%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC100+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 : n001.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 20:49:39 EDT 2023 % Result : Theorem 22.56s 3.83s % Output : Proof 33.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC100+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.33 % Computer : n001.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.33 % DateTime : Mon Aug 28 18:18:20 EDT 2023 % 0.17/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.15/1.55 Prover 1: Preprocessing ... % 5.15/1.55 Prover 4: Preprocessing ... % 5.85/1.58 Prover 3: Preprocessing ... % 5.85/1.58 Prover 2: Preprocessing ... % 5.85/1.58 Prover 5: Preprocessing ... % 5.85/1.58 Prover 6: Preprocessing ... % 5.85/1.60 Prover 0: Preprocessing ... % 15.41/2.90 Prover 2: Proving ... % 15.41/2.93 Prover 1: Constructing countermodel ... % 15.41/2.94 Prover 5: Constructing countermodel ... % 16.32/3.02 Prover 3: Constructing countermodel ... % 16.57/3.05 Prover 6: Proving ... % 21.37/3.67 Prover 4: Constructing countermodel ... % 22.56/3.83 Prover 3: proved (3196ms) % 22.56/3.83 % 22.56/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.56/3.83 % 22.56/3.83 Prover 2: stopped % 22.56/3.83 Prover 6: stopped % 22.56/3.84 Prover 5: stopped % 22.76/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.76/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.76/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.76/3.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.21/3.95 Prover 0: Proving ... % 23.21/3.96 Prover 0: stopped % 23.54/3.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.08/4.19 Prover 10: Preprocessing ... % 24.08/4.22 Prover 8: Preprocessing ... % 25.30/4.25 Prover 7: Preprocessing ... % 25.82/4.29 Prover 11: Preprocessing ... % 26.17/4.38 Prover 13: Preprocessing ... % 26.79/4.42 Prover 10: Constructing countermodel ... % 26.79/4.48 Prover 7: Constructing countermodel ... % 28.36/4.66 Prover 8: Warning: ignoring some quantifiers % 28.36/4.69 Prover 8: Constructing countermodel ... % 29.05/4.72 Prover 13: Constructing countermodel ... % 31.89/5.18 Prover 1: Found proof (size 117) % 31.89/5.18 Prover 1: proved (4560ms) % 31.89/5.18 Prover 7: stopped % 31.89/5.18 Prover 8: stopped % 31.89/5.18 Prover 4: stopped % 31.89/5.18 Prover 13: stopped % 31.89/5.18 Prover 10: stopped % 33.00/5.38 Prover 11: Constructing countermodel ... % 33.00/5.40 Prover 11: stopped % 33.00/5.40 % 33.00/5.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.00/5.40 % 33.00/5.42 % SZS output start Proof for theBenchmark % 33.00/5.43 Assumptions after simplification: % 33.00/5.43 --------------------------------- % 33.00/5.43 % 33.00/5.43 (ax15) % 33.00/5.47 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 33.00/5.47 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 33.00/5.47 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 33.00/5.47 % 33.00/5.47 (ax17) % 33.00/5.47 ssList(nil) = 0 & $i(nil) % 33.00/5.47 % 33.00/5.47 (ax5) % 33.00/5.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 33.00/5.48 ( ~ (frontsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 33.00/5.48 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 & % 33.00/5.48 app(v1, v3) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v1, % 33.00/5.48 v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) % 33.00/5.48 = v4)))))) % 33.00/5.48 % 33.00/5.48 (ax83) % 33.00/5.48 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 33.00/5.48 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 33.00/5.48 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 33.00/5.48 = nil) | ~ (v0 = nil) | v2 = nil)))) % 33.00/5.48 % 33.00/5.48 (co1) % 33.00/5.48 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 33.00/5.48 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (frontsegP(v2, v0) = v4 % 33.00/5.48 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5: any] : % 33.00/5.48 (strictorderedP(v0) = v5 & ? [v6: $i] : (v5 = 0 & ssList(v6) = 0 & % 33.00/5.48 app(v0, v6) = v2 & $i(v6) & ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v7, % 33.00/5.48 nil) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & % 33.00/5.48 ssItem(v7) = v9) | ! [v9: $i] : ( ~ (app(v8, v9) = v6) | ~ % 33.00/5.48 $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) = v10) | ! % 33.00/5.48 [v10: $i] : ! [v11: $i] : ( ~ (cons(v10, nil) = v11) | ~ $i(v10) % 33.00/5.48 | ? [v12: any] : ? [v13: any] : (lt(v10, v7) = v13 & % 33.00/5.48 ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14: $i] : ( ~ (v13 = % 33.00/5.48 0) | ~ (app(v14, v11) = v0) | ~ $i(v14) | ? [v15: % 33.00/5.48 int] : ( ~ (v15 = 0) & ssList(v14) = v15)))))))) & ( ~ % 33.00/5.48 (v0 = nil) | v2 = nil) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0))) | (v2 % 33.00/5.48 = nil & ~ (v0 = nil)))))) % 33.00/5.48 % 33.00/5.48 (function-axioms) % 33.00/5.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 33.00/5.49 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.00/5.49 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.00/5.49 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.00/5.49 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.00/5.49 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 33.00/5.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 33.00/5.49 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 33.00/5.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 33.00/5.49 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 33.00/5.49 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 33.00/5.49 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 33.00/5.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.00/5.49 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 33.00/5.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 33.00/5.49 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 33.00/5.49 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 33.00/5.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 33.00/5.49 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 33.00/5.49 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 33.00/5.49 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 33.00/5.49 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 33.00/5.49 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 33.00/5.49 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 33.00/5.49 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 33.00/5.49 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 33.00/5.49 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 33.00/5.49 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 33.00/5.49 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 33.00/5.49 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 33.00/5.49 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 33.00/5.49 % 33.00/5.49 Further assumptions not needed in the proof: % 33.00/5.49 -------------------------------------------- % 33.00/5.50 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 33.00/5.50 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, % 33.00/5.50 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, % 33.00/5.50 ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, % 33.00/5.50 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, % 33.00/5.50 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 33.00/5.50 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 33.00/5.50 % 33.00/5.50 Those formulas are unsatisfiable: % 33.00/5.50 --------------------------------- % 33.00/5.50 % 33.00/5.50 Begin of proof % 33.00/5.50 | % 33.00/5.50 | ALPHA: (ax17) implies: % 33.00/5.50 | (1) ssList(nil) = 0 % 33.00/5.50 | % 33.00/5.50 | ALPHA: (ax83) implies: % 33.00/5.50 | (2) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 33.00/5.50 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 33.00/5.50 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 33.00/5.50 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 33.00/5.50 | % 33.00/5.50 | ALPHA: (co1) implies: % 33.00/5.50 | (3) $i(nil) % 33.00/5.50 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 33.00/5.50 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (frontsegP(v2, % 33.00/5.50 | v0) = v4 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5: % 33.00/5.50 | any] : (strictorderedP(v0) = v5 & ? [v6: $i] : (v5 = 0 & % 33.00/5.50 | ssList(v6) = 0 & app(v0, v6) = v2 & $i(v6) & ! [v7: $i] : ! % 33.00/5.50 | [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: int] % 33.00/5.50 | : ( ~ (v9 = 0) & ssItem(v7) = v9) | ! [v9: $i] : ( ~ % 33.00/5.50 | (app(v8, v9) = v6) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = % 33.00/5.50 | 0) & ssList(v9) = v10) | ! [v10: $i] : ! [v11: $i] : % 33.00/5.50 | ( ~ (cons(v10, nil) = v11) | ~ $i(v10) | ? [v12: any] : % 33.00/5.50 | ? [v13: any] : (lt(v10, v7) = v13 & ssItem(v10) = v12 & ( % 33.00/5.50 | ~ (v12 = 0) | ! [v14: $i] : ( ~ (v13 = 0) | ~ % 33.00/5.50 | (app(v14, v11) = v0) | ~ $i(v14) | ? [v15: int] : % 33.00/5.50 | ( ~ (v15 = 0) & ssList(v14) = v15)))))))) & ( ~ (v0 % 33.00/5.50 | = nil) | v2 = nil) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0))) % 33.00/5.50 | | (v2 = nil & ~ (v0 = nil)))))) % 33.00/5.50 | % 33.00/5.50 | ALPHA: (function-axioms) implies: % 33.84/5.50 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.84/5.50 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 33.84/5.50 | % 33.84/5.51 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives: % 33.84/5.51 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & % 33.84/5.51 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(v0, all_93_1) = % 33.84/5.51 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] : % 33.84/5.51 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : (v3 = 0 & ssList(v4) = % 33.84/5.51 | 0 & app(all_93_1, v4) = v0 & $i(v4) & ! [v5: $i] : ! [v6: $i] : % 33.84/5.51 | ( ~ (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = % 33.84/5.51 | 0) & ssItem(v5) = v7) | ! [v7: $i] : ( ~ (app(v6, v7) = % 33.84/5.51 | v4) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v7) % 33.84/5.51 | = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (cons(v8, nil) = % 33.84/5.51 | v9) | ~ $i(v8) | ? [v10: any] : ? [v11: any] : (lt(v8, % 33.84/5.51 | v5) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | ! [v12: % 33.84/5.51 | $i] : ( ~ (v11 = 0) | ~ (app(v12, v9) = all_93_1) | % 33.84/5.51 | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) & % 33.84/5.51 | ssList(v12) = v13)))))))) & ( ~ (all_93_1 = nil) | % 33.84/5.51 | v0 = nil) & ((v1 = 0 & ( ~ (v2 = 0) | ~ (all_93_0 = 0))) | (v0 = % 33.84/5.51 | nil & ~ (all_93_1 = nil))))) % 33.84/5.51 | % 33.84/5.51 | ALPHA: (6) implies: % 33.84/5.51 | (7) $i(all_93_1) % 33.84/5.51 | (8) neq(all_93_1, nil) = all_93_0 % 33.84/5.51 | (9) ssList(all_93_1) = 0 % 33.84/5.51 | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(v0, all_93_1) = % 33.84/5.51 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] : % 33.84/5.51 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : (v3 = 0 & ssList(v4) % 33.84/5.51 | = 0 & app(all_93_1, v4) = v0 & $i(v4) & ! [v5: $i] : ! [v6: % 33.84/5.51 | $i] : ( ~ (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: int] : ( % 33.84/5.51 | ~ (v7 = 0) & ssItem(v5) = v7) | ! [v7: $i] : ( ~ (app(v6, % 33.84/5.51 | v7) = v4) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 33.84/5.51 | ssList(v7) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ % 33.84/5.51 | (cons(v8, nil) = v9) | ~ $i(v8) | ? [v10: any] : ? % 33.84/5.51 | [v11: any] : (lt(v8, v5) = v11 & ssItem(v8) = v10 & ( ~ % 33.84/5.51 | (v10 = 0) | ! [v12: $i] : ( ~ (v11 = 0) | ~ % 33.84/5.51 | (app(v12, v9) = all_93_1) | ~ $i(v12) | ? [v13: % 33.84/5.51 | int] : ( ~ (v13 = 0) & ssList(v12) = v13)))))))) & % 33.84/5.51 | ( ~ (all_93_1 = nil) | v0 = nil) & ((v1 = 0 & ( ~ (v2 = 0) | ~ % 33.84/5.51 | (all_93_0 = 0))) | (v0 = nil & ~ (all_93_1 = nil))))) % 33.84/5.51 | % 33.84/5.51 | DELTA: instantiating (10) with fresh symbols all_97_0, all_97_1, all_97_2 % 33.84/5.51 | gives: % 33.84/5.52 | (11) frontsegP(all_97_2, all_93_1) = all_97_0 & ssList(all_97_2) = 0 & % 33.84/5.52 | neq(all_97_2, nil) = all_97_1 & $i(all_97_2) & ? [v0: any] : % 33.84/5.52 | (strictorderedP(all_93_1) = v0 & ? [v1: $i] : (v0 = 0 & ssList(v1) = % 33.84/5.52 | 0 & app(all_93_1, v1) = all_97_2 & $i(v1) & ! [v2: $i] : ! [v3: % 33.84/5.52 | $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ % 33.84/5.52 | (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) = % 33.84/5.52 | v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v4) = % 33.84/5.52 | v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, nil) = v6) | % 33.84/5.52 | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (lt(v5, v2) = v8 & % 33.84/5.52 | ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9: $i] : ( ~ (v8 = % 33.84/5.52 | 0) | ~ (app(v9, v6) = all_93_1) | ~ $i(v9) | ? % 33.84/5.52 | [v10: int] : ( ~ (v10 = 0) & ssList(v9) = v10)))))))) % 33.84/5.52 | & ( ~ (all_93_1 = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~ % 33.84/5.52 | (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ % 33.84/5.52 | (all_93_1 = nil)))) % 33.84/5.52 | % 33.84/5.52 | ALPHA: (11) implies: % 33.84/5.52 | (12) $i(all_97_2) % 33.84/5.52 | (13) neq(all_97_2, nil) = all_97_1 % 33.84/5.52 | (14) ssList(all_97_2) = 0 % 33.84/5.52 | (15) frontsegP(all_97_2, all_93_1) = all_97_0 % 33.84/5.52 | (16) ? [v0: any] : (strictorderedP(all_93_1) = v0 & ? [v1: $i] : (v0 = 0 % 33.84/5.52 | & ssList(v1) = 0 & app(all_93_1, v1) = all_97_2 & $i(v1) & ! [v2: % 33.84/5.52 | $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? % 33.84/5.52 | [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ % 33.84/5.52 | (app(v3, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 33.84/5.52 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, % 33.84/5.52 | nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : % 33.84/5.52 | (lt(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9: % 33.84/5.52 | $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_1) | ~ % 33.84/5.52 | $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) = % 33.84/5.52 | v10)))))))) & ( ~ (all_93_1 = nil) | all_97_2 = nil) % 33.84/5.52 | & ((all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | % 33.84/5.52 | (all_97_2 = nil & ~ (all_93_1 = nil)))) % 33.84/5.52 | % 33.84/5.52 | DELTA: instantiating (16) with fresh symbol all_99_0 gives: % 33.84/5.52 | (17) strictorderedP(all_93_1) = all_99_0 & ? [v0: $i] : (all_99_0 = 0 & % 33.84/5.52 | ssList(v0) = 0 & app(all_93_1, v0) = all_97_2 & $i(v0) & ! [v1: $i] % 33.84/5.52 | : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] % 33.84/5.52 | : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) % 33.84/5.53 | = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = % 33.84/5.53 | v4) | ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | % 33.84/5.53 | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 & % 33.84/5.53 | ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) % 33.84/5.53 | | ~ (app(v8, v5) = all_93_1) | ~ $i(v8) | ? [v9: int] % 33.84/5.53 | : ( ~ (v9 = 0) & ssList(v8) = v9)))))))) & ( ~ (all_93_1 % 33.84/5.53 | = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~ (all_97_0 = 0) | % 33.84/5.53 | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ (all_93_1 = nil))) % 33.84/5.53 | % 33.84/5.53 | ALPHA: (17) implies: % 33.84/5.53 | (18) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = % 33.84/5.53 | nil & ~ (all_93_1 = nil)) % 33.84/5.53 | (19) ~ (all_93_1 = nil) | all_97_2 = nil % 33.84/5.53 | (20) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_93_1, v0) = % 33.84/5.53 | all_97_2 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = % 33.84/5.53 | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) % 33.84/5.53 | | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ $i(v3) | ? [v4: int] % 33.84/5.53 | : ( ~ (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] : % 33.84/5.53 | ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 33.84/5.53 | any] : (lt(v4, v1) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) | % 33.84/5.53 | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, v5) = all_93_1) | % 33.84/5.53 | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) = % 33.84/5.53 | v9)))))))) % 33.84/5.53 | % 33.84/5.53 | DELTA: instantiating (20) with fresh symbol all_101_0 gives: % 33.84/5.53 | (21) all_99_0 = 0 & ssList(all_101_0) = 0 & app(all_93_1, all_101_0) = % 33.84/5.53 | all_97_2 & $i(all_101_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 33.84/5.53 | nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 33.84/5.53 | ssItem(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = all_101_0) | % 33.84/5.53 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | ! % 33.84/5.53 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? % 33.84/5.53 | [v5: any] : ? [v6: any] : (lt(v3, v0) = v6 & ssItem(v3) = v5 & % 33.84/5.53 | ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) = % 33.84/5.53 | all_93_1) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 33.84/5.53 | ssList(v7) = v8))))))) % 33.84/5.53 | % 33.84/5.53 | ALPHA: (21) implies: % 33.84/5.53 | (22) $i(all_101_0) % 33.84/5.53 | (23) app(all_93_1, all_101_0) = all_97_2 % 33.84/5.53 | (24) ssList(all_101_0) = 0 % 33.84/5.53 | % 33.84/5.53 | GROUND_INST: instantiating (2) with all_93_1, simplifying with (7), (9) gives: % 33.84/5.53 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_93_1, v0) = v1) | ~ $i(v0) | % 33.84/5.53 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) | % 33.84/5.53 | (v0 = nil & all_93_1 = nil)) & ( ~ (v0 = nil) | ~ (all_93_1 = % 33.84/5.53 | nil) | v1 = nil))) % 33.84/5.53 | % 33.84/5.53 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (7), (9) % 33.84/5.53 | gives: % 33.84/5.53 | (26) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0) % 33.84/5.53 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 33.84/5.53 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1))) % 33.84/5.53 | % 33.84/5.53 | GROUND_INST: instantiating (ax5) with all_97_2, simplifying with (12), (14) % 33.84/5.54 | gives: % 33.84/5.54 | (27) ! [v0: $i] : ! [v1: any] : ( ~ (frontsegP(all_97_2, v0) = v1) | ~ % 33.84/5.54 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 33.84/5.54 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v0, v2) = all_97_2 & % 33.84/5.54 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v0, v2) = % 33.84/5.54 | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 33.84/5.54 | ssList(v2) = v3))))) % 33.84/5.54 | % 33.84/5.54 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (12), (14) % 33.84/5.54 | gives: % 33.84/5.54 | (28) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0) % 33.84/5.54 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 33.84/5.54 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2))) % 33.84/5.54 | % 33.84/5.54 | GROUND_INST: instantiating (26) with nil, all_93_0, simplifying with (3), (8) % 33.84/5.54 | gives: % 33.84/5.54 | (29) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0) % 33.84/5.54 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil)) % 33.84/5.54 | % 33.84/5.54 | GROUND_INST: instantiating (28) with nil, all_97_1, simplifying with (3), (13) % 33.84/5.54 | gives: % 33.84/5.54 | (30) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0) % 33.84/5.54 | | ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil)) % 33.84/5.54 | % 33.84/5.54 | GROUND_INST: instantiating (27) with all_93_1, all_97_0, simplifying with (7), % 33.84/5.54 | (15) gives: % 33.84/5.54 | (31) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 % 33.84/5.54 | = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(all_93_1, v0) = % 33.84/5.54 | all_97_2 & $i(v0))) & (all_97_0 = 0 | ! [v0: $i] : ( ~ % 33.84/5.54 | (app(all_93_1, v0) = all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ % 33.84/5.54 | (v1 = 0) & ssList(v0) = v1)))) % 33.84/5.54 | % 33.84/5.54 | GROUND_INST: instantiating (25) with all_101_0, all_97_2, simplifying with % 33.84/5.54 | (22), (23) gives: % 33.84/5.54 | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (( ~ % 33.84/5.54 | (all_101_0 = nil) | ~ (all_93_1 = nil) | all_97_2 = nil) & ( ~ % 33.84/5.54 | (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil))) % 33.84/5.54 | % 33.84/5.54 | BETA: splitting (19) gives: % 33.84/5.54 | % 33.84/5.54 | Case 1: % 33.84/5.54 | | % 33.84/5.54 | | (33) ~ (all_93_1 = nil) % 33.84/5.54 | | % 33.84/5.54 | | BETA: splitting (29) gives: % 33.84/5.54 | | % 33.84/5.54 | | Case 1: % 33.84/5.54 | | | % 33.84/5.54 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 33.84/5.54 | | | % 33.84/5.54 | | | DELTA: instantiating (34) with fresh symbol all_357_0 gives: % 33.84/5.54 | | | (35) ~ (all_357_0 = 0) & ssList(nil) = all_357_0 % 33.84/5.54 | | | % 33.84/5.54 | | | ALPHA: (35) implies: % 33.84/5.54 | | | (36) ~ (all_357_0 = 0) % 33.84/5.54 | | | (37) ssList(nil) = all_357_0 % 33.84/5.54 | | | % 33.84/5.54 | | | GROUND_INST: instantiating (5) with 0, all_357_0, nil, simplifying with % 33.84/5.54 | | | (1), (37) gives: % 33.84/5.54 | | | (38) all_357_0 = 0 % 33.84/5.54 | | | % 33.84/5.54 | | | REDUCE: (36), (38) imply: % 33.84/5.55 | | | (39) $false % 33.84/5.55 | | | % 33.84/5.55 | | | CLOSE: (39) is inconsistent. % 33.84/5.55 | | | % 33.84/5.55 | | Case 2: % 33.84/5.55 | | | % 33.84/5.55 | | | (40) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | % 33.84/5.55 | | | all_93_1 = nil) % 33.84/5.55 | | | % 33.84/5.55 | | | ALPHA: (40) implies: % 33.84/5.55 | | | (41) all_93_0 = 0 | all_93_1 = nil % 33.84/5.55 | | | % 33.84/5.55 | | | BETA: splitting (32) gives: % 33.84/5.55 | | | % 33.84/5.55 | | | Case 1: % 33.84/5.55 | | | | % 33.84/5.55 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) % 33.84/5.55 | | | | % 33.84/5.55 | | | | DELTA: instantiating (42) with fresh symbol all_366_0 gives: % 33.84/5.55 | | | | (43) ~ (all_366_0 = 0) & ssList(all_101_0) = all_366_0 % 33.84/5.55 | | | | % 33.84/5.55 | | | | ALPHA: (43) implies: % 33.84/5.55 | | | | (44) ~ (all_366_0 = 0) % 33.84/5.55 | | | | (45) ssList(all_101_0) = all_366_0 % 33.84/5.55 | | | | % 33.84/5.55 | | | | GROUND_INST: instantiating (5) with 0, all_366_0, all_101_0, simplifying % 33.84/5.55 | | | | with (24), (45) gives: % 33.84/5.55 | | | | (46) all_366_0 = 0 % 33.84/5.55 | | | | % 33.84/5.55 | | | | REDUCE: (44), (46) imply: % 33.84/5.55 | | | | (47) $false % 33.84/5.55 | | | | % 33.84/5.55 | | | | CLOSE: (47) is inconsistent. % 33.84/5.55 | | | | % 33.84/5.55 | | | Case 2: % 33.84/5.55 | | | | % 33.84/5.55 | | | | (48) ( ~ (all_101_0 = nil) | ~ (all_93_1 = nil) | all_97_2 = nil) & % 33.84/5.55 | | | | ( ~ (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil)) % 33.84/5.55 | | | | % 33.84/5.55 | | | | ALPHA: (48) implies: % 33.84/5.55 | | | | (49) ~ (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil) % 33.84/5.55 | | | | % 33.84/5.55 | | | | BETA: splitting (49) gives: % 33.84/5.55 | | | | % 33.84/5.55 | | | | Case 1: % 33.84/5.55 | | | | | % 33.84/5.55 | | | | | (50) ~ (all_97_2 = nil) % 33.84/5.55 | | | | | % 33.84/5.55 | | | | | BETA: splitting (18) gives: % 33.84/5.55 | | | | | % 33.84/5.55 | | | | | Case 1: % 33.84/5.55 | | | | | | % 33.84/5.55 | | | | | | (51) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0)) % 33.84/5.55 | | | | | | % 33.84/5.55 | | | | | | ALPHA: (51) implies: % 33.84/5.55 | | | | | | (52) ~ (all_97_0 = 0) | ~ (all_93_0 = 0) % 33.84/5.55 | | | | | | % 33.84/5.55 | | | | | | BETA: splitting (41) gives: % 33.84/5.55 | | | | | | % 33.84/5.55 | | | | | | Case 1: % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | (53) all_93_1 = nil % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | REDUCE: (33), (53) imply: % 33.84/5.55 | | | | | | | (54) $false % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | CLOSE: (54) is inconsistent. % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | Case 2: % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | (55) all_93_0 = 0 % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | BETA: splitting (52) gives: % 33.84/5.55 | | | | | | | % 33.84/5.55 | | | | | | | Case 1: % 33.84/5.55 | | | | | | | | % 33.84/5.55 | | | | | | | | (56) ~ (all_97_0 = 0) % 33.84/5.55 | | | | | | | | % 33.84/5.55 | | | | | | | | BETA: splitting (31) gives: % 33.84/5.55 | | | | | | | | % 33.84/5.55 | | | | | | | | Case 1: % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | DELTA: instantiating (57) with fresh symbol all_391_0 gives: % 33.84/5.55 | | | | | | | | | (58) ~ (all_391_0 = 0) & ssList(all_93_1) = all_391_0 % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | ALPHA: (58) implies: % 33.84/5.55 | | | | | | | | | (59) ~ (all_391_0 = 0) % 33.84/5.55 | | | | | | | | | (60) ssList(all_93_1) = all_391_0 % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_391_0, all_93_1, % 33.84/5.55 | | | | | | | | | simplifying with (9), (60) gives: % 33.84/5.55 | | | | | | | | | (61) all_391_0 = 0 % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | REDUCE: (59), (61) imply: % 33.84/5.55 | | | | | | | | | (62) $false % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | CLOSE: (62) is inconsistent. % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | Case 2: % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | (63) ( ~ (all_97_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 33.84/5.55 | | | | | | | | | app(all_93_1, v0) = all_97_2 & $i(v0))) & % 33.84/5.55 | | | | | | | | | (all_97_0 = 0 | ! [v0: $i] : ( ~ (app(all_93_1, v0) = % 33.84/5.55 | | | | | | | | | all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 33.84/5.55 | | | | | | | | | 0) & ssList(v0) = v1))) % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | ALPHA: (63) implies: % 33.84/5.55 | | | | | | | | | (64) all_97_0 = 0 | ! [v0: $i] : ( ~ (app(all_93_1, v0) = % 33.84/5.55 | | | | | | | | | all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 33.84/5.55 | | | | | | | | | 0) & ssList(v0) = v1)) % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | BETA: splitting (64) gives: % 33.84/5.55 | | | | | | | | | % 33.84/5.55 | | | | | | | | | Case 1: % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | (65) all_97_0 = 0 % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | REDUCE: (56), (65) imply: % 33.84/5.55 | | | | | | | | | | (66) $false % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | CLOSE: (66) is inconsistent. % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | Case 2: % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | (67) ! [v0: $i] : ( ~ (app(all_93_1, v0) = all_97_2) | % 33.84/5.55 | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 33.84/5.55 | | | | | | | | | | ssList(v0) = v1)) % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | GROUND_INST: instantiating (67) with all_101_0, simplifying % 33.84/5.55 | | | | | | | | | | with (22), (23) gives: % 33.84/5.55 | | | | | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = % 33.84/5.55 | | | | | | | | | | v0) % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | DELTA: instantiating (68) with fresh symbol all_395_0 gives: % 33.84/5.55 | | | | | | | | | | (69) ~ (all_395_0 = 0) & ssList(all_101_0) = all_395_0 % 33.84/5.55 | | | | | | | | | | % 33.84/5.55 | | | | | | | | | | ALPHA: (69) implies: % 33.84/5.55 | | | | | | | | | | (70) ~ (all_395_0 = 0) % 33.84/5.55 | | | | | | | | | | (71) ssList(all_101_0) = all_395_0 % 33.84/5.55 | | | | | | | | | | % 33.84/5.56 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_395_0, all_101_0, % 33.84/5.56 | | | | | | | | | | simplifying with (24), (71) gives: % 33.84/5.56 | | | | | | | | | | (72) all_395_0 = 0 % 33.84/5.56 | | | | | | | | | | % 33.84/5.56 | | | | | | | | | | REDUCE: (70), (72) imply: % 33.84/5.56 | | | | | | | | | | (73) $false % 33.84/5.56 | | | | | | | | | | % 33.84/5.56 | | | | | | | | | | CLOSE: (73) is inconsistent. % 33.84/5.56 | | | | | | | | | | % 33.84/5.56 | | | | | | | | | End of split % 33.84/5.56 | | | | | | | | | % 33.84/5.56 | | | | | | | | End of split % 33.84/5.56 | | | | | | | | % 33.84/5.56 | | | | | | | Case 2: % 33.84/5.56 | | | | | | | | % 33.84/5.56 | | | | | | | | (74) ~ (all_93_0 = 0) % 33.84/5.56 | | | | | | | | % 33.84/5.56 | | | | | | | | REDUCE: (55), (74) imply: % 33.84/5.56 | | | | | | | | (75) $false % 33.84/5.56 | | | | | | | | % 33.84/5.56 | | | | | | | | CLOSE: (75) is inconsistent. % 33.84/5.56 | | | | | | | | % 33.84/5.56 | | | | | | | End of split % 33.84/5.56 | | | | | | | % 33.84/5.56 | | | | | | End of split % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | Case 2: % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | | (76) all_97_2 = nil & ~ (all_93_1 = nil) % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | | ALPHA: (76) implies: % 33.84/5.56 | | | | | | (77) all_97_2 = nil % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | | REDUCE: (50), (77) imply: % 33.84/5.56 | | | | | | (78) $false % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | | CLOSE: (78) is inconsistent. % 33.84/5.56 | | | | | | % 33.84/5.56 | | | | | End of split % 33.84/5.56 | | | | | % 33.84/5.56 | | | | Case 2: % 33.84/5.56 | | | | | % 33.84/5.56 | | | | | (79) all_97_2 = nil % 33.84/5.56 | | | | | (80) all_101_0 = nil & all_93_1 = nil % 33.84/5.56 | | | | | % 33.84/5.56 | | | | | ALPHA: (80) implies: % 33.84/5.56 | | | | | (81) all_93_1 = nil % 33.84/5.56 | | | | | % 33.84/5.56 | | | | | REF_CLOSE: (1), (5), (18), (30), (79), (81) are inconsistent by % 33.84/5.56 | | | | | sub-proof #1. % 33.84/5.56 | | | | | % 33.84/5.56 | | | | End of split % 33.84/5.56 | | | | % 33.84/5.56 | | | End of split % 33.84/5.56 | | | % 33.84/5.56 | | End of split % 33.84/5.56 | | % 33.84/5.56 | Case 2: % 33.84/5.56 | | % 33.84/5.56 | | (82) all_93_1 = nil % 33.84/5.56 | | (83) all_97_2 = nil % 33.84/5.56 | | % 33.84/5.56 | | REF_CLOSE: (1), (5), (18), (30), (82), (83) are inconsistent by sub-proof % 33.84/5.56 | | #1. % 33.84/5.56 | | % 33.84/5.56 | End of split % 33.84/5.56 | % 33.84/5.56 End of proof % 33.84/5.56 % 33.84/5.56 Sub-proof #1 shows that the following formulas are inconsistent: % 33.84/5.56 ---------------------------------------------------------------- % 33.84/5.56 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.84/5.56 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 33.84/5.56 (2) ssList(nil) = 0 % 33.84/5.56 (3) all_93_1 = nil % 33.84/5.56 (4) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = % 33.84/5.56 nil & ~ (all_93_1 = nil)) % 33.84/5.56 (5) all_97_2 = nil % 33.84/5.56 (6) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0) | % 33.84/5.56 ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil)) % 33.84/5.56 % 33.84/5.56 Begin of proof % 33.84/5.56 | % 33.84/5.56 | BETA: splitting (4) gives: % 33.84/5.56 | % 33.84/5.56 | Case 1: % 33.84/5.56 | | % 33.84/5.56 | | (7) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0)) % 33.84/5.56 | | % 33.84/5.56 | | ALPHA: (7) implies: % 33.84/5.56 | | (8) all_97_1 = 0 % 33.84/5.56 | | % 33.84/5.56 | | BETA: splitting (6) gives: % 33.84/5.56 | | % 33.84/5.56 | | Case 1: % 33.84/5.56 | | | % 33.84/5.56 | | | (9) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 33.84/5.56 | | | % 33.84/5.56 | | | DELTA: instantiating (9) with fresh symbol all_361_0 gives: % 33.84/5.56 | | | (10) ~ (all_361_0 = 0) & ssList(nil) = all_361_0 % 33.84/5.56 | | | % 33.84/5.56 | | | ALPHA: (10) implies: % 33.84/5.56 | | | (11) ~ (all_361_0 = 0) % 33.84/5.56 | | | (12) ssList(nil) = all_361_0 % 33.84/5.56 | | | % 33.84/5.56 | | | DELTA: instantiating (9) with fresh symbol all_366_0 gives: % 33.84/5.56 | | | (13) ~ (all_366_0 = 0) & ssList(nil) = all_366_0 % 33.84/5.56 | | | % 33.84/5.56 | | | ALPHA: (13) implies: % 33.84/5.56 | | | (14) ssList(nil) = all_366_0 % 33.84/5.56 | | | % 33.84/5.56 | | | GROUND_INST: instantiating (1) with 0, all_366_0, nil, simplifying with % 33.84/5.56 | | | (2), (14) gives: % 33.84/5.56 | | | (15) all_366_0 = 0 % 33.84/5.56 | | | % 33.84/5.56 | | | GROUND_INST: instantiating (1) with all_361_0, all_366_0, nil, simplifying % 33.84/5.56 | | | with (12), (14) gives: % 33.84/5.56 | | | (16) all_366_0 = all_361_0 % 33.84/5.56 | | | % 33.84/5.56 | | | COMBINE_EQS: (15), (16) imply: % 33.84/5.56 | | | (17) all_361_0 = 0 % 33.84/5.56 | | | % 33.84/5.56 | | | REDUCE: (11), (17) imply: % 33.84/5.56 | | | (18) $false % 33.84/5.56 | | | % 33.84/5.56 | | | CLOSE: (18) is inconsistent. % 33.84/5.56 | | | % 33.84/5.56 | | Case 2: % 33.84/5.56 | | | % 33.84/5.56 | | | (19) ( ~ (all_97_1 = 0) | ~ (all_97_2 = nil)) & (all_97_1 = 0 | % 33.84/5.56 | | | all_97_2 = nil) % 33.84/5.56 | | | % 33.84/5.56 | | | ALPHA: (19) implies: % 33.84/5.56 | | | (20) ~ (all_97_1 = 0) | ~ (all_97_2 = nil) % 33.84/5.56 | | | % 33.84/5.56 | | | BETA: splitting (20) gives: % 33.84/5.56 | | | % 33.84/5.56 | | | Case 1: % 33.84/5.56 | | | | % 33.84/5.56 | | | | (21) ~ (all_97_2 = nil) % 33.84/5.56 | | | | % 33.84/5.56 | | | | REDUCE: (5), (21) imply: % 33.84/5.56 | | | | (22) $false % 33.84/5.56 | | | | % 33.84/5.56 | | | | CLOSE: (22) is inconsistent. % 33.84/5.56 | | | | % 33.84/5.56 | | | Case 2: % 33.84/5.56 | | | | % 33.84/5.56 | | | | (23) ~ (all_97_1 = 0) % 33.84/5.56 | | | | % 33.84/5.56 | | | | REDUCE: (8), (23) imply: % 33.84/5.56 | | | | (24) $false % 33.84/5.56 | | | | % 33.84/5.56 | | | | CLOSE: (24) is inconsistent. % 33.84/5.56 | | | | % 33.84/5.56 | | | End of split % 33.84/5.56 | | | % 33.84/5.56 | | End of split % 33.84/5.56 | | % 33.84/5.56 | Case 2: % 33.84/5.56 | | % 33.84/5.56 | | (25) all_97_2 = nil & ~ (all_93_1 = nil) % 33.84/5.56 | | % 33.84/5.56 | | ALPHA: (25) implies: % 33.84/5.56 | | (26) ~ (all_93_1 = nil) % 33.84/5.56 | | % 33.84/5.56 | | REDUCE: (3), (26) imply: % 33.84/5.56 | | (27) $false % 33.84/5.56 | | % 33.84/5.56 | | CLOSE: (27) is inconsistent. % 33.84/5.56 | | % 33.84/5.56 | End of split % 33.84/5.56 | % 33.84/5.56 End of proof % 33.84/5.56 % SZS output end Proof for theBenchmark % 33.84/5.56 % 33.84/5.56 4963ms %------------------------------------------------------------------------------