%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC112+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 : n020.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 20:49:43 EDT 2023 % Result : Theorem 26.30s 5.98s % Output : Proof 60.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWC112+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Mon Aug 28 17:41:28 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.66 Running up to 7 provers in parallel. % 0.60/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.60/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.60/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.60/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.60/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.60/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.60/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 5.26/1.80 Prover 1: Preprocessing ... % 5.26/1.81 Prover 4: Preprocessing ... % 5.66/1.85 Prover 5: Preprocessing ... % 5.66/1.85 Prover 0: Preprocessing ... % 5.66/1.85 Prover 3: Preprocessing ... % 5.66/1.85 Prover 2: Preprocessing ... % 5.66/1.86 Prover 6: Preprocessing ... % 15.19/3.74 Prover 1: Constructing countermodel ... % 15.19/3.77 Prover 2: Proving ... % 15.19/3.80 Prover 5: Constructing countermodel ... % 15.19/3.83 Prover 3: Constructing countermodel ... % 15.92/3.91 Prover 6: Proving ... % 23.29/5.33 Prover 4: Constructing countermodel ... % 24.74/5.63 Prover 0: Proving ... % 26.30/5.98 Prover 3: proved (5302ms) % 26.30/5.98 % 26.30/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.30/5.98 % 26.30/5.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.30/5.99 Prover 5: stopped % 26.30/5.99 Prover 2: stopped % 26.76/6.01 Prover 0: stopped % 26.76/6.02 Prover 6: stopped % 26.76/6.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.76/6.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.76/6.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.76/6.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.90/6.40 Prover 7: Preprocessing ... % 28.90/6.48 Prover 8: Preprocessing ... % 29.39/6.50 Prover 10: Preprocessing ... % 29.39/6.50 Prover 11: Preprocessing ... % 29.39/6.52 Prover 13: Preprocessing ... % 30.48/6.74 Prover 7: Constructing countermodel ... % 30.48/6.78 Prover 10: Constructing countermodel ... % 31.41/6.98 Prover 13: Constructing countermodel ... % 32.48/7.17 Prover 8: Warning: ignoring some quantifiers % 32.48/7.19 Prover 8: Constructing countermodel ... % 39.22/8.39 Prover 11: Constructing countermodel ... % 52.74/10.87 Prover 13: stopped % 53.10/10.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 53.45/11.09 Prover 16: Preprocessing ... % 55.19/11.30 Prover 16: Constructing countermodel ... % 59.16/12.08 Prover 1: Found proof (size 138) % 59.16/12.08 Prover 1: proved (11401ms) % 59.16/12.08 Prover 8: stopped % 59.16/12.08 Prover 4: stopped % 59.16/12.08 Prover 16: stopped % 59.58/12.08 Prover 11: stopped % 59.58/12.09 Prover 7: stopped % 59.58/12.09 Prover 10: stopped % 59.58/12.09 % 59.58/12.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 59.58/12.09 % 59.58/12.10 % SZS output start Proof for theBenchmark % 59.65/12.10 Assumptions after simplification: % 59.65/12.10 --------------------------------- % 59.65/12.10 % 59.65/12.10 (ax15) % 59.70/12.13 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 59.70/12.13 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 59.70/12.13 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 59.70/12.13 % 59.70/12.13 (ax17) % 59.70/12.13 ssList(nil) = 0 & $i(nil) % 59.70/12.13 % 59.70/12.13 (ax58) % 59.70/12.13 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ % 59.70/12.13 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 59.70/12.14 = nil) & ( ~ (v0 = nil) | v1 = 0))) % 59.70/12.14 % 59.70/12.14 (ax7) % 59.70/12.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 59.70/12.14 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 59.70/12.14 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 59.70/12.14 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 59.70/12.14 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 59.70/12.14 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 59.70/12.14 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 59.70/12.14 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 59.70/12.14 ssList(v5) = v6))))))) % 59.70/12.14 % 59.70/12.14 (co1) % 59.70/12.15 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 59.70/12.15 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2, v0) = v4 % 59.70/12.15 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5: any] : % 59.70/12.15 (strictorderedP(v0) = v5 & ? [v6: $i] : ? [v7: $i] : (ssList(v6) = 0 & % 59.70/12.15 app(v6, v0) = v7 & $i(v7) & $i(v6) & ? [v8: $i] : (v5 = 0 & % 59.70/12.15 ssList(v8) = 0 & app(v7, v8) = v2 & $i(v8) & ! [v9: $i] : ! [v10: % 59.70/12.15 $i] : ( ~ (cons(v9, nil) = v10) | ~ $i(v9) | ? [v11: int] : ( ~ % 59.70/12.15 (v11 = 0) & ssItem(v9) = v11) | ! [v11: $i] : ( ~ (app(v11, % 59.70/12.15 v10) = v6) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0) & % 59.70/12.15 ssList(v11) = v12) | ! [v12: $i] : ! [v13: $i] : ( ~ % 59.70/12.15 (cons(v12, nil) = v13) | ~ $i(v12) | ? [v14: any] : ? [v15: % 59.70/12.15 any] : (lt(v9, v12) = v15 & ssItem(v12) = v14 & ( ~ (v14 = % 59.70/12.15 0) | ! [v16: $i] : ( ~ (v15 = 0) | ~ (app(v13, v16) = % 59.70/12.15 v0) | ~ $i(v16) | ? [v17: int] : ( ~ (v17 = 0) & % 59.70/12.15 ssList(v16) = v17))))))) & ! [v9: $i] : ! [v10: $i] % 59.70/12.15 : ( ~ (cons(v9, nil) = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = % 59.70/12.15 0) & ssItem(v9) = v11) | ! [v11: $i] : ( ~ (app(v10, v11) = % 59.70/12.15 v8) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0) & ssList(v11) % 59.70/12.15 = v12) | ! [v12: $i] : ! [v13: $i] : ( ~ (cons(v12, nil) = % 59.70/12.15 v13) | ~ $i(v12) | ? [v14: any] : ? [v15: any] : (lt(v12, % 59.70/12.15 v9) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | ! [v16: % 59.70/12.15 $i] : ( ~ (v15 = 0) | ~ (app(v16, v13) = v0) | ~ % 59.70/12.15 $i(v16) | ? [v17: int] : ( ~ (v17 = 0) & ssList(v16) = % 59.70/12.15 v17))))))))) & ( ~ (v0 = nil) | v2 = nil) & ((v3 = 0 & % 59.70/12.15 ( ~ (v4 = 0) | ~ (v1 = 0))) | (v2 = nil & ~ (v0 = nil)))))) % 59.70/12.15 % 59.70/12.15 (function-axioms) % 59.70/12.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 59.70/12.16 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 59.70/12.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 59.70/12.16 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 59.70/12.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 59.70/12.16 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 59.70/12.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 59.70/12.16 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 59.70/12.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 59.70/12.16 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 59.70/12.16 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 59.70/12.16 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 59.70/12.16 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 59.70/12.16 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 59.70/12.16 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 59.70/12.16 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 59.70/12.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 59.70/12.16 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 59.70/12.16 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 59.70/12.16 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 59.70/12.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 59.70/12.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 59.70/12.16 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 59.70/12.16 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 59.70/12.16 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 59.70/12.16 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 59.70/12.16 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 59.70/12.16 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 59.70/12.16 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 59.70/12.16 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 59.70/12.16 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 59.70/12.16 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 59.70/12.16 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 59.70/12.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 59.70/12.16 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 59.70/12.16 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 59.70/12.16 % 59.70/12.16 Further assumptions not needed in the proof: % 59.70/12.16 -------------------------------------------- % 59.70/12.17 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 59.70/12.17 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, % 59.70/12.17 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, % 59.70/12.17 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, % 59.70/12.17 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, % 59.70/12.17 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, % 59.70/12.17 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 59.70/12.17 % 59.70/12.17 Those formulas are unsatisfiable: % 59.70/12.17 --------------------------------- % 59.70/12.17 % 59.70/12.17 Begin of proof % 59.70/12.17 | % 59.70/12.17 | ALPHA: (ax17) implies: % 59.70/12.17 | (1) ssList(nil) = 0 % 59.70/12.17 | % 59.70/12.17 | ALPHA: (ax58) implies: % 59.70/12.17 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) | % 59.70/12.17 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 = % 59.70/12.17 | nil) & ( ~ (v0 = nil) | v1 = 0))) % 59.70/12.17 | % 59.70/12.17 | ALPHA: (co1) implies: % 59.70/12.17 | (3) $i(nil) % 59.70/12.18 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 59.70/12.18 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2, % 59.70/12.18 | v0) = v4 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5: % 59.70/12.18 | any] : (strictorderedP(v0) = v5 & ? [v6: $i] : ? [v7: $i] : % 59.70/12.18 | (ssList(v6) = 0 & app(v6, v0) = v7 & $i(v7) & $i(v6) & ? [v8: % 59.70/12.18 | $i] : (v5 = 0 & ssList(v8) = 0 & app(v7, v8) = v2 & $i(v8) & % 59.70/12.18 | ! [v9: $i] : ! [v10: $i] : ( ~ (cons(v9, nil) = v10) | ~ % 59.70/12.18 | $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssItem(v9) = v11) % 59.70/12.18 | | ! [v11: $i] : ( ~ (app(v11, v10) = v6) | ~ $i(v11) | ? % 59.70/12.18 | [v12: int] : ( ~ (v12 = 0) & ssList(v11) = v12) | ! % 59.70/12.18 | [v12: $i] : ! [v13: $i] : ( ~ (cons(v12, nil) = v13) | % 59.70/12.18 | ~ $i(v12) | ? [v14: any] : ? [v15: any] : (lt(v9, % 59.70/12.18 | v12) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | ! % 59.70/12.18 | [v16: $i] : ( ~ (v15 = 0) | ~ (app(v13, v16) = v0) % 59.70/12.18 | | ~ $i(v16) | ? [v17: int] : ( ~ (v17 = 0) & % 59.70/12.18 | ssList(v16) = v17))))))) & ! [v9: $i] : ! % 59.70/12.18 | [v10: $i] : ( ~ (cons(v9, nil) = v10) | ~ $i(v9) | ? [v11: % 59.70/12.18 | int] : ( ~ (v11 = 0) & ssItem(v9) = v11) | ! [v11: $i] : % 59.70/12.18 | ( ~ (app(v10, v11) = v8) | ~ $i(v11) | ? [v12: int] : ( ~ % 59.70/12.18 | (v12 = 0) & ssList(v11) = v12) | ! [v12: $i] : ! % 59.70/12.18 | [v13: $i] : ( ~ (cons(v12, nil) = v13) | ~ $i(v12) | ? % 59.70/12.18 | [v14: any] : ? [v15: any] : (lt(v12, v9) = v15 & % 59.70/12.18 | ssItem(v12) = v14 & ( ~ (v14 = 0) | ! [v16: $i] : ( % 59.70/12.18 | ~ (v15 = 0) | ~ (app(v16, v13) = v0) | ~ % 59.70/12.18 | $i(v16) | ? [v17: int] : ( ~ (v17 = 0) & % 59.70/12.18 | ssList(v16) = v17))))))))) & ( ~ (v0 = nil) | % 59.70/12.18 | v2 = nil) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0))) | (v2 = nil % 59.70/12.18 | & ~ (v0 = nil)))))) % 59.70/12.18 | % 59.70/12.18 | ALPHA: (function-axioms) implies: % 59.70/12.19 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 59.70/12.19 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 59.70/12.19 | % 59.70/12.19 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives: % 59.70/12.19 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & % 59.70/12.19 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1) = v2 % 59.70/12.19 | & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] : % 59.70/12.19 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : ? [v5: $i] : % 59.70/12.19 | (ssList(v4) = 0 & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ? % 59.70/12.19 | [v6: $i] : (v3 = 0 & ssList(v6) = 0 & app(v5, v6) = v0 & $i(v6) & % 59.70/12.19 | ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ % 59.70/12.19 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssItem(v7) = v9) | ! % 59.70/12.19 | [v9: $i] : ( ~ (app(v9, v8) = v4) | ~ $i(v9) | ? [v10: int] % 59.70/12.19 | : ( ~ (v10 = 0) & ssList(v9) = v10) | ! [v10: $i] : ! % 59.70/12.19 | [v11: $i] : ( ~ (cons(v10, nil) = v11) | ~ $i(v10) | ? % 59.70/12.19 | [v12: any] : ? [v13: any] : (lt(v7, v10) = v13 & % 59.70/12.19 | ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14: $i] : ( ~ % 59.70/12.19 | (v13 = 0) | ~ (app(v11, v14) = all_93_1) | ~ % 59.70/12.19 | $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & % 59.70/12.19 | ssList(v14) = v15))))))) & ! [v7: $i] : ! [v8: % 59.70/12.19 | $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: int] : ( % 59.70/12.19 | ~ (v9 = 0) & ssItem(v7) = v9) | ! [v9: $i] : ( ~ (app(v8, % 59.70/12.19 | v9) = v6) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & % 59.70/12.19 | ssList(v9) = v10) | ! [v10: $i] : ! [v11: $i] : ( ~ % 59.70/12.19 | (cons(v10, nil) = v11) | ~ $i(v10) | ? [v12: any] : ? % 59.70/12.19 | [v13: any] : (lt(v10, v7) = v13 & ssItem(v10) = v12 & ( ~ % 59.70/12.19 | (v12 = 0) | ! [v14: $i] : ( ~ (v13 = 0) | ~ % 59.70/12.19 | (app(v14, v11) = all_93_1) | ~ $i(v14) | ? [v15: % 59.70/12.19 | int] : ( ~ (v15 = 0) & ssList(v14) = v15))))))))) % 59.70/12.19 | & ( ~ (all_93_1 = nil) | v0 = nil) & ((v1 = 0 & ( ~ (v2 = 0) | ~ % 59.70/12.19 | (all_93_0 = 0))) | (v0 = nil & ~ (all_93_1 = nil))))) % 59.70/12.19 | % 59.70/12.19 | ALPHA: (6) implies: % 59.70/12.19 | (7) $i(all_93_1) % 59.70/12.19 | (8) neq(all_93_1, nil) = all_93_0 % 59.70/12.19 | (9) ssList(all_93_1) = 0 % 59.70/12.20 | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1) = % 59.70/12.20 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] : % 59.70/12.20 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : ? [v5: $i] : % 59.70/12.20 | (ssList(v4) = 0 & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ? % 59.70/12.20 | [v6: $i] : (v3 = 0 & ssList(v6) = 0 & app(v5, v6) = v0 & $i(v6) % 59.70/12.20 | & ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ % 59.70/12.20 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssItem(v7) = v9) | ! % 59.70/12.20 | [v9: $i] : ( ~ (app(v9, v8) = v4) | ~ $i(v9) | ? [v10: % 59.70/12.20 | int] : ( ~ (v10 = 0) & ssList(v9) = v10) | ! [v10: $i] % 59.70/12.20 | : ! [v11: $i] : ( ~ (cons(v10, nil) = v11) | ~ $i(v10) | % 59.70/12.20 | ? [v12: any] : ? [v13: any] : (lt(v7, v10) = v13 & % 59.70/12.20 | ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14: $i] : ( ~ % 59.70/12.20 | (v13 = 0) | ~ (app(v11, v14) = all_93_1) | ~ % 59.70/12.20 | $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & % 59.70/12.20 | ssList(v14) = v15))))))) & ! [v7: $i] : ! [v8: % 59.70/12.20 | $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: int] : % 59.70/12.20 | ( ~ (v9 = 0) & ssItem(v7) = v9) | ! [v9: $i] : ( ~ (app(v8, % 59.70/12.20 | v9) = v6) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) % 59.70/12.20 | & ssList(v9) = v10) | ! [v10: $i] : ! [v11: $i] : ( ~ % 59.70/12.20 | (cons(v10, nil) = v11) | ~ $i(v10) | ? [v12: any] : ? % 59.70/12.20 | [v13: any] : (lt(v10, v7) = v13 & ssItem(v10) = v12 & ( % 59.70/12.20 | ~ (v12 = 0) | ! [v14: $i] : ( ~ (v13 = 0) | ~ % 59.70/12.20 | (app(v14, v11) = all_93_1) | ~ $i(v14) | ? [v15: % 59.70/12.20 | int] : ( ~ (v15 = 0) & ssList(v14) = % 59.70/12.20 | v15))))))))) & ( ~ (all_93_1 = nil) | v0 = nil) % 59.70/12.20 | & ((v1 = 0 & ( ~ (v2 = 0) | ~ (all_93_0 = 0))) | (v0 = nil & ~ % 59.70/12.20 | (all_93_1 = nil))))) % 59.70/12.20 | % 59.70/12.20 | DELTA: instantiating (10) with fresh symbols all_97_0, all_97_1, all_97_2 % 59.70/12.20 | gives: % 59.70/12.21 | (11) segmentP(all_97_2, all_93_1) = all_97_0 & ssList(all_97_2) = 0 & % 59.70/12.21 | neq(all_97_2, nil) = all_97_1 & $i(all_97_2) & ? [v0: any] : % 59.70/12.21 | (strictorderedP(all_93_1) = v0 & ? [v1: $i] : ? [v2: $i] : % 59.70/12.21 | (ssList(v1) = 0 & app(v1, all_93_1) = v2 & $i(v2) & $i(v1) & ? [v3: % 59.70/12.21 | $i] : (v0 = 0 & ssList(v3) = 0 & app(v2, v3) = all_97_2 & $i(v3) % 59.70/12.21 | & ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ % 59.70/12.21 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! % 59.70/12.21 | [v6: $i] : ( ~ (app(v6, v5) = v1) | ~ $i(v6) | ? [v7: int] : % 59.70/12.21 | ( ~ (v7 = 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] % 59.70/12.21 | : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? % 59.70/12.21 | [v10: any] : (lt(v4, v7) = v10 & ssItem(v7) = v9 & ( ~ (v9 % 59.70/12.21 | = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v8, % 59.70/12.21 | v11) = all_93_1) | ~ $i(v11) | ? [v12: int] : % 59.70/12.21 | ( ~ (v12 = 0) & ssList(v11) = v12))))))) & ! [v4: % 59.70/12.21 | $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? % 59.70/12.21 | [v6: int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( % 59.70/12.21 | ~ (app(v5, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = % 59.70/12.21 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] : ( ~ % 59.70/12.21 | (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: % 59.70/12.21 | any] : (lt(v7, v4) = v10 & ssItem(v7) = v9 & ( ~ (v9 = % 59.70/12.21 | 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v11, v8) % 59.70/12.21 | = all_93_1) | ~ $i(v11) | ? [v12: int] : ( ~ % 59.70/12.21 | (v12 = 0) & ssList(v11) = v12))))))))) & ( ~ % 59.70/12.21 | (all_93_1 = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~ % 60.10/12.21 | (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ % 60.10/12.21 | (all_93_1 = nil)))) % 60.10/12.21 | % 60.10/12.21 | ALPHA: (11) implies: % 60.10/12.21 | (12) $i(all_97_2) % 60.10/12.21 | (13) neq(all_97_2, nil) = all_97_1 % 60.10/12.21 | (14) ssList(all_97_2) = 0 % 60.10/12.21 | (15) segmentP(all_97_2, all_93_1) = all_97_0 % 60.10/12.22 | (16) ? [v0: any] : (strictorderedP(all_93_1) = v0 & ? [v1: $i] : ? [v2: % 60.10/12.22 | $i] : (ssList(v1) = 0 & app(v1, all_93_1) = v2 & $i(v2) & $i(v1) & % 60.10/12.22 | ? [v3: $i] : (v0 = 0 & ssList(v3) = 0 & app(v2, v3) = all_97_2 & % 60.10/12.22 | $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | % 60.10/12.22 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! % 60.10/12.22 | [v6: $i] : ( ~ (app(v6, v5) = v1) | ~ $i(v6) | ? [v7: int] : % 60.10/12.22 | ( ~ (v7 = 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] % 60.10/12.22 | : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? % 60.10/12.22 | [v10: any] : (lt(v4, v7) = v10 & ssItem(v7) = v9 & ( ~ (v9 % 60.10/12.22 | = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v8, % 60.10/12.22 | v11) = all_93_1) | ~ $i(v11) | ? [v12: int] : % 60.10/12.22 | ( ~ (v12 = 0) & ssList(v11) = v12))))))) & ! [v4: % 60.10/12.22 | $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? % 60.10/12.22 | [v6: int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( % 60.10/12.22 | ~ (app(v5, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = % 60.10/12.22 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] : ( ~ % 60.10/12.22 | (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: % 60.10/12.22 | any] : (lt(v7, v4) = v10 & ssItem(v7) = v9 & ( ~ (v9 = % 60.10/12.22 | 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v11, v8) % 60.10/12.22 | = all_93_1) | ~ $i(v11) | ? [v12: int] : ( ~ % 60.10/12.22 | (v12 = 0) & ssList(v11) = v12))))))))) & ( ~ % 60.10/12.22 | (all_93_1 = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~ % 60.10/12.22 | (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ % 60.10/12.22 | (all_93_1 = nil)))) % 60.10/12.22 | % 60.10/12.22 | DELTA: instantiating (16) with fresh symbol all_99_0 gives: % 60.10/12.22 | (17) strictorderedP(all_93_1) = all_99_0 & ? [v0: $i] : ? [v1: $i] : % 60.10/12.22 | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: % 60.10/12.22 | $i] : (all_99_0 = 0 & ssList(v2) = 0 & app(v1, v2) = all_97_2 & % 60.10/12.22 | $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ % 60.10/12.22 | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! % 60.10/12.22 | [v5: $i] : ( ~ (app(v5, v4) = v0) | ~ $i(v5) | ? [v6: int] : ( % 60.10/12.22 | ~ (v6 = 0) & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : % 60.10/12.22 | ( ~ (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 60.10/12.22 | any] : (lt(v3, v6) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) | % 60.10/12.22 | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v7, v10) = % 60.10/12.22 | all_93_1) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 60.10/12.22 | 0) & ssList(v10) = v11))))))) & ! [v3: $i] : ! % 60.10/12.22 | [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: int] : ( % 60.10/12.22 | ~ (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : ( ~ (app(v4, v5) % 60.10/12.22 | = v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v5) % 60.10/12.22 | = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v6, nil) = v7) % 60.10/12.22 | | ~ $i(v6) | ? [v8: any] : ? [v9: any] : (lt(v6, v3) = v9 % 60.10/12.22 | & ssItem(v6) = v8 & ( ~ (v8 = 0) | ! [v10: $i] : ( ~ (v9 % 60.10/12.22 | = 0) | ~ (app(v10, v7) = all_93_1) | ~ $i(v10) | % 60.10/12.22 | ? [v11: int] : ( ~ (v11 = 0) & ssList(v10) = % 60.10/12.22 | v11))))))))) & ( ~ (all_93_1 = nil) | all_97_2 = % 60.10/12.22 | nil) & ((all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | % 60.10/12.22 | (all_97_2 = nil & ~ (all_93_1 = nil))) % 60.10/12.22 | % 60.10/12.22 | ALPHA: (17) implies: % 60.10/12.22 | (18) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = % 60.10/12.22 | nil & ~ (all_93_1 = nil)) % 60.10/12.22 | (19) ~ (all_93_1 = nil) | all_97_2 = nil % 60.10/12.23 | (20) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_93_1) = v1 & % 60.10/12.23 | $i(v1) & $i(v0) & ? [v2: $i] : (all_99_0 = 0 & ssList(v2) = 0 & % 60.10/12.23 | app(v1, v2) = all_97_2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ % 60.10/12.23 | (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 60.10/12.23 | ssItem(v3) = v5) | ! [v5: $i] : ( ~ (app(v5, v4) = v0) | ~ % 60.10/12.23 | $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v5) = v6) | ! % 60.10/12.23 | [v6: $i] : ! [v7: $i] : ( ~ (cons(v6, nil) = v7) | ~ $i(v6) % 60.10/12.23 | | ? [v8: any] : ? [v9: any] : (lt(v3, v6) = v9 & % 60.10/12.23 | ssItem(v6) = v8 & ( ~ (v8 = 0) | ! [v10: $i] : ( ~ (v9 = % 60.10/12.23 | 0) | ~ (app(v7, v10) = all_93_1) | ~ $i(v10) | ? % 60.10/12.23 | [v11: int] : ( ~ (v11 = 0) & ssList(v10) = v11))))))) % 60.10/12.23 | & ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) % 60.10/12.23 | | ? [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : % 60.10/12.23 | ( ~ (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 60.10/12.23 | & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 60.10/12.23 | (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 60.10/12.23 | any] : (lt(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) | % 60.10/12.23 | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) = % 60.10/12.23 | all_93_1) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 60.10/12.23 | 0) & ssList(v10) = v11))))))))) % 60.10/12.23 | % 60.10/12.23 | DELTA: instantiating (20) with fresh symbols all_101_0, all_101_1 gives: % 60.10/12.23 | (21) ssList(all_101_1) = 0 & app(all_101_1, all_93_1) = all_101_0 & % 60.10/12.23 | $i(all_101_0) & $i(all_101_1) & ? [v0: $i] : (all_99_0 = 0 & % 60.10/12.23 | ssList(v0) = 0 & app(all_101_0, v0) = all_97_2 & $i(v0) & ! [v1: % 60.10/12.23 | $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: % 60.10/12.23 | int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] : ( ~ % 60.10/12.23 | (app(v3, v2) = all_101_1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 60.10/12.23 | 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 60.10/12.23 | (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] % 60.10/12.23 | : (lt(v1, v4) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8: % 60.10/12.23 | $i] : ( ~ (v7 = 0) | ~ (app(v5, v8) = all_93_1) | ~ % 60.10/12.23 | $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) = % 60.10/12.23 | v9))))))) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, % 60.10/12.23 | nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 60.10/12.23 | ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ % 60.10/12.23 | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = v4) | ! % 60.10/12.23 | [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | % 60.10/12.23 | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 & ssItem(v4) = % 60.10/12.23 | v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, % 60.10/12.23 | v5) = all_93_1) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 % 60.10/12.23 | = 0) & ssList(v8) = v9)))))))) % 60.10/12.23 | % 60.10/12.23 | ALPHA: (21) implies: % 60.10/12.23 | (22) $i(all_101_1) % 60.10/12.23 | (23) app(all_101_1, all_93_1) = all_101_0 % 60.10/12.23 | (24) ssList(all_101_1) = 0 % 60.10/12.24 | (25) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_101_0, v0) = % 60.10/12.24 | all_97_2 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = % 60.10/12.24 | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) % 60.10/12.24 | | ! [v3: $i] : ( ~ (app(v3, v2) = all_101_1) | ~ $i(v3) | ? % 60.10/12.24 | [v4: int] : ( ~ (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! % 60.10/12.24 | [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : % 60.10/12.24 | ? [v7: any] : (lt(v1, v4) = v7 & ssItem(v4) = v6 & ( ~ (v6 = % 60.10/12.24 | 0) | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v5, v8) = % 60.10/12.24 | all_93_1) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & % 60.10/12.24 | ssList(v8) = v9))))))) & ! [v1: $i] : ! [v2: $i] : ( % 60.10/12.24 | ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 60.10/12.24 | ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ % 60.10/12.24 | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = v4) | ! % 60.10/12.24 | [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | % 60.10/12.24 | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 & ssItem(v4) = % 60.10/12.24 | v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, % 60.10/12.24 | v5) = all_93_1) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 % 60.10/12.24 | = 0) & ssList(v8) = v9)))))))) % 60.10/12.24 | % 60.10/12.24 | DELTA: instantiating (25) with fresh symbol all_103_0 gives: % 60.10/12.24 | (26) all_99_0 = 0 & ssList(all_103_0) = 0 & app(all_101_0, all_103_0) = % 60.10/12.24 | all_97_2 & $i(all_103_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 60.10/12.24 | nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 60.10/12.24 | ssItem(v0) = v2) | ! [v2: $i] : ( ~ (app(v2, v1) = all_101_1) | % 60.10/12.24 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | ! % 60.10/12.24 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? % 60.10/12.24 | [v5: any] : ? [v6: any] : (lt(v0, v3) = v6 & ssItem(v3) = v5 & % 60.10/12.24 | ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (v6 = 0) | ~ (app(v4, v7) = % 60.10/12.24 | all_93_1) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 60.10/12.24 | ssList(v7) = v8))))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 60.10/12.24 | (cons(v0, nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 60.10/12.24 | ssItem(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = all_103_0) | % 60.10/12.24 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | ! % 60.10/12.24 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? % 60.10/12.24 | [v5: any] : ? [v6: any] : (lt(v3, v0) = v6 & ssItem(v3) = v5 & % 60.10/12.24 | ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) = % 60.10/12.24 | all_93_1) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 60.10/12.24 | ssList(v7) = v8))))))) % 60.10/12.24 | % 60.10/12.24 | ALPHA: (26) implies: % 60.10/12.24 | (27) $i(all_103_0) % 60.10/12.24 | (28) app(all_101_0, all_103_0) = all_97_2 % 60.10/12.24 | (29) ssList(all_103_0) = 0 % 60.10/12.24 | % 60.10/12.24 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (7), (9) % 60.10/12.24 | gives: % 60.10/12.24 | (30) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0) % 60.10/12.24 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 60.10/12.24 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1))) % 60.10/12.24 | % 60.10/12.24 | GROUND_INST: instantiating (ax7) with all_97_2, simplifying with (12), (14) % 60.10/12.24 | gives: % 60.10/12.24 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_97_2, v0) = v1) | ~ % 60.10/12.24 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 60.10/12.24 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 60.10/12.24 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 60.10/12.25 | app(v3, v4) = all_97_2 & $i(v4)))) & (v1 = 0 | ! [v2: $i] : % 60.10/12.25 | ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] % 60.10/12.25 | : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, % 60.10/12.25 | v4) = all_97_2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = % 60.10/12.25 | 0) & ssList(v4) = v5)))))) % 60.10/12.25 | % 60.10/12.25 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (12), (14) % 60.10/12.25 | gives: % 60.10/12.25 | (32) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0) % 60.10/12.25 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 60.10/12.25 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2))) % 60.10/12.25 | % 60.10/12.25 | GROUND_INST: instantiating (32) with nil, all_97_1, simplifying with (3), (13) % 60.10/12.25 | gives: % 60.10/12.25 | (33) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0) % 60.10/12.25 | | ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil)) % 60.10/12.25 | % 60.10/12.25 | GROUND_INST: instantiating (31) with all_93_1, all_97_0, simplifying with (7), % 60.10/12.25 | (15) gives: % 60.10/12.25 | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 % 60.10/12.25 | = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 60.10/12.25 | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = % 60.10/12.25 | 0 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_0 = 0 | ! % 60.10/12.25 | [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) % 60.10/12.25 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : % 60.10/12.25 | ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ % 60.10/12.25 | (v3 = 0) & ssList(v2) = v3))))) % 60.10/12.25 | % 60.10/12.25 | GROUND_INST: instantiating (30) with nil, all_93_0, simplifying with (3), (8) % 60.10/12.25 | gives: % 60.10/12.25 | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0) % 60.10/12.25 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil)) % 60.10/12.25 | % 60.10/12.25 | BETA: splitting (18) gives: % 60.10/12.25 | % 60.10/12.25 | Case 1: % 60.10/12.25 | | % 60.10/12.25 | | (36) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0)) % 60.10/12.25 | | % 60.10/12.25 | | ALPHA: (36) implies: % 60.10/12.25 | | (37) all_97_1 = 0 % 60.10/12.25 | | (38) ~ (all_97_0 = 0) | ~ (all_93_0 = 0) % 60.10/12.25 | | % 60.10/12.25 | | BETA: splitting (33) gives: % 60.10/12.25 | | % 60.10/12.25 | | Case 1: % 60.10/12.25 | | | % 60.10/12.25 | | | (39) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 60.10/12.25 | | | % 60.10/12.25 | | | REF_CLOSE: (1), (5), (39) are inconsistent by sub-proof #3. % 60.10/12.25 | | | % 60.10/12.25 | | Case 2: % 60.10/12.25 | | | % 60.10/12.25 | | | (40) ( ~ (all_97_1 = 0) | ~ (all_97_2 = nil)) & (all_97_1 = 0 | % 60.10/12.25 | | | all_97_2 = nil) % 60.10/12.25 | | | % 60.10/12.25 | | | ALPHA: (40) implies: % 60.10/12.25 | | | (41) ~ (all_97_1 = 0) | ~ (all_97_2 = nil) % 60.10/12.25 | | | % 60.10/12.25 | | | BETA: splitting (41) gives: % 60.10/12.25 | | | % 60.10/12.25 | | | Case 1: % 60.10/12.25 | | | | % 60.10/12.25 | | | | (42) ~ (all_97_2 = nil) % 60.10/12.25 | | | | % 60.10/12.25 | | | | BETA: splitting (19) gives: % 60.10/12.25 | | | | % 60.10/12.25 | | | | Case 1: % 60.10/12.25 | | | | | % 60.10/12.25 | | | | | (43) ~ (all_93_1 = nil) % 60.10/12.25 | | | | | % 60.10/12.25 | | | | | BETA: splitting (35) gives: % 60.10/12.25 | | | | | % 60.10/12.25 | | | | | Case 1: % 60.10/12.25 | | | | | | % 60.10/12.25 | | | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 60.10/12.25 | | | | | | % 60.10/12.25 | | | | | | REF_CLOSE: (1), (5), (44) are inconsistent by sub-proof #3. % 60.10/12.25 | | | | | | % 60.10/12.25 | | | | | Case 2: % 60.10/12.25 | | | | | | % 60.10/12.26 | | | | | | (45) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | % 60.10/12.26 | | | | | | all_93_1 = nil) % 60.10/12.26 | | | | | | % 60.10/12.26 | | | | | | ALPHA: (45) implies: % 60.10/12.26 | | | | | | (46) all_93_0 = 0 | all_93_1 = nil % 60.10/12.26 | | | | | | % 60.10/12.26 | | | | | | BETA: splitting (46) gives: % 60.10/12.26 | | | | | | % 60.10/12.26 | | | | | | Case 1: % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | (47) all_93_1 = nil % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | REDUCE: (43), (47) imply: % 60.10/12.26 | | | | | | | (48) $false % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | CLOSE: (48) is inconsistent. % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | Case 2: % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | (49) all_93_0 = 0 % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | BETA: splitting (38) gives: % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | | Case 1: % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | | (50) ~ (all_97_0 = 0) % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | | REF_CLOSE: (5), (9), (22), (23), (24), (27), (28), (29), (34), % 60.10/12.26 | | | | | | | | (50) are inconsistent by sub-proof #1. % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | Case 2: % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | | (51) ~ (all_93_0 = 0) % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | | REDUCE: (49), (51) imply: % 60.10/12.26 | | | | | | | | (52) $false % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | | CLOSE: (52) is inconsistent. % 60.10/12.26 | | | | | | | | % 60.10/12.26 | | | | | | | End of split % 60.10/12.26 | | | | | | | % 60.10/12.26 | | | | | | End of split % 60.10/12.26 | | | | | | % 60.10/12.26 | | | | | End of split % 60.10/12.26 | | | | | % 60.10/12.26 | | | | Case 2: % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | (53) all_97_2 = nil % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | REDUCE: (42), (53) imply: % 60.10/12.26 | | | | | (54) $false % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | CLOSE: (54) is inconsistent. % 60.10/12.26 | | | | | % 60.10/12.26 | | | | End of split % 60.10/12.26 | | | | % 60.10/12.26 | | | Case 2: % 60.10/12.26 | | | | % 60.10/12.26 | | | | (55) ~ (all_97_1 = 0) % 60.10/12.26 | | | | % 60.10/12.26 | | | | REDUCE: (37), (55) imply: % 60.10/12.26 | | | | (56) $false % 60.10/12.26 | | | | % 60.10/12.26 | | | | CLOSE: (56) is inconsistent. % 60.10/12.26 | | | | % 60.10/12.26 | | | End of split % 60.10/12.26 | | | % 60.10/12.26 | | End of split % 60.10/12.26 | | % 60.10/12.26 | Case 2: % 60.10/12.26 | | % 60.10/12.26 | | (57) all_97_2 = nil & ~ (all_93_1 = nil) % 60.10/12.26 | | % 60.10/12.26 | | ALPHA: (57) implies: % 60.10/12.26 | | (58) all_97_2 = nil % 60.10/12.26 | | (59) ~ (all_93_1 = nil) % 60.10/12.26 | | % 60.10/12.26 | | REDUCE: (15), (58) imply: % 60.10/12.26 | | (60) segmentP(nil, all_93_1) = all_97_0 % 60.10/12.26 | | % 60.10/12.26 | | BETA: splitting (33) gives: % 60.10/12.26 | | % 60.10/12.26 | | Case 1: % 60.10/12.26 | | | % 60.10/12.26 | | | (61) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 60.10/12.26 | | | % 60.10/12.26 | | | REF_CLOSE: (1), (5), (61) are inconsistent by sub-proof #3. % 60.10/12.26 | | | % 60.10/12.26 | | Case 2: % 60.10/12.26 | | | % 60.10/12.26 | | | % 60.10/12.26 | | | GROUND_INST: instantiating (2) with all_93_1, all_97_0, simplifying with % 60.10/12.26 | | | (7), (60) gives: % 60.10/12.26 | | | (62) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ % 60.10/12.26 | | | (all_97_0 = 0) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | % 60.10/12.26 | | | all_97_0 = 0)) % 60.10/12.26 | | | % 60.10/12.26 | | | BETA: splitting (62) gives: % 60.10/12.26 | | | % 60.10/12.26 | | | Case 1: % 60.10/12.26 | | | | % 60.10/12.26 | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 60.10/12.26 | | | | % 60.10/12.26 | | | | REF_CLOSE: (5), (9), (63) are inconsistent by sub-proof #2. % 60.10/12.26 | | | | % 60.10/12.26 | | | Case 2: % 60.10/12.26 | | | | % 60.10/12.26 | | | | (64) ( ~ (all_97_0 = 0) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | % 60.10/12.26 | | | | all_97_0 = 0) % 60.10/12.26 | | | | % 60.10/12.26 | | | | ALPHA: (64) implies: % 60.10/12.26 | | | | (65) ~ (all_97_0 = 0) | all_93_1 = nil % 60.10/12.26 | | | | % 60.10/12.26 | | | | BETA: splitting (65) gives: % 60.10/12.26 | | | | % 60.10/12.26 | | | | Case 1: % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | (66) ~ (all_97_0 = 0) % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | REF_CLOSE: (5), (9), (22), (23), (24), (27), (28), (29), (34), (66) % 60.10/12.26 | | | | | are inconsistent by sub-proof #1. % 60.10/12.26 | | | | | % 60.10/12.26 | | | | Case 2: % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | (67) all_93_1 = nil % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | REDUCE: (59), (67) imply: % 60.10/12.26 | | | | | (68) $false % 60.10/12.26 | | | | | % 60.10/12.26 | | | | | CLOSE: (68) is inconsistent. % 60.10/12.26 | | | | | % 60.10/12.26 | | | | End of split % 60.10/12.26 | | | | % 60.10/12.26 | | | End of split % 60.10/12.26 | | | % 60.10/12.26 | | End of split % 60.10/12.26 | | % 60.10/12.26 | End of split % 60.10/12.26 | % 60.10/12.26 End of proof % 60.10/12.26 % 60.10/12.26 Sub-proof #1 shows that the following formulas are inconsistent: % 60.10/12.26 ---------------------------------------------------------------- % 60.10/12.26 (1) $i(all_101_1) % 60.10/12.27 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 60.10/12.27 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 60.10/12.27 (3) ssList(all_103_0) = 0 % 60.10/12.27 (4) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 = % 60.10/12.27 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 60.10/12.27 all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 % 60.10/12.27 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_0 = 0 | ! [v0: % 60.10/12.27 $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) | ? % 60.10/12.27 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ % 60.10/12.27 (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 60.10/12.27 0) & ssList(v2) = v3))))) % 60.10/12.27 (5) $i(all_103_0) % 60.10/12.27 (6) app(all_101_1, all_93_1) = all_101_0 % 60.10/12.27 (7) ssList(all_93_1) = 0 % 60.10/12.27 (8) app(all_101_0, all_103_0) = all_97_2 % 60.10/12.27 (9) ssList(all_101_1) = 0 % 60.10/12.27 (10) ~ (all_97_0 = 0) % 60.10/12.27 % 60.10/12.27 Begin of proof % 60.10/12.27 | % 60.10/12.27 | BETA: splitting (4) gives: % 60.10/12.27 | % 60.10/12.27 | Case 1: % 60.10/12.27 | | % 60.10/12.27 | | (11) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 60.10/12.27 | | % 60.10/12.27 | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #2. % 60.10/12.27 | | % 60.10/12.27 | Case 2: % 60.10/12.27 | | % 60.10/12.27 | | (12) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & % 60.10/12.27 | | app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 60.10/12.27 | | (ssList(v2) = 0 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_0 % 60.10/12.27 | | = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | % 60.10/12.27 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 60.10/12.27 | | [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: % 60.10/12.27 | | int] : ( ~ (v3 = 0) & ssList(v2) = v3)))) % 60.10/12.27 | | % 60.10/12.27 | | ALPHA: (12) implies: % 60.10/12.27 | | (13) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = % 60.10/12.27 | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) % 60.10/12.27 | | | ! [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: % 60.10/12.27 | | int] : ( ~ (v3 = 0) & ssList(v2) = v3))) % 60.10/12.27 | | % 60.10/12.27 | | BETA: splitting (13) gives: % 60.10/12.27 | | % 60.10/12.27 | | Case 1: % 60.10/12.27 | | | % 60.10/12.27 | | | (14) all_97_0 = 0 % 60.10/12.27 | | | % 60.10/12.27 | | | REDUCE: (10), (14) imply: % 60.10/12.27 | | | (15) $false % 60.10/12.27 | | | % 60.10/12.27 | | | CLOSE: (15) is inconsistent. % 60.10/12.27 | | | % 60.10/12.27 | | Case 2: % 60.10/12.27 | | | % 60.10/12.27 | | | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ % 60.10/12.27 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 60.10/12.27 | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: % 60.10/12.28 | | | int] : ( ~ (v3 = 0) & ssList(v2) = v3))) % 60.10/12.28 | | | % 60.10/12.28 | | | GROUND_INST: instantiating (16) with all_101_1, all_101_0, simplifying % 60.10/12.28 | | | with (1), (6) gives: % 60.10/12.28 | | | (17) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_1) = v0) | ! [v0: % 60.10/12.28 | | | $i] : ( ~ (app(all_101_0, v0) = all_97_2) | ~ $i(v0) | ? [v1: % 60.10/12.28 | | | int] : ( ~ (v1 = 0) & ssList(v0) = v1)) % 60.10/12.28 | | | % 60.10/12.28 | | | BETA: splitting (17) gives: % 60.10/12.28 | | | % 60.10/12.28 | | | Case 1: % 60.10/12.28 | | | | % 60.10/12.28 | | | | (18) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_1) = v0) % 60.10/12.28 | | | | % 60.10/12.28 | | | | DELTA: instantiating (18) with fresh symbol all_473_0 gives: % 60.10/12.28 | | | | (19) ~ (all_473_0 = 0) & ssList(all_101_1) = all_473_0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | ALPHA: (19) implies: % 60.10/12.28 | | | | (20) ~ (all_473_0 = 0) % 60.10/12.28 | | | | (21) ssList(all_101_1) = all_473_0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | GROUND_INST: instantiating (2) with 0, all_473_0, all_101_1, simplifying % 60.10/12.28 | | | | with (9), (21) gives: % 60.10/12.28 | | | | (22) all_473_0 = 0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | REDUCE: (20), (22) imply: % 60.10/12.28 | | | | (23) $false % 60.10/12.28 | | | | % 60.10/12.28 | | | | CLOSE: (23) is inconsistent. % 60.10/12.28 | | | | % 60.10/12.28 | | | Case 2: % 60.10/12.28 | | | | % 60.10/12.28 | | | | (24) ! [v0: $i] : ( ~ (app(all_101_0, v0) = all_97_2) | ~ $i(v0) | % 60.10/12.28 | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1)) % 60.10/12.28 | | | | % 60.10/12.28 | | | | GROUND_INST: instantiating (24) with all_103_0, simplifying with (5), % 60.10/12.28 | | | | (8) gives: % 60.10/12.28 | | | | (25) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_103_0) = v0) % 60.10/12.28 | | | | % 60.10/12.28 | | | | DELTA: instantiating (25) with fresh symbol all_474_0 gives: % 60.10/12.28 | | | | (26) ~ (all_474_0 = 0) & ssList(all_103_0) = all_474_0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | ALPHA: (26) implies: % 60.10/12.28 | | | | (27) ~ (all_474_0 = 0) % 60.10/12.28 | | | | (28) ssList(all_103_0) = all_474_0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | GROUND_INST: instantiating (2) with 0, all_474_0, all_103_0, simplifying % 60.10/12.28 | | | | with (3), (28) gives: % 60.10/12.28 | | | | (29) all_474_0 = 0 % 60.10/12.28 | | | | % 60.10/12.28 | | | | REDUCE: (27), (29) imply: % 60.10/12.28 | | | | (30) $false % 60.10/12.28 | | | | % 60.10/12.28 | | | | CLOSE: (30) is inconsistent. % 60.10/12.28 | | | | % 60.10/12.28 | | | End of split % 60.10/12.28 | | | % 60.10/12.28 | | End of split % 60.10/12.28 | | % 60.10/12.28 | End of split % 60.10/12.28 | % 60.10/12.28 End of proof % 60.10/12.28 % 60.10/12.28 Sub-proof #2 shows that the following formulas are inconsistent: % 60.10/12.28 ---------------------------------------------------------------- % 60.10/12.28 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 60.10/12.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 60.10/12.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 60.10/12.28 (3) ssList(all_93_1) = 0 % 60.10/12.28 % 60.10/12.28 Begin of proof % 60.10/12.28 | % 60.10/12.28 | DELTA: instantiating (1) with fresh symbol all_406_0 gives: % 60.10/12.28 | (4) ~ (all_406_0 = 0) & ssList(all_93_1) = all_406_0 % 60.10/12.28 | % 60.10/12.28 | ALPHA: (4) implies: % 60.10/12.28 | (5) ~ (all_406_0 = 0) % 60.10/12.28 | (6) ssList(all_93_1) = all_406_0 % 60.10/12.28 | % 60.10/12.28 | GROUND_INST: instantiating (2) with 0, all_406_0, all_93_1, simplifying with % 60.10/12.28 | (3), (6) gives: % 60.10/12.28 | (7) all_406_0 = 0 % 60.10/12.28 | % 60.10/12.28 | REDUCE: (5), (7) imply: % 60.10/12.28 | (8) $false % 60.10/12.28 | % 60.10/12.28 | CLOSE: (8) is inconsistent. % 60.10/12.28 | % 60.10/12.28 End of proof % 60.10/12.28 % 60.10/12.28 Sub-proof #3 shows that the following formulas are inconsistent: % 60.10/12.28 ---------------------------------------------------------------- % 60.10/12.28 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 60.10/12.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 60.10/12.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 60.10/12.28 (3) ssList(nil) = 0 % 60.10/12.28 % 60.10/12.28 Begin of proof % 60.10/12.28 | % 60.10/12.28 | DELTA: instantiating (1) with fresh symbol all_374_0 gives: % 60.10/12.28 | (4) ~ (all_374_0 = 0) & ssList(nil) = all_374_0 % 60.10/12.28 | % 60.10/12.28 | ALPHA: (4) implies: % 60.10/12.28 | (5) ~ (all_374_0 = 0) % 60.10/12.28 | (6) ssList(nil) = all_374_0 % 60.10/12.28 | % 60.10/12.28 | DELTA: instantiating (1) with fresh symbol all_376_0 gives: % 60.10/12.28 | (7) ~ (all_376_0 = 0) & ssList(nil) = all_376_0 % 60.10/12.28 | % 60.10/12.28 | ALPHA: (7) implies: % 60.10/12.28 | (8) ssList(nil) = all_376_0 % 60.10/12.28 | % 60.10/12.28 | GROUND_INST: instantiating (2) with 0, all_376_0, nil, simplifying with (3), % 60.10/12.28 | (8) gives: % 60.10/12.28 | (9) all_376_0 = 0 % 60.10/12.28 | % 60.10/12.28 | GROUND_INST: instantiating (2) with all_374_0, all_376_0, nil, simplifying % 60.10/12.28 | with (6), (8) gives: % 60.10/12.28 | (10) all_376_0 = all_374_0 % 60.10/12.28 | % 60.10/12.28 | COMBINE_EQS: (9), (10) imply: % 60.10/12.28 | (11) all_374_0 = 0 % 60.10/12.28 | % 60.10/12.28 | REDUCE: (5), (11) imply: % 60.10/12.28 | (12) $false % 60.10/12.28 | % 60.10/12.28 | CLOSE: (12) is inconsistent. % 60.10/12.28 | % 60.10/12.28 End of proof % 60.10/12.28 % SZS output end Proof for theBenchmark % 60.10/12.29 % 60.10/12.29 11640ms %------------------------------------------------------------------------------