7: int] : (Nat$(v3) & ((v6 = 0 & ~ % 55.35/8.36 | (v7 = 0) & fun_app$k(of_nat$, v3) = v4 & nat$($sum(v4, 1)) = % 55.35/8.36 | v5 & fun_app$c(v0, v5) = 0 & fun_app$c(v0, v3) = v7 & % 55.35/8.36 | Nat$(v5)) | (v2 = 0 & fun_app$c(v0, all_337_0) = 0)))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (57) implies: % 55.35/8.36 | (58) nat$(0) = all_337_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (15) with fresh symbol all_343_0 gives: % 55.35/8.36 | (59) nat$(0) = all_343_0 & Nat$(all_343_0) & ! [v0: Nat_bool_fun$] : ! % 55.35/8.36 | [v1: Nat$] : ! [v2: int] : (v2 = 0 | ~ (fun_app$c(v0, v1) = v2) | ~ % 55.35/8.36 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v3: int] : ? [v4: Nat$] : ? % 55.35/8.36 | [v5: int] : ? [v6: int] : ? [v7: Nat$] : ? [v8: int] : (Nat$(v4) % 55.35/8.36 | & ((v5 = 0 & ~ (v8 = 0) & fun_app$k(of_nat$, v4) = v6 & % 55.35/8.36 | nat$($sum(v6, 1)) = v7 & fun_app$c(v0, v7) = v8 & % 55.35/8.36 | fun_app$c(v0, v4) = 0 & Nat$(v7)) | ( ~ (v3 = 0) & % 55.35/8.36 | fun_app$c(v0, all_343_0) = v3)))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (59) implies: % 55.35/8.36 | (60) nat$(0) = all_343_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (19) with fresh symbol all_346_0 gives: % 55.35/8.36 | (61) nat$(0) = all_346_0 & Nat$(all_346_0) & ! [v0: Nat_a_set_fun$] : ! % 55.35/8.36 | [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: Nat$] : ! [v4: % 55.35/8.36 | A_set_list$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 55.35/8.36 | (subsequence$(v0, all_346_0, v3) = v4) | ~ (foldl$(af_letter$, v1, % 55.35/8.36 | v4) = v5) | ~ (gF_advice$(v5, v2) = v6) | ~ Nat_a_set_fun$(v0) % 55.35/8.36 | | ~ A_ltln$(v1) | ~ A_ltln_set$(v2) | ~ Nat$(v3) | ? [v7: % 55.35/8.36 | A_ltln$] : ? [v8: any] : ? [v9: Nat_a_set_fun$] : ? [v10: any] % 55.35/8.36 | : (suffix$(v3, v0) = v9 & gF_advice$(v1, v2) = v7 & % 55.35/8.36 | semantics_ltln$(v9, v6) = v10 & semantics_ltln$(v0, v7) = v8 & % 55.35/8.36 | Nat_a_set_fun$(v9) & A_ltln$(v7) & ( ~ (v8 = 0) | v10 = 0))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (61) implies: % 55.35/8.36 | (62) nat$(0) = all_346_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (12) with fresh symbol all_349_0 gives: % 55.35/8.36 | (63) nat$(0) = all_349_0 & Nat$(all_349_0) & ! [v0: Nat$] : ! [v1: % 55.35/8.36 | Nat_a_set_fun$] : ! [v2: A_ltln$] : ! [v3: A_ltln_set$] : ! [v4: % 55.35/8.36 | A_set_list$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 55.35/8.36 | (subsequence$(v1, all_349_0, v0) = v4) | ~ (foldl$(af_letter$, v2, % 55.35/8.36 | v4) = v5) | ~ (fG_advice$(v5, v3) = v6) | ~ Nat_a_set_fun$(v1) % 55.35/8.36 | | ~ A_ltln$(v2) | ~ A_ltln_set$(v3) | ~ Nat$(v0) | ? [v7: % 55.35/8.36 | Nat_a_set_fun$] : ? [v8: any] : ? [v9: A_ltln$] : ? [v10: any] % 55.35/8.36 | : (fG_advice$(v2, v3) = v9 & suffix$(v0, v1) = v7 & % 55.35/8.36 | semantics_ltln$(v7, v6) = v8 & semantics_ltln$(v1, v9) = v10 & % 55.35/8.36 | Nat_a_set_fun$(v7) & A_ltln$(v9) & ( ~ (v8 = 0) | v10 = 0))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (63) implies: % 55.35/8.36 | (64) nat$(0) = all_349_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (34) with fresh symbols all_352_0, all_352_1, all_352_2, % 55.35/8.36 | all_352_3, all_352_4, all_352_5, all_352_6, all_352_7, all_352_8 gives: % 55.35/8.36 | (65) ~ (all_352_0 = 0) & suffix$(all_352_8, w$) = all_352_7 & % 55.35/8.36 | fun_app$h(af_letter$, all_352_6) = all_352_5 & nat$(1) = all_352_8 & % 55.35/8.36 | nat$(0) = all_352_4 & fun_app$j(w$, all_352_4) = all_352_3 & % 55.35/8.36 | fun_app$g(all_352_5, all_352_3) = all_352_2 & fun_app$i(next_ltln$, % 55.35/8.36 | phi$) = all_352_6 & gF_advice$(all_352_2, x$) = all_352_1 & % 55.35/8.36 | semantics_ltln$(all_352_7, all_352_1) = all_352_0 & % 55.35/8.36 | Nat_a_set_fun$(all_352_7) & A_ltln$(all_352_1) & A_ltln$(all_352_2) & % 55.35/8.36 | A_ltln$(all_352_6) & A_set$(all_352_3) & A_set_a_ltln_fun$(all_352_5) % 55.35/8.36 | & Nat$(all_352_4) & Nat$(all_352_8) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (65) implies: % 55.35/8.36 | (66) ~ (all_352_0 = 0) % 55.35/8.36 | (67) A_ltln$(all_352_2) % 55.35/8.36 | (68) semantics_ltln$(all_352_7, all_352_1) = all_352_0 % 55.35/8.36 | (69) gF_advice$(all_352_2, x$) = all_352_1 % 55.35/8.36 | (70) fun_app$i(next_ltln$, phi$) = all_352_6 % 55.35/8.36 | (71) fun_app$g(all_352_5, all_352_3) = all_352_2 % 55.35/8.36 | (72) fun_app$j(w$, all_352_4) = all_352_3 % 55.35/8.36 | (73) nat$(0) = all_352_4 % 55.35/8.36 | (74) nat$(1) = all_352_8 % 55.35/8.36 | (75) fun_app$h(af_letter$, all_352_6) = all_352_5 % 55.35/8.36 | (76) suffix$(all_352_8, w$) = all_352_7 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (20) with fresh symbol all_354_0 gives: % 55.35/8.36 | (77) nat$(0) = all_354_0 & Nat$(all_354_0) & ! [v0: Nat_a_set_fun$] : ! % 55.35/8.36 | [v1: A_ltln$] : ! [v2: A_ltln_set$] : ! [v3: A_ltln$] : ! [v4: % 55.35/8.36 | A_ltln$] : ( ~ (fun_app$i(id$, v1) = v3) | ~ (gF_advice$(v3, v2) = % 55.35/8.36 | v4) | ~ (semantics_ltln$(v0, v4) = 0) | ~ Nat_a_set_fun$(v0) | % 55.35/8.36 | ~ A_ltln$(v1) | ~ A_ltln_set$(v2) | ? [v5: Nat$] : ? [v6: % 55.35/8.36 | Nat_a_set_fun$] : ? [v7: A_set_list$] : ? [v8: A_ltln$] : ? % 55.35/8.36 | [v9: A_ltln$] : (subsequence$(v0, all_354_0, v5) = v7 & % 55.35/8.36 | foldl$(af_letter$, v1, v7) = v8 & suffix$(v5, v0) = v6 & % 55.35/8.36 | gF_advice$(v8, v2) = v9 & semantics_ltln$(v6, v9) = 0 & % 55.35/8.36 | Nat_a_set_fun$(v6) & A_ltln$(v9) & A_ltln$(v8) & A_set_list$(v7) & % 55.35/8.36 | Nat$(v5))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (77) implies: % 55.35/8.36 | (78) nat$(0) = all_354_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (11) with fresh symbol all_363_0 gives: % 55.35/8.36 | (79) nat$(1) = all_363_0 & Nat$(all_363_0) & ! [v0: Nat$] : ! [v1: % 55.35/8.36 | Nat_bool_fun$] : ! [v2: int] : (v2 = 0 | ~ (fun_app$c(v1, v0) = % 55.35/8.36 | v2) | ~ Nat_bool_fun$(v1) | ~ Nat$(v0) | ? [v3: int] : ? [v4: % 55.35/8.36 | any] : ? [v5: Nat$] : ? [v6: int] : ? [v7: int] : ? [v8: Nat$] % 55.35/8.36 | : ? [v9: int] : (Nat$(v5) & ((v7 = 0 & ~ (v9 = 0) & $lesseq(1, v6) % 55.35/8.36 | & fun_app$k(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v8 & % 55.35/8.36 | fun_app$c(v1, v8) = v9 & fun_app$c(v1, v5) = 0 & Nat$(v8)) | % 55.35/8.36 | (fun_app$k(of_nat$, v0) = v3 & fun_app$c(v1, all_363_0) = v4 & ( % 55.35/8.36 | ~ (v4 = 0) | ~ ($lesseq(1, v3))))))) % 55.35/8.36 | % 55.35/8.36 | ALPHA: (79) implies: % 55.35/8.36 | (80) nat$(1) = all_363_0 % 55.35/8.36 | % 55.35/8.36 | DELTA: instantiating (8) with fresh symbol all_369_0 gives: % 55.35/8.37 | (81) nat$(0) = all_369_0 & Nat$(all_369_0) & ! [v0: % 55.35/8.37 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! [v2: % 55.35/8.37 | Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! [v5: % 55.35/8.37 | A_ltln$] : ! [v6: A_ltln$] : ( ~ (gF_advice_congruent$(v0, v1) = 0) % 55.35/8.37 | | ~ (fun_app$i(v1, v3) = v5) | ~ (gF_advice$(v5, v4) = v6) | ~ % 55.35/8.37 | (semantics_ltln$(v2, v6) = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | % 55.35/8.37 | ~ Nat_a_set_fun$(v2) | ~ A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ % 55.35/8.37 | A_ltln_a_ltln_fun$(v1) | ? [v7: Nat$] : ? [v8: Nat_a_set_fun$] : % 55.35/8.37 | ? [v9: A_set_list$] : ? [v10: A_ltln$] : ? [v11: A_ltln$] : % 55.35/8.37 | (subsequence$(v2, all_369_0, v7) = v9 & foldl$(af_letter$, v3, v9) = % 55.35/8.37 | v10 & suffix$(v7, v2) = v8 & gF_advice$(v10, v4) = v11 & % 55.35/8.37 | semantics_ltln$(v8, v11) = 0 & Nat_a_set_fun$(v8) & A_ltln$(v11) & % 55.35/8.37 | A_ltln$(v10) & A_set_list$(v9) & Nat$(v7))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (81) implies: % 55.35/8.37 | (82) nat$(0) = all_369_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (16) with fresh symbol all_372_0 gives: % 55.35/8.37 | (83) nat$(0) = all_372_0 & Nat$(all_372_0) & ! [v0: Nat_bool_fun$] : ! % 55.35/8.37 | [v1: Nat$] : ! [v2: int] : (v2 = 0 | ~ (fun_app$c(v0, v1) = v2) | ~ % 55.35/8.37 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v3: int] : ? [v4: Nat$] : ? % 55.35/8.37 | [v5: int] : ? [v6: int] : (Nat$(v4) & (( ~ (v6 = 0) & $lesseq(1, % 55.35/8.37 | v5) & fun_app$k(of_nat$, v4) = v5 & fun_app$c(v0, v4) = v6 & % 55.35/8.37 | ! [v7: Nat$] : ! [v8: int] : (v8 = 0 | ~ (fun_app$c(v0, v7) % 55.35/8.37 | = v8) | ~ Nat$(v7) | ? [v9: int] : ($lesseq(v5, v9) & % 55.35/8.37 | fun_app$k(of_nat$, v7) = v9)) & ! [v7: Nat$] : ! [v8: % 55.35/8.37 | int] : ( ~ ($lesseq(1, $difference(v5, v8))) | ~ % 55.35/8.37 | (fun_app$k(of_nat$, v7) = v8) | ~ Nat$(v7) | fun_app$c(v0, % 55.35/8.37 | v7) = 0)) | ( ~ (v3 = 0) & fun_app$c(v0, all_372_0) = % 55.35/8.37 | v3)))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (83) implies: % 55.35/8.37 | (84) nat$(0) = all_372_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (2) with fresh symbols all_375_0, all_375_1, all_375_2, % 55.35/8.37 | all_375_3, all_375_4, all_375_5, all_375_6, all_375_7, all_375_8, % 55.35/8.37 | all_375_9, all_375_10 gives: % 55.35/8.37 | (85) suffix$(all_375_7, w$) = all_375_6 & fun_app$h(af_letter$, phi$) = % 55.35/8.37 | all_375_5 & nat$(1) = all_375_7 & nat$(0) = all_375_4 & fun_app$j(w$, % 55.35/8.37 | all_375_4) = all_375_3 & fun_app$g(all_375_5, all_375_3) = all_375_2 % 55.35/8.37 | & fun_app$i(unf$, phi$) = all_375_10 & gF_advice$(all_375_2, x$) = % 55.35/8.37 | all_375_1 & gF_advice$(all_375_10, x$) = all_375_9 & % 55.35/8.37 | semantics_ltln$(all_375_6, all_375_1) = all_375_0 & % 55.35/8.37 | semantics_ltln$(w$, all_375_9) = all_375_8 & Nat_a_set_fun$(all_375_6) % 55.35/8.37 | & A_ltln$(all_375_1) & A_ltln$(all_375_2) & A_ltln$(all_375_9) & % 55.35/8.37 | A_ltln$(all_375_10) & A_set$(all_375_3) & A_set_a_ltln_fun$(all_375_5) % 55.35/8.37 | & Nat$(all_375_4) & Nat$(all_375_7) & ( ~ (all_375_8 = 0) | all_375_0 % 55.35/8.37 | = 0) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (85) implies: % 55.35/8.37 | (86) A_set$(all_375_3) % 55.35/8.37 | (87) Nat_a_set_fun$(all_375_6) % 55.35/8.37 | (88) fun_app$j(w$, all_375_4) = all_375_3 % 55.35/8.37 | (89) nat$(0) = all_375_4 % 55.35/8.37 | (90) nat$(1) = all_375_7 % 55.35/8.37 | (91) suffix$(all_375_7, w$) = all_375_6 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (25) with fresh symbol all_377_0 gives: % 55.35/8.37 | (92) nat$(0) = all_377_0 & Nat$(all_377_0) & ! [v0: A_ltln$] : ! [v1: % 55.35/8.37 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.37 | A_ltln_set$] : ( ~ (g_F$(v0, v3) = v4) | ~ (suffix$(v2, v1) = v3) | % 55.35/8.37 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | A_set_list$] : ? [v6: A_ltln$] : (g_F$(v6, v3) = v4 & % 55.35/8.37 | subsequence$(v1, all_377_0, v2) = v5 & foldl$(af_letter$, v0, v5) % 55.35/8.37 | = v6 & A_ltln$(v6) & A_set_list$(v5) & A_ltln_set$(v4))) & ! [v0: % 55.35/8.37 | A_ltln$] : ! [v1: Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: % 55.35/8.37 | A_set_list$] : ! [v4: A_ltln$] : ( ~ (subsequence$(v1, all_377_0, % 55.35/8.37 | v2) = v3) | ~ (foldl$(af_letter$, v0, v3) = v4) | ~ % 55.35/8.37 | Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | Nat_a_set_fun$] : ? [v6: A_ltln_set$] : (g_F$(v4, v5) = v6 & % 55.35/8.37 | g_F$(v0, v5) = v6 & suffix$(v2, v1) = v5 & Nat_a_set_fun$(v5) & % 55.35/8.37 | A_ltln_set$(v6))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (92) implies: % 55.35/8.37 | (93) nat$(0) = all_377_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (23) with fresh symbol all_380_0 gives: % 55.35/8.37 | (94) nat$(0) = all_380_0 & Nat$(all_380_0) & ! [v0: A_ltln$] : ! [v1: % 55.35/8.37 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.37 | A_ltln_set$] : ( ~ (g$(v0, v3) = v4) | ~ (suffix$(v2, v1) = v3) | % 55.35/8.37 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | A_set_list$] : ? [v6: A_ltln$] : (g$(v6, v3) = v4 & % 55.35/8.37 | subsequence$(v1, all_380_0, v2) = v5 & foldl$(af_letter$, v0, v5) % 55.35/8.37 | = v6 & A_ltln$(v6) & A_set_list$(v5) & A_ltln_set$(v4))) & ! [v0: % 55.35/8.37 | A_ltln$] : ! [v1: Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: % 55.35/8.37 | A_set_list$] : ! [v4: A_ltln$] : ( ~ (subsequence$(v1, all_380_0, % 55.35/8.37 | v2) = v3) | ~ (foldl$(af_letter$, v0, v3) = v4) | ~ % 55.35/8.37 | Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | Nat_a_set_fun$] : ? [v6: A_ltln_set$] : (g$(v4, v5) = v6 & g$(v0, % 55.35/8.37 | v5) = v6 & suffix$(v2, v1) = v5 & Nat_a_set_fun$(v5) & % 55.35/8.37 | A_ltln_set$(v6))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (94) implies: % 55.35/8.37 | (95) nat$(0) = all_380_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (22) with fresh symbol all_383_0 gives: % 55.35/8.37 | (96) nat$(0) = all_383_0 & Nat$(all_383_0) & ! [v0: A_ltln$] : ! [v1: % 55.35/8.37 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.37 | A_ltln_set$] : ( ~ (f$(v0, v3) = v4) | ~ (suffix$(v2, v1) = v3) | % 55.35/8.37 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | A_set_list$] : ? [v6: A_ltln$] : (f$(v6, v3) = v4 & % 55.35/8.37 | subsequence$(v1, all_383_0, v2) = v5 & foldl$(af_letter$, v0, v5) % 55.35/8.37 | = v6 & A_ltln$(v6) & A_set_list$(v5) & A_ltln_set$(v4))) & ! [v0: % 55.35/8.37 | A_ltln$] : ! [v1: Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: % 55.35/8.37 | A_set_list$] : ! [v4: A_ltln$] : ( ~ (subsequence$(v1, all_383_0, % 55.35/8.37 | v2) = v3) | ~ (foldl$(af_letter$, v0, v3) = v4) | ~ % 55.35/8.37 | Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | Nat_a_set_fun$] : ? [v6: A_ltln_set$] : (f$(v4, v5) = v6 & f$(v0, % 55.35/8.37 | v5) = v6 & suffix$(v2, v1) = v5 & Nat_a_set_fun$(v5) & % 55.35/8.37 | A_ltln_set$(v6))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (96) implies: % 55.35/8.37 | (97) nat$(0) = all_383_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (24) with fresh symbol all_386_0 gives: % 55.35/8.37 | (98) nat$(0) = all_386_0 & Nat$(all_386_0) & ! [v0: A_ltln$] : ! [v1: % 55.35/8.37 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: Nat_a_set_fun$] : ! [v4: % 55.35/8.37 | A_ltln_set$] : ( ~ (f_G$(v0, v3) = v4) | ~ (suffix$(v2, v1) = v3) | % 55.35/8.37 | ~ Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | A_set_list$] : ? [v6: A_ltln$] : (f_G$(v6, v3) = v4 & % 55.35/8.37 | subsequence$(v1, all_386_0, v2) = v5 & foldl$(af_letter$, v0, v5) % 55.35/8.37 | = v6 & A_ltln$(v6) & A_set_list$(v5) & A_ltln_set$(v4))) & ! [v0: % 55.35/8.37 | A_ltln$] : ! [v1: Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: % 55.35/8.37 | A_set_list$] : ! [v4: A_ltln$] : ( ~ (subsequence$(v1, all_386_0, % 55.35/8.37 | v2) = v3) | ~ (foldl$(af_letter$, v0, v3) = v4) | ~ % 55.35/8.37 | Nat_a_set_fun$(v1) | ~ A_ltln$(v0) | ~ Nat$(v2) | ? [v5: % 55.35/8.37 | Nat_a_set_fun$] : ? [v6: A_ltln_set$] : (f_G$(v4, v5) = v6 & % 55.35/8.37 | f_G$(v0, v5) = v6 & suffix$(v2, v1) = v5 & Nat_a_set_fun$(v5) & % 55.35/8.37 | A_ltln_set$(v6))) % 55.35/8.37 | % 55.35/8.37 | ALPHA: (98) implies: % 55.35/8.37 | (99) nat$(0) = all_386_0 % 55.35/8.37 | % 55.35/8.37 | DELTA: instantiating (26) with fresh symbol all_389_0 gives: % 55.35/8.38 | (100) nat$(0) = all_389_0 & Nat$(all_389_0) & ! [v0: Nat_bool_fun$] : ! % 55.35/8.38 | [v1: Nat$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : ! [v5: % 55.35/8.38 | Nat$] : ! [v6: any] : ( ~ (fun_app$k(of_nat$, v2) = v3) | ~ % 55.35/8.38 | (fun_app$k(of_nat$, v1) = v4) | ~ (nat$($difference(v4, v3)) = v5) % 55.35/8.38 | | ~ (fun_app$c(v0, v5) = v6) | ~ Nat_bool_fun$(v0) | ~ Nat$(v2) % 55.35/8.38 | | ~ Nat$(v1) | ? [v7: any] : ? [v8: any] : ? [v9: Nat$] : ? % 55.35/8.38 | [v10: int] : ? [v11: Nat$] : ? [v12: int] : ? [v13: int] : % 55.35/8.38 | (Nat$(v9) & ((v12 = 0 & ~ (v13 = 0) & fun_app$k(of_nat$, v9) = v10 % 55.35/8.38 | & nat$($sum(v10, 1)) = v11 & fun_app$c(v0, v11) = 0 & % 55.35/8.38 | fun_app$c(v0, v9) = v13 & Nat$(v11)) | (fun_app$c(v0, v1) = % 55.35/8.38 | v7 & fun_app$c(v0, all_389_0) = v8 & ( ~ (v7 = 0) | ((v8 = 0 % 55.35/8.38 | | ~ ($lesseq(1, $difference(v3, v4)))) & (v6 = 0 | ~ % 55.35/8.38 | ($lesseq(v3, v4))))))))) % 55.35/8.38 | % 55.35/8.38 | ALPHA: (100) implies: % 55.35/8.38 | (101) nat$(0) = all_389_0 % 55.35/8.38 | % 55.35/8.38 | DELTA: instantiating (29) with fresh symbol all_392_0 gives: % 55.35/8.38 | (102) nat$(0) = all_392_0 & Nat$(all_392_0) & ! [v0: Nat$] : ! [v1: % 55.35/8.38 | Nat_nat_fun$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : ! [v4: % 55.35/8.38 | Nat$] : (v4 = v0 | ~ (case_nat$(v0, v1) = v3) | ~ (fun_app$e(v3, % 55.35/8.38 | v2) = v4) | ~ Nat$(v2) | ~ Nat$(v0) | ~ Nat_nat_fun$(v1) | % 55.35/8.38 | ? [v5: int] : ( ~ (v5 = 0) & fun_app$k(of_nat$, v2) = v5)) & ! % 55.35/8.38 | [v0: Nat$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat$] : ! [v3: % 55.35/8.38 | Nat_nat_fun$] : ! [v4: Nat$] : ( ~ (case_nat$(v0, v1) = v3) | ~ % 55.35/8.38 | (fun_app$e(v3, v2) = v4) | ~ Nat$(v2) | ~ Nat$(v0) | ~ % 55.35/8.38 | Nat_nat_fun$(v1) | ? [v5: int] : ? [v6: Nat$] : ? [v7: Nat$] : % 55.35/8.38 | ? [v8: Nat$] : (fun_app$k(of_nat$, v2) = v5 & nat$($sum(v5, -1)) = % 55.35/8.38 | v7 & fun_app$e(v1, v7) = v8 & fun_app$e(v1, all_392_0) = v6 & % 55.35/8.38 | Nat$(v8) & Nat$(v7) & Nat$(v6) & (v5 = 0 | ((v8 = v4 | ~ % 55.35/8.38 | ($lesseq(1, v5))) & (v6 = v4 | ~ ($lesseq(v5, -1))))))) % 55.35/8.38 | % 55.35/8.38 | ALPHA: (102) implies: % 55.35/8.38 | (103) nat$(0) = all_392_0 % 55.35/8.38 | % 55.35/8.38 | DELTA: instantiating (28) with fresh symbols all_395_0, all_395_1, all_395_2, % 55.35/8.38 | all_395_3 gives: % 55.35/8.38 | (104) case_nat$(all_395_3, uud$) = all_395_2 & fun_app$k(of_nat$, % 55.35/8.38 | all_395_1) = all_395_0 & nat$(0) = all_395_3 & fun_app$e(all_395_2, % 55.35/8.38 | all_395_3) = all_395_1 & Nat$(all_395_1) & Nat$(all_395_3) & % 55.35/8.38 | Nat_nat_fun$(all_395_2) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: % 55.35/8.38 | int] : ! [v3: int] : ! [v4: Nat$] : (all_395_0 = 0 | ~ % 55.35/8.38 | ($lesseq(1, $difference(v2, v3))) | ~ (fun_app$k(of_nat$, v1) = % 55.35/8.38 | v2) | ~ (fun_app$k(of_nat$, v0) = v3) | ~ (nat$($difference(v3, % 55.35/8.38 | v2)) = v4) | ~ Nat$(v1) | ~ Nat$(v0)) & ! [v0: Nat$] : ! % 55.35/8.38 | [v1: Nat$] : ! [v2: int] : ! [v3: int] : ! [v4: Nat$] : ( ~ % 55.35/8.38 | ($lesseq(1, $difference(v3, v2))) | ~ (fun_app$k(of_nat$, v1) = % 55.35/8.38 | v2) | ~ (fun_app$k(of_nat$, v0) = v3) | ~ (nat$($difference(v3, % 55.35/8.38 | v2)) = v4) | ~ Nat$(v1) | ~ Nat$(v0) | ? [v5: Nat$] : % 55.35/8.38 | (fun_app$k(of_nat$, v5) = $sum($difference(v3, v2), -1) & % 55.35/8.38 | fun_app$e(all_395_2, v4) = v5 & Nat$(v5))) & ! [v0: Nat$] : ! % 55.35/8.38 | [v1: Nat$] : ! [v2: int] : (all_395_0 = 0 | ~ (fun_app$k(of_nat$, % 55.35/8.38 | v1) = v2) | ~ (fun_app$k(of_nat$, v0) = v2) | ~ Nat$(v1) | ~ % 55.35/8.38 | Nat$(v0)) % 55.35/8.38 | % 55.35/8.38 | ALPHA: (104) implies: % 55.35/8.38 | (105) nat$(0) = all_395_3 % 55.35/8.38 | % 55.35/8.38 | DELTA: instantiating (3) with fresh symbol all_398_0 gives: % 55.67/8.38 | (106) nat$(1) = all_398_0 & Nat$(all_398_0) & ! [v0: Nat_a_set_fun$] : ! % 55.67/8.38 | [v1: A_ltln$] : ! [v2: Nat_a_set_fun$] : ! [v3: int] : (v3 = 0 | ~ % 55.67/8.38 | (suffix$(all_398_0, v0) = v2) | ~ (semantics_ltln$(v2, v1) = v3) | % 55.67/8.38 | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ? [v4: A_ltln$] : ? [v5: % 55.67/8.38 | int] : ( ~ (v5 = 0) & fun_app$i(next_ltln$, v1) = v4 & % 55.67/8.38 | semantics_ltln$(v0, v4) = v5 & A_ltln$(v4))) & ! [v0: % 55.67/8.38 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ! [v3: % 55.67/8.38 | int] : (v3 = 0 | ~ (fun_app$i(next_ltln$, v1) = v2) | ~ % 55.67/8.38 | (semantics_ltln$(v0, v2) = v3) | ~ Nat_a_set_fun$(v0) | ~ % 55.67/8.38 | A_ltln$(v1) | ? [v4: Nat_a_set_fun$] : ? [v5: int] : ( ~ (v5 = 0) % 55.67/8.38 | & suffix$(all_398_0, v0) = v4 & semantics_ltln$(v4, v1) = v5 & % 55.67/8.38 | Nat_a_set_fun$(v4))) & ! [v0: Nat_a_set_fun$] : ! [v1: A_ltln$] % 55.67/8.38 | : ! [v2: Nat_a_set_fun$] : ( ~ (suffix$(all_398_0, v0) = v2) | ~ % 55.67/8.38 | (semantics_ltln$(v2, v1) = 0) | ~ Nat_a_set_fun$(v0) | ~ % 55.67/8.38 | A_ltln$(v1) | ? [v3: A_ltln$] : (fun_app$i(next_ltln$, v1) = v3 & % 55.67/8.38 | semantics_ltln$(v0, v3) = 0 & A_ltln$(v3))) & ! [v0: % 55.67/8.38 | Nat_a_set_fun$] : ! [v1: A_ltln$] : ! [v2: A_ltln$] : ( ~ % 55.67/8.38 | (fun_app$i(next_ltln$, v1) = v2) | ~ (semantics_ltln$(v0, v2) = 0) % 55.67/8.38 | | ~ Nat_a_set_fun$(v0) | ~ A_ltln$(v1) | ? [v3: Nat_a_set_fun$] % 55.67/8.38 | : (suffix$(all_398_0, v0) = v3 & semantics_ltln$(v3, v1) = 0 & % 55.67/8.38 | Nat_a_set_fun$(v3))) % 55.67/8.38 | % 55.67/8.38 | ALPHA: (106) implies: % 55.67/8.38 | (107) nat$(1) = all_398_0 % 55.67/8.38 | % 55.67/8.38 | DELTA: instantiating (14) with fresh symbol all_404_0 gives: % 55.67/8.38 | (108) nat$(0) = all_404_0 & Nat$(all_404_0) & ! [v0: % 55.67/8.38 | Nat_nat_bool_fun_fun$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: % 55.67/8.38 | Nat_bool_fun$] : ! [v4: int] : (v4 = 0 | ~ (fun_app$n(v0, v1) = % 55.67/8.38 | v3) | ~ (fun_app$c(v3, v2) = v4) | ~ Nat$(v2) | ~ Nat$(v1) | % 55.67/8.38 | ~ Nat_nat_bool_fun_fun$(v0) | ? [v5: Nat_bool_fun$] : ? [v6: % 55.67/8.38 | Nat$] : ? [v7: int] : ? [v8: Nat$] : ? [v9: int] : ? [v10: % 55.67/8.38 | Nat$] : ? [v11: Nat$] : ? [v12: Nat_bool_fun$] : ? [v13: int] % 55.67/8.38 | : ? [v14: int] : ? [v15: Nat$] : ? [v16: Nat_bool_fun$] : ? % 55.67/8.38 | [v17: int] : ? [v18: Nat$] : ? [v19: int] : ? [v20: Nat$] : ? % 55.67/8.38 | [v21: Nat_bool_fun$] : ? [v22: int] : (Nat$(v20) & Nat$(v11) & % 55.67/8.38 | Nat$(v10) & Nat$(v6) & ((v13 = 0 & ~ (v19 = 0) & fun_app$n(v0, % 55.67/8.38 | v15) = v16 & fun_app$n(v0, v10) = v12 & fun_app$k(of_nat$, % 55.67/8.38 | v11) = v17 & fun_app$k(of_nat$, v10) = v14 & nat$($sum(v17, % 55.67/8.38 | 1)) = v18 & nat$($sum(v14, 1)) = v15 & fun_app$c(v16, % 55.67/8.38 | v18) = v19 & fun_app$c(v12, v11) = 0 & Nat_bool_fun$(v16) & % 55.67/8.38 | Nat_bool_fun$(v12) & Nat$(v18) & Nat$(v15)) | ( ~ (v22 = 0) & % 55.67/8.38 | fun_app$n(v0, v20) = v21 & fun_app$c(v21, all_404_0) = v22 & % 55.67/8.38 | Nat_bool_fun$(v21)) | ( ~ (v9 = 0) & fun_app$n(v0, all_404_0) % 55.67/8.38 | = v5 & fun_app$k(of_nat$, v6) = v7 & nat$($sum(v7, 1)) = v8 & % 55.67/8.38 | fun_app$c(v5, v8) = v9 & Nat_bool_fun$(v5) & Nat$(v8))))) % 55.67/8.38 | % 55.67/8.38 | ALPHA: (108) implies: % 55.67/8.38 | (109) nat$(0) = all_404_0 % 55.67/8.38 | % 55.67/8.38 | DELTA: instantiating (27) with fresh symbol all_407_0 gives: % 55.67/8.39 | (110) nat$(0) = all_407_0 & Nat$(all_407_0) & ! [v0: Nat$] : ! [v1: % 55.67/8.39 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : ! % 55.67/8.39 | [v5: Nat_a_set_fun$] : ! [v6: Nat$] : ! [v7: A_set_list$] : ( ~ % 55.67/8.39 | ($lesseq(v3, v4)) | ~ (subsequence$(v5, all_407_0, v6) = v7) | ~ % 55.67/8.39 | (fun_app$k(of_nat$, v2) = v4) | ~ (fun_app$k(of_nat$, v0) = v3) | % 55.67/8.39 | ~ (suffix$(v0, v1) = v5) | ~ (nat$($difference(v4, v3)) = v6) | ~ % 55.67/8.39 | Nat_a_set_fun$(v1) | ~ Nat$(v2) | ~ Nat$(v0) | (subsequence$(v1, % 55.67/8.39 | v0, v2) = v7 & A_set_list$(v7))) & ! [v0: Nat$] : ! [v1: % 55.67/8.39 | Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: A_set_list$] : ( ~ % 55.67/8.39 | (subsequence$(v1, v0, v2) = v3) | ~ Nat_a_set_fun$(v1) | ~ % 55.67/8.39 | Nat$(v2) | ~ Nat$(v0) | ? [v4: int] : ? [v5: int] : ? [v6: % 55.67/8.39 | Nat_a_set_fun$] : ? [v7: Nat$] : ? [v8: A_set_list$] : % 55.67/8.39 | (subsequence$(v6, all_407_0, v7) = v8 & fun_app$k(of_nat$, v2) = v5 % 55.67/8.39 | & fun_app$k(of_nat$, v0) = v4 & suffix$(v0, v1) = v6 & % 55.67/8.39 | nat$($difference(v5, v4)) = v7 & Nat_a_set_fun$(v6) & % 55.67/8.39 | A_set_list$(v8) & Nat$(v7) & (v8 = v3 | ~ ($lesseq(v4, v5))))) & % 55.67/8.39 | ! [v0: Nat$] : ! [v1: Nat_a_set_fun$] : ! [v2: Nat$] : ! [v3: % 55.67/8.39 | A_set_list$] : ( ~ (subsequence$(v1, v0, v2) = v3) | ~ % 55.67/8.39 | Nat_a_set_fun$(v1) | ~ Nat$(v2) | ~ Nat$(v0) | ? [v4: int] : ? % 55.67/8.39 | [v5: int] : ? [v6: Nat_a_set_fun$] : ? [v7: A_set_list$] : % 55.67/8.39 | (subsequence$(v6, all_407_0, all_407_0) = v7 & fun_app$k(of_nat$, % 55.67/8.39 | v2) = v5 & fun_app$k(of_nat$, v0) = v4 & suffix$(v0, v1) = v6 & % 55.67/8.39 | Nat_a_set_fun$(v6) & A_set_list$(v7) & (v7 = v3 | ~ ($lesseq(1, % 55.67/8.39 | $difference(v4, v5)))))) % 55.67/8.39 | % 55.67/8.39 | ALPHA: (110) implies: % 55.67/8.39 | (111) nat$(0) = all_407_0 % 55.67/8.39 | % 55.67/8.39 | DELTA: instantiating (10) with fresh symbol all_410_0 gives: % 55.67/8.39 | (112) nat$(0) = all_410_0 & Nat$(all_410_0) & ! [v0: Nat$] : ! [v1: % 55.67/8.39 | Nat_bool_fun$] : ! [v2: int] : ! [v3: int] : ! [v4: Nat$] : ! % 55.67/8.39 | [v5: int] : (v3 = 0 | ~ ($lesseq(v5, v2)) | ~ (fun_app$k(of_nat$, % 55.67/8.39 | v4) = v5) | ~ (fun_app$k(of_nat$, v0) = v2) | ~ % 55.67/8.39 | (fun_app$c(v1, all_410_0) = v3) | ~ Nat_bool_fun$(v1) | ~ % 55.67/8.39 | Nat$(v4) | ~ Nat$(v0) | ? [v6: Nat$] : ? [v7: int] : ? [v8: % 55.67/8.39 | Nat$] : ? [v9: int] : ? [v10: int] : (Nat$(v6) & ((v9 = 0 & % 55.67/8.39 | $lesseq(1, $difference(v2, v7)) & fun_app$k(of_nat$, v6) = v7 % 55.67/8.39 | & nat$($sum(v7, 1)) = v8 & fun_app$c(v1, v8) = 0 & Nat$(v8)) % 55.67/8.39 | | ( ~ (v10 = 0) & fun_app$c(v1, v4) = v10)))) & ! [v0: Nat$] : % 55.67/8.39 | ! [v1: Nat_bool_fun$] : ! [v2: MultipleValueBool] : ! [v3: int] : % 55.67/8.39 | ! [v4: Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v3, v5))) | % 55.67/8.39 | ~ (fun_app$k(of_nat$, v4) = v5) | ~ (fun_app$k(of_nat$, v0) = v3) % 55.67/8.39 | | ~ (fun_app$c(v1, all_410_0) = v2) | ~ Nat_bool_fun$(v1) | ~ % 55.67/8.39 | Nat$(v4) | ~ Nat$(v0) | ? [v6: Nat$] : ? [v7: int] : ? [v8: % 55.67/8.39 | int] : ? [v9: Nat$] : ? [v10: int] : (Nat$(v6) & ((v8 = 0 & % 55.67/8.39 | $lesseq(v7, v3) & fun_app$k(of_nat$, v6) = v7 & fun_app$c(v1, % 55.67/8.39 | v6) = 0) | ( ~ (v10 = 0) & nat$($sum(v5, 1)) = v9 & % 55.67/8.39 | fun_app$c(v1, v9) = v10 & Nat$(v9))))) & ! [v0: Nat$] : ! % 55.67/8.39 | [v1: Nat_bool_fun$] : ! [v2: int] : ! [v3: int] : ! [v4: Nat$] : % 55.67/8.39 | (v3 = 0 | ~ (fun_app$k(of_nat$, v0) = v2) | ~ (fun_app$c(v1, v4) = % 55.67/8.39 | 0) | ~ (fun_app$c(v1, all_410_0) = v3) | ~ Nat_bool_fun$(v1) | % 55.67/8.39 | ~ Nat$(v4) | ~ Nat$(v0) | ? [v5: Nat$] : ? [v6: int] : ? [v7: % 55.67/8.39 | Nat$] : ? [v8: int] : ? [v9: int] : (Nat$(v5) & ((v8 = 0 & % 55.67/8.39 | $lesseq(1, $difference(v2, v6)) & fun_app$k(of_nat$, v5) = v6 % 55.67/8.39 | & nat$($sum(v6, 1)) = v7 & fun_app$c(v1, v7) = 0 & Nat$(v7)) % 55.67/8.39 | | ($lesseq(1, $difference(v9, v2)) & fun_app$k(of_nat$, v4) = % 55.67/8.39 | v9)))) & ! [v0: Nat$] : ! [v1: Nat_bool_fun$] : ! [v2: % 55.67/8.39 | int] : ( ~ (fun_app$k(of_nat$, v0) = v2) | ~ (fun_app$c(v1, % 55.67/8.39 | all_410_0) = 0) | ~ Nat_bool_fun$(v1) | ~ Nat$(v0) | ? [v3: % 55.67/8.39 | Nat$] : ? [v4: int] : ($lesseq(v4, v2) & fun_app$k(of_nat$, v3) % 55.67/8.39 | = v4 & fun_app$c(v1, v3) = 0 & Nat$(v3))) % 55.67/8.39 | % 55.67/8.39 | ALPHA: (112) implies: % 55.67/8.39 | (113) nat$(0) = all_410_0 % 55.67/8.39 | % 55.67/8.39 | DELTA: instantiating (9) with fresh symbol all_413_0 gives: % 55.67/8.39 | (114) nat$(0) = all_413_0 & Nat$(all_413_0) & ! [v0: Nat$] : ! [v1: % 55.67/8.39 | Nat_bool_fun$] : ! [v2: int] : ! [v3: MultipleValueBool] : ! % 55.67/8.39 | [v4: Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v2, v5))) | % 55.67/8.39 | ~ (fun_app$k(of_nat$, v4) = v5) | ~ (fun_app$k(of_nat$, v0) = v2) % 55.67/8.39 | | ~ (fun_app$c(v1, all_413_0) = v3) | ~ Nat_bool_fun$(v1) | ~ % 55.67/8.39 | Nat$(v4) | ~ Nat$(v0) | ? [v6: Nat$] : ? [v7: int] : ? [v8: % 55.67/8.39 | Nat$] : ? [v9: int] : ? [v10: int] : (Nat$(v8) & ((v7 = 0 & % 55.67/8.39 | nat$($sum(v5, 1)) = v6 & fun_app$c(v1, v6) = 0 & Nat$(v6)) | % 55.67/8.39 | ( ~ (v10 = 0) & $lesseq(v9, v2) & fun_app$k(of_nat$, v8) = v9 & % 55.67/8.39 | fun_app$c(v1, v8) = v10)))) & ! [v0: Nat$] : ! [v1: % 55.67/8.39 | Nat_bool_fun$] : ! [v2: int] : ! [v3: Nat$] : ! [v4: int] : (v4 % 55.67/8.39 | = 0 | ~ (fun_app$k(of_nat$, v0) = v2) | ~ (fun_app$c(v1, v3) = % 55.67/8.39 | v4) | ~ (fun_app$c(v1, all_413_0) = 0) | ~ Nat_bool_fun$(v1) | % 55.67/8.39 | ~ Nat$(v3) | ~ Nat$(v0) | ? [v5: int] : ? [v6: Nat$] : ? [v7: % 55.67/8.39 | int] : ? [v8: Nat$] : ? [v9: int] : (Nat$(v6) & (( ~ (v9 = 0) & % 55.67/8.39 | $lesseq(1, $difference(v2, v7)) & fun_app$k(of_nat$, v6) = v7 % 55.67/8.39 | & nat$($sum(v7, 1)) = v8 & fun_app$c(v1, v8) = v9 & Nat$(v8)) % 55.67/8.39 | | ($lesseq(1, $difference(v5, v2)) & fun_app$k(of_nat$, v3) = % 55.67/8.39 | v5)))) & ! [v0: Nat$] : ! [v1: Nat_bool_fun$] : ! [v2: % 55.67/8.39 | int] : ! [v3: Nat$] : ! [v4: int] : ( ~ ($lesseq(v4, v2)) | ~ % 55.67/8.39 | (fun_app$k(of_nat$, v3) = v4) | ~ (fun_app$k(of_nat$, v0) = v2) | % 55.67/8.39 | ~ (fun_app$c(v1, all_413_0) = 0) | ~ Nat_bool_fun$(v1) | ~ % 55.67/8.39 | Nat$(v3) | ~ Nat$(v0) | ? [v5: int] : ? [v6: Nat$] : ? [v7: % 55.67/8.39 | int] : ? [v8: Nat$] : ? [v9: int] : (Nat$(v6) & ((v5 = 0 & % 55.67/8.39 | fun_app$c(v1, v3) = 0) | ( ~ (v9 = 0) & $lesseq(1, % 55.67/8.39 | $difference(v2, v7)) & fun_app$k(of_nat$, v6) = v7 & % 55.67/8.39 | nat$($sum(v7, 1)) = v8 & fun_app$c(v1, v8) = v9 & % 55.67/8.39 | Nat$(v8))))) & ! [v0: Nat$] : ! [v1: Nat_bool_fun$] : ! % 55.67/8.39 | [v2: int] : ! [v3: int] : (v3 = 0 | ~ (fun_app$k(of_nat$, v0) = v2) % 55.67/8.39 | | ~ (fun_app$c(v1, all_413_0) = v3) | ~ Nat_bool_fun$(v1) | ~ % 55.67/8.39 | Nat$(v0) | ? [v4: Nat$] : ? [v5: int] : ? [v6: int] : ( ~ (v6 = % 55.67/8.39 | 0) & $lesseq(v5, v2) & fun_app$k(of_nat$, v4) = v5 & % 55.67/8.39 | fun_app$c(v1, v4) = v6 & Nat$(v4))) % 55.67/8.39 | % 55.67/8.39 | ALPHA: (114) implies: % 55.67/8.39 | (115) nat$(0) = all_413_0 % 55.67/8.39 | % 55.67/8.39 | DELTA: instantiating (18) with fresh symbol all_416_0 gives: % 55.67/8.40 | (116) nat$(0) = all_416_0 & Nat$(all_416_0) & ! [v0: % 55.67/8.40 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.40 | [v2: int] : (v2 = 0 | ~ (gF_advice_congruent_axioms$(v0, v1) = v2) | % 55.67/8.40 | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? % 55.67/8.40 | [v3: A_ltln$] : ? [v4: A_ltln$] : ? [v5: A_ltln_set$] : ? [v6: % 55.67/8.40 | A_ltln_bool_fun$] : ? [v7: int] : ? [v8: A_ltln$] : ? [v9: % 55.67/8.40 | A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: A_ltln$] : ? % 55.67/8.40 | [v12: A_ltln$] : ? [v13: int] : ? [v14: Nat_a_set_fun$] : ? % 55.67/8.40 | [v15: A_ltln$] : ? [v16: A_ltln_set$] : ? [v17: A_ltln$] : ? % 55.67/8.40 | [v18: A_ltln$] : ? [v19: int] : ? [v20: Nat_a_set_fun$] : ? % 55.67/8.40 | [v21: A_ltln$] : ? [v22: A_ltln_set$] : ? [v23: A_ltln$] : ? % 55.67/8.40 | [v24: int] : ? [v25: A_ltln$] : ? [v26: A_ltln$] : ? [v27: int] % 55.67/8.40 | : ? [v28: A_ltln$] : ? [v29: A_ltln_bool_fun$] : ? [v30: % 55.67/8.40 | A_ltln$] : ? [v31: int] : (Nat_a_set_fun$(v20) & % 55.67/8.40 | Nat_a_set_fun$(v14) & A_ltln$(v28) & A_ltln$(v21) & A_ltln$(v15) % 55.67/8.40 | & A_ltln$(v4) & A_ltln$(v3) & A_ltln_set$(v22) & A_ltln_set$(v16) % 55.67/8.40 | & A_ltln_set$(v5) & ((v24 = 0 & ~ (v27 = 0) & fun_app$i(v1, v21) % 55.67/8.40 | = v25 & gF_advice$(v25, v22) = v26 & gF_advice$(v21, v22) = % 55.67/8.40 | v23 & semantics_ltln$(v20, v26) = v27 & semantics_ltln$(v20, % 55.67/8.40 | v23) = 0 & A_ltln$(v26) & A_ltln$(v25) & A_ltln$(v23)) | % 55.67/8.40 | (v19 = 0 & fun_app$i(v1, v15) = v17 & gF_advice$(v17, v16) = % 55.67/8.40 | v18 & semantics_ltln$(v14, v18) = 0 & A_ltln$(v18) & % 55.67/8.40 | A_ltln$(v17) & ! [v32: Nat$] : ! [v33: A_set_list$] : ( ~ % 55.67/8.40 | (subsequence$(v14, all_416_0, v32) = v33) | ~ Nat$(v32) | % 55.67/8.40 | ? [v34: Nat_a_set_fun$] : ? [v35: A_ltln$] : ? [v36: % 55.67/8.40 | A_ltln$] : ? [v37: int] : ( ~ (v37 = 0) & % 55.67/8.40 | foldl$(af_letter$, v15, v33) = v35 & suffix$(v32, v14) = % 55.67/8.40 | v34 & gF_advice$(v35, v16) = v36 & semantics_ltln$(v34, % 55.67/8.40 | v36) = v37 & Nat_a_set_fun$(v34) & A_ltln$(v36) & % 55.67/8.40 | A_ltln$(v35))) & ! [v32: Nat$] : ! [v33: % 55.67/8.40 | Nat_a_set_fun$] : ( ~ (suffix$(v32, v14) = v33) | ~ % 55.67/8.40 | Nat$(v32) | ? [v34: A_set_list$] : ? [v35: A_ltln$] : ? % 55.67/8.40 | [v36: A_ltln$] : ? [v37: int] : ( ~ (v37 = 0) & % 55.67/8.40 | subsequence$(v14, all_416_0, v32) = v34 & % 55.67/8.40 | foldl$(af_letter$, v15, v34) = v35 & gF_advice$(v35, v16) % 55.67/8.40 | = v36 & semantics_ltln$(v33, v36) = v37 & A_ltln$(v36) & % 55.67/8.40 | A_ltln$(v35) & A_set_list$(v34)))) | (v7 = 0 & ~ (v13 = % 55.67/8.40 | 0) & fun_app$m(v0, v9) = v10 & fun_app$m(v0, v3) = v6 & % 55.67/8.40 | fun_app$l(v10, v12) = v13 & fun_app$l(v6, v4) = 0 & % 55.67/8.40 | fun_app$i(v1, v4) = v11 & fun_app$i(v1, v3) = v8 & % 55.67/8.40 | gF_advice$(v11, v5) = v12 & gF_advice$(v8, v5) = v9 & % 55.67/8.40 | A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v9) & A_ltln$(v8) & % 55.67/8.40 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v6)) | ( ~ (v31 = 0) % 55.67/8.40 | & fun_app$m(v0, v28) = v29 & fun_app$l(v29, v30) = v31 & % 55.67/8.40 | fun_app$i(v1, v28) = v30 & A_ltln$(v30) & % 55.67/8.40 | A_ltln_bool_fun$(v29))))) % 55.67/8.40 | % 55.67/8.40 | ALPHA: (116) implies: % 55.67/8.40 | (117) nat$(0) = all_416_0 % 55.67/8.40 | % 55.67/8.40 | DELTA: instantiating (21) with fresh symbol all_419_0 gives: % 55.67/8.40 | (118) nat$(0) = all_419_0 & Nat$(all_419_0) & ! [v0: Nat_nat_fun$] : ! % 55.67/8.40 | [v1: Nat$] : ! [v2: int] : ( ~ (idx_sequence$(v0) = 0) | ~ % 55.67/8.40 | (fun_app$k(of_nat$, v1) = v2) | ~ Nat$(v1) | ~ Nat_nat_fun$(v0) | % 55.67/8.40 | ? [v3: Nat$] : ? [v4: Nat$] : ? [v5: int] : ? [v6: Nat$] : ? % 55.67/8.40 | [v7: int] : ($lesseq(1, $difference(v5, v7)) & fun_app$k(of_nat$, % 55.67/8.40 | v6) = v7 & fun_app$k(of_nat$, v4) = v5 & nat$($sum(v2, 1)) = v3 % 55.67/8.40 | & fun_app$e(v0, v3) = v4 & fun_app$e(v0, v1) = v6 & Nat$(v6) & % 55.67/8.40 | Nat$(v4) & Nat$(v3))) & ! [v0: Nat_nat_fun$] : ! [v1: Nat$] : % 55.67/8.40 | ! [v2: Nat$] : ( ~ (idx_sequence$(v0) = 0) | ~ (fun_app$e(v0, v1) = % 55.67/8.40 | v2) | ~ Nat$(v1) | ~ Nat_nat_fun$(v0) | ? [v3: int] : ? [v4: % 55.67/8.40 | Nat$] : ? [v5: Nat$] : ? [v6: int] : ? [v7: int] : ($lesseq(1, % 55.67/8.40 | $difference(v6, v7)) & fun_app$k(of_nat$, v5) = v6 & % 55.67/8.40 | fun_app$k(of_nat$, v2) = v7 & fun_app$k(of_nat$, v1) = v3 & % 55.67/8.40 | nat$($sum(v3, 1)) = v4 & fun_app$e(v0, v4) = v5 & Nat$(v5) & % 55.67/8.40 | Nat$(v4))) & ! [v0: Nat_nat_fun$] : ! [v1: int] : (v1 = 0 | ~ % 55.67/8.40 | (idx_sequence$(v0) = v1) | ~ Nat_nat_fun$(v0) | ? [v2: Nat$] : ? % 55.67/8.40 | [v3: int] : ? [v4: Nat$] : ? [v5: int] : ? [v6: Nat$] : ? [v7: % 55.67/8.40 | Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : (Nat$(v4) % 55.67/8.40 | & (( ~ (v3 = 0) & fun_app$k(of_nat$, v2) = v3 & fun_app$e(v0, % 55.67/8.40 | all_419_0) = v2 & Nat$(v2)) | ($lesseq(v8, v10) & % 55.67/8.40 | fun_app$k(of_nat$, v9) = v10 & fun_app$k(of_nat$, v7) = v8 & % 55.67/8.40 | fun_app$k(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = v6 & % 55.67/8.40 | fun_app$e(v0, v6) = v7 & fun_app$e(v0, v4) = v9 & Nat$(v9) & % 55.67/8.40 | Nat$(v7) & Nat$(v6))))) & ! [v0: Nat_nat_fun$] : ! [v1: % 55.67/8.40 | Nat$] : ( ~ (fun_app$e(v0, all_419_0) = v1) | ~ Nat_nat_fun$(v0) | % 55.67/8.40 | ? [v2: int] : ? [v3: any] : ? [v4: Nat$] : ? [v5: int] : ? % 55.67/8.40 | [v6: Nat$] : ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? % 55.67/8.40 | [v10: int] : (Nat$(v4) & (($lesseq(v8, v10) & fun_app$k(of_nat$, % 55.67/8.40 | v9) = v10 & fun_app$k(of_nat$, v7) = v8 & % 55.67/8.40 | fun_app$k(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = v6 & % 55.67/8.40 | fun_app$e(v0, v6) = v7 & fun_app$e(v0, v4) = v9 & Nat$(v9) & % 55.67/8.40 | Nat$(v7) & Nat$(v6)) | (idx_sequence$(v0) = v3 & % 55.67/8.40 | fun_app$k(of_nat$, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))))) & ! % 55.67/8.40 | [v0: Nat_nat_fun$] : ! [v1: Nat$] : ( ~ (fun_app$e(v0, all_419_0) = % 55.67/8.40 | v1) | ~ Nat_nat_fun$(v0) | ? [v2: any] : ? [v3: int] : % 55.67/8.40 | (idx_sequence$(v0) = v2 & fun_app$k(of_nat$, v1) = v3 & ( ~ (v2 = % 55.67/8.40 | 0) | (v3 = 0 & ! [v4: Nat$] : ! [v5: int] : ( ~ % 55.67/8.40 | (fun_app$k(of_nat$, v4) = v5) | ~ Nat$(v4) | ? [v6: Nat$] % 55.67/8.40 | : ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: % 55.67/8.40 | int] : ($lesseq(1, $difference(v8, v10)) & % 55.67/8.40 | fun_app$k(of_nat$, v9) = v10 & fun_app$k(of_nat$, v7) = % 55.67/8.40 | v8 & nat$($sum(v5, 1)) = v6 & fun_app$e(v0, v6) = v7 & % 55.67/8.40 | fun_app$e(v0, v4) = v9 & Nat$(v9) & Nat$(v7) & Nat$(v6))) % 55.67/8.40 | & ! [v4: Nat$] : ! [v5: Nat$] : ( ~ (fun_app$e(v0, v4) = % 55.67/8.40 | v5) | ~ Nat$(v4) | ? [v6: int] : ? [v7: Nat$] : ? % 55.67/8.40 | [v8: Nat$] : ? [v9: int] : ? [v10: int] : ($lesseq(1, % 55.67/8.40 | $difference(v9, v10)) & fun_app$k(of_nat$, v8) = v9 & % 55.67/8.40 | fun_app$k(of_nat$, v5) = v10 & fun_app$k(of_nat$, v4) = % 55.67/8.40 | v6 & nat$($sum(v6, 1)) = v7 & fun_app$e(v0, v7) = v8 & % 55.67/8.40 | Nat$(v8) & Nat$(v7))))))) & ! [v0: Nat_nat_fun$] : ( ~ % 55.67/8.40 | (idx_sequence$(v0) = 0) | ~ Nat_nat_fun$(v0) | ? [v1: Nat$] : % 55.67/8.40 | (fun_app$k(of_nat$, v1) = 0 & fun_app$e(v0, all_419_0) = v1 & % 55.67/8.40 | Nat$(v1))) % 55.67/8.40 | % 55.67/8.40 | ALPHA: (118) implies: % 55.67/8.40 | (119) nat$(0) = all_419_0 % 55.67/8.40 | % 55.67/8.40 | DELTA: instantiating (17) with fresh symbol all_422_0 gives: % 55.67/8.41 | (120) nat$(0) = all_422_0 & Nat$(all_422_0) & ! [v0: % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: A_ltln$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! [v5: % 55.67/8.41 | A_ltln$] : ! [v6: A_ltln$] : ! [v7: A_ltln_bool_fun$] : ! [v8: % 55.67/8.41 | A_ltln$] : ! [v9: A_ltln$] : ! [v10: int] : (v10 = 0 | ~ % 55.67/8.41 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$m(v0, v6) = % 55.67/8.41 | v7) | ~ (fun_app$l(v7, v9) = v10) | ~ (fun_app$i(v1, v3) = v8) % 55.67/8.41 | | ~ (fun_app$i(v1, v2) = v5) | ~ (gF_advice$(v8, v4) = v9) | ~ % 55.67/8.41 | (gF_advice$(v5, v4) = v6) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ % 55.67/8.41 | A_ltln$(v3) | ~ A_ltln$(v2) | ~ A_ltln_set$(v4) | ~ % 55.67/8.41 | A_ltln_a_ltln_fun$(v1) | ? [v11: A_ltln_bool_fun$] : ? [v12: int] % 55.67/8.41 | : ( ~ (v12 = 0) & fun_app$m(v0, v2) = v11 & fun_app$l(v11, v3) = % 55.67/8.41 | v12 & A_ltln_bool_fun$(v11))) & ! [v0: % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! % 55.67/8.41 | [v5: A_ltln$] : ! [v6: A_ltln$] : ! [v7: int] : (v7 = 0 | ~ % 55.67/8.41 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$i(v1, v3) = % 55.67/8.41 | v5) | ~ (gF_advice$(v5, v4) = v6) | ~ (semantics_ltln$(v2, v6) % 55.67/8.41 | = v7) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ % 55.67/8.41 | Nat_a_set_fun$(v2) | ~ A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ % 55.67/8.41 | A_ltln_a_ltln_fun$(v1) | ? [v8: A_ltln$] : ? [v9: int] : ( ~ (v9 % 55.67/8.41 | = 0) & gF_advice$(v3, v4) = v8 & semantics_ltln$(v2, v8) = v9 & % 55.67/8.41 | A_ltln$(v8))) & ! [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: % 55.67/8.41 | A_ltln_a_ltln_fun$] : ! [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : % 55.67/8.41 | ! [v4: A_ltln_set$] : ! [v5: A_ltln$] : ! [v6: A_ltln$] : ( ~ % 55.67/8.41 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$i(v1, v3) = % 55.67/8.41 | v5) | ~ (gF_advice$(v5, v4) = v6) | ~ (semantics_ltln$(v2, v6) % 55.67/8.41 | = 0) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) % 55.67/8.41 | | ~ A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | % 55.67/8.41 | ? [v7: Nat$] : ? [v8: Nat_a_set_fun$] : ? [v9: A_set_list$] : ? % 55.67/8.41 | [v10: A_ltln$] : ? [v11: A_ltln$] : (subsequence$(v2, all_422_0, % 55.67/8.41 | v7) = v9 & foldl$(af_letter$, v3, v9) = v10 & suffix$(v7, v2) = % 55.67/8.41 | v8 & gF_advice$(v10, v4) = v11 & semantics_ltln$(v8, v11) = 0 & % 55.67/8.41 | Nat_a_set_fun$(v8) & A_ltln$(v11) & A_ltln$(v10) & % 55.67/8.41 | A_set_list$(v9) & Nat$(v7))) & ! [v0: % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: Nat_a_set_fun$] : ! [v3: A_ltln$] : ! [v4: A_ltln_set$] : ! % 55.67/8.41 | [v5: A_ltln$] : ( ~ (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ % 55.67/8.41 | (gF_advice$(v3, v4) = v5) | ~ (semantics_ltln$(v2, v5) = 0) | ~ % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$(v0) | ~ Nat_a_set_fun$(v2) | ~ % 55.67/8.41 | A_ltln$(v3) | ~ A_ltln_set$(v4) | ~ A_ltln_a_ltln_fun$(v1) | ? % 55.67/8.41 | [v6: A_ltln$] : ? [v7: A_ltln$] : (fun_app$i(v1, v3) = v6 & % 55.67/8.41 | gF_advice$(v6, v4) = v7 & semantics_ltln$(v2, v7) = 0 & % 55.67/8.41 | A_ltln$(v7) & A_ltln$(v6))) & ! [v0: % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: A_ltln$] : ! [v3: A_ltln_bool_fun$] : ( ~ % 55.67/8.41 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$m(v0, v2) = % 55.67/8.41 | v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) | ~ % 55.67/8.41 | A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln$] : (fun_app$l(v3, v4) = 0 % 55.67/8.41 | & fun_app$i(v1, v2) = v4 & A_ltln$(v4))) & ! [v0: % 55.67/8.41 | A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: A_ltln$] : ! [v3: A_ltln$] : ( ~ % 55.67/8.41 | (gF_advice_congruent_axioms$(v0, v1) = 0) | ~ (fun_app$i(v1, v2) = % 55.67/8.41 | v3) | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln$(v2) | ~ % 55.67/8.41 | A_ltln_a_ltln_fun$(v1) | ? [v4: A_ltln_bool_fun$] : (fun_app$m(v0, % 55.67/8.41 | v2) = v4 & fun_app$l(v4, v3) = 0 & A_ltln_bool_fun$(v4))) & ! % 55.67/8.41 | [v0: A_ltln_a_ltln_bool_fun_fun$] : ! [v1: A_ltln_a_ltln_fun$] : ! % 55.67/8.41 | [v2: int] : (v2 = 0 | ~ (gF_advice_congruent_axioms$(v0, v1) = v2) | % 55.67/8.41 | ~ A_ltln_a_ltln_bool_fun_fun$(v0) | ~ A_ltln_a_ltln_fun$(v1) | ? % 55.67/8.41 | [v3: A_ltln$] : ? [v4: A_ltln$] : ? [v5: A_ltln_set$] : ? [v6: % 55.67/8.41 | A_ltln_bool_fun$] : ? [v7: int] : ? [v8: A_ltln$] : ? [v9: % 55.67/8.41 | A_ltln$] : ? [v10: A_ltln_bool_fun$] : ? [v11: A_ltln$] : ? % 55.67/8.41 | [v12: A_ltln$] : ? [v13: int] : ? [v14: Nat_a_set_fun$] : ? % 55.67/8.41 | [v15: A_ltln$] : ? [v16: A_ltln_set$] : ? [v17: A_ltln$] : ? % 55.67/8.41 | [v18: A_ltln$] : ? [v19: int] : ? [v20: Nat_a_set_fun$] : ? % 55.67/8.41 | [v21: A_ltln$] : ? [v22: A_ltln_set$] : ? [v23: A_ltln$] : ? % 55.67/8.41 | [v24: int] : ? [v25: A_ltln$] : ? [v26: A_ltln$] : ? [v27: int] % 55.67/8.41 | : ? [v28: A_ltln$] : ? [v29: A_ltln_bool_fun$] : ? [v30: % 55.67/8.41 | A_ltln$] : ? [v31: int] : (Nat_a_set_fun$(v20) & % 55.67/8.41 | Nat_a_set_fun$(v14) & A_ltln$(v28) & A_ltln$(v21) & A_ltln$(v15) % 55.67/8.41 | & A_ltln$(v4) & A_ltln$(v3) & A_ltln_set$(v22) & A_ltln_set$(v16) % 55.67/8.41 | & A_ltln_set$(v5) & ((v24 = 0 & ~ (v27 = 0) & fun_app$i(v1, v21) % 55.67/8.41 | = v25 & gF_advice$(v25, v22) = v26 & gF_advice$(v21, v22) = % 55.67/8.41 | v23 & semantics_ltln$(v20, v26) = v27 & semantics_ltln$(v20, % 55.67/8.41 | v23) = 0 & A_ltln$(v26) & A_ltln$(v25) & A_ltln$(v23)) | % 55.67/8.41 | (v19 = 0 & fun_app$i(v1, v15) = v17 & gF_advice$(v17, v16) = % 55.67/8.41 | v18 & semantics_ltln$(v14, v18) = 0 & A_ltln$(v18) & % 55.67/8.41 | A_ltln$(v17) & ! [v32: Nat$] : ! [v33: A_set_list$] : ( ~ % 55.67/8.41 | (subsequence$(v14, all_422_0, v32) = v33) | ~ Nat$(v32) | % 55.67/8.41 | ? [v34: Nat_a_set_fun$] : ? [v35: A_ltln$] : ? [v36: % 55.67/8.41 | A_ltln$] : ? [v37: int] : ( ~ (v37 = 0) & % 55.67/8.41 | foldl$(af_letter$, v15, v33) = v35 & suffix$(v32, v14) = % 55.67/8.41 | v34 & gF_advice$(v35, v16) = v36 & semantics_ltln$(v34, % 55.67/8.41 | v36) = v37 & Nat_a_set_fun$(v34) & A_ltln$(v36) & % 55.67/8.41 | A_ltln$(v35))) & ! [v32: Nat$] : ! [v33: % 55.67/8.41 | Nat_a_set_fun$] : ( ~ (suffix$(v32, v14) = v33) | ~ % 55.67/8.41 | Nat$(v32) | ? [v34: A_set_list$] : ? [v35: A_ltln$] : ? % 55.67/8.41 | [v36: A_ltln$] : ? [v37: int] : ( ~ (v37 = 0) & % 55.67/8.41 | subsequence$(v14, all_422_0, v32) = v34 & % 55.67/8.41 | foldl$(af_letter$, v15, v34) = v35 & gF_advice$(v35, v16) % 55.67/8.41 | = v36 & semantics_ltln$(v33, v36) = v37 & A_ltln$(v36) & % 55.67/8.41 | A_ltln$(v35) & A_set_list$(v34)))) | (v7 = 0 & ~ (v13 = % 55.67/8.41 | 0) & fun_app$m(v0, v9) = v10 & fun_app$m(v0, v3) = v6 & % 55.67/8.41 | fun_app$l(v10, v12) = v13 & fun_app$l(v6, v4) = 0 & % 55.67/8.41 | fun_app$i(v1, v4) = v11 & fun_app$i(v1, v3) = v8 & % 55.67/8.41 | gF_advice$(v11, v5) = v12 & gF_advice$(v8, v5) = v9 & % 55.67/8.41 | A_ltln$(v12) & A_ltln$(v11) & A_ltln$(v9) & A_ltln$(v8) & % 55.67/8.41 | A_ltln_bool_fun$(v10) & A_ltln_bool_fun$(v6)) | ( ~ (v31 = 0) % 55.67/8.41 | & fun_app$m(v0, v28) = v29 & fun_app$l(v29, v30) = v31 & % 55.67/8.41 | fun_app$i(v1, v28) = v30 & A_ltln$(v30) & % 55.67/8.41 | A_ltln_bool_fun$(v29))))) % 55.67/8.41 | % 55.67/8.41 | ALPHA: (120) implies: % 55.67/8.41 | (121) nat$(0) = all_422_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (38) with all_322_2, all_352_6, phi$, next_ltln$, % 55.67/8.41 | simplifying with (47), (70) gives: % 55.67/8.41 | (122) all_352_6 = all_322_2 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_328_1, all_334_0, 0, simplifying with % 55.67/8.41 | (50), (56) gives: % 55.67/8.41 | (123) all_334_0 = all_328_1 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_334_0, all_337_0, 0, simplifying with % 55.67/8.41 | (56), (58) gives: % 55.67/8.41 | (124) all_337_0 = all_334_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_352_4, all_372_0, 0, simplifying with % 55.67/8.41 | (73), (84) gives: % 55.67/8.41 | (125) all_372_0 = all_352_4 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_372_0, all_375_4, 0, simplifying with % 55.67/8.41 | (84), (89) gives: % 55.67/8.41 | (126) all_375_4 = all_372_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_375_4, all_377_0, 0, simplifying with % 55.67/8.41 | (89), (93) gives: % 55.67/8.41 | (127) all_377_0 = all_375_4 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_372_0, all_380_0, 0, simplifying with % 55.67/8.41 | (84), (95) gives: % 55.67/8.41 | (128) all_380_0 = all_372_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_377_0, all_383_0, 0, simplifying with % 55.67/8.41 | (93), (97) gives: % 55.67/8.41 | (129) all_383_0 = all_377_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_354_0, all_404_0, 0, simplifying with % 55.67/8.41 | (78), (109) gives: % 55.67/8.41 | (130) all_404_0 = all_354_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_352_4, all_404_0, 0, simplifying with % 55.67/8.41 | (73), (109) gives: % 55.67/8.41 | (131) all_404_0 = all_352_4 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_346_0, all_404_0, 0, simplifying with % 55.67/8.41 | (62), (109) gives: % 55.67/8.41 | (132) all_404_0 = all_346_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_380_0, all_407_0, 0, simplifying with % 55.67/8.41 | (95), (111) gives: % 55.67/8.41 | (133) all_407_0 = all_380_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_369_0, all_407_0, 0, simplifying with % 55.67/8.41 | (82), (111) gives: % 55.67/8.41 | (134) all_407_0 = all_369_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_410_0, all_413_0, 0, simplifying with % 55.67/8.41 | (113), (115) gives: % 55.67/8.41 | (135) all_413_0 = all_410_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_389_0, all_413_0, 0, simplifying with % 55.67/8.41 | (101), (115) gives: % 55.67/8.41 | (136) all_413_0 = all_389_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_308_0, all_413_0, 0, simplifying with % 55.67/8.41 | (43), (115) gives: % 55.67/8.41 | (137) all_413_0 = all_308_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_404_0, all_416_0, 0, simplifying with % 55.67/8.41 | (109), (117) gives: % 55.67/8.41 | (138) all_416_0 = all_404_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_395_3, all_416_0, 0, simplifying with % 55.67/8.41 | (105), (117) gives: % 55.67/8.41 | (139) all_416_0 = all_395_3 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_349_0, all_416_0, 0, simplifying with % 55.67/8.41 | (64), (117) gives: % 55.67/8.41 | (140) all_416_0 = all_349_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_346_0, all_419_0, 0, simplifying with % 55.67/8.41 | (62), (119) gives: % 55.67/8.41 | (141) all_419_0 = all_346_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_343_0, all_419_0, 0, simplifying with % 55.67/8.41 | (60), (119) gives: % 55.67/8.41 | (142) all_419_0 = all_343_0 % 55.67/8.41 | % 55.67/8.41 | GROUND_INST: instantiating (35) with all_337_0, all_419_0, 0, simplifying with % 55.67/8.41 | (58), (119) gives: % 55.67/8.42 | (143) all_419_0 = all_337_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_392_0, all_422_0, 0, simplifying with % 55.67/8.42 | (103), (121) gives: % 55.67/8.42 | (144) all_422_0 = all_392_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_389_0, all_422_0, 0, simplifying with % 55.67/8.42 | (101), (121) gives: % 55.67/8.42 | (145) all_422_0 = all_389_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_386_0, all_422_0, 0, simplifying with % 55.67/8.42 | (99), (121) gives: % 55.67/8.42 | (146) all_422_0 = all_386_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_383_0, all_422_0, 0, simplifying with % 55.67/8.42 | (97), (121) gives: % 55.67/8.42 | (147) all_422_0 = all_383_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_328_0, all_363_0, 1, simplifying with % 55.67/8.42 | (51), (80) gives: % 55.67/8.42 | (148) all_363_0 = all_328_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_363_0, all_375_7, 1, simplifying with % 55.67/8.42 | (80), (90) gives: % 55.67/8.42 | (149) all_375_7 = all_363_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_352_8, all_375_7, 1, simplifying with % 55.67/8.42 | (74), (90) gives: % 55.67/8.42 | (150) all_375_7 = all_352_8 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_363_0, all_398_0, 1, simplifying with % 55.67/8.42 | (80), (107) gives: % 55.67/8.42 | (151) all_398_0 = all_363_0 % 55.67/8.42 | % 55.67/8.42 | GROUND_INST: instantiating (35) with all_331_0, all_398_0, 1, simplifying with % 55.67/8.42 | (54), (107) gives: % 55.67/8.42 | (152) all_398_0 = all_331_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (144), (147) imply: % 55.67/8.42 | (153) all_392_0 = all_383_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (144), (146) imply: % 55.67/8.42 | (154) all_392_0 = all_386_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (144), (145) imply: % 55.67/8.42 | (155) all_392_0 = all_389_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (142), (143) imply: % 55.67/8.42 | (156) all_343_0 = all_337_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (141), (142) imply: % 55.67/8.42 | (157) all_346_0 = all_343_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (157) implies: % 55.67/8.42 | (158) all_346_0 = all_343_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (139), (140) imply: % 55.67/8.42 | (159) all_395_3 = all_349_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (138), (139) imply: % 55.67/8.42 | (160) all_404_0 = all_395_3 % 55.67/8.42 | % 55.67/8.42 | SIMP: (160) implies: % 55.67/8.42 | (161) all_404_0 = all_395_3 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (135), (137) imply: % 55.67/8.42 | (162) all_410_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (135), (136) imply: % 55.67/8.42 | (163) all_410_0 = all_389_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (162), (163) imply: % 55.67/8.42 | (164) all_389_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (164) implies: % 55.67/8.42 | (165) all_389_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (133), (134) imply: % 55.67/8.42 | (166) all_380_0 = all_369_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (166) implies: % 55.67/8.42 | (167) all_380_0 = all_369_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (130), (161) imply: % 55.67/8.42 | (168) all_395_3 = all_354_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (168) implies: % 55.67/8.42 | (169) all_395_3 = all_354_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (130), (132) imply: % 55.67/8.42 | (170) all_354_0 = all_346_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (130), (131) imply: % 55.67/8.42 | (171) all_354_0 = all_352_4 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (151), (152) imply: % 55.67/8.42 | (172) all_363_0 = all_331_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (172) implies: % 55.67/8.42 | (173) all_363_0 = all_331_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (159), (169) imply: % 55.67/8.42 | (174) all_354_0 = all_349_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (174) implies: % 55.67/8.42 | (175) all_354_0 = all_349_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (154), (155) imply: % 55.67/8.42 | (176) all_389_0 = all_386_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (176) implies: % 55.67/8.42 | (177) all_389_0 = all_386_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (153), (154) imply: % 55.67/8.42 | (178) all_386_0 = all_383_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (165), (177) imply: % 55.67/8.42 | (179) all_386_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (179) implies: % 55.67/8.42 | (180) all_386_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (178), (180) imply: % 55.67/8.42 | (181) all_383_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (181) implies: % 55.67/8.42 | (182) all_383_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (129), (182) imply: % 55.67/8.42 | (183) all_377_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (183) implies: % 55.67/8.42 | (184) all_377_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (128), (167) imply: % 55.67/8.42 | (185) all_372_0 = all_369_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (185) implies: % 55.67/8.42 | (186) all_372_0 = all_369_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (127), (184) imply: % 55.67/8.42 | (187) all_375_4 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (187) implies: % 55.67/8.42 | (188) all_375_4 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (126), (188) imply: % 55.67/8.42 | (189) all_372_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (189) implies: % 55.67/8.42 | (190) all_372_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (149), (150) imply: % 55.67/8.42 | (191) all_363_0 = all_352_8 % 55.67/8.42 | % 55.67/8.42 | SIMP: (191) implies: % 55.67/8.42 | (192) all_363_0 = all_352_8 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (125), (186) imply: % 55.67/8.42 | (193) all_369_0 = all_352_4 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (186), (190) imply: % 55.67/8.42 | (194) all_369_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (193), (194) imply: % 55.67/8.42 | (195) all_352_4 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (195) implies: % 55.67/8.42 | (196) all_352_4 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (148), (192) imply: % 55.67/8.42 | (197) all_352_8 = all_328_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (173), (192) imply: % 55.67/8.42 | (198) all_352_8 = all_331_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (171), (175) imply: % 55.67/8.42 | (199) all_352_4 = all_349_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (199) implies: % 55.67/8.42 | (200) all_352_4 = all_349_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (170), (175) imply: % 55.67/8.42 | (201) all_349_0 = all_346_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (196), (200) imply: % 55.67/8.42 | (202) all_349_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (202) implies: % 55.67/8.42 | (203) all_349_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (197), (198) imply: % 55.67/8.42 | (204) all_331_0 = all_328_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (201), (203) imply: % 55.67/8.42 | (205) all_346_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (205) implies: % 55.67/8.42 | (206) all_346_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (158), (206) imply: % 55.67/8.42 | (207) all_343_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (207) implies: % 55.67/8.42 | (208) all_343_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (156), (208) imply: % 55.67/8.42 | (209) all_337_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (209) implies: % 55.67/8.42 | (210) all_337_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (124), (210) imply: % 55.67/8.42 | (211) all_334_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (211) implies: % 55.67/8.42 | (212) all_334_0 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (123), (212) imply: % 55.67/8.42 | (213) all_328_1 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | SIMP: (213) implies: % 55.67/8.42 | (214) all_328_1 = all_308_0 % 55.67/8.42 | % 55.67/8.42 | COMBINE_EQS: (150), (197) imply: % 55.67/8.42 | (215) all_375_7 = all_328_0 % 55.67/8.42 | % 55.67/8.42 | REDUCE: (91), (215) imply: % 55.67/8.43 | (216) suffix$(all_328_0, w$) = all_375_6 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (76), (197) imply: % 55.67/8.43 | (217) suffix$(all_328_0, w$) = all_352_7 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (75), (122) imply: % 55.67/8.43 | (218) fun_app$h(af_letter$, all_322_2) = all_352_5 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (88), (188) imply: % 55.67/8.43 | (219) fun_app$j(w$, all_308_0) = all_375_3 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (72), (196) imply: % 55.67/8.43 | (220) fun_app$j(w$, all_308_0) = all_352_3 % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (39) with all_352_3, all_375_3, all_308_0, w$, % 55.67/8.43 | simplifying with (219), (220) gives: % 55.67/8.43 | (221) all_375_3 = all_352_3 % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (40) with all_352_7, all_375_6, w$, all_328_0, % 55.67/8.43 | simplifying with (216), (217) gives: % 55.67/8.43 | (222) all_375_6 = all_352_7 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (87), (222) imply: % 55.67/8.43 | (223) Nat_a_set_fun$(all_352_7) % 55.67/8.43 | % 55.67/8.43 | REDUCE: (86), (221) imply: % 55.67/8.43 | (224) A_set$(all_352_3) % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (4) with all_352_2, x$, all_352_1, simplifying with % 55.67/8.43 | (31), (67), (69) gives: % 55.67/8.43 | (225) ? [v0: A_ltln$] : ? [v1: A_ltln$] : (fun_app$i(next_ltln$, % 55.67/8.43 | all_352_1) = v1 & fun_app$i(next_ltln$, all_352_2) = v0 & % 55.67/8.43 | gF_advice$(v0, x$) = v1 & A_ltln$(v1) & A_ltln$(v0)) % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (6) with phi$, all_322_2, simplifying with (32), % 55.67/8.43 | (47) gives: % 55.67/8.43 | (226) fun_app$i(unf$, all_322_2) = all_322_2 & A_ltln$(all_322_2) % 55.67/8.43 | % 55.67/8.43 | ALPHA: (226) implies: % 55.67/8.43 | (227) A_ltln$(all_322_2) % 55.67/8.43 | (228) fun_app$i(unf$, all_322_2) = all_322_2 % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (7) with all_352_3, all_352_7, all_322_2, x$, % 55.67/8.43 | all_352_5, all_352_2, all_352_1, all_352_0, simplifying with % 55.67/8.43 | (31), (68), (69), (71), (218), (223), (224), (227) gives: % 55.67/8.43 | (229) all_352_0 = 0 | ? [v0: Nat_a_set_fun$] : ? [v1: A_ltln$] : ? [v2: % 55.67/8.43 | int] : ( ~ (v2 = 0) & build$(all_352_3, all_352_7) = v0 & % 55.67/8.43 | gF_advice$(all_322_2, x$) = v1 & semantics_ltln$(v0, v1) = v2 & % 55.67/8.43 | Nat_a_set_fun$(v0) & A_ltln$(v1)) % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (5) with phi$, all_352_3, all_322_2, all_352_5, % 55.67/8.43 | all_352_2, simplifying with (32), (47), (71), (218), (224) gives: % 55.67/8.43 | (230) all_352_2 = phi$ % 55.67/8.43 | % 55.67/8.43 | GROUND_INST: instantiating (52) with w$, all_352_7, simplifying with (33), % 55.67/8.43 | (217) gives: % 55.67/8.43 | (231) ? [v0: A_set$] : (build$(v0, all_352_7) = w$ & fun_app$j(w$, % 55.67/8.43 | all_328_1) = v0 & A_set$(v0)) % 55.67/8.43 | % 55.67/8.43 | DELTA: instantiating (231) with fresh symbol all_464_0 gives: % 55.67/8.43 | (232) build$(all_464_0, all_352_7) = w$ & fun_app$j(w$, all_328_1) = % 55.67/8.43 | all_464_0 & A_set$(all_464_0) % 55.67/8.43 | % 55.67/8.43 | ALPHA: (232) implies: % 55.67/8.43 | (233) fun_app$j(w$, all_328_1) = all_464_0 % 55.67/8.43 | (234) build$(all_464_0, all_352_7) = w$ % 55.67/8.43 | % 55.67/8.43 | DELTA: instantiating (225) with fresh symbols all_486_0, all_486_1 gives: % 55.67/8.43 | (235) fun_app$i(next_ltln$, all_352_1) = all_486_0 & fun_app$i(next_ltln$, % 55.67/8.43 | all_352_2) = all_486_1 & gF_advice$(all_486_1, x$) = all_486_0 & % 55.67/8.43 | A_ltln$(all_486_0) & A_ltln$(all_486_1) % 55.67/8.43 | % 55.67/8.43 | ALPHA: (235) implies: % 55.67/8.43 | (236) gF_advice$(all_486_1, x$) = all_486_0 % 55.67/8.43 | (237) fun_app$i(next_ltln$, all_352_2) = all_486_1 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (214), (233) imply: % 55.67/8.43 | (238) fun_app$j(w$, all_308_0) = all_464_0 % 55.67/8.43 | % 55.67/8.43 | REDUCE: (230), (237) imply: % 55.67/8.43 | (239) fun_app$i(next_ltln$, phi$) = all_486_1 % 55.67/8.43 | % 55.67/8.43 | BETA: splitting (229) gives: % 55.67/8.43 | % 55.67/8.43 | Case 1: % 55.67/8.43 | | % 55.67/8.43 | | (240) all_352_0 = 0 % 55.67/8.43 | | % 55.67/8.43 | | REDUCE: (66), (240) imply: % 55.67/8.43 | | (241) $false % 55.67/8.43 | | % 55.67/8.43 | | CLOSE: (241) is inconsistent. % 55.67/8.43 | | % 55.67/8.43 | Case 2: % 55.67/8.43 | | % 55.67/8.43 | | (242) ? [v0: Nat_a_set_fun$] : ? [v1: A_ltln$] : ? [v2: int] : ( ~ (v2 % 55.67/8.43 | | = 0) & build$(all_352_3, all_352_7) = v0 & % 55.67/8.43 | | gF_advice$(all_322_2, x$) = v1 & semantics_ltln$(v0, v1) = v2 & % 55.67/8.43 | | Nat_a_set_fun$(v0) & A_ltln$(v1)) % 55.67/8.43 | | % 55.67/8.43 | | DELTA: instantiating (242) with fresh symbols all_570_0, all_570_1, % 55.67/8.43 | | all_570_2 gives: % 55.67/8.43 | | (243) ~ (all_570_0 = 0) & build$(all_352_3, all_352_7) = all_570_2 & % 55.67/8.43 | | gF_advice$(all_322_2, x$) = all_570_1 & semantics_ltln$(all_570_2, % 55.67/8.43 | | all_570_1) = all_570_0 & Nat_a_set_fun$(all_570_2) & % 55.67/8.43 | | A_ltln$(all_570_1) % 55.67/8.43 | | % 55.67/8.43 | | ALPHA: (243) implies: % 55.67/8.43 | | (244) ~ (all_570_0 = 0) % 55.67/8.43 | | (245) semantics_ltln$(all_570_2, all_570_1) = all_570_0 % 55.67/8.43 | | (246) gF_advice$(all_322_2, x$) = all_570_1 % 55.67/8.43 | | (247) build$(all_352_3, all_352_7) = all_570_2 % 55.67/8.43 | | % 55.67/8.43 | | GROUND_INST: instantiating (38) with all_322_2, all_486_1, phi$, next_ltln$, % 55.67/8.43 | | simplifying with (47), (239) gives: % 55.67/8.43 | | (248) all_486_1 = all_322_2 % 55.67/8.43 | | % 55.67/8.43 | | GROUND_INST: instantiating (38) with all_322_1, all_322_2, all_322_2, unf$, % 55.67/8.43 | | simplifying with (48), (228) gives: % 55.67/8.43 | | (249) all_322_1 = all_322_2 % 55.67/8.43 | | % 55.67/8.43 | | GROUND_INST: instantiating (39) with all_352_3, all_464_0, all_308_0, w$, % 55.67/8.43 | | simplifying with (220), (238) gives: % 55.67/8.43 | | (250) all_464_0 = all_352_3 % 55.67/8.43 | | % 55.67/8.43 | | REDUCE: (234), (250) imply: % 55.67/8.43 | | (251) build$(all_352_3, all_352_7) = w$ % 55.67/8.43 | | % 55.67/8.43 | | REDUCE: (236), (248) imply: % 55.67/8.43 | | (252) gF_advice$(all_322_2, x$) = all_486_0 % 55.67/8.43 | | % 55.67/8.43 | | REDUCE: (46), (249) imply: % 55.67/8.43 | | (253) gF_advice$(all_322_2, x$) = all_322_0 % 55.67/8.43 | | % 55.67/8.43 | | GROUND_INST: instantiating (37) with all_570_1, all_322_0, x$, all_322_2, % 55.67/8.43 | | simplifying with (246), (253) gives: % 55.67/8.43 | | (254) all_570_1 = all_322_0 % 55.67/8.43 | | % 55.67/8.43 | | GROUND_INST: instantiating (37) with all_570_1, all_486_0, x$, all_322_2, % 55.67/8.43 | | simplifying with (246), (252) gives: % 55.67/8.43 | | (255) all_570_1 = all_486_0 % 55.67/8.43 | | % 55.67/8.44 | | GROUND_INST: instantiating (41) with all_570_2, w$, all_352_7, all_352_3, % 55.67/8.44 | | simplifying with (247), (251) gives: % 55.67/8.44 | | (256) all_570_2 = w$ % 55.67/8.44 | | % 55.67/8.44 | | COMBINE_EQS: (254), (255) imply: % 55.67/8.44 | | (257) all_486_0 = all_322_0 % 55.67/8.44 | | % 55.67/8.44 | | REDUCE: (245), (254), (256) imply: % 55.67/8.44 | | (258) semantics_ltln$(w$, all_322_0) = all_570_0 % 55.67/8.44 | | % 55.67/8.44 | | GROUND_INST: instantiating (36) with 0, all_570_0, all_322_0, w$, % 55.67/8.44 | | simplifying with (45), (258) gives: % 55.67/8.44 | | (259) all_570_0 = 0 % 55.67/8.44 | | % 55.67/8.44 | | REDUCE: (244), (259) imply: % 55.67/8.44 | | (260) $false % 55.67/8.44 | | % 55.67/8.44 | | CLOSE: (260) is inconsistent. % 55.67/8.44 | | % 55.67/8.44 | End of split % 55.67/8.44 | % 55.67/8.44 End of proof % 55.67/8.44 % SZS output end Proof for theBenchmark % 55.67/8.44 % 55.67/8.44 7825ms %------------------------------------------------------------------------------