%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 04:12:02 EDT 2023 % Result : Theorem 39.52s 6.08s % Output : Proof 98.40s % 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 % 0.17/0.34 % Computer : n022.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Sun Aug 27 12:22:24 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 13.89/2.65 Prover 0: Preprocessing ... % 13.89/2.65 Prover 6: Preprocessing ... % 13.89/2.65 Prover 5: Preprocessing ... % 13.89/2.66 Prover 3: Preprocessing ... % 13.89/2.67 Prover 2: Preprocessing ... % 13.89/2.69 Prover 1: Preprocessing ... % 13.89/2.70 Prover 4: Preprocessing ... % 31.91/5.09 Prover 6: Proving ... % 32.52/5.18 Prover 1: Warning: ignoring some quantifiers % 33.07/5.24 Prover 3: Warning: ignoring some quantifiers % 33.46/5.28 Prover 3: Constructing countermodel ... % 33.46/5.31 Prover 1: Constructing countermodel ... % 34.17/5.40 Prover 4: Warning: ignoring some quantifiers % 35.37/5.53 Prover 5: Proving ... % 35.37/5.57 Prover 4: Constructing countermodel ... % 37.51/5.84 Prover 0: Proving ... % 38.26/5.98 Prover 2: Proving ... % 39.48/6.08 Prover 3: proved (5436ms) % 39.52/6.08 % 39.52/6.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 39.52/6.08 % 39.52/6.09 Prover 0: stopped % 39.52/6.09 Prover 6: stopped % 39.52/6.09 Prover 5: stopped % 39.52/6.10 Prover 2: stopped % 39.52/6.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 39.52/6.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.52/6.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.52/6.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.52/6.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 46.25/7.02 Prover 10: Preprocessing ... % 46.25/7.14 Prover 7: Preprocessing ... % 46.25/7.14 Prover 11: Preprocessing ... % 46.25/7.15 Prover 8: Preprocessing ... % 46.25/7.17 Prover 13: Preprocessing ... % 55.55/8.25 Prover 10: Warning: ignoring some quantifiers % 56.23/8.35 Prover 10: Constructing countermodel ... % 56.23/8.38 Prover 8: Warning: ignoring some quantifiers % 56.23/8.39 Prover 7: Warning: ignoring some quantifiers % 56.95/8.47 Prover 8: Constructing countermodel ... % 57.75/8.50 Prover 7: Constructing countermodel ... % 59.42/8.74 Prover 13: Warning: ignoring some quantifiers % 59.42/8.80 Prover 11: Warning: ignoring some quantifiers % 60.16/8.85 Prover 13: Constructing countermodel ... % 60.16/8.90 Prover 11: Constructing countermodel ... % 75.85/10.89 Prover 13: stopped % 75.85/10.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 80.79/11.53 Prover 16: Preprocessing ... % 87.09/12.37 Prover 16: Warning: ignoring some quantifiers % 87.78/12.46 Prover 16: Constructing countermodel ... % 97.85/13.71 Prover 4: Found proof (size 99) % 97.85/13.71 Prover 4: proved (13065ms) % 97.85/13.71 Prover 7: stopped % 97.85/13.71 Prover 10: stopped % 97.85/13.71 Prover 16: stopped % 97.85/13.71 Prover 11: stopped % 97.85/13.71 Prover 1: stopped % 97.85/13.71 Prover 8: stopped % 97.85/13.71 % 97.85/13.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 97.85/13.72 % 97.97/13.73 % SZS output start Proof for theBenchmark % 97.97/13.75 Assumptions after simplification: % 97.97/13.75 --------------------------------- % 97.97/13.75 % 97.97/13.75 (axiom48) % 97.97/13.77 Nat_int_fun$(of_nat$) & Nat_nat_fun$(f$) & Nat_nat_fun$(g$) & ? [v0: % 97.97/13.77 Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! [v1: Nat$] : % 97.97/13.77 ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ Nat$(v1) | ? [v3: int] : % 97.97/13.77 ? [v4: Nat$] : ? [v5: int] : ($lesseq(v3, v5) & fun_app$c(g$, v1) = v4 & % 97.97/13.77 fun_app$b(of_nat$, v4) = v5 & fun_app$b(of_nat$, v2) = v3 & Nat$(v4))) & % 97.97/13.77 ! [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | % 97.97/13.77 ? [v3: Nat$] : ? [v4: int] : ? [v5: int] : ($lesseq(v4, v5) & % 97.97/13.77 fun_app$c(v0, v1) = v3 & fun_app$b(of_nat$, v3) = v4 & % 97.97/13.77 fun_app$b(of_nat$, v2) = v5 & Nat$(v3)))) % 97.97/13.77 % 97.97/13.77 (axiom49) % 97.97/13.77 Nat_int_fun$(of_nat$) & Nat_nat_fun$(f$) & Nat_nat_fun$(g$) & ? [v0: % 97.97/13.77 Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! [v1: Nat$] : % 97.97/13.77 ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ Nat$(v1) | ? [v3: Nat$] : % 97.97/13.77 ? [v4: int] : ? [v5: int] : ($lesseq(v4, v5) & fun_app$c(g$, v1) = v3 & % 97.97/13.77 fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, v2) = v5 & Nat$(v3))) & % 97.97/13.77 ! [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | % 97.97/13.77 ? [v3: int] : ? [v4: Nat$] : ? [v5: int] : ($lesseq(v3, v5) & % 97.97/13.77 fun_app$c(v0, v1) = v4 & fun_app$b(of_nat$, v4) = v5 & % 97.97/13.77 fun_app$b(of_nat$, v2) = v3 & Nat$(v4)))) % 97.97/13.77 % 97.97/13.77 (axiom50) % 97.97/13.77 Nat_int_fun$(of_nat$) & Nat_nat_fun$(f$) & Nat_nat_fun$(g$) & ? [v0: % 97.97/13.77 Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! [v1: Nat$] : % 97.97/13.77 ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ Nat$(v1) | ? [v3: int] : % 97.97/13.77 ? [v4: Nat$] : ? [v5: int] : ($lesseq(v3, v5) & fun_app$c(g$, v1) = v4 & % 97.97/13.77 fun_app$b(of_nat$, v4) = v5 & fun_app$b(of_nat$, v2) = v3 & Nat$(v4))) & % 97.97/13.77 ! [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | % 97.97/13.77 ? [v3: Nat$] : ? [v4: int] : ? [v5: int] : ($lesseq(v4, v5) & % 97.97/13.77 fun_app$c(v0, v1) = v3 & fun_app$b(of_nat$, v3) = v4 & % 97.97/13.77 fun_app$b(of_nat$, v2) = v5 & Nat$(v3)))) % 97.97/13.77 % 97.97/13.77 (axiom51) % 97.97/13.78 Nat_int_fun$(of_nat$) & Nat_nat_fun$(f$) & Nat_nat_fun$(g$) & ? [v0: % 97.97/13.78 Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! [v1: Nat$] : % 97.97/13.78 ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ Nat$(v1) | ? [v3: Nat$] : % 97.97/13.78 ? [v4: int] : ? [v5: int] : ($lesseq(v4, v5) & fun_app$c(g$, v1) = v3 & % 97.97/13.78 fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, v2) = v5 & Nat$(v3))) & % 97.97/13.78 ! [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | % 97.97/13.78 ? [v3: int] : ? [v4: Nat$] : ? [v5: int] : ($lesseq(v3, v5) & % 97.97/13.78 fun_app$c(v0, v1) = v4 & fun_app$b(of_nat$, v4) = v5 & % 97.97/13.78 fun_app$b(of_nat$, v2) = v3 & Nat$(v4)))) % 97.97/13.78 % 97.97/13.78 (axiom528) % 97.97/13.78 Nat_int_fun$(of_nat$) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: % 97.97/13.78 int] : ! [v4: Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v3, v5))) % 97.97/13.78 | ~ ($lesseq(v1, v0)) | ~ (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ % 97.97/13.78 (fun_app$b(of_nat$, v4) = v5) | ~ (fun_app$b(of_nat$, v2) = v3)) & ! [v0: % 97.97/13.78 int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: % 97.97/13.78 int] : ( ~ ($lesseq(1, $difference(v3, v5))) | ~ ($lesseq(v1, 0) | ~ % 97.97/13.78 (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ (fun_app$b(of_nat$, v4) = v5) | % 97.97/13.78 ~ (fun_app$b(of_nat$, v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: % 97.97/13.78 Nat$] : ! [v3: int] : ! [v4: Nat$] : ! [v5: int] : ( ~ ($lesseq(v3, % 97.97/13.78 v5)) | ~ ($lesseq(1, $difference(v1, v0))) | ~ ($lesseq(1, v1)) | ~ % 97.97/13.78 (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ (fun_app$b(of_nat$, v4) = v5) | % 97.97/13.78 ~ (fun_app$b(of_nat$, v2) = v3)) % 97.97/13.78 % 97.97/13.78 (axiom539) % 97.97/13.78 Nat_int_fun$(of_nat$) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: % 97.97/13.78 int] : ! [v4: Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v5, v3))) % 97.97/13.78 | ~ ($lesseq(v0, v1)) | ~ (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ % 97.97/13.78 (fun_app$b(of_nat$, v4) = v5) | ~ (fun_app$b(of_nat$, v2) = v3)) % 97.97/13.78 % 97.97/13.78 (axiom649) % 97.97/13.78 Nat_int_fun$(of_nat$) & ! [v0: Nat$] : ! [v1: int] : ( ~ (fun_app$b(of_nat$, % 97.97/13.78 v0) = v1) | ~ Nat$(v0) | nat$(v1) = v0) % 97.97/13.78 % 97.97/13.78 (conjecture46) % 97.97/13.78 Nat_int_fun$(of_nat$) & Nat$(n$) & Nat_nat_fun$(f$) & Nat_nat_fun$(g$) & ? % 97.97/13.78 [v0: Nat$] : ? [v1: int] : ? [v2: Nat_nat_fun$] : ? [v3: Nat$] : ? [v4: % 97.97/13.78 int] : ( ~ (v4 = v1) & dil_inverse$(f$) = v2 & fun_app$c(v2, n$) = v3 & % 97.97/13.78 fun_app$c(g$, n$) = v0 & fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, % 97.97/13.78 v0) = v1 & Nat$(v3) & Nat$(v0) & Nat_nat_fun$(v2)) % 97.97/13.78 % 97.97/13.79 (function-axioms) % 97.97/13.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.97/13.81 Nat_nat_fun$] : ! [v3: A_run$] : ! [v4: A_run$] : ! [v5: Nat_nat_fun$] : % 97.97/13.81 (v1 = v0 | ~ (contracting$(v5, v4, v3, v2) = v1) | ~ (contracting$(v5, v4, % 97.97/13.81 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 97.97/13.81 : ! [v2: A_run$] : ! [v3: A_run$] : ! [v4: Nat_nat_fun$] : (v1 = v0 | ~ % 97.97/13.81 (dilating$(v4, v3, v2) = v1) | ~ (dilating$(v4, v3, v2) = v0)) & ! [v0: % 97.97/13.81 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Nat_set$] : ! [v3: % 97.97/13.81 Int_nat_set_bool_fun_fun$] : ! [v4: Int_set$] : (v1 = v0 | ~ (uuz$(v4, v3, % 97.97/13.81 v2) = v1) | ~ (uuz$(v4, v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! % 97.97/13.81 [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : ! [v3: Nat_nat_set_bool_fun_fun$] : % 97.97/13.81 ! [v4: Nat_set$] : (v1 = v0 | ~ (uux$(v4, v3, v2) = v1) | ~ (uux$(v4, v3, % 97.97/13.81 v2) = v0)) & ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: % 97.97/13.81 Clock$] : ! [v3: A_run$] : (v1 = v0 | ~ (tick_count_strict$(v3, v2) = v1) % 97.97/13.81 | ~ (tick_count_strict$(v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! [v1: % 97.97/13.81 Nat_bool_fun$] : ! [v2: Nat_nat_bool_fun_fun$] : ! [v3: % 97.97/13.81 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (ordering_top$a(v3, v2) = v1) | ~ % 97.97/13.81 (ordering_top$a(v3, v2) = v0)) & ! [v0: Nat_set_bool_fun$] : ! [v1: % 97.97/13.81 Nat_set_bool_fun$] : ! [v2: Nat_set_nat_set_bool_fun_fun$] : ! [v3: % 97.97/13.81 Nat_set_nat_set_bool_fun_fun$] : (v1 = v0 | ~ (ordering_top$(v3, v2) = v1) % 97.97/13.81 | ~ (ordering_top$(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: % 97.97/13.81 Nat_set$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ (arg_min_on$a(v3, v2) = % 97.97/13.81 v1) | ~ (arg_min_on$a(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 97.97/13.81 [v2: Int_set$] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ (arg_min_on$(v3, v2) = % 97.97/13.81 v1) | ~ (arg_min_on$(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 97.97/13.81 [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | % 97.97/13.81 ~ (fun_app$s(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: % 97.97/13.81 Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (def_8(v3, v2) = v1) | ~ % 97.97/13.81 (def_8(v3, v2) = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : % 97.97/13.81 ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (def_7(v3, v2) = v1) | ~ (def_7(v3, v2) % 97.97/13.81 = v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_5(v3, v2) = v1) | ~ (def_5(v3, v2) = % 97.97/13.81 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_6(v3, v2) = v1) | ~ (def_6(v3, v2) = % 97.97/13.81 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_3(v3, v2) = v1) | ~ (def_3(v3, v2) = % 97.97/13.81 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_4(v3, v2) = v1) | ~ (def_4(v3, v2) = % 97.97/13.81 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_1(v3, v2) = v1) | ~ (def_1(v3, v2) = % 97.97/13.81 v0)) & ! [v0: tlbool] : ! [v1: tlbool] : ! [v2: Nat$] : ! [v3: % 97.97/13.81 Nat_bool_fun$] : (v1 = v0 | ~ (def_2(v3, v2) = v1) | ~ (def_2(v3, v2) = % 97.97/13.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.97/13.81 tlbool] : ! [v3: tlbool] : (v1 = v0 | ~ (less_eq$g(v3, v2) = v1) | ~ % 97.97/13.81 (less_eq$g(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.97/13.81 MultipleValueBool] : ! [v2: Int_bool_fun$] : ! [v3: Int_bool_fun$] : (v1 = % 97.97/13.81 v0 | ~ (less_eq$f(v3, v2) = v1) | ~ (less_eq$f(v3, v2) = v0)) & ! [v0: % 97.97/13.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_bool_fun$] : % 97.97/13.81 ! [v3: Int_bool_fun$] : (v1 = v0 | ~ (less$f(v3, v2) = v1) | ~ (less$f(v3, % 97.97/13.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 97.97/13.81 ! [v2: Nat_bool_fun$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (less$e(v3, v2) % 97.97/13.81 = v1) | ~ (less$e(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.97/13.81 MultipleValueBool] : ! [v2: Nat_bool_fun_set$] : ! [v3: Nat_bool_fun$] : % 97.97/13.81 (v1 = v0 | ~ (member$d(v3, v2) = v1) | ~ (member$d(v3, v2) = v0)) & ! [v0: % 97.97/13.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_bool_fun$] : % 97.97/13.81 ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (less_eq$e(v3, v2) = v1) | ~ % 97.97/13.81 (less_eq$e(v3, v2) = v0)) & ! [v0: Int_int_bool_fun_fun$] : ! [v1: % 97.97/13.81 Int_int_bool_fun_fun$] : ! [v2: Int_int_bool_fun_fun$] : ! [v3: Int_set$] % 97.97/13.81 : (v1 = v0 | ~ (uuv$(v3, v2) = v1) | ~ (uuv$(v3, v2) = v0)) & ! [v0: % 97.97/13.81 Nat_int_bool_fun_fun$] : ! [v1: Nat_int_bool_fun_fun$] : ! [v2: % 97.97/13.81 Int_nat_bool_fun_fun$] : ! [v3: Int_set$] : (v1 = v0 | ~ (uuu$(v3, v2) = % 97.97/13.81 v1) | ~ (uuu$(v3, v2) = v0)) & ! [v0: Int_set_int_bool_fun_fun$] : ! % 97.97/13.81 [v1: Int_set_int_bool_fun_fun$] : ! [v2: Int_int_set_bool_fun_fun$] : ! [v3: % 97.97/13.81 Int_set$] : (v1 = v0 | ~ (uuy$(v3, v2) = v1) | ~ (uuy$(v3, v2) = v0)) & ! % 97.97/13.81 [v0: Nat_set_bool_fun$] : ! [v1: Nat_set_bool_fun$] : ! [v2: int] : ! [v3: % 97.97/13.81 Int_nat_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1) | ~ % 97.97/13.81 (fun_app$r(v3, v2) = v0)) & ! [v0: Int_nat_bool_fun_fun$] : ! [v1: % 97.97/13.81 Int_nat_bool_fun_fun$] : ! [v2: Nat_int_bool_fun_fun$] : ! [v3: Nat_set$] % 97.97/13.81 : (v1 = v0 | ~ (uut$(v3, v2) = v1) | ~ (uut$(v3, v2) = v0)) & ! [v0: % 97.97/13.81 Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: int] : ! [v3: % 97.97/13.81 Int_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$p(v3, v2) = v1) | ~ % 97.97/13.81 (fun_app$p(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] % 97.97/13.81 : ! [v2: Nat$] : ! [v3: Nat_int_bool_fun_fun$] : (v1 = v0 | ~ % 97.97/13.81 (fun_app$q(v3, v2) = v1) | ~ (fun_app$q(v3, v2) = v0)) & ! [v0: % 97.97/13.81 Nat_nat_bool_fun_fun$] : ! [v1: Nat_nat_bool_fun_fun$] : ! [v2: % 97.97/13.81 Nat_nat_bool_fun_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~ (uus$(v3, v2) = % 97.97/13.81 v1) | ~ (uus$(v3, v2) = v0)) & ! [v0: Int_set_nat_bool_fun_fun$] : ! % 97.97/13.81 [v1: Int_set_nat_bool_fun_fun$] : ! [v2: Nat_int_set_bool_fun_fun$] : ! [v3: % 97.97/13.81 Nat_set$] : (v1 = v0 | ~ (uuw$(v3, v2) = v1) | ~ (uuw$(v3, v2) = v0)) & ! % 97.97/13.81 [v0: Int_int_set_bool_fun_fun$] : ! [v1: Int_int_set_bool_fun_fun$] : ! [v2: % 97.97/13.81 Int_set_int_bool_fun_fun$] : ! [v3: Int_set_set$] : (v1 = v0 | ~ (uvb$(v3, % 97.97/13.81 v2) = v1) | ~ (uvb$(v3, v2) = v0)) & ! [v0: Nat_int_set_bool_fun_fun$] % 97.97/13.81 : ! [v1: Nat_int_set_bool_fun_fun$] : ! [v2: Int_set_nat_bool_fun_fun$] : ! % 97.97/13.81 [v3: Int_set_set$] : (v1 = v0 | ~ (uva$(v3, v2) = v1) | ~ (uva$(v3, v2) = % 97.97/13.81 v0)) & ! [v0: Int_set_bool_fun$] : ! [v1: Int_set_bool_fun$] : ! [v2: % 97.97/13.81 Nat$] : ! [v3: Nat_int_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$n(v3, % 97.97/13.81 v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! % 97.97/13.81 [v1: Nat_bool_fun$] : ! [v2: Int_set$] : ! [v3: Int_set_nat_bool_fun_fun$] : % 97.97/13.81 (v1 = v0 | ~ (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! % 97.97/13.81 [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Int_bool_fun$] : ! % 97.97/13.81 [v3: Int_bool_fun$] : (v1 = v0 | ~ (uuf$(v3, v2) = v1) | ~ (uuf$(v3, v2) = % 97.97/13.81 v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 97.97/13.81 Nat_bool_fun$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ (uue$(v3, v2) = v1) % 97.97/13.81 | ~ (uue$(v3, v2) = v0)) & ! [v0: Int_set_bool_fun$] : ! [v1: % 97.97/13.81 Int_set_bool_fun$] : ! [v2: Int_set_bool_fun$] : ! [v3: Int_set_bool_fun$] % 97.97/13.81 : (v1 = v0 | ~ (uuc$(v3, v2) = v1) | ~ (uuc$(v3, v2) = v0)) & ! [v0: % 97.97/13.81 Nat_set_bool_fun$] : ! [v1: Nat_set_bool_fun$] : ! [v2: Nat_set_bool_fun$] % 97.97/13.81 : ! [v3: Nat_set_bool_fun$] : (v1 = v0 | ~ (uud$(v3, v2) = v1) | ~ % 97.97/13.81 (uud$(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! % 97.97/13.81 [v2: Int_bool_fun$] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~ (uuj$(v3, v2) = % 97.97/13.81 v1) | ~ (uuj$(v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! [v1: % 97.97/13.81 Nat_bool_fun$] : ! [v2: Nat_bool_fun$] : ! [v3: Nat_bool_fun$] : (v1 = v0 % 97.97/13.81 | ~ (uui$(v3, v2) = v1) | ~ (uui$(v3, v2) = v0)) & ! [v0: % 97.97/13.81 Int_set_bool_fun$] : ! [v1: Int_set_bool_fun$] : ! [v2: Int_set_bool_fun$] % 97.97/13.81 : ! [v3: Int_set_bool_fun$] : (v1 = v0 | ~ (uug$(v3, v2) = v1) | ~ % 97.97/13.81 (uug$(v3, v2) = v0)) & ! [v0: Nat_set_bool_fun$] : ! [v1: % 97.97/13.81 Nat_set_bool_fun$] : ! [v2: Nat_set_bool_fun$] : ! [v3: Nat_set_bool_fun$] % 97.97/13.82 : (v1 = v0 | ~ (uuh$(v3, v2) = v1) | ~ (uuh$(v3, v2) = v0)) & ! [v0: % 97.97/13.82 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: Int_bool_fun$] : ! [v3: % 97.97/13.82 Int_set$] : (v1 = v0 | ~ (uvf$(v3, v2) = v1) | ~ (uvf$(v3, v2) = v0)) & ! % 97.97/13.82 [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat_bool_fun$] : ! % 97.97/13.82 [v3: Nat_set$] : (v1 = v0 | ~ (uve$(v3, v2) = v1) | ~ (uve$(v3, v2) = v0)) & % 97.97/13.82 ! [v0: Int_set_bool_fun$] : ! [v1: Int_set_bool_fun$] : ! [v2: % 97.97/13.82 Int_set_bool_fun$] : ! [v3: Int_set_set$] : (v1 = v0 | ~ (uvc$(v3, v2) = % 97.97/13.82 v1) | ~ (uvc$(v3, v2) = v0)) & ! [v0: Nat_set_bool_fun$] : ! [v1: % 97.97/13.82 Nat_set_bool_fun$] : ! [v2: Nat_set_bool_fun$] : ! [v3: Nat_set_set$] : % 97.97/13.82 (v1 = v0 | ~ (uvd$(v3, v2) = v1) | ~ (uvd$(v3, v2) = v0)) & ! [v0: % 97.97/13.82 Int_set_bool_fun$] : ! [v1: Int_set_bool_fun$] : ! [v2: int] : ! [v3: % 97.97/13.82 Int_int_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$m(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$m(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] % 97.97/13.82 : ! [v2: Int_set$] : ! [v3: Int_set_int_bool_fun_fun$] : (v1 = v0 | ~ % 97.97/13.82 (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: % 97.97/13.82 Nat_set_bool_fun$] : ! [v1: Nat_set_bool_fun$] : ! [v2: Nat$] : ! [v3: % 97.97/13.82 Nat_nat_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$k(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$k(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] % 97.97/13.82 : ! [v2: int] : ! [v3: Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$j(v3, % 97.97/13.82 v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 97.97/13.82 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | % 97.97/13.82 ~ (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0: % 97.97/13.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set$] : ! % 97.97/13.82 [v3: Int_set_bool_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$h(v3, v2) = v0)) & ! [v0: Nat_set_bool_fun$] : ! [v1: % 97.97/13.82 Nat_set_bool_fun$] : ! [v2: Nat_set$] : ! [v3: % 97.97/13.82 Nat_set_nat_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$g(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$g(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.97/13.82 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat_set_bool_fun$] : (v1 = % 97.97/13.82 v0 | ~ (fun_app$f(v3, v2) = v1) | ~ (fun_app$f(v3, v2) = v0)) & ! [v0: % 97.97/13.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_set_set$] : ! % 97.97/13.82 [v3: Int_set_set_bool_fun$] : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$e(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.97/13.82 MultipleValueBool] : ! [v2: Nat_set_set$] : ! [v3: Nat_set_set_bool_fun$] % 97.97/13.82 : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! % 97.97/13.82 [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: % 97.97/13.82 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ % 97.97/13.82 (fun_app$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.97/13.82 MultipleValueBool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0 | ~ % 97.97/13.82 (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0: Nat$] : ! % 97.97/13.82 [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ % 97.97/13.82 (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: int] : ! % 97.97/13.82 [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ % 97.97/13.82 (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! [v0: Int_set$] % 97.97/13.82 : ! [v1: Int_set$] : ! [v2: Int_set$] : (v1 = v0 | ~ (uminus$b(v2) = v1) | % 97.97/13.82 ~ (uminus$b(v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : % 97.97/13.82 ! [v2: Int_bool_fun$] : (v1 = v0 | ~ (uminus$c(v2) = v1) | ~ (uminus$c(v2) = % 97.97/13.82 v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 97.97/13.82 Nat_bool_fun$] : (v1 = v0 | ~ (uminus$a(v2) = v1) | ~ (uminus$a(v2) = v0)) % 97.97/13.82 & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: Nat_set$] : (v1 = v0 | ~ % 97.97/13.82 (uminus$(v2) = v1) | ~ (uminus$(v2) = v0)) & ! [v0: MultipleValueBool] : % 97.97/13.82 ! [v1: MultipleValueBool] : ! [v2: Nat_bool_fun_set$] : (v1 = v0 | ~ % 97.97/13.82 (finite$f(v2) = v1) | ~ (finite$f(v2) = v0)) & ! [v0: Int_set_bool_fun$] : % 97.97/13.82 ! [v1: Int_set_bool_fun$] : ! [v2: Int_set$] : (v1 = v0 | ~ (less$d(v2) = % 97.97/13.82 v1) | ~ (less$d(v2) = v0)) & ! [v0: Nat_set_set_bool_fun$] : ! [v1: % 97.97/13.82 Nat_set_set_bool_fun$] : ! [v2: Nat_set_set$] : (v1 = v0 | ~ (less$c(v2) = % 97.97/13.82 v1) | ~ (less$c(v2) = v0)) & ! [v0: Int_set_set_bool_fun$] : ! [v1: % 97.97/13.82 Int_set_set_bool_fun$] : ! [v2: Int_set_set$] : (v1 = v0 | ~ (less$b(v2) = % 97.97/13.82 v1) | ~ (less$b(v2) = v0)) & ! [v0: Nat_set_set_set$] : ! [v1: % 97.97/13.82 Nat_set_set_set$] : ! [v2: Nat_set_set_bool_fun$] : (v1 = v0 | ~ % 97.97/13.82 (collect$e(v2) = v1) | ~ (collect$e(v2) = v0)) & ! [v0: MultipleValueBool] % 97.97/13.82 : ! [v1: MultipleValueBool] : ! [v2: Nat_set_set_set$] : (v1 = v0 | ~ % 97.97/13.82 (finite$e(v2) = v1) | ~ (finite$e(v2) = v0)) & ! [v0: Int_set_set_set$] : % 97.97/13.82 ! [v1: Int_set_set_set$] : ! [v2: Int_set_set_bool_fun$] : (v1 = v0 | ~ % 97.97/13.82 (collect$d(v2) = v1) | ~ (collect$d(v2) = v0)) & ! [v0: MultipleValueBool] % 97.97/13.82 : ! [v1: MultipleValueBool] : ! [v2: Int_set_set_set$] : (v1 = v0 | ~ % 97.97/13.82 (finite$d(v2) = v1) | ~ (finite$d(v2) = v0)) & ! [v0: Int_set$] : ! [v1: % 97.97/13.82 Int_set$] : ! [v2: Int_bool_fun$] : (v1 = v0 | ~ (collect$c(v2) = v1) | ~ % 98.40/13.82 (collect$c(v2) = v0)) & ! [v0: Nat_set_set$] : ! [v1: Nat_set_set$] : ! % 98.40/13.82 [v2: Nat_set_bool_fun$] : (v1 = v0 | ~ (collect$b(v2) = v1) | ~ % 98.40/13.82 (collect$b(v2) = v0)) & ! [v0: Int_set_set$] : ! [v1: Int_set_set$] : ! % 98.40/13.82 [v2: Int_set_bool_fun$] : (v1 = v0 | ~ (collect$a(v2) = v1) | ~ % 98.40/13.82 (collect$a(v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2: % 98.40/13.82 Nat_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) = v0)) % 98.40/13.82 & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) % 98.40/13.82 | ~ (nat$(v2) = v0)) & ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! % 98.40/13.82 [v2: Nat_nat_fun$] : (v1 = v0 | ~ (dil_inverse$(v2) = v1) | ~ % 98.40/13.82 (dil_inverse$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 98.40/13.82 MultipleValueBool] : ! [v2: A_run$] : (v1 = v0 | ~ (dense_run$(v2) = v1) | % 98.40/13.82 ~ (dense_run$(v2) = v0)) & ! [v0: Int_int_bool_fun_fun$] : ! [v1: % 98.40/13.82 Int_int_bool_fun_fun$] : ! [v2: int] : (v1 = v0 | ~ (uvm$(v2) = v1) | ~ % 98.40/13.82 (uvm$(v2) = v0)) & ! [v0: Int_int_bool_fun_fun$] : ! [v1: % 98.40/13.82 Int_int_bool_fun_fun$] : ! [v2: int] : (v1 = v0 | ~ (uvn$(v2) = v1) | ~ % 98.40/13.82 (uvn$(v2) = v0)) & ! [v0: Int_int_bool_fun_fun$] : ! [v1: % 98.40/13.82 Int_int_bool_fun_fun$] : ! [v2: int] : (v1 = v0 | ~ (uvo$(v2) = v1) | ~ % 98.40/13.82 (uvo$(v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: % 98.40/13.82 Int_bool_fun$] : (v1 = v0 | ~ (uvq$(v2) = v1) | ~ (uvq$(v2) = v0)) & ! % 98.40/13.82 [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat_bool_fun$] : (v1 = % 98.40/13.82 v0 | ~ (uvp$(v2) = v1) | ~ (uvp$(v2) = v0)) & ! [v0: Nat_bool_fun$] : ! % 98.40/13.82 [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (uvr$(v2) = v1) | ~ % 98.40/13.82 (uvr$(v2) = v0)) & ! [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: % 98.40/13.82 Nat_set$] : (v1 = v0 | ~ (uuq$(v2) = v1) | ~ (uuq$(v2) = v0)) & ! [v0: % 98.40/13.82 Int_set_set_bool_fun$] : ! [v1: Int_set_set_bool_fun$] : ! [v2: Int_set$] % 98.40/13.82 : (v1 = v0 | ~ (member$a(v2) = v1) | ~ (member$a(v2) = v0)) & ! [v0: % 98.40/13.82 Int_set_bool_fun$] : ! [v1: Int_set_bool_fun$] : ! [v2: Int_set_set$] : % 98.40/13.82 (v1 = v0 | ~ (uuo$(v2) = v1) | ~ (uuo$(v2) = v0)) & ! [v0: % 98.40/13.82 Nat_set_set_bool_fun$] : ! [v1: Nat_set_set_bool_fun$] : ! [v2: Nat_set$] % 98.40/13.82 : (v1 = v0 | ~ (member$(v2) = v1) | ~ (member$(v2) = v0)) & ! [v0: % 98.40/13.82 Nat_set_bool_fun$] : ! [v1: Nat_set_bool_fun$] : ! [v2: Nat_set_set$] : % 98.40/13.82 (v1 = v0 | ~ (uup$(v2) = v1) | ~ (uup$(v2) = v0)) & ! [v0: % 98.40/13.82 Nat_set_bool_fun$] : ! [v1: Nat_set_bool_fun$] : ! [v2: Nat_set$] : (v1 = % 98.40/13.82 v0 | ~ (less$(v2) = v1) | ~ (less$(v2) = v0)) & ! [v0: Int_set_bool_fun$] % 98.40/13.82 : ! [v1: Int_set_bool_fun$] : ! [v2: Int_set$] : (v1 = v0 | ~ % 98.40/13.82 (less_eq$c(v2) = v1) | ~ (less_eq$c(v2) = v0)) & ! [v0: Int_set_bool_fun$] % 98.40/13.82 : ! [v1: Int_set_bool_fun$] : ! [v2: Int_set$] : (v1 = v0 | ~ (uun$(v2) = % 98.40/13.82 v1) | ~ (uun$(v2) = v0)) & ! [v0: Nat_set_bool_fun$] : ! [v1: % 98.40/13.82 Nat_set_bool_fun$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (less_eq$b(v2) = v1) % 98.40/13.82 | ~ (less_eq$b(v2) = v0)) & ! [v0: Int_set_set_bool_fun$] : ! [v1: % 98.40/13.82 Int_set_set_bool_fun$] : ! [v2: Int_set_set$] : (v1 = v0 | ~ % 98.40/13.82 (less_eq$a(v2) = v1) | ~ (less_eq$a(v2) = v0)) & ! [v0: % 98.40/13.82 Int_set_set_bool_fun$] : ! [v1: Int_set_set_bool_fun$] : ! [v2: % 98.40/13.82 Int_set_set$] : (v1 = v0 | ~ (uuk$(v2) = v1) | ~ (uuk$(v2) = v0)) & ! % 98.40/13.82 [v0: Nat_set_set_bool_fun$] : ! [v1: Nat_set_set_bool_fun$] : ! [v2: % 98.40/13.82 Nat_set_set$] : (v1 = v0 | ~ (less_eq$(v2) = v1) | ~ (less_eq$(v2) = v0)) % 98.40/13.82 & ! [v0: Nat_set_set_bool_fun$] : ! [v1: Nat_set_set_bool_fun$] : ! [v2: % 98.40/13.82 Nat_set_set$] : (v1 = v0 | ~ (uul$(v2) = v1) | ~ (uul$(v2) = v0)) % 98.40/13.82 % 98.40/13.82 Further assumptions not needed in the proof: % 98.40/13.82 -------------------------------------------- % 98.40/13.82 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, % 98.40/13.82 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, % 98.40/13.82 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, % 98.40/13.82 axiom12, axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, % 98.40/13.82 axiom127, axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, % 98.40/13.82 axiom134, axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, % 98.40/13.82 axiom141, axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, % 98.40/13.82 axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, % 98.40/13.82 axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, % 98.40/13.82 axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17, % 98.40/13.82 axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177, % 98.40/13.82 axiom178, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, % 98.40/13.82 axiom185, axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, % 98.40/13.82 axiom192, axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, % 98.40/13.82 axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, axiom205, % 98.40/13.82 axiom206, axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212, % 98.40/13.82 axiom213, axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22, % 98.40/13.82 axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227, % 98.40/13.82 axiom228, axiom229, axiom23, axiom230, axiom231, axiom232, axiom233, axiom234, % 98.40/13.82 axiom235, axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241, % 98.40/13.82 axiom242, axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249, % 98.40/13.82 axiom25, axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256, % 98.40/13.82 axiom257, axiom258, axiom259, axiom26, axiom260, axiom261, axiom262, axiom263, % 98.40/13.82 axiom264, axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270, % 98.40/13.82 axiom271, axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278, % 98.40/13.82 axiom279, axiom28, axiom280, axiom281, axiom282, axiom283, axiom284, axiom285, % 98.40/13.82 axiom286, axiom287, axiom288, axiom289, axiom29, axiom290, axiom291, axiom292, % 98.40/13.82 axiom293, axiom294, axiom295, axiom296, axiom297, axiom298, axiom299, axiom3, % 98.40/13.82 axiom30, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, axiom306, % 98.40/13.82 axiom307, axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, axiom313, % 98.40/13.82 axiom314, axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320, % 98.40/13.82 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328, % 98.40/13.82 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335, % 98.40/13.82 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342, % 98.40/13.82 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35, % 98.40/13.82 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357, % 98.40/13.82 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364, % 98.40/13.82 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371, % 98.40/13.82 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom378, axiom379, % 98.40/13.82 axiom38, axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, % 98.40/13.82 axiom387, axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, % 98.40/13.82 axiom394, axiom395, axiom396, axiom397, axiom398, axiom399, axiom4, axiom40, % 98.40/13.82 axiom400, axiom401, axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, % 98.40/13.82 axiom408, axiom409, axiom41, axiom410, axiom411, axiom412, axiom413, axiom414, % 98.40/13.82 axiom415, axiom416, axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, % 98.40/13.82 axiom422, axiom423, axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, % 98.40/13.82 axiom43, axiom430, axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, % 98.40/13.82 axiom437, axiom438, axiom439, axiom44, axiom440, axiom441, axiom442, axiom443, % 98.40/13.82 axiom444, axiom445, axiom446, axiom447, axiom448, axiom449, axiom45, axiom450, % 98.40/13.82 axiom451, axiom452, axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, % 98.40/13.82 axiom459, axiom460, axiom461, axiom462, axiom463, axiom464, axiom465, axiom466, % 98.40/13.82 axiom467, axiom468, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473, % 98.40/13.82 axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, axiom480, axiom481, % 98.40/13.82 axiom482, axiom483, axiom484, axiom485, axiom486, axiom487, axiom488, axiom489, % 98.40/13.82 axiom490, axiom491, axiom492, axiom493, axiom494, axiom495, axiom496, axiom497, % 98.40/13.82 axiom498, axiom499, axiom5, axiom500, axiom501, axiom502, axiom503, axiom504, % 98.40/13.82 axiom505, axiom506, axiom507, axiom508, axiom509, axiom510, axiom511, axiom512, % 98.40/13.82 axiom513, axiom514, axiom515, axiom516, axiom517, axiom518, axiom519, axiom52, % 98.40/13.82 axiom520, axiom521, axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, % 98.40/13.82 axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535, % 98.40/13.82 axiom536, axiom537, axiom538, axiom54, axiom540, axiom541, axiom542, axiom543, % 98.40/13.82 axiom544, axiom545, axiom546, axiom547, axiom548, axiom549, axiom55, axiom550, % 98.40/13.82 axiom551, axiom552, axiom553, axiom554, axiom555, axiom556, axiom557, axiom558, % 98.40/13.82 axiom559, axiom56, axiom560, axiom561, axiom562, axiom563, axiom564, axiom565, % 98.40/13.82 axiom566, axiom567, axiom568, axiom569, axiom57, axiom570, axiom571, axiom572, % 98.40/13.82 axiom573, axiom574, axiom575, axiom576, axiom577, axiom578, axiom579, axiom58, % 98.40/13.82 axiom580, axiom581, axiom582, axiom583, axiom584, axiom585, axiom586, axiom587, % 98.40/13.82 axiom588, axiom589, axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, % 98.40/13.82 axiom595, axiom596, axiom597, axiom598, axiom599, axiom6, axiom60, axiom600, % 98.40/13.82 axiom601, axiom602, axiom603, axiom604, axiom605, axiom606, axiom607, axiom608, % 98.40/13.82 axiom609, axiom61, axiom610, axiom611, axiom612, axiom613, axiom614, axiom615, % 98.40/13.82 axiom616, axiom617, axiom618, axiom619, axiom62, axiom620, axiom621, axiom622, % 98.40/13.82 axiom623, axiom624, axiom625, axiom626, axiom627, axiom628, axiom629, axiom63, % 98.40/13.82 axiom630, axiom631, axiom632, axiom633, axiom634, axiom635, axiom636, axiom637, % 98.40/13.82 axiom638, axiom639, axiom64, axiom640, axiom641, axiom642, axiom643, axiom644, % 98.40/13.82 axiom645, axiom646, axiom647, axiom648, axiom65, axiom650, axiom66, axiom67, % 98.40/13.82 axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, % 98.40/13.82 axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81, axiom82, axiom83, % 98.40/13.82 axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, axiom91, % 98.40/13.82 axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, axiom99, % 98.40/13.82 formula_652, formula_653, formula_654, formula_655, formula_656, formula_657, % 98.40/13.82 formula_658, formula_659, formula_660, formula_661 % 98.40/13.82 % 98.40/13.82 Those formulas are unsatisfiable: % 98.40/13.82 --------------------------------- % 98.40/13.82 % 98.40/13.82 Begin of proof % 98.40/13.82 | % 98.40/13.82 | ALPHA: (axiom50) implies: % 98.40/13.82 | (1) ? [v0: Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! % 98.40/13.82 | [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ % 98.40/13.82 | Nat$(v1) | ? [v3: int] : ? [v4: Nat$] : ? [v5: int] : % 98.40/13.82 | ($lesseq(v3, v5) & fun_app$c(g$, v1) = v4 & fun_app$b(of_nat$, v4) % 98.40/13.82 | = v5 & fun_app$b(of_nat$, v2) = v3 & Nat$(v4))) & ! [v1: Nat$] : % 98.40/13.82 | ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | ? [v3: % 98.40/13.82 | Nat$] : ? [v4: int] : ? [v5: int] : ($lesseq(v4, v5) & % 98.40/13.82 | fun_app$c(v0, v1) = v3 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.82 | fun_app$b(of_nat$, v2) = v5 & Nat$(v3)))) % 98.40/13.82 | % 98.40/13.83 | ALPHA: (axiom51) implies: % 98.40/13.83 | (2) ? [v0: Nat_nat_fun$] : (dil_inverse$(f$) = v0 & Nat_nat_fun$(v0) & ! % 98.40/13.83 | [v1: Nat$] : ! [v2: Nat$] : ( ~ (fun_app$c(v0, v1) = v2) | ~ % 98.40/13.83 | Nat$(v1) | ? [v3: Nat$] : ? [v4: int] : ? [v5: int] : % 98.40/13.83 | ($lesseq(v4, v5) & fun_app$c(g$, v1) = v3 & fun_app$b(of_nat$, v3) % 98.40/13.83 | = v4 & fun_app$b(of_nat$, v2) = v5 & Nat$(v3))) & ! [v1: Nat$] : % 98.40/13.83 | ! [v2: Nat$] : ( ~ (fun_app$c(g$, v1) = v2) | ~ Nat$(v1) | ? [v3: % 98.40/13.83 | int] : ? [v4: Nat$] : ? [v5: int] : ($lesseq(v3, v5) & % 98.40/13.83 | fun_app$c(v0, v1) = v4 & fun_app$b(of_nat$, v4) = v5 & % 98.40/13.83 | fun_app$b(of_nat$, v2) = v3 & Nat$(v4)))) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (axiom528) implies: % 98.40/13.83 | (3) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: int] : ! [v4: % 98.40/13.83 | Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v3, v5))) | ~ % 98.40/13.83 | ($lesseq(v1, v0)) | ~ (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ % 98.40/13.83 | (fun_app$b(of_nat$, v4) = v5) | ~ (fun_app$b(of_nat$, v2) = v3)) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (axiom539) implies: % 98.40/13.83 | (4) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: int] : ! [v4: % 98.40/13.83 | Nat$] : ! [v5: int] : ( ~ ($lesseq(1, $difference(v5, v3))) | ~ % 98.40/13.83 | ($lesseq(v0, v1)) | ~ (nat$(v1) = v2) | ~ (nat$(v0) = v4) | ~ % 98.40/13.83 | (fun_app$b(of_nat$, v4) = v5) | ~ (fun_app$b(of_nat$, v2) = v3)) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (axiom649) implies: % 98.40/13.83 | (5) ! [v0: Nat$] : ! [v1: int] : ( ~ (fun_app$b(of_nat$, v0) = v1) | ~ % 98.40/13.83 | Nat$(v0) | nat$(v1) = v0) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (conjecture46) implies: % 98.40/13.83 | (6) Nat$(n$) % 98.40/13.83 | (7) ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat_nat_fun$] : ? [v3: Nat$] : % 98.40/13.83 | ? [v4: int] : ( ~ (v4 = v1) & dil_inverse$(f$) = v2 & fun_app$c(v2, n$) % 98.40/13.83 | = v3 & fun_app$c(g$, n$) = v0 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.83 | fun_app$b(of_nat$, v0) = v1 & Nat$(v3) & Nat$(v0) & Nat_nat_fun$(v2)) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (function-axioms) implies: % 98.40/13.83 | (8) ! [v0: Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : % 98.40/13.83 | (v1 = v0 | ~ (dil_inverse$(v2) = v1) | ~ (dil_inverse$(v2) = v0)) % 98.40/13.83 | (9) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : % 98.40/13.83 | (v1 = v0 | ~ (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) % 98.40/13.83 | % 98.40/13.83 | DELTA: instantiating (7) with fresh symbols all_534_0, all_534_1, all_534_2, % 98.40/13.83 | all_534_3, all_534_4 gives: % 98.40/13.83 | (10) ~ (all_534_0 = all_534_3) & dil_inverse$(f$) = all_534_2 & % 98.40/13.83 | fun_app$c(all_534_2, n$) = all_534_1 & fun_app$c(g$, n$) = all_534_4 & % 98.40/13.83 | fun_app$b(of_nat$, all_534_1) = all_534_0 & fun_app$b(of_nat$, % 98.40/13.83 | all_534_4) = all_534_3 & Nat$(all_534_1) & Nat$(all_534_4) & % 98.40/13.83 | Nat_nat_fun$(all_534_2) % 98.40/13.83 | % 98.40/13.83 | ALPHA: (10) implies: % 98.40/13.83 | (11) ~ (all_534_0 = all_534_3) % 98.40/13.83 | (12) Nat$(all_534_4) % 98.40/13.83 | (13) Nat$(all_534_1) % 98.40/13.83 | (14) fun_app$b(of_nat$, all_534_4) = all_534_3 % 98.40/13.83 | (15) fun_app$b(of_nat$, all_534_1) = all_534_0 % 98.40/13.83 | (16) fun_app$c(g$, n$) = all_534_4 % 98.40/13.83 | (17) fun_app$c(all_534_2, n$) = all_534_1 % 98.40/13.83 | (18) dil_inverse$(f$) = all_534_2 % 98.40/13.83 | % 98.40/13.83 | DELTA: instantiating (2) with fresh symbol all_543_0 gives: % 98.40/13.84 | (19) dil_inverse$(f$) = all_543_0 & Nat_nat_fun$(all_543_0) & ! [v0: Nat$] % 98.40/13.84 | : ! [v1: Nat$] : ( ~ (fun_app$c(all_543_0, v0) = v1) | ~ Nat$(v0) | % 98.40/13.84 | ? [v2: Nat$] : ? [v3: int] : ? [v4: int] : ($lesseq(v3, v4) & % 98.40/13.84 | fun_app$c(g$, v0) = v2 & fun_app$b(of_nat$, v2) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v4 & Nat$(v2))) & ! [v0: Nat$] : ! [v1: % 98.40/13.84 | Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ Nat$(v0) | ? [v2: int] : % 98.40/13.84 | ? [v3: Nat$] : ? [v4: int] : ($lesseq(v2, v4) & % 98.40/13.84 | fun_app$c(all_543_0, v0) = v3 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v2 & Nat$(v3))) % 98.40/13.84 | % 98.40/13.84 | ALPHA: (19) implies: % 98.40/13.84 | (20) dil_inverse$(f$) = all_543_0 % 98.40/13.84 | (21) ! [v0: Nat$] : ! [v1: Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ % 98.40/13.84 | Nat$(v0) | ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : % 98.40/13.84 | ($lesseq(v2, v4) & fun_app$c(all_543_0, v0) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, v1) = v2 & % 98.40/13.84 | Nat$(v3))) % 98.40/13.84 | % 98.40/13.84 | DELTA: instantiating (2) with fresh symbol all_546_0 gives: % 98.40/13.84 | (22) dil_inverse$(f$) = all_546_0 & Nat_nat_fun$(all_546_0) & ! [v0: Nat$] % 98.40/13.84 | : ! [v1: Nat$] : ( ~ (fun_app$c(all_546_0, v0) = v1) | ~ Nat$(v0) | % 98.40/13.84 | ? [v2: Nat$] : ? [v3: int] : ? [v4: int] : ($lesseq(v3, v4) & % 98.40/13.84 | fun_app$c(g$, v0) = v2 & fun_app$b(of_nat$, v2) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v4 & Nat$(v2))) & ! [v0: Nat$] : ! [v1: % 98.40/13.84 | Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ Nat$(v0) | ? [v2: int] : % 98.40/13.84 | ? [v3: Nat$] : ? [v4: int] : ($lesseq(v2, v4) & % 98.40/13.84 | fun_app$c(all_546_0, v0) = v3 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v2 & Nat$(v3))) % 98.40/13.84 | % 98.40/13.84 | ALPHA: (22) implies: % 98.40/13.84 | (23) dil_inverse$(f$) = all_546_0 % 98.40/13.84 | (24) ! [v0: Nat$] : ! [v1: Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ % 98.40/13.84 | Nat$(v0) | ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : % 98.40/13.84 | ($lesseq(v2, v4) & fun_app$c(all_546_0, v0) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, v1) = v2 & % 98.40/13.84 | Nat$(v3))) % 98.40/13.84 | % 98.40/13.84 | DELTA: instantiating (1) with fresh symbol all_549_0 gives: % 98.40/13.84 | (25) dil_inverse$(f$) = all_549_0 & Nat_nat_fun$(all_549_0) & ! [v0: Nat$] % 98.40/13.84 | : ! [v1: Nat$] : ( ~ (fun_app$c(all_549_0, v0) = v1) | ~ Nat$(v0) | % 98.40/13.84 | ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : ($lesseq(v2, v4) & % 98.40/13.84 | fun_app$c(g$, v0) = v3 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v2 & Nat$(v3))) & ! [v0: Nat$] : ! [v1: % 98.40/13.84 | Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ Nat$(v0) | ? [v2: Nat$] : % 98.40/13.84 | ? [v3: int] : ? [v4: int] : ($lesseq(v3, v4) & % 98.40/13.84 | fun_app$c(all_549_0, v0) = v2 & fun_app$b(of_nat$, v2) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v4 & Nat$(v2))) % 98.40/13.84 | % 98.40/13.84 | ALPHA: (25) implies: % 98.40/13.84 | (26) dil_inverse$(f$) = all_549_0 % 98.40/13.84 | (27) ! [v0: Nat$] : ! [v1: Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ % 98.40/13.84 | Nat$(v0) | ? [v2: Nat$] : ? [v3: int] : ? [v4: int] : % 98.40/13.84 | ($lesseq(v3, v4) & fun_app$c(all_549_0, v0) = v2 & % 98.40/13.84 | fun_app$b(of_nat$, v2) = v3 & fun_app$b(of_nat$, v1) = v4 & % 98.40/13.84 | Nat$(v2))) % 98.40/13.84 | % 98.40/13.84 | DELTA: instantiating (1) with fresh symbol all_552_0 gives: % 98.40/13.84 | (28) dil_inverse$(f$) = all_552_0 & Nat_nat_fun$(all_552_0) & ! [v0: Nat$] % 98.40/13.84 | : ! [v1: Nat$] : ( ~ (fun_app$c(all_552_0, v0) = v1) | ~ Nat$(v0) | % 98.40/13.84 | ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : ($lesseq(v2, v4) & % 98.40/13.84 | fun_app$c(g$, v0) = v3 & fun_app$b(of_nat$, v3) = v4 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v2 & Nat$(v3))) & ! [v0: Nat$] : ! [v1: % 98.40/13.84 | Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ Nat$(v0) | ? [v2: Nat$] : % 98.40/13.84 | ? [v3: int] : ? [v4: int] : ($lesseq(v3, v4) & % 98.40/13.84 | fun_app$c(all_552_0, v0) = v2 & fun_app$b(of_nat$, v2) = v3 & % 98.40/13.84 | fun_app$b(of_nat$, v1) = v4 & Nat$(v2))) % 98.40/13.84 | % 98.40/13.84 | ALPHA: (28) implies: % 98.40/13.84 | (29) dil_inverse$(f$) = all_552_0 % 98.40/13.84 | (30) ! [v0: Nat$] : ! [v1: Nat$] : ( ~ (fun_app$c(g$, v0) = v1) | ~ % 98.40/13.84 | Nat$(v0) | ? [v2: Nat$] : ? [v3: int] : ? [v4: int] : % 98.40/13.84 | ($lesseq(v3, v4) & fun_app$c(all_552_0, v0) = v2 & % 98.40/13.84 | fun_app$b(of_nat$, v2) = v3 & fun_app$b(of_nat$, v1) = v4 & % 98.40/13.84 | Nat$(v2))) % 98.40/13.84 | % 98.40/13.85 | GROUND_INST: instantiating (8) with all_546_0, all_549_0, f$, simplifying with % 98.40/13.85 | (23), (26) gives: % 98.40/13.85 | (31) all_549_0 = all_546_0 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (8) with all_534_2, all_549_0, f$, simplifying with % 98.40/13.85 | (18), (26) gives: % 98.40/13.85 | (32) all_549_0 = all_534_2 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (8) with all_549_0, all_552_0, f$, simplifying with % 98.40/13.85 | (26), (29) gives: % 98.40/13.85 | (33) all_552_0 = all_549_0 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (8) with all_543_0, all_552_0, f$, simplifying with % 98.40/13.85 | (20), (29) gives: % 98.40/13.85 | (34) all_552_0 = all_543_0 % 98.40/13.85 | % 98.40/13.85 | COMBINE_EQS: (33), (34) imply: % 98.40/13.85 | (35) all_549_0 = all_543_0 % 98.40/13.85 | % 98.40/13.85 | SIMP: (35) implies: % 98.40/13.85 | (36) all_549_0 = all_543_0 % 98.40/13.85 | % 98.40/13.85 | COMBINE_EQS: (31), (32) imply: % 98.40/13.85 | (37) all_546_0 = all_534_2 % 98.40/13.85 | % 98.40/13.85 | COMBINE_EQS: (31), (36) imply: % 98.40/13.85 | (38) all_546_0 = all_543_0 % 98.40/13.85 | % 98.40/13.85 | COMBINE_EQS: (37), (38) imply: % 98.40/13.85 | (39) all_543_0 = all_534_2 % 98.40/13.85 | % 98.40/13.85 | SIMP: (39) implies: % 98.40/13.85 | (40) all_543_0 = all_534_2 % 98.40/13.85 | % 98.40/13.85 | COMBINE_EQS: (34), (40) imply: % 98.40/13.85 | (41) all_552_0 = all_534_2 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (5) with all_534_4, all_534_3, simplifying with % 98.40/13.85 | (12), (14) gives: % 98.40/13.85 | (42) nat$(all_534_3) = all_534_4 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (5) with all_534_1, all_534_0, simplifying with % 98.40/13.85 | (13), (15) gives: % 98.40/13.85 | (43) nat$(all_534_0) = all_534_1 % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (30) with n$, all_534_4, simplifying with (6), (16) % 98.40/13.85 | gives: % 98.40/13.85 | (44) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ($lesseq(v1, v2) & % 98.40/13.85 | fun_app$c(all_552_0, n$) = v0 & fun_app$b(of_nat$, v0) = v1 & % 98.40/13.85 | fun_app$b(of_nat$, all_534_4) = v2 & Nat$(v0)) % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (27) with n$, all_534_4, simplifying with (6), (16) % 98.40/13.85 | gives: % 98.40/13.85 | (45) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ($lesseq(v1, v2) & % 98.40/13.85 | fun_app$c(all_549_0, n$) = v0 & fun_app$b(of_nat$, v0) = v1 & % 98.40/13.85 | fun_app$b(of_nat$, all_534_4) = v2 & Nat$(v0)) % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (24) with n$, all_534_4, simplifying with (6), (16) % 98.40/13.85 | gives: % 98.40/13.85 | (46) ? [v0: int] : ? [v1: Nat$] : ? [v2: int] : ($lesseq(v0, v2) & % 98.40/13.85 | fun_app$c(all_546_0, n$) = v1 & fun_app$b(of_nat$, v1) = v2 & % 98.40/13.85 | fun_app$b(of_nat$, all_534_4) = v0 & Nat$(v1)) % 98.40/13.85 | % 98.40/13.85 | GROUND_INST: instantiating (21) with n$, all_534_4, simplifying with (6), (16) % 98.40/13.85 | gives: % 98.40/13.85 | (47) ? [v0: int] : ? [v1: Nat$] : ? [v2: int] : ($lesseq(v0, v2) & % 98.40/13.85 | fun_app$c(all_543_0, n$) = v1 & fun_app$b(of_nat$, v1) = v2 & % 98.40/13.85 | fun_app$b(of_nat$, all_534_4) = v0 & Nat$(v1)) % 98.40/13.85 | % 98.40/13.85 | DELTA: instantiating (47) with fresh symbols all_630_0, all_630_1, all_630_2 % 98.40/13.85 | gives: % 98.40/13.85 | (48) $lesseq(all_630_2, all_630_0) & fun_app$c(all_543_0, n$) = all_630_1 & % 98.40/13.85 | fun_app$b(of_nat$, all_630_1) = all_630_0 & fun_app$b(of_nat$, % 98.40/13.85 | all_534_4) = all_630_2 & Nat$(all_630_1) % 98.40/13.85 | % 98.40/13.85 | ALPHA: (48) implies: % 98.40/13.85 | (49) fun_app$b(of_nat$, all_630_1) = all_630_0 % 98.40/13.85 | (50) fun_app$c(all_543_0, n$) = all_630_1 % 98.40/13.85 | % 98.40/13.85 | DELTA: instantiating (46) with fresh symbols all_633_0, all_633_1, all_633_2 % 98.40/13.85 | gives: % 98.40/13.85 | (51) $lesseq(all_633_2, all_633_0) & fun_app$c(all_546_0, n$) = all_633_1 & % 98.40/13.85 | fun_app$b(of_nat$, all_633_1) = all_633_0 & fun_app$b(of_nat$, % 98.40/13.85 | all_534_4) = all_633_2 & Nat$(all_633_1) % 98.40/13.85 | % 98.40/13.85 | ALPHA: (51) implies: % 98.40/13.85 | (52) $lesseq(all_633_2, all_633_0) % 98.40/13.85 | (53) fun_app$b(of_nat$, all_534_4) = all_633_2 % 98.40/13.85 | (54) fun_app$b(of_nat$, all_633_1) = all_633_0 % 98.40/13.85 | (55) fun_app$c(all_546_0, n$) = all_633_1 % 98.40/13.85 | % 98.40/13.85 | DELTA: instantiating (45) with fresh symbols all_638_0, all_638_1, all_638_2 % 98.40/13.85 | gives: % 98.40/13.85 | (56) $lesseq(all_638_1, all_638_0) & fun_app$c(all_549_0, n$) = all_638_2 & % 98.40/13.85 | fun_app$b(of_nat$, all_638_2) = all_638_1 & fun_app$b(of_nat$, % 98.40/13.85 | all_534_4) = all_638_0 & Nat$(all_638_2) % 98.40/13.85 | % 98.40/13.85 | ALPHA: (56) implies: % 98.40/13.85 | (57) fun_app$b(of_nat$, all_638_2) = all_638_1 % 98.40/13.85 | (58) fun_app$c(all_549_0, n$) = all_638_2 % 98.40/13.85 | % 98.40/13.85 | DELTA: instantiating (44) with fresh symbols all_641_0, all_641_1, all_641_2 % 98.40/13.85 | gives: % 98.40/13.85 | (59) $lesseq(all_641_1, all_641_0) & fun_app$c(all_552_0, n$) = all_641_2 & % 98.40/13.85 | fun_app$b(of_nat$, all_641_2) = all_641_1 & fun_app$b(of_nat$, % 98.40/13.85 | all_534_4) = all_641_0 & Nat$(all_641_2) % 98.40/13.85 | % 98.40/13.85 | ALPHA: (59) implies: % 98.40/13.85 | (60) $lesseq(all_641_1, all_641_0) % 98.40/13.85 | (61) fun_app$b(of_nat$, all_534_4) = all_641_0 % 98.40/13.85 | (62) fun_app$b(of_nat$, all_641_2) = all_641_1 % 98.40/13.85 | (63) fun_app$c(all_552_0, n$) = all_641_2 % 98.40/13.85 | % 98.40/13.85 | REDUCE: (41), (63) imply: % 98.40/13.86 | (64) fun_app$c(all_534_2, n$) = all_641_2 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (32), (58) imply: % 98.40/13.86 | (65) fun_app$c(all_534_2, n$) = all_638_2 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (37), (55) imply: % 98.40/13.86 | (66) fun_app$c(all_534_2, n$) = all_633_1 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (40), (50) imply: % 98.40/13.86 | (67) fun_app$c(all_534_2, n$) = all_630_1 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (9) with all_633_1, all_638_2, n$, all_534_2, % 98.40/13.86 | simplifying with (65), (66) gives: % 98.40/13.86 | (68) all_638_2 = all_633_1 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (9) with all_630_1, all_638_2, n$, all_534_2, % 98.40/13.86 | simplifying with (65), (67) gives: % 98.40/13.86 | (69) all_638_2 = all_630_1 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (9) with all_534_1, all_641_2, n$, all_534_2, % 98.40/13.86 | simplifying with (17), (64) gives: % 98.40/13.86 | (70) all_641_2 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (9) with all_633_1, all_641_2, n$, all_534_2, % 98.40/13.86 | simplifying with (64), (66) gives: % 98.40/13.86 | (71) all_641_2 = all_633_1 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_3, all_534_3, all_534_4, % 98.40/13.86 | all_633_2, all_534_4, all_641_0, simplifying with (42), (53), % 98.40/13.86 | (61) gives: % 98.40/13.86 | (72) $lesseq(all_633_2, all_641_0) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_3, all_534_3, all_534_4, % 98.40/13.86 | all_633_2, all_534_4, all_641_0, simplifying with (42), (53), % 98.40/13.86 | (61) gives: % 98.40/13.86 | (73) $lesseq(all_641_0, all_633_2) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_3, all_534_3, all_534_4, % 98.40/13.86 | all_534_3, all_534_4, all_641_0, simplifying with (14), (42), % 98.40/13.86 | (61) gives: % 98.40/13.86 | (74) $lesseq(all_534_3, all_641_0) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_3, all_534_3, all_534_4, % 98.40/13.86 | all_534_3, all_534_4, all_641_0, simplifying with (14), (42), % 98.40/13.86 | (61) gives: % 98.40/13.86 | (75) $lesseq(all_641_0, all_534_3) % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (70), (71) imply: % 98.40/13.86 | (76) all_633_1 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | SIMP: (76) implies: % 98.40/13.86 | (77) all_633_1 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (68), (69) imply: % 98.40/13.86 | (78) all_633_1 = all_630_1 % 98.40/13.86 | % 98.40/13.86 | SIMP: (78) implies: % 98.40/13.86 | (79) all_633_1 = all_630_1 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (77), (79) imply: % 98.40/13.86 | (80) all_630_1 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | SIMP: (80) implies: % 98.40/13.86 | (81) all_630_1 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (69), (81) imply: % 98.40/13.86 | (82) all_638_2 = all_534_1 % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (72), (73) imply: % 98.40/13.86 | (83) all_641_0 = all_633_2 % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (74), (75) imply: % 98.40/13.86 | (84) all_641_0 = all_534_3 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (83), (84) imply: % 98.40/13.86 | (85) all_633_2 = all_534_3 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (60), (84) imply: % 98.40/13.86 | (86) $lesseq(all_641_1, all_534_3) % 98.40/13.86 | % 98.40/13.86 | REDUCE: (52), (85) imply: % 98.40/13.86 | (87) $lesseq(all_534_3, all_633_0) % 98.40/13.86 | % 98.40/13.86 | REDUCE: (62), (70) imply: % 98.40/13.86 | (88) fun_app$b(of_nat$, all_534_1) = all_641_1 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (57), (82) imply: % 98.40/13.86 | (89) fun_app$b(of_nat$, all_534_1) = all_638_1 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (54), (77) imply: % 98.40/13.86 | (90) fun_app$b(of_nat$, all_534_1) = all_633_0 % 98.40/13.86 | % 98.40/13.86 | REDUCE: (49), (81) imply: % 98.40/13.86 | (91) fun_app$b(of_nat$, all_534_1) = all_630_0 % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_534_0, all_534_1, all_641_1, simplifying with (15), (43), % 98.40/13.86 | (88) gives: % 98.40/13.86 | (92) $lesseq(all_534_0, all_641_1) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_534_0, all_534_1, all_641_1, simplifying with (15), (43), % 98.40/13.86 | (88) gives: % 98.40/13.86 | (93) $lesseq(all_641_1, all_534_0) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_638_1, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (89) gives: % 98.40/13.86 | (94) $lesseq(all_638_1, all_641_1) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_638_1, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (89) gives: % 98.40/13.86 | (95) $lesseq(all_641_1, all_638_1) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_633_0, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (90) gives: % 98.40/13.86 | (96) $lesseq(all_633_0, all_641_1) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_633_0, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (90) gives: % 98.40/13.86 | (97) $lesseq(all_641_1, all_633_0) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (3) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_630_0, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (91) gives: % 98.40/13.86 | (98) $lesseq(all_630_0, all_641_1) % 98.40/13.86 | % 98.40/13.86 | GROUND_INST: instantiating (4) with all_534_0, all_534_0, all_534_1, % 98.40/13.86 | all_630_0, all_534_1, all_641_1, simplifying with (43), (88), % 98.40/13.86 | (91) gives: % 98.40/13.86 | (99) $lesseq(all_641_1, all_630_0) % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (94), (95) imply: % 98.40/13.86 | (100) all_641_1 = all_638_1 % 98.40/13.86 | % 98.40/13.86 | COMBINE_INEQS: (86), (94) imply: % 98.40/13.86 | (101) $lesseq(all_638_1, all_534_3) % 98.40/13.86 | % 98.40/13.86 | COMBINE_INEQS: (95), (96) imply: % 98.40/13.86 | (102) $lesseq(all_633_0, all_638_1) % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (96), (97) imply: % 98.40/13.86 | (103) all_641_1 = all_633_0 % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (98), (99) imply: % 98.40/13.86 | (104) all_641_1 = all_630_0 % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (92), (93) imply: % 98.40/13.86 | (105) all_641_1 = all_534_0 % 98.40/13.86 | % 98.40/13.86 | COMBINE_INEQS: (101), (102) imply: % 98.40/13.86 | (106) $lesseq(all_633_0, all_534_3) % 98.40/13.86 | % 98.40/13.86 | ANTI_SYMM: (87), (106) imply: % 98.40/13.86 | (107) all_633_0 = all_534_3 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (100), (103) imply: % 98.40/13.86 | (108) all_638_1 = all_633_0 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (100), (105) imply: % 98.40/13.86 | (109) all_638_1 = all_534_0 % 98.40/13.86 | % 98.40/13.86 | COMBINE_EQS: (100), (104) imply: % 98.40/13.87 | (110) all_638_1 = all_630_0 % 98.40/13.87 | % 98.40/13.87 | COMBINE_EQS: (108), (110) imply: % 98.40/13.87 | (111) all_633_0 = all_630_0 % 98.40/13.87 | % 98.40/13.87 | COMBINE_EQS: (108), (109) imply: % 98.40/13.87 | (112) all_633_0 = all_534_0 % 98.40/13.87 | % 98.40/13.87 | COMBINE_EQS: (107), (111) imply: % 98.40/13.87 | (113) all_630_0 = all_534_3 % 98.40/13.87 | % 98.40/13.87 | COMBINE_EQS: (111), (112) imply: % 98.40/13.87 | (114) all_630_0 = all_534_0 % 98.40/13.87 | % 98.40/13.87 | COMBINE_EQS: (113), (114) imply: % 98.40/13.87 | (115) all_534_0 = all_534_3 % 98.40/13.87 | % 98.40/13.87 | REDUCE: (11), (115) imply: % 98.40/13.87 | (116) $false % 98.40/13.87 | % 98.40/13.87 | CLOSE: (116) is inconsistent. % 98.40/13.87 | % 98.40/13.87 End of proof % 98.40/13.87 % SZS output end Proof for theBenchmark % 98.40/13.87 % 98.40/13.87 13245ms %------------------------------------------------------------------------------