%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC384+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 20:51:09 EDT 2023 % Result : Theorem 44.06s 6.69s % Output : Proof 109.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWC384+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 18:04:39 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.66 ________ _____ % 0.19/0.66 ___ __ \_________(_)________________________________ % 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.66 % 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.66 (2023-06-19) % 0.19/0.66 % 0.19/0.66 (c) Philipp Rümmer, 2009-2023 % 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.66 Amanda Stjerna. % 0.19/0.66 Free software under BSD-3-Clause. % 0.19/0.66 % 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.66 % 0.19/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.67 Running up to 7 provers in parallel. % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.05/1.66 Prover 4: Preprocessing ... % 6.58/1.69 Prover 1: Preprocessing ... % 6.58/1.72 Prover 5: Preprocessing ... % 6.58/1.72 Prover 0: Preprocessing ... % 6.58/1.72 Prover 3: Preprocessing ... % 6.58/1.72 Prover 2: Preprocessing ... % 6.58/1.72 Prover 6: Preprocessing ... % 16.80/3.07 Prover 2: Proving ... % 16.80/3.09 Prover 5: Constructing countermodel ... % 16.80/3.14 Prover 1: Constructing countermodel ... % 17.42/3.16 Prover 6: Proving ... % 18.09/3.24 Prover 3: Constructing countermodel ... % 23.61/4.05 Prover 4: Constructing countermodel ... % 24.38/4.15 Prover 0: Proving ... % 44.06/6.68 Prover 3: proved (6005ms) % 44.06/6.69 % 44.06/6.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 44.06/6.69 % 44.06/6.69 Prover 2: stopped % 44.40/6.69 Prover 0: stopped % 44.40/6.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 44.40/6.70 Prover 5: stopped % 44.40/6.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 44.40/6.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 44.40/6.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 44.40/6.74 Prover 6: stopped % 44.88/6.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 45.71/6.92 Prover 11: Preprocessing ... % 45.71/6.93 Prover 7: Preprocessing ... % 45.71/6.94 Prover 13: Preprocessing ... % 45.71/6.94 Prover 8: Preprocessing ... % 45.71/6.97 Prover 10: Preprocessing ... % 47.68/7.13 Prover 7: Constructing countermodel ... % 47.68/7.14 Prover 10: Constructing countermodel ... % 48.69/7.27 Prover 13: Constructing countermodel ... % 48.89/7.28 Prover 8: Warning: ignoring some quantifiers % 48.89/7.29 Prover 8: Constructing countermodel ... % 53.65/7.95 Prover 11: Constructing countermodel ... % 81.05/11.43 Prover 13: stopped % 81.05/11.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 81.21/11.50 Prover 16: Preprocessing ... % 82.09/11.60 Prover 16: Constructing countermodel ... % 108.96/15.09 Prover 1: Found proof (size 176) % 108.96/15.09 Prover 1: proved (14410ms) % 108.96/15.09 Prover 8: stopped % 108.96/15.09 Prover 11: stopped % 108.96/15.09 Prover 7: stopped % 108.96/15.09 Prover 16: stopped % 108.96/15.09 Prover 4: stopped % 108.96/15.09 Prover 10: stopped % 108.96/15.09 % 108.96/15.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 108.96/15.09 % 109.23/15.11 % SZS output start Proof for theBenchmark % 109.23/15.11 Assumptions after simplification: % 109.23/15.11 --------------------------------- % 109.23/15.11 % 109.23/15.11 (ax15) % 109.23/15.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 109.23/15.14 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 109.23/15.14 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 109.23/15.14 % 109.23/15.14 (ax17) % 109.23/15.14 ssList(nil) = 0 & $i(nil) % 109.23/15.14 % 109.23/15.14 (ax20) % 109.23/15.15 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 109.23/15.15 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 109.23/15.15 ssItem(v2) = 0 & $i(v2)))) % 109.23/15.15 % 109.23/15.15 (ax23) % 109.23/15.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 109.23/15.15 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 109.23/15.15 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 109.23/15.15 % 109.23/15.15 (ax25) % 109.23/15.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 109.23/15.15 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 109.23/15.15 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 109.23/15.15 % 109.23/15.15 (ax4) % 109.23/15.15 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | % 109.23/15.15 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i] % 109.23/15.15 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2: % 109.23/15.15 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 109.23/15.15 0) & ssItem(v2) = v3))))) % 109.23/15.15 % 109.23/15.15 (ax59) % 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.16 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 109.23/15.16 (v2 = 0) | v3 = 0))) % 109.23/15.16 % 109.23/15.16 (ax61) % 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.16 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 109.23/15.16 (v2 = 0) | v3 = 0))) % 109.23/15.16 % 109.23/15.16 (ax63) % 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.16 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 109.23/15.16 (v2 = 0) | v3 = 0))) % 109.23/15.16 % 109.23/15.16 (ax65) % 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.16 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 109.23/15.16 (v2 = 0) | v3 = 0))) % 109.23/15.16 % 109.23/15.16 (ax68) % 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.16 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 109.23/15.16 ~ (v2 = 0) | v3 = 0))) % 109.23/15.16 % 109.23/15.16 (ax7) % 109.23/15.16 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 109.23/15.16 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 109.23/15.16 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 109.23/15.16 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 109.23/15.16 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 109.23/15.16 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 109.23/15.16 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 109.23/15.16 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 109.23/15.16 ssList(v5) = v6))))))) % 109.23/15.16 % 109.23/15.16 (ax71) % 109.23/15.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.17 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 109.23/15.17 ~ (v2 = 0) | v3 = 0))) % 109.23/15.17 % 109.23/15.17 (ax73) % 109.23/15.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 109.23/15.17 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 109.23/15.17 (v2 = 0) | v3 = 0))) % 109.23/15.17 % 109.23/15.17 (co1) % 109.23/15.17 $i(nil) & ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 109.23/15.17 $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & ssList(v2) = % 109.23/15.17 0 & neq(v2, nil) = 0 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & ( ? [v4: $i] % 109.23/15.17 : ? [v5: $i] : (cons(v4, nil) = v5 & ssItem(v4) = 0 & $i(v5) & $i(v4) & % 109.23/15.17 ? [v6: $i] : ? [v7: $i] : (ssList(v6) = 0 & app(v6, v0) = v7 & % 109.23/15.17 $i(v7) & $i(v6) & ? [v8: $i] : (v5 = v0 & ssList(v8) = 0 & app(v7, % 109.23/15.17 v8) = v2 & $i(v8) & ! [v9: $i] : ( ~ (memberP(v8, v9) = 0) | ~ % 109.23/15.17 $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v9, v4) = v11 & % 109.23/15.17 ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v9: % 109.23/15.17 $i] : ( ~ (memberP(v6, v9) = 0) | ~ $i(v9) | ? [v10: any] : ? % 109.23/15.17 [v11: any] : (lt(v4, v9) = v11 & ssItem(v9) = v10 & ( ~ (v11 = % 109.23/15.17 0) | ~ (v10 = 0))))))) | (v2 = nil & v0 = nil)))) % 109.23/15.17 % 109.23/15.17 (function-axioms) % 109.23/15.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 109.23/15.18 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.23/15.18 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.23/15.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.23/15.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.23/15.18 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 109.23/15.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 109.23/15.18 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 109.23/15.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 109.23/15.18 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 109.23/15.18 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 109.23/15.18 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 109.23/15.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 109.23/15.18 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 109.23/15.18 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 109.23/15.18 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 109.23/15.18 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 109.23/15.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 109.23/15.18 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 109.23/15.18 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 109.23/15.18 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 109.23/15.18 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 109.23/15.18 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 109.23/15.18 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 109.23/15.18 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 109.23/15.18 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 109.23/15.18 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 109.23/15.18 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 109.23/15.18 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 109.23/15.18 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 109.23/15.18 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 109.23/15.18 % 109.23/15.18 Further assumptions not needed in the proof: % 109.23/15.18 -------------------------------------------- % 109.23/15.18 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax24, % 109.23/15.18 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, % 109.23/15.18 ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 109.23/15.18 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, % 109.23/15.18 ax66, ax67, ax69, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, % 109.23/15.18 ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 109.23/15.18 ax93, ax94, ax95 % 109.23/15.18 % 109.23/15.18 Those formulas are unsatisfiable: % 109.23/15.18 --------------------------------- % 109.23/15.18 % 109.23/15.18 Begin of proof % 109.23/15.18 | % 109.23/15.18 | ALPHA: (ax4) implies: % 109.23/15.18 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ? % 109.23/15.18 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: % 109.23/15.18 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 % 109.23/15.18 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: % 109.23/15.18 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3))))) % 109.23/15.18 | % 109.23/15.18 | ALPHA: (ax17) implies: % 109.23/15.18 | (2) ssList(nil) = 0 % 109.23/15.18 | % 109.23/15.18 | ALPHA: (ax20) implies: % 109.23/15.19 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 109.23/15.19 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 109.23/15.19 | ssItem(v2) = 0 & $i(v2)))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax59) implies: % 109.23/15.19 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 109.23/15.19 | ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax61) implies: % 109.23/15.19 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax63) implies: % 109.23/15.19 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax65) implies: % 109.23/15.19 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax68) implies: % 109.23/15.19 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax71) implies: % 109.23/15.19 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (ax73) implies: % 109.23/15.19 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.19 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0))) % 109.23/15.19 | % 109.23/15.19 | ALPHA: (co1) implies: % 109.23/15.19 | (11) $i(nil) % 109.23/15.20 | (12) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 109.23/15.20 | $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & % 109.23/15.20 | ssList(v2) = 0 & neq(v2, nil) = 0 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 109.23/15.20 | = 0)) & ( ? [v4: $i] : ? [v5: $i] : (cons(v4, nil) = v5 & % 109.23/15.20 | ssItem(v4) = 0 & $i(v5) & $i(v4) & ? [v6: $i] : ? [v7: $i] : % 109.23/15.20 | (ssList(v6) = 0 & app(v6, v0) = v7 & $i(v7) & $i(v6) & ? [v8: % 109.23/15.20 | $i] : (v5 = v0 & ssList(v8) = 0 & app(v7, v8) = v2 & % 109.23/15.20 | $i(v8) & ! [v9: $i] : ( ~ (memberP(v8, v9) = 0) | ~ % 109.23/15.20 | $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v9, v4) = % 109.23/15.20 | v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 109.23/15.20 | 0)))) & ! [v9: $i] : ( ~ (memberP(v6, v9) = 0) | % 109.23/15.20 | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v4, v9) = % 109.23/15.20 | v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 109.23/15.20 | 0))))))) | (v2 = nil & v0 = nil)))) % 109.23/15.20 | % 109.23/15.20 | ALPHA: (function-axioms) implies: % 109.23/15.20 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 109.23/15.20 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 109.23/15.20 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 109.23/15.20 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 109.23/15.20 | % 109.23/15.20 | DELTA: instantiating (12) with fresh symbols all_93_0, all_93_1 gives: % 109.23/15.20 | (15) singletonP(all_93_1) = all_93_0 & ssList(all_93_1) = 0 & $i(all_93_1) % 109.23/15.20 | & ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 & % 109.23/15.20 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0) & ( ~ (v1 = 0) | ~ % 109.23/15.20 | (all_93_0 = 0)) & ( ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) = v3 % 109.23/15.20 | & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] : % 109.23/15.20 | (ssList(v4) = 0 & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ? % 109.23/15.20 | [v6: $i] : (v3 = all_93_1 & ssList(v6) = 0 & app(v5, v6) = v0 % 109.23/15.20 | & $i(v6) & ! [v7: $i] : ( ~ (memberP(v6, v7) = 0) | ~ % 109.23/15.20 | $i(v7) | ? [v8: any] : ? [v9: any] : (lt(v7, v2) = v9 & % 109.23/15.20 | ssItem(v7) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! % 109.23/15.20 | [v7: $i] : ( ~ (memberP(v4, v7) = 0) | ~ $i(v7) | ? [v8: % 109.23/15.20 | any] : ? [v9: any] : (lt(v2, v7) = v9 & ssItem(v7) = v8 % 109.23/15.20 | & ( ~ (v9 = 0) | ~ (v8 = 0))))))) | (v0 = nil & % 109.23/15.20 | all_93_1 = nil))) % 109.23/15.20 | % 109.23/15.20 | ALPHA: (15) implies: % 109.23/15.20 | (16) $i(all_93_1) % 109.23/15.20 | (17) ssList(all_93_1) = 0 % 109.23/15.20 | (18) singletonP(all_93_1) = all_93_0 % 109.23/15.21 | (19) ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 & ssList(v0) % 109.23/15.21 | = 0 & neq(v0, nil) = 0 & $i(v0) & ( ~ (v1 = 0) | ~ (all_93_0 = 0)) % 109.23/15.21 | & ( ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 % 109.23/15.21 | & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] : (ssList(v4) = 0 % 109.23/15.21 | & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ? [v6: $i] : (v3 % 109.23/15.21 | = all_93_1 & ssList(v6) = 0 & app(v5, v6) = v0 & $i(v6) & ! % 109.23/15.21 | [v7: $i] : ( ~ (memberP(v6, v7) = 0) | ~ $i(v7) | ? [v8: % 109.23/15.21 | any] : ? [v9: any] : (lt(v7, v2) = v9 & ssItem(v7) = v8 % 109.23/15.21 | & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v7: $i] : ( ~ % 109.23/15.21 | (memberP(v4, v7) = 0) | ~ $i(v7) | ? [v8: any] : ? [v9: % 109.23/15.21 | any] : (lt(v2, v7) = v9 & ssItem(v7) = v8 & ( ~ (v9 = 0) % 109.23/15.21 | | ~ (v8 = 0))))))) | (v0 = nil & all_93_1 = nil))) % 109.23/15.21 | % 109.23/15.21 | DELTA: instantiating (19) with fresh symbols all_97_0, all_97_1 gives: % 109.23/15.21 | (20) segmentP(all_97_1, all_93_1) = all_97_0 & ssList(all_97_1) = 0 & % 109.23/15.21 | neq(all_97_1, nil) = 0 & $i(all_97_1) & ( ~ (all_97_0 = 0) | ~ % 109.23/15.21 | (all_93_0 = 0)) & ( ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & % 109.23/15.21 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : % 109.23/15.21 | (ssList(v2) = 0 & app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? % 109.23/15.21 | [v4: $i] : (v1 = all_93_1 & ssList(v4) = 0 & app(v3, v4) = % 109.23/15.21 | all_97_1 & $i(v4) & ! [v5: $i] : ( ~ (memberP(v4, v5) = 0) | % 109.23/15.21 | ~ $i(v5) | ? [v6: any] : ? [v7: any] : (lt(v5, v0) = v7 & % 109.23/15.21 | ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5: % 109.23/15.21 | $i] : ( ~ (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : % 109.23/15.21 | ? [v7: any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 % 109.23/15.21 | = 0) | ~ (v6 = 0))))))) | (all_97_1 = nil & all_93_1 % 109.23/15.21 | = nil)) % 109.23/15.21 | % 109.23/15.21 | ALPHA: (20) implies: % 109.23/15.21 | (21) $i(all_97_1) % 109.23/15.21 | (22) neq(all_97_1, nil) = 0 % 109.23/15.21 | (23) ssList(all_97_1) = 0 % 109.23/15.21 | (24) segmentP(all_97_1, all_93_1) = all_97_0 % 109.23/15.21 | (25) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 109.23/15.21 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & % 109.23/15.21 | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 = % 109.23/15.21 | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_1 & $i(v4) & ! % 109.23/15.21 | [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] % 109.23/15.21 | : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7 % 109.23/15.21 | = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2, % 109.23/15.21 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : % 109.23/15.21 | (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 109.23/15.21 | 0))))))) | (all_97_1 = nil & all_93_1 = nil) % 109.23/15.21 | (26) ~ (all_97_0 = 0) | ~ (all_93_0 = 0) % 109.23/15.21 | % 109.23/15.21 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (11) gives: % 109.23/15.22 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.22 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 109.23/15.22 | ( ~ (v2 = 0) | v3 = nil))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (11) gives: % 109.23/15.22 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 109.23/15.22 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 109.23/15.22 | ( ~ (v2 = 0) | v3 = v0))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (3) with all_97_1, simplifying with (21), (23) % 109.23/15.22 | gives: % 109.23/15.22 | (29) all_97_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 109.23/15.22 | : (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (ax7) with all_97_1, simplifying with (21), (23) % 109.23/15.22 | gives: % 109.23/15.22 | (30) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_97_1, v0) = v1) | ~ % 109.23/15.22 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 109.23/15.22 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 109.23/15.22 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 109.23/15.22 | app(v3, v4) = all_97_1 & $i(v4)))) & (v1 = 0 | ! [v2: $i] : % 109.23/15.22 | ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] % 109.23/15.22 | : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, % 109.23/15.22 | v4) = all_97_1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = % 109.23/15.22 | 0) & ssList(v4) = v5)))))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (21), (23) % 109.23/15.22 | gives: % 109.23/15.22 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0) % 109.23/15.22 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 109.23/15.22 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (1) with all_93_1, all_93_0, simplifying with (16), % 109.23/15.22 | (18) gives: % 109.23/15.22 | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_93_0 % 109.23/15.22 | = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & ssItem(v0) = 0 % 109.23/15.22 | & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = % 109.23/15.22 | all_93_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 109.23/15.22 | ssItem(v0) = v1)))) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (31) with nil, 0, simplifying with (11) gives: % 109.23/15.22 | (33) ~ (all_97_1 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0 % 109.23/15.22 | = 0) & ssList(nil) = v0) % 109.23/15.22 | % 109.23/15.22 | GROUND_INST: instantiating (30) with all_93_1, all_97_0, simplifying with % 109.23/15.22 | (16), (24) gives: % 109.23/15.23 | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 % 109.23/15.23 | = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 109.23/15.23 | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = % 109.23/15.23 | 0 & app(v1, v2) = all_97_1 & $i(v2)))) & (all_97_0 = 0 | ! % 109.23/15.23 | [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) % 109.23/15.23 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : % 109.23/15.23 | ( ~ (app(v1, v2) = all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~ % 109.23/15.23 | (v3 = 0) & ssList(v2) = v3))))) % 109.23/15.23 | % 109.23/15.23 | BETA: splitting (25) gives: % 109.23/15.23 | % 109.23/15.23 | Case 1: % 109.23/15.23 | | % 109.23/15.23 | | (35) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 109.23/15.23 | | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & % 109.23/15.23 | | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 = % 109.23/15.23 | | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_1 & $i(v4) & % 109.23/15.23 | | ! [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: % 109.23/15.23 | | any] : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & % 109.23/15.23 | | ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ % 109.23/15.23 | | (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: % 109.23/15.23 | | any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | % 109.23/15.23 | | ~ (v6 = 0))))))) % 109.23/15.23 | | % 109.23/15.23 | | DELTA: instantiating (35) with fresh symbols all_298_0, all_298_1 gives: % 109.23/15.23 | | (36) cons(all_298_1, nil) = all_298_0 & ssItem(all_298_1) = 0 & % 109.23/15.23 | | $i(all_298_0) & $i(all_298_1) & ? [v0: $i] : ? [v1: $i] : % 109.23/15.23 | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: % 109.23/15.23 | | $i] : (all_298_0 = all_93_1 & ssList(v2) = 0 & app(v1, v2) = % 109.23/15.23 | | all_97_1 & $i(v2) & ! [v3: $i] : ( ~ (memberP(v2, v3) = 0) | ~ % 109.23/15.23 | | $i(v3) | ? [v4: any] : ? [v5: any] : (lt(v3, all_298_1) = v5 % 109.23/15.23 | | & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v3: % 109.23/15.23 | | $i] : ( ~ (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: any] : % 109.23/15.23 | | ? [v5: any] : (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~ % 109.23/15.23 | | (v5 = 0) | ~ (v4 = 0)))))) % 109.23/15.23 | | % 109.23/15.23 | | ALPHA: (36) implies: % 109.23/15.23 | | (37) $i(all_298_1) % 109.23/15.23 | | (38) ssItem(all_298_1) = 0 % 109.23/15.23 | | (39) cons(all_298_1, nil) = all_298_0 % 109.23/15.23 | | (40) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_93_1) = v1 % 109.23/15.23 | | & $i(v1) & $i(v0) & ? [v2: $i] : (all_298_0 = all_93_1 & % 109.23/15.23 | | ssList(v2) = 0 & app(v1, v2) = all_97_1 & $i(v2) & ! [v3: $i] : % 109.23/15.23 | | ( ~ (memberP(v2, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: % 109.23/15.23 | | any] : (lt(v3, all_298_1) = v5 & ssItem(v3) = v4 & ( ~ (v5 = % 109.23/15.23 | | 0) | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ (memberP(v0, v3) % 109.23/15.23 | | = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 109.23/15.23 | | (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ % 109.23/15.23 | | (v4 = 0)))))) % 109.23/15.23 | | % 109.23/15.23 | | DELTA: instantiating (40) with fresh symbols all_300_0, all_300_1 gives: % 109.23/15.24 | | (41) ssList(all_300_1) = 0 & app(all_300_1, all_93_1) = all_300_0 & % 109.23/15.24 | | $i(all_300_0) & $i(all_300_1) & ? [v0: $i] : (all_298_0 = all_93_1 % 109.23/15.24 | | & ssList(v0) = 0 & app(all_300_0, v0) = all_97_1 & $i(v0) & ! % 109.23/15.24 | | [v1: $i] : ( ~ (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : % 109.23/15.24 | | ? [v3: any] : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~ % 109.23/15.24 | | (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 109.23/15.24 | | (memberP(all_300_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? % 109.23/15.24 | | [v3: any] : (lt(all_298_1, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 % 109.23/15.24 | | = 0) | ~ (v2 = 0))))) % 109.23/15.24 | | % 109.23/15.24 | | ALPHA: (41) implies: % 109.23/15.24 | | (42) $i(all_300_1) % 109.23/15.24 | | (43) app(all_300_1, all_93_1) = all_300_0 % 109.23/15.24 | | (44) ssList(all_300_1) = 0 % 109.23/15.24 | | (45) ? [v0: $i] : (all_298_0 = all_93_1 & ssList(v0) = 0 & % 109.23/15.24 | | app(all_300_0, v0) = all_97_1 & $i(v0) & ! [v1: $i] : ( ~ % 109.23/15.24 | | (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] % 109.23/15.24 | | : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ % 109.23/15.24 | | (v2 = 0)))) & ! [v1: $i] : ( ~ (memberP(all_300_1, v1) = 0) % 109.23/15.24 | | | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (lt(all_298_1, v1) = % 109.23/15.24 | | v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 109.23/15.24 | | % 109.23/15.24 | | DELTA: instantiating (45) with fresh symbol all_302_0 gives: % 109.23/15.24 | | (46) all_298_0 = all_93_1 & ssList(all_302_0) = 0 & app(all_300_0, % 109.23/15.24 | | all_302_0) = all_97_1 & $i(all_302_0) & ! [v0: $i] : ( ~ % 109.23/15.24 | | (memberP(all_302_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 109.23/15.24 | | any] : (lt(v0, all_298_1) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) % 109.23/15.24 | | | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ (memberP(all_300_1, v0) = % 109.23/15.24 | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (lt(all_298_1, % 109.23/15.24 | | v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 109.23/15.24 | | % 109.23/15.24 | | ALPHA: (46) implies: % 109.23/15.24 | | (47) all_298_0 = all_93_1 % 109.23/15.24 | | (48) $i(all_302_0) % 109.23/15.24 | | (49) app(all_300_0, all_302_0) = all_97_1 % 109.23/15.24 | | (50) ssList(all_302_0) = 0 % 109.23/15.24 | | % 109.23/15.24 | | REDUCE: (39), (47) imply: % 109.23/15.24 | | (51) cons(all_298_1, nil) = all_93_1 % 109.23/15.24 | | % 109.23/15.24 | | BETA: splitting (26) gives: % 109.23/15.24 | | % 109.23/15.24 | | Case 1: % 109.23/15.24 | | | % 109.23/15.24 | | | (52) ~ (all_97_0 = 0) % 109.23/15.24 | | | % 109.23/15.24 | | | BETA: splitting (34) gives: % 109.23/15.24 | | | % 109.23/15.24 | | | Case 1: % 109.23/15.24 | | | | % 109.23/15.24 | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 109.23/15.24 | | | | % 109.23/15.24 | | | | DELTA: instantiating (53) with fresh symbol all_314_0 gives: % 109.23/15.24 | | | | (54) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0 % 109.54/15.24 | | | | % 109.54/15.25 | | | | REF_CLOSE: (14), (17), (54) are inconsistent by sub-proof #2. % 109.54/15.25 | | | | % 109.54/15.25 | | | Case 2: % 109.54/15.25 | | | | % 109.54/15.25 | | | | (55) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 % 109.54/15.25 | | | | & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 109.54/15.25 | | | | (ssList(v2) = 0 & app(v1, v2) = all_97_1 & $i(v2)))) & % 109.54/15.25 | | | | (all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, % 109.54/15.25 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 109.54/15.25 | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = % 109.54/15.25 | | | | all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 109.54/15.25 | | | | ssList(v2) = v3)))) % 109.54/15.25 | | | | % 109.54/15.25 | | | | ALPHA: (55) implies: % 109.54/15.25 | | | | (56) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, % 109.54/15.25 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 109.54/15.25 | | | | & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = % 109.54/15.25 | | | | all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 109.54/15.25 | | | | ssList(v2) = v3))) % 109.54/15.25 | | | | % 109.54/15.25 | | | | BETA: splitting (56) gives: % 109.54/15.25 | | | | % 109.54/15.25 | | | | Case 1: % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | (57) all_97_0 = 0 % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | REDUCE: (52), (57) imply: % 109.54/15.25 | | | | | (58) $false % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | CLOSE: (58) is inconsistent. % 109.54/15.25 | | | | | % 109.54/15.25 | | | | Case 2: % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ % 109.54/15.25 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 109.54/15.25 | | | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_1) | ~ $i(v2) | ? % 109.54/15.25 | | | | | [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3))) % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | GROUND_INST: instantiating (59) with all_300_1, all_300_0, simplifying % 109.54/15.25 | | | | | with (42), (43) gives: % 109.54/15.25 | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0) | ! % 109.54/15.25 | | | | | [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_1) | ~ $i(v0) | % 109.54/15.25 | | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1)) % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | BETA: splitting (60) gives: % 109.54/15.25 | | | | | % 109.54/15.25 | | | | | Case 1: % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0) % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | DELTA: instantiating (61) with fresh symbol all_1019_0 gives: % 109.54/15.25 | | | | | | (62) ~ (all_1019_0 = 0) & ssList(all_300_1) = all_1019_0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | ALPHA: (62) implies: % 109.54/15.25 | | | | | | (63) ~ (all_1019_0 = 0) % 109.54/15.25 | | | | | | (64) ssList(all_300_1) = all_1019_0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | GROUND_INST: instantiating (14) with 0, all_1019_0, all_300_1, % 109.54/15.25 | | | | | | simplifying with (44), (64) gives: % 109.54/15.25 | | | | | | (65) all_1019_0 = 0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | REDUCE: (63), (65) imply: % 109.54/15.25 | | | | | | (66) $false % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | CLOSE: (66) is inconsistent. % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | Case 2: % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | (67) ! [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_1) | ~ % 109.54/15.25 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1)) % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | GROUND_INST: instantiating (67) with all_302_0, simplifying with % 109.54/15.25 | | | | | | (48), (49) gives: % 109.54/15.25 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_302_0) = v0) % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | DELTA: instantiating (68) with fresh symbol all_1016_0 gives: % 109.54/15.25 | | | | | | (69) ~ (all_1016_0 = 0) & ssList(all_302_0) = all_1016_0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | ALPHA: (69) implies: % 109.54/15.25 | | | | | | (70) ~ (all_1016_0 = 0) % 109.54/15.25 | | | | | | (71) ssList(all_302_0) = all_1016_0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | GROUND_INST: instantiating (14) with 0, all_1016_0, all_302_0, % 109.54/15.25 | | | | | | simplifying with (50), (71) gives: % 109.54/15.25 | | | | | | (72) all_1016_0 = 0 % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | REDUCE: (70), (72) imply: % 109.54/15.25 | | | | | | (73) $false % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | | CLOSE: (73) is inconsistent. % 109.54/15.25 | | | | | | % 109.54/15.25 | | | | | End of split % 109.54/15.25 | | | | | % 109.54/15.25 | | | | End of split % 109.54/15.25 | | | | % 109.54/15.26 | | | End of split % 109.54/15.26 | | | % 109.54/15.26 | | Case 2: % 109.54/15.26 | | | % 109.54/15.26 | | | (74) ~ (all_93_0 = 0) % 109.54/15.26 | | | % 109.54/15.26 | | | BETA: splitting (32) gives: % 109.54/15.26 | | | % 109.54/15.26 | | | Case 1: % 109.54/15.26 | | | | % 109.54/15.26 | | | | (75) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 109.54/15.26 | | | | % 109.54/15.26 | | | | DELTA: instantiating (75) with fresh symbol all_314_0 gives: % 109.54/15.26 | | | | (76) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0 % 109.54/15.26 | | | | % 109.54/15.26 | | | | REF_CLOSE: (14), (17), (76) are inconsistent by sub-proof #2. % 109.54/15.26 | | | | % 109.54/15.26 | | | Case 2: % 109.54/15.26 | | | | % 109.54/15.26 | | | | (77) ( ~ (all_93_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & % 109.54/15.26 | | | | ssItem(v0) = 0 & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( % 109.54/15.26 | | | | ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? [v1: int] : ( % 109.54/15.26 | | | | ~ (v1 = 0) & ssItem(v0) = v1))) % 109.54/15.26 | | | | % 109.54/15.26 | | | | ALPHA: (77) implies: % 109.54/15.26 | | | | (78) all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ % 109.54/15.26 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 109.54/15.26 | | | | % 109.54/15.26 | | | | BETA: splitting (78) gives: % 109.54/15.26 | | | | % 109.54/15.26 | | | | Case 1: % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | (79) all_93_0 = 0 % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | REDUCE: (74), (79) imply: % 109.54/15.26 | | | | | (80) $false % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | CLOSE: (80) is inconsistent. % 109.54/15.26 | | | | | % 109.54/15.26 | | | | Case 2: % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | (81) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? % 109.54/15.26 | | | | | [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | BETA: splitting (29) gives: % 109.54/15.26 | | | | | % 109.54/15.26 | | | | | Case 1: % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | (82) all_97_1 = nil % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | REDUCE: (22), (82) imply: % 109.54/15.26 | | | | | | (83) neq(nil, nil) = 0 % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | REF_CLOSE: (2), (14), (33), (82), (83) are inconsistent by sub-proof % 109.54/15.26 | | | | | | #1. % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | Case 2: % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (81) with all_298_1, simplifying with % 109.54/15.26 | | | | | | (37), (51) gives: % 109.54/15.26 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_298_1) = v0) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (27) with all_298_1, all_93_1, % 109.54/15.26 | | | | | | simplifying with (37), (51) gives: % 109.54/15.26 | | | | | | (85) ? [v0: any] : ? [v1: $i] : (tl(all_93_1) = v1 & % 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 109.54/15.26 | | | | | | nil)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (28) with all_298_1, all_93_1, % 109.54/15.26 | | | | | | simplifying with (37), (51) gives: % 109.54/15.26 | | | | | | (86) ? [v0: any] : ? [v1: $i] : (hd(all_93_1) = v1 & % 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 109.54/15.26 | | | | | | all_298_1)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (10) with all_298_1, all_93_1, % 109.54/15.26 | | | | | | simplifying with (37), (51) gives: % 109.54/15.26 | | | | | | (87) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_1) = v1 & % 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (9) with all_298_1, all_93_1, simplifying % 109.54/15.26 | | | | | | with (37), (51) gives: % 109.54/15.26 | | | | | | (88) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_1) = v1 % 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (8) with all_298_1, all_93_1, simplifying % 109.54/15.26 | | | | | | with (37), (51) gives: % 109.54/15.26 | | | | | | (89) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_1) = v1 % 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (7) with all_298_1, all_93_1, simplifying % 109.54/15.26 | | | | | | with (37), (51) gives: % 109.54/15.26 | | | | | | (90) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_1) = v1 % 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (6) with all_298_1, all_93_1, simplifying % 109.54/15.26 | | | | | | with (37), (51) gives: % 109.54/15.26 | | | | | | (91) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_1) = v1 & % 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.26 | | | | | | % 109.54/15.26 | | | | | | GROUND_INST: instantiating (5) with all_298_1, all_93_1, simplifying % 109.54/15.26 | | | | | | with (37), (51) gives: % 109.54/15.27 | | | | | | (92) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_1) = v1 & % 109.54/15.27 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (4) with all_298_1, all_93_1, simplifying % 109.54/15.27 | | | | | | with (37), (51) gives: % 109.54/15.27 | | | | | | (93) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_1) = v1 & % 109.54/15.27 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (84) with fresh symbol all_1119_0 gives: % 109.54/15.27 | | | | | | (94) ~ (all_1119_0 = 0) & ssItem(all_298_1) = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (94) implies: % 109.54/15.27 | | | | | | (95) ~ (all_1119_0 = 0) % 109.54/15.27 | | | | | | (96) ssItem(all_298_1) = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (93) with fresh symbols all_1121_0, all_1121_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (97) cyclefreeP(all_93_1) = all_1121_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1121_1 & ( ~ (all_1121_1 = 0) | all_1121_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (97) implies: % 109.54/15.27 | | | | | | (98) ssItem(all_298_1) = all_1121_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (91) with fresh symbols all_1123_0, all_1123_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (99) strictorderP(all_93_1) = all_1123_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1123_1 & ( ~ (all_1123_1 = 0) | all_1123_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (99) implies: % 109.54/15.27 | | | | | | (100) ssItem(all_298_1) = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (90) with fresh symbols all_1125_0, all_1125_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (101) totalorderedP(all_93_1) = all_1125_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1125_1 & ( ~ (all_1125_1 = 0) | all_1125_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (101) implies: % 109.54/15.27 | | | | | | (102) ssItem(all_298_1) = all_1125_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (92) with fresh symbols all_1127_0, all_1127_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (103) totalorderP(all_93_1) = all_1127_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1127_1 & ( ~ (all_1127_1 = 0) | all_1127_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (103) implies: % 109.54/15.27 | | | | | | (104) ssItem(all_298_1) = all_1127_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (89) with fresh symbols all_1129_0, all_1129_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (105) strictorderedP(all_93_1) = all_1129_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1129_1 & ( ~ (all_1129_1 = 0) | all_1129_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (105) implies: % 109.54/15.27 | | | | | | (106) ssItem(all_298_1) = all_1129_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (87) with fresh symbols all_1131_0, all_1131_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (107) equalelemsP(all_93_1) = all_1131_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1131_1 & ( ~ (all_1131_1 = 0) | all_1131_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (107) implies: % 109.54/15.27 | | | | | | (108) ssItem(all_298_1) = all_1131_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (88) with fresh symbols all_1133_0, all_1133_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (109) duplicatefreeP(all_93_1) = all_1133_0 & ssItem(all_298_1) = % 109.54/15.27 | | | | | | all_1133_1 & ( ~ (all_1133_1 = 0) | all_1133_0 = 0) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (109) implies: % 109.54/15.27 | | | | | | (110) ssItem(all_298_1) = all_1133_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (86) with fresh symbols all_1135_0, all_1135_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (111) hd(all_93_1) = all_1135_0 & ssItem(all_298_1) = all_1135_1 % 109.54/15.27 | | | | | | & $i(all_1135_0) & ( ~ (all_1135_1 = 0) | all_1135_0 = % 109.54/15.27 | | | | | | all_298_1) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (111) implies: % 109.54/15.27 | | | | | | (112) ssItem(all_298_1) = all_1135_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | DELTA: instantiating (85) with fresh symbols all_1137_0, all_1137_1 % 109.54/15.27 | | | | | | gives: % 109.54/15.27 | | | | | | (113) tl(all_93_1) = all_1137_0 & ssItem(all_298_1) = all_1137_1 % 109.54/15.27 | | | | | | & $i(all_1137_0) & ( ~ (all_1137_1 = 0) | all_1137_0 = nil) % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | ALPHA: (113) implies: % 109.54/15.27 | | | | | | (114) ssItem(all_298_1) = all_1137_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with 0, all_1125_1, all_298_1, % 109.54/15.27 | | | | | | simplifying with (38), (102) gives: % 109.54/15.27 | | | | | | (115) all_1125_1 = 0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1125_1, all_1129_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (102), (106) gives: % 109.54/15.27 | | | | | | (116) all_1129_1 = all_1125_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1121_1, all_1129_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (98), (106) gives: % 109.54/15.27 | | | | | | (117) all_1129_1 = all_1121_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1131_1, all_1133_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (108), (110) gives: % 109.54/15.27 | | | | | | (118) all_1133_1 = all_1131_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1127_1, all_1133_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (104), (110) gives: % 109.54/15.27 | | | | | | (119) all_1133_1 = all_1127_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1129_1, all_1135_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (106), (112) gives: % 109.54/15.27 | | | | | | (120) all_1135_1 = all_1129_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1127_1, all_1135_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (104), (112) gives: % 109.54/15.27 | | | | | | (121) all_1135_1 = all_1127_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1123_1, all_1135_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (100), (112) gives: % 109.54/15.27 | | | | | | (122) all_1135_1 = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1133_1, all_1137_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (110), (114) gives: % 109.54/15.27 | | | | | | (123) all_1137_1 = all_1133_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1119_0, all_1137_1, % 109.54/15.27 | | | | | | all_298_1, simplifying with (96), (114) gives: % 109.54/15.27 | | | | | | (124) all_1137_1 = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | COMBINE_EQS: (123), (124) imply: % 109.54/15.27 | | | | | | (125) all_1133_1 = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | SIMP: (125) implies: % 109.54/15.27 | | | | | | (126) all_1133_1 = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | COMBINE_EQS: (120), (122) imply: % 109.54/15.27 | | | | | | (127) all_1129_1 = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | SIMP: (127) implies: % 109.54/15.27 | | | | | | (128) all_1129_1 = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | COMBINE_EQS: (121), (122) imply: % 109.54/15.27 | | | | | | (129) all_1127_1 = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | SIMP: (129) implies: % 109.54/15.27 | | | | | | (130) all_1127_1 = all_1123_1 % 109.54/15.27 | | | | | | % 109.54/15.27 | | | | | | COMBINE_EQS: (118), (126) imply: % 109.54/15.27 | | | | | | (131) all_1131_1 = all_1119_0 % 109.54/15.27 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (118), (119) imply: % 109.54/15.28 | | | | | | (132) all_1131_1 = all_1127_1 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (131), (132) imply: % 109.54/15.28 | | | | | | (133) all_1127_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (133) implies: % 109.54/15.28 | | | | | | (134) all_1127_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (116), (117) imply: % 109.54/15.28 | | | | | | (135) all_1125_1 = all_1121_1 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (135) implies: % 109.54/15.28 | | | | | | (136) all_1125_1 = all_1121_1 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (117), (128) imply: % 109.54/15.28 | | | | | | (137) all_1123_1 = all_1121_1 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (137) implies: % 109.54/15.28 | | | | | | (138) all_1123_1 = all_1121_1 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (130), (134) imply: % 109.54/15.28 | | | | | | (139) all_1123_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (139) implies: % 109.54/15.28 | | | | | | (140) all_1123_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (115), (136) imply: % 109.54/15.28 | | | | | | (141) all_1121_1 = 0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (141) implies: % 109.54/15.28 | | | | | | (142) all_1121_1 = 0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (138), (140) imply: % 109.54/15.28 | | | | | | (143) all_1121_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | SIMP: (143) implies: % 109.54/15.28 | | | | | | (144) all_1121_1 = all_1119_0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | COMBINE_EQS: (142), (144) imply: % 109.54/15.28 | | | | | | (145) all_1119_0 = 0 % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | REDUCE: (95), (145) imply: % 109.54/15.28 | | | | | | (146) $false % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | | CLOSE: (146) is inconsistent. % 109.54/15.28 | | | | | | % 109.54/15.28 | | | | | End of split % 109.54/15.28 | | | | | % 109.54/15.28 | | | | End of split % 109.54/15.28 | | | | % 109.54/15.28 | | | End of split % 109.54/15.28 | | | % 109.54/15.28 | | End of split % 109.54/15.28 | | % 109.54/15.28 | Case 2: % 109.54/15.28 | | % 109.54/15.28 | | (147) all_97_1 = nil & all_93_1 = nil % 109.54/15.28 | | % 109.54/15.28 | | ALPHA: (147) implies: % 109.54/15.28 | | (148) all_93_1 = nil % 109.54/15.28 | | (149) all_97_1 = nil % 109.54/15.28 | | % 109.54/15.28 | | REDUCE: (22), (149) imply: % 109.54/15.28 | | (150) neq(nil, nil) = 0 % 109.54/15.28 | | % 109.54/15.28 | | REF_CLOSE: (2), (14), (33), (149), (150) are inconsistent by sub-proof #1. % 109.54/15.28 | | % 109.54/15.28 | End of split % 109.54/15.28 | % 109.54/15.28 End of proof % 109.54/15.28 % 109.54/15.28 Sub-proof #1 shows that the following formulas are inconsistent: % 109.54/15.28 ---------------------------------------------------------------- % 109.54/15.28 (1) neq(nil, nil) = 0 % 109.54/15.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 109.54/15.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 109.54/15.28 (3) ~ (all_97_1 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0 = % 109.54/15.28 0) & ssList(nil) = v0) % 109.54/15.28 (4) all_97_1 = nil % 109.54/15.28 (5) ssList(nil) = 0 % 109.54/15.28 % 109.54/15.28 Begin of proof % 109.54/15.28 | % 109.54/15.28 | BETA: splitting (3) gives: % 109.54/15.28 | % 109.54/15.28 | Case 1: % 109.54/15.28 | | % 109.54/15.28 | | (6) ~ (neq(nil, nil) = 0) % 109.54/15.28 | | % 109.54/15.28 | | PRED_UNIFY: (1), (6) imply: % 109.54/15.28 | | (7) $false % 109.54/15.28 | | % 109.54/15.28 | | CLOSE: (7) is inconsistent. % 109.54/15.28 | | % 109.54/15.28 | Case 2: % 109.54/15.28 | | % 109.54/15.28 | | (8) ~ (all_97_1 = nil) | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 109.54/15.28 | | % 109.54/15.28 | | BETA: splitting (8) gives: % 109.54/15.28 | | % 109.54/15.28 | | Case 1: % 109.54/15.28 | | | % 109.54/15.28 | | | (9) ~ (all_97_1 = nil) % 109.54/15.28 | | | % 109.54/15.28 | | | REDUCE: (4), (9) imply: % 109.54/15.28 | | | (10) $false % 109.54/15.28 | | | % 109.54/15.28 | | | CLOSE: (10) is inconsistent. % 109.54/15.28 | | | % 109.54/15.28 | | Case 2: % 109.54/15.28 | | | % 109.54/15.28 | | | (11) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 109.54/15.28 | | | % 109.54/15.28 | | | DELTA: instantiating (11) with fresh symbol all_286_0 gives: % 109.54/15.28 | | | (12) ~ (all_286_0 = 0) & ssList(nil) = all_286_0 % 109.54/15.28 | | | % 109.54/15.28 | | | ALPHA: (12) implies: % 109.54/15.28 | | | (13) ~ (all_286_0 = 0) % 109.54/15.28 | | | (14) ssList(nil) = all_286_0 % 109.54/15.28 | | | % 109.54/15.28 | | | DELTA: instantiating (11) with fresh symbol all_288_0 gives: % 109.54/15.28 | | | (15) ~ (all_288_0 = 0) & ssList(nil) = all_288_0 % 109.54/15.28 | | | % 109.54/15.28 | | | ALPHA: (15) implies: % 109.54/15.28 | | | (16) ssList(nil) = all_288_0 % 109.54/15.28 | | | % 109.54/15.28 | | | GROUND_INST: instantiating (2) with 0, all_288_0, nil, simplifying with % 109.54/15.28 | | | (5), (16) gives: % 109.54/15.28 | | | (17) all_288_0 = 0 % 109.54/15.28 | | | % 109.54/15.28 | | | GROUND_INST: instantiating (2) with all_286_0, all_288_0, nil, simplifying % 109.54/15.28 | | | with (14), (16) gives: % 109.54/15.28 | | | (18) all_288_0 = all_286_0 % 109.54/15.28 | | | % 109.54/15.28 | | | COMBINE_EQS: (17), (18) imply: % 109.54/15.28 | | | (19) all_286_0 = 0 % 109.54/15.28 | | | % 109.54/15.28 | | | REDUCE: (13), (19) imply: % 109.54/15.28 | | | (20) $false % 109.54/15.28 | | | % 109.54/15.28 | | | CLOSE: (20) is inconsistent. % 109.54/15.28 | | | % 109.54/15.28 | | End of split % 109.54/15.28 | | % 109.54/15.28 | End of split % 109.54/15.28 | % 109.54/15.28 End of proof % 109.54/15.28 % 109.54/15.28 Sub-proof #2 shows that the following formulas are inconsistent: % 109.54/15.28 ---------------------------------------------------------------- % 109.54/15.28 (1) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0 % 109.54/15.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 109.54/15.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 109.54/15.28 (3) ssList(all_93_1) = 0 % 109.54/15.28 % 109.54/15.28 Begin of proof % 109.54/15.28 | % 109.54/15.28 | ALPHA: (1) implies: % 109.54/15.28 | (4) ~ (all_314_0 = 0) % 109.54/15.28 | (5) ssList(all_93_1) = all_314_0 % 109.54/15.28 | % 109.54/15.28 | GROUND_INST: instantiating (2) with 0, all_314_0, all_93_1, simplifying with % 109.54/15.28 | (3), (5) gives: % 109.54/15.29 | (6) all_314_0 = 0 % 109.54/15.29 | % 109.54/15.29 | REDUCE: (4), (6) imply: % 109.54/15.29 | (7) $false % 109.54/15.29 | % 109.54/15.29 | CLOSE: (7) is inconsistent. % 109.54/15.29 | % 109.54/15.29 End of proof % 109.54/15.29 % SZS output end Proof for theBenchmark % 109.54/15.29 % 109.54/15.29 14628ms %------------------------------------------------------------------------------