%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC017+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 : n014.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 20:49:12 EDT 2023 % Result : Theorem 39.02s 6.02s % Output : Proof 109.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC017+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 16:11:01 EDT 2023 % 0.13/0.34 % 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 % 4.37/1.38 Prover 1: Preprocessing ... % 4.37/1.38 Prover 4: Preprocessing ... % 4.37/1.42 Prover 3: Preprocessing ... % 4.37/1.42 Prover 6: Preprocessing ... % 4.37/1.43 Prover 2: Preprocessing ... % 4.37/1.43 Prover 0: Preprocessing ... % 4.37/1.43 Prover 5: Preprocessing ... % 14.76/2.78 Prover 2: Proving ... % 15.16/2.95 Prover 6: Proving ... % 15.16/2.96 Prover 5: Constructing countermodel ... % 16.46/2.99 Prover 1: Constructing countermodel ... % 16.46/3.02 Prover 3: Constructing countermodel ... % 22.97/3.96 Prover 0: Proving ... % 23.80/4.00 Prover 4: Constructing countermodel ... % 39.02/6.02 Prover 3: proved (5394ms) % 39.02/6.02 % 39.02/6.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 39.02/6.02 % 39.02/6.02 Prover 5: stopped % 39.02/6.03 Prover 2: stopped % 39.02/6.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.02/6.03 Prover 6: stopped % 39.58/6.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 39.58/6.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.58/6.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.58/6.06 Prover 0: stopped % 39.79/6.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 40.43/6.20 Prover 7: Preprocessing ... % 41.23/6.27 Prover 8: Preprocessing ... % 41.23/6.31 Prover 10: Preprocessing ... % 41.23/6.34 Prover 13: Preprocessing ... % 41.23/6.34 Prover 11: Preprocessing ... % 41.81/6.48 Prover 7: Constructing countermodel ... % 42.21/6.54 Prover 10: Constructing countermodel ... % 43.90/6.66 Prover 13: Constructing countermodel ... % 44.61/6.77 Prover 8: Warning: ignoring some quantifiers % 45.14/6.79 Prover 8: Constructing countermodel ... % 50.70/7.53 Prover 11: Constructing countermodel ... % 75.30/10.88 Prover 13: stopped % 75.30/10.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 75.60/10.97 Prover 16: Preprocessing ... % 78.36/11.16 Prover 16: Constructing countermodel ... % 107.50/15.11 Prover 8: Found proof (size 267) % 107.50/15.11 Prover 8: proved (8957ms) % 107.50/15.12 Prover 1: stopped % 107.50/15.12 Prover 7: stopped % 107.50/15.12 Prover 11: stopped % 107.50/15.12 Prover 10: stopped % 107.50/15.12 Prover 4: stopped % 107.50/15.12 Prover 16: stopped % 107.50/15.12 % 107.50/15.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 107.50/15.12 % 107.50/15.13 % SZS output start Proof for theBenchmark % 108.63/15.14 Assumptions after simplification: % 108.63/15.14 --------------------------------- % 108.63/15.14 % 108.63/15.14 (ax15) % 108.63/15.17 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 108.63/15.17 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 108.63/15.17 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 108.63/15.17 % 108.63/15.17 (ax17) % 108.63/15.17 ssList(nil) = 0 & $i(nil) % 108.63/15.17 % 108.63/15.17 (ax2) % 108.63/15.17 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 108.63/15.17 ssItem(v1) = 0 & $i(v1))) % 108.63/15.17 % 108.63/15.17 (ax20) % 108.63/15.17 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 108.63/15.17 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 108.63/15.17 ssItem(v2) = 0 & $i(v2)))) % 108.63/15.17 % 108.63/15.17 (ax23) % 108.63/15.17 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 108.63/15.17 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 108.63/15.17 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 108.63/15.17 % 108.63/15.17 (ax25) % 108.63/15.17 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 108.63/15.17 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 108.63/15.17 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 108.63/15.17 % 108.63/15.17 (ax41) % 108.63/15.18 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 108.63/15.18 (frontsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 108.63/15.18 (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 108.63/15.18 % 108.63/15.18 (ax42) % 108.63/15.18 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ~ $i(v0) % 108.63/15.18 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 108.63/15.18 % 108.63/15.18 (ax44) % 108.63/15.18 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) % 108.63/15.18 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) | % 108.63/15.18 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] % 108.63/15.18 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~ % 108.63/15.18 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : % 108.63/15.18 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = % 108.63/15.18 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = % 108.63/15.18 v0))))))))) % 108.63/15.18 % 108.63/15.18 (ax46) % 108.63/15.18 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (frontsegP(nil, v0) = v1) | ~ % 108.63/15.18 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 108.63/15.18 = nil) & ( ~ (v0 = nil) | v1 = 0))) % 108.63/15.18 % 108.63/15.18 (co1) % 108.63/15.19 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 108.63/15.19 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: $i] : ? [v4: any] % 108.63/15.19 : (ssList(v3) = 0 & neq(v3, nil) = v4 & $i(v3) & ? [v5: any] : (v3 = v0 & % 108.63/15.19 frontsegP(v1, v0) = v5 & ((v5 = 0 & v4 = 0) | (v1 = nil & v0 = nil)) & % 108.63/15.19 ((v2 = 0 & ! [v6: $i] : ( ~ (neq(v6, nil) = 0) | ~ $i(v6) | ? [v7: % 108.63/15.19 any] : ? [v8: any] : ? [v9: any] : (frontsegP(v1, v6) = v8 & % 108.63/15.19 frontsegP(v0, v6) = v9 & ssList(v6) = v7 & ( ~ (v9 = 0) | ~ % 108.63/15.19 (v8 = 0) | ~ (v7 = 0))))) | (v1 = nil & ~ (v0 = nil))))))) % 108.63/15.19 % 108.63/15.19 (function-axioms) % 108.63/15.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 108.63/15.20 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 108.63/15.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 108.63/15.20 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 108.63/15.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 108.63/15.20 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 108.63/15.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 108.63/15.20 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 108.63/15.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 108.63/15.20 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 108.63/15.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 108.63/15.20 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 108.63/15.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 108.63/15.20 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 108.63/15.20 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 108.63/15.20 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 108.63/15.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 108.63/15.20 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 108.63/15.20 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 108.63/15.20 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 108.63/15.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 108.63/15.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 108.63/15.20 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 108.63/15.20 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 108.63/15.20 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 108.63/15.20 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 108.63/15.20 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 108.63/15.20 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 108.63/15.20 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 108.63/15.20 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 108.63/15.20 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 108.63/15.20 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 108.63/15.20 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 108.63/15.20 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 108.63/15.20 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 108.63/15.20 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 108.63/15.20 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 108.63/15.20 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 108.63/15.20 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 108.63/15.20 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 108.63/15.20 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 108.63/15.20 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 108.63/15.20 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 108.63/15.20 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 108.63/15.20 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 108.63/15.20 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 108.63/15.20 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 108.63/15.20 (hd(v0) = v1 & $i(v1)) % 108.63/15.20 % 108.63/15.20 Further assumptions not needed in the proof: % 108.63/15.20 -------------------------------------------- % 108.63/15.20 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax21, ax22, ax24, ax26, % 108.63/15.20 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 108.63/15.20 ax39, ax4, ax40, ax43, ax45, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, % 108.63/15.20 ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, % 108.63/15.20 ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, % 108.63/15.20 ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, % 108.63/15.20 ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 108.63/15.20 % 108.63/15.20 Those formulas are unsatisfiable: % 108.63/15.20 --------------------------------- % 108.63/15.20 % 108.63/15.20 Begin of proof % 108.93/15.20 | % 108.93/15.20 | ALPHA: (ax17) implies: % 108.93/15.20 | (1) ssList(nil) = 0 % 108.93/15.20 | % 108.93/15.20 | ALPHA: (ax20) implies: % 108.93/15.20 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 108.93/15.20 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 108.93/15.20 | ssItem(v2) = 0 & $i(v2)))) % 108.93/15.20 | % 108.93/15.20 | ALPHA: (ax46) implies: % 108.93/15.20 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (frontsegP(nil, v0) = v1) | ~ $i(v0) % 108.93/15.20 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 108.93/15.20 | = nil) & ( ~ (v0 = nil) | v1 = 0))) % 108.93/15.20 | % 108.93/15.20 | ALPHA: (co1) implies: % 108.93/15.21 | (4) $i(nil) % 108.93/15.21 | (5) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 108.93/15.21 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: $i] : ? [v4: % 108.93/15.21 | any] : (ssList(v3) = 0 & neq(v3, nil) = v4 & $i(v3) & ? [v5: % 108.93/15.21 | any] : (v3 = v0 & frontsegP(v1, v0) = v5 & ((v5 = 0 & v4 = 0) | % 108.93/15.21 | (v1 = nil & v0 = nil)) & ((v2 = 0 & ! [v6: $i] : ( ~ % 108.93/15.21 | (neq(v6, nil) = 0) | ~ $i(v6) | ? [v7: any] : ? [v8: % 108.93/15.21 | any] : ? [v9: any] : (frontsegP(v1, v6) = v8 & % 108.93/15.21 | frontsegP(v0, v6) = v9 & ssList(v6) = v7 & ( ~ (v9 = 0) % 108.93/15.21 | | ~ (v8 = 0) | ~ (v7 = 0))))) | (v1 = nil & ~ (v0 % 108.93/15.21 | = nil))))))) % 108.93/15.21 | % 108.93/15.21 | ALPHA: (function-axioms) implies: % 108.93/15.21 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 108.93/15.21 | (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 108.93/15.21 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 108.93/15.21 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 108.93/15.21 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 108.93/15.21 | ! [v3: $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ % 108.93/15.21 | (frontsegP(v3, v2) = v0)) % 108.93/15.21 | % 108.93/15.21 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives: % 108.93/15.21 | (9) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 = % 108.93/15.21 | all_137_0) & ssItem(v0) = 0 & $i(v0)) % 108.93/15.21 | % 108.93/15.21 | ALPHA: (9) implies: % 108.93/15.21 | (10) $i(all_137_0) % 108.93/15.21 | (11) ssItem(all_137_0) = 0 % 108.93/15.21 | % 108.93/15.21 | DELTA: instantiating (5) with fresh symbol all_139_0 gives: % 108.93/15.21 | (12) ssList(all_139_0) = 0 & $i(all_139_0) & ? [v0: $i] : ? [v1: any] : % 108.93/15.21 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v2: $i] : ? [v3: % 108.93/15.21 | any] : (ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v4: any] % 108.93/15.21 | : (v2 = all_139_0 & frontsegP(v0, all_139_0) = v4 & ((v4 = 0 & v3 % 108.93/15.21 | = 0) | (v0 = nil & all_139_0 = nil)) & ((v1 = 0 & ! [v5: % 108.93/15.21 | $i] : ( ~ (neq(v5, nil) = 0) | ~ $i(v5) | ? [v6: any] : % 108.93/15.21 | ? [v7: any] : ? [v8: any] : (frontsegP(v0, v5) = v7 & % 108.93/15.21 | frontsegP(all_139_0, v5) = v8 & ssList(v5) = v6 & ( ~ % 108.93/15.21 | (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) | (v0 = nil & % 108.93/15.21 | ~ (all_139_0 = nil)))))) % 108.93/15.21 | % 108.93/15.21 | ALPHA: (12) implies: % 108.93/15.22 | (13) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 108.93/15.22 | $i(v0) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, nil) % 108.93/15.22 | = v3 & $i(v2) & ? [v4: any] : (v2 = all_139_0 & frontsegP(v0, % 108.93/15.22 | all_139_0) = v4 & ((v4 = 0 & v3 = 0) | (v0 = nil & all_139_0 = % 108.93/15.22 | nil)) & ((v1 = 0 & ! [v5: $i] : ( ~ (neq(v5, nil) = 0) | ~ % 108.93/15.22 | $i(v5) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 108.93/15.22 | (frontsegP(v0, v5) = v7 & frontsegP(all_139_0, v5) = v8 & % 108.93/15.22 | ssList(v5) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 108.93/15.22 | 0))))) | (v0 = nil & ~ (all_139_0 = nil)))))) % 108.93/15.22 | % 108.93/15.22 | DELTA: instantiating (13) with fresh symbols all_143_0, all_143_1 gives: % 108.93/15.22 | (14) ssList(all_143_1) = 0 & neq(all_143_1, nil) = all_143_0 & % 108.93/15.22 | $i(all_143_1) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, % 108.93/15.22 | nil) = v1 & $i(v0) & ? [v2: any] : (v0 = all_139_0 & % 108.93/15.22 | frontsegP(all_143_1, all_139_0) = v2 & ((v2 = 0 & v1 = 0) | % 108.93/15.22 | (all_143_1 = nil & all_139_0 = nil)) & ((all_143_0 = 0 & ! [v3: % 108.93/15.22 | $i] : ( ~ (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ? % 108.93/15.22 | [v5: any] : ? [v6: any] : (frontsegP(all_143_1, v3) = v5 & % 108.93/15.22 | frontsegP(all_139_0, v3) = v6 & ssList(v3) = v4 & ( ~ (v6 % 108.93/15.22 | = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (all_143_1 = % 108.93/15.22 | nil & ~ (all_139_0 = nil))))) % 108.93/15.22 | % 108.93/15.22 | ALPHA: (14) implies: % 108.93/15.22 | (15) $i(all_143_1) % 108.93/15.22 | (16) neq(all_143_1, nil) = all_143_0 % 108.93/15.22 | (17) ssList(all_143_1) = 0 % 108.93/15.22 | (18) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 108.93/15.22 | $i(v0) & ? [v2: any] : (v0 = all_139_0 & frontsegP(all_143_1, % 108.93/15.22 | all_139_0) = v2 & ((v2 = 0 & v1 = 0) | (all_143_1 = nil & % 108.93/15.22 | all_139_0 = nil)) & ((all_143_0 = 0 & ! [v3: $i] : ( ~ % 108.93/15.22 | (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] % 108.93/15.22 | : ? [v6: any] : (frontsegP(all_143_1, v3) = v5 & % 108.93/15.22 | frontsegP(all_139_0, v3) = v6 & ssList(v3) = v4 & ( ~ (v6 % 108.93/15.22 | = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (all_143_1 = % 108.93/15.22 | nil & ~ (all_139_0 = nil))))) % 108.93/15.22 | % 108.93/15.22 | DELTA: instantiating (18) with fresh symbols all_145_0, all_145_1 gives: % 108.93/15.22 | (19) ssList(all_145_1) = 0 & neq(all_145_1, nil) = all_145_0 & % 108.93/15.22 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_0 & % 108.93/15.22 | frontsegP(all_143_1, all_139_0) = v0 & ((v0 = 0 & all_145_0 = 0) | % 108.93/15.22 | (all_143_1 = nil & all_139_0 = nil)) & ((all_143_0 = 0 & ! [v1: % 108.93/15.22 | $i] : ( ~ (neq(v1, nil) = 0) | ~ $i(v1) | ? [v2: any] : ? % 108.93/15.22 | [v3: any] : ? [v4: any] : (frontsegP(all_143_1, v1) = v3 & % 108.93/15.22 | frontsegP(all_139_0, v1) = v4 & ssList(v1) = v2 & ( ~ (v4 = % 108.93/15.22 | 0) | ~ (v3 = 0) | ~ (v2 = 0))))) | (all_143_1 = nil & % 108.93/15.22 | ~ (all_139_0 = nil)))) % 108.93/15.22 | % 108.93/15.22 | ALPHA: (19) implies: % 108.93/15.22 | (20) $i(all_145_1) % 108.93/15.22 | (21) neq(all_145_1, nil) = all_145_0 % 108.93/15.22 | (22) ssList(all_145_1) = 0 % 108.93/15.22 | (23) ? [v0: any] : (all_145_1 = all_139_0 & frontsegP(all_143_1, % 108.93/15.22 | all_139_0) = v0 & ((v0 = 0 & all_145_0 = 0) | (all_143_1 = nil & % 108.93/15.22 | all_139_0 = nil)) & ((all_143_0 = 0 & ! [v1: $i] : ( ~ (neq(v1, % 108.93/15.22 | nil) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : ? % 108.93/15.22 | [v4: any] : (frontsegP(all_143_1, v1) = v3 & % 108.93/15.22 | frontsegP(all_139_0, v1) = v4 & ssList(v1) = v2 & ( ~ (v4 = % 108.93/15.22 | 0) | ~ (v3 = 0) | ~ (v2 = 0))))) | (all_143_1 = nil & % 108.93/15.22 | ~ (all_139_0 = nil)))) % 108.93/15.22 | % 108.93/15.22 | DELTA: instantiating (23) with fresh symbol all_147_0 gives: % 108.93/15.23 | (24) all_145_1 = all_139_0 & frontsegP(all_143_1, all_139_0) = all_147_0 & % 108.93/15.23 | ((all_147_0 = 0 & all_145_0 = 0) | (all_143_1 = nil & all_139_0 = % 108.93/15.23 | nil)) & ((all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | % 108.93/15.23 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 108.93/15.23 | (frontsegP(all_143_1, v0) = v2 & frontsegP(all_139_0, v0) = v3 & % 108.93/15.23 | ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) % 108.93/15.23 | | (all_143_1 = nil & ~ (all_139_0 = nil))) % 108.93/15.23 | % 108.93/15.23 | ALPHA: (24) implies: % 108.93/15.23 | (25) all_145_1 = all_139_0 % 108.93/15.23 | (26) frontsegP(all_143_1, all_139_0) = all_147_0 % 108.93/15.23 | (27) (all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? % 108.93/15.23 | [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_143_1, % 108.93/15.23 | v0) = v2 & frontsegP(all_139_0, v0) = v3 & ssList(v0) = v1 & ( % 108.93/15.23 | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_143_1 = nil % 108.93/15.23 | & ~ (all_139_0 = nil)) % 108.93/15.23 | (28) (all_147_0 = 0 & all_145_0 = 0) | (all_143_1 = nil & all_139_0 = nil) % 108.93/15.23 | % 108.93/15.23 | REDUCE: (22), (25) imply: % 108.93/15.23 | (29) ssList(all_139_0) = 0 % 108.93/15.23 | % 108.93/15.23 | REDUCE: (21), (25) imply: % 108.93/15.23 | (30) neq(all_139_0, nil) = all_145_0 % 108.93/15.23 | % 108.93/15.23 | REDUCE: (20), (25) imply: % 108.93/15.23 | (31) $i(all_139_0) % 108.93/15.23 | % 108.93/15.23 | GROUND_INST: instantiating (ax41) with nil, simplifying with (1), (4) gives: % 108.93/15.23 | (32) ! [v0: $i] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ~ $i(v0) | ? % 108.93/15.23 | [v1: any] : ? [v2: any] : (frontsegP(v0, nil) = v2 & ssList(v0) = % 108.93/15.23 | v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 108.93/15.23 | % 108.93/15.23 | GROUND_INST: instantiating (2) with all_139_0, simplifying with (29), (31) % 108.93/15.23 | gives: % 108.93/15.23 | (33) all_139_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 108.93/15.23 | : (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & $i(v1))) % 108.93/15.23 | % 108.93/15.23 | GROUND_INST: instantiating (ax15) with all_139_0, simplifying with (29), (31) % 108.93/15.23 | gives: % 108.93/15.23 | (34) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_139_0, v0) = v1) | ~ $i(v0) % 108.93/15.23 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 108.93/15.23 | ~ (v0 = all_139_0)) & (v1 = 0 | v0 = all_139_0))) % 108.93/15.23 | % 108.93/15.23 | GROUND_INST: instantiating (2) with all_143_1, simplifying with (15), (17) % 108.93/15.23 | gives: % 108.93/15.23 | (35) all_143_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 108.93/15.23 | : (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 108.93/15.23 | % 108.93/15.23 | GROUND_INST: instantiating (ax15) with all_143_1, simplifying with (15), (17) % 108.93/15.23 | gives: % 108.93/15.24 | (36) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_1, v0) = v1) | ~ $i(v0) % 108.93/15.24 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 108.93/15.24 | ~ (v0 = all_143_1)) & (v1 = 0 | v0 = all_143_1))) % 108.93/15.24 | % 108.93/15.24 | GROUND_INST: instantiating (36) with nil, all_143_0, simplifying with (4), % 108.93/15.24 | (16) gives: % 108.93/15.24 | (37) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_143_0 = 0) % 108.93/15.24 | | ~ (all_143_1 = nil)) & (all_143_0 = 0 | all_143_1 = nil)) % 108.93/15.24 | % 108.93/15.24 | GROUND_INST: instantiating (34) with nil, all_145_0, simplifying with (4), % 108.93/15.24 | (30) gives: % 108.93/15.24 | (38) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_145_0 = 0) % 108.93/15.24 | | ~ (all_139_0 = nil)) & (all_145_0 = 0 | all_139_0 = nil)) % 108.93/15.24 | % 108.93/15.24 | BETA: splitting (27) gives: % 108.93/15.24 | % 108.93/15.24 | Case 1: % 108.93/15.24 | | % 108.93/15.24 | | (39) all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | % 108.93/15.24 | | ? [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_143_1, % 108.93/15.24 | | v0) = v2 & frontsegP(all_139_0, v0) = v3 & ssList(v0) = v1 & ( % 108.93/15.24 | | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) % 108.93/15.24 | | % 108.93/15.24 | | ALPHA: (39) implies: % 108.93/15.24 | | (40) all_143_0 = 0 % 108.93/15.24 | | (41) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ? % 108.93/15.24 | | [v2: any] : ? [v3: any] : (frontsegP(all_143_1, v0) = v2 & % 108.93/15.24 | | frontsegP(all_139_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | % 108.93/15.24 | | ~ (v2 = 0) | ~ (v1 = 0)))) % 108.93/15.24 | | % 108.93/15.24 | | BETA: splitting (37) gives: % 108.93/15.24 | | % 108.93/15.24 | | Case 1: % 108.93/15.24 | | | % 108.93/15.24 | | | (42) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.93/15.24 | | | % 108.93/15.24 | | | REF_CLOSE: (1), (7), (42) are inconsistent by sub-proof #1. % 108.93/15.24 | | | % 108.93/15.24 | | Case 2: % 108.93/15.24 | | | % 108.93/15.24 | | | (43) ( ~ (all_143_0 = 0) | ~ (all_143_1 = nil)) & (all_143_0 = 0 | % 108.93/15.24 | | | all_143_1 = nil) % 108.93/15.24 | | | % 108.93/15.24 | | | ALPHA: (43) implies: % 108.93/15.24 | | | (44) ~ (all_143_0 = 0) | ~ (all_143_1 = nil) % 108.93/15.24 | | | % 108.93/15.24 | | | BETA: splitting (44) gives: % 108.93/15.24 | | | % 108.93/15.24 | | | Case 1: % 108.93/15.24 | | | | % 108.93/15.24 | | | | (45) ~ (all_143_1 = nil) % 108.93/15.24 | | | | % 108.93/15.24 | | | | BETA: splitting (28) gives: % 108.93/15.24 | | | | % 108.93/15.24 | | | | Case 1: % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | (46) all_147_0 = 0 & all_145_0 = 0 % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | ALPHA: (46) implies: % 108.93/15.24 | | | | | (47) all_145_0 = 0 % 108.93/15.24 | | | | | (48) all_147_0 = 0 % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | REDUCE: (26), (48) imply: % 108.93/15.24 | | | | | (49) frontsegP(all_143_1, all_139_0) = 0 % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | REDUCE: (30), (47) imply: % 108.93/15.24 | | | | | (50) neq(all_139_0, nil) = 0 % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | BETA: splitting (38) gives: % 108.93/15.24 | | | | | % 108.93/15.24 | | | | | Case 1: % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | REF_CLOSE: (1), (7), (51) are inconsistent by sub-proof #1. % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | Case 2: % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | (52) ( ~ (all_145_0 = 0) | ~ (all_139_0 = nil)) & (all_145_0 = 0 % 108.93/15.24 | | | | | | | all_139_0 = nil) % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | ALPHA: (52) implies: % 108.93/15.24 | | | | | | (53) ~ (all_145_0 = 0) | ~ (all_139_0 = nil) % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | BETA: splitting (35) gives: % 108.93/15.24 | | | | | | % 108.93/15.24 | | | | | | Case 1: % 108.93/15.24 | | | | | | | % 108.93/15.24 | | | | | | | (54) all_143_1 = nil % 108.93/15.24 | | | | | | | % 108.93/15.24 | | | | | | | REDUCE: (45), (54) imply: % 108.93/15.24 | | | | | | | (55) $false % 108.93/15.24 | | | | | | | % 108.93/15.24 | | | | | | | CLOSE: (55) is inconsistent. % 108.93/15.24 | | | | | | | % 108.93/15.25 | | | | | | Case 2: % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | (56) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 108.93/15.25 | | | | | | | (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | DELTA: instantiating (56) with fresh symbol all_365_0 gives: % 108.93/15.25 | | | | | | | (57) ssList(all_365_0) = 0 & $i(all_365_0) & ? [v0: $i] : % 108.93/15.25 | | | | | | | (cons(v0, all_365_0) = all_143_1 & ssItem(v0) = 0 & % 108.93/15.25 | | | | | | | $i(v0)) % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | ALPHA: (57) implies: % 108.93/15.25 | | | | | | | (58) $i(all_365_0) % 108.93/15.25 | | | | | | | (59) ssList(all_365_0) = 0 % 108.93/15.25 | | | | | | | (60) ? [v0: $i] : (cons(v0, all_365_0) = all_143_1 & % 108.93/15.25 | | | | | | | ssItem(v0) = 0 & $i(v0)) % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | DELTA: instantiating (60) with fresh symbol all_367_0 gives: % 108.93/15.25 | | | | | | | (61) cons(all_367_0, all_365_0) = all_143_1 & ssItem(all_367_0) % 108.93/15.25 | | | | | | | = 0 & $i(all_367_0) % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | ALPHA: (61) implies: % 108.93/15.25 | | | | | | | (62) $i(all_367_0) % 108.93/15.25 | | | | | | | (63) ssItem(all_367_0) = 0 % 108.93/15.25 | | | | | | | (64) cons(all_367_0, all_365_0) = all_143_1 % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | BETA: splitting (53) gives: % 108.93/15.25 | | | | | | | % 108.93/15.25 | | | | | | | Case 1: % 108.93/15.25 | | | | | | | | % 108.93/15.25 | | | | | | | | (65) ~ (all_139_0 = nil) % 108.93/15.25 | | | | | | | | % 108.93/15.25 | | | | | | | | BETA: splitting (33) gives: % 108.93/15.25 | | | | | | | | % 108.93/15.25 | | | | | | | | Case 1: % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | (66) all_139_0 = nil % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | REDUCE: (65), (66) imply: % 108.93/15.25 | | | | | | | | | (67) $false % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | CLOSE: (67) is inconsistent. % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | Case 2: % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | (68) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 108.93/15.25 | | | | | | | | | (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & % 108.93/15.25 | | | | | | | | | $i(v1))) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | DELTA: instantiating (68) with fresh symbol all_378_0 gives: % 108.93/15.25 | | | | | | | | | (69) ssList(all_378_0) = 0 & $i(all_378_0) & ? [v0: $i] : % 108.93/15.25 | | | | | | | | | (cons(v0, all_378_0) = all_139_0 & ssItem(v0) = 0 & % 108.93/15.25 | | | | | | | | | $i(v0)) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | ALPHA: (69) implies: % 108.93/15.25 | | | | | | | | | (70) $i(all_378_0) % 108.93/15.25 | | | | | | | | | (71) ssList(all_378_0) = 0 % 108.93/15.25 | | | | | | | | | (72) ? [v0: $i] : (cons(v0, all_378_0) = all_139_0 & % 108.93/15.25 | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | DELTA: instantiating (72) with fresh symbol all_380_0 gives: % 108.93/15.25 | | | | | | | | | (73) cons(all_380_0, all_378_0) = all_139_0 & % 108.93/15.25 | | | | | | | | | ssItem(all_380_0) = 0 & $i(all_380_0) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | ALPHA: (73) implies: % 108.93/15.25 | | | | | | | | | (74) $i(all_380_0) % 108.93/15.25 | | | | | | | | | (75) ssItem(all_380_0) = 0 % 108.93/15.25 | | | | | | | | | (76) cons(all_380_0, all_378_0) = all_139_0 % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | GROUND_INST: instantiating (ax44) with all_367_0, simplifying % 108.93/15.25 | | | | | | | | | with (62), (63) gives: % 108.93/15.25 | | | | | | | | | (77) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! % 108.93/15.25 | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (cons(all_367_0, v1) = % 108.93/15.25 | | | | | | | | | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 108.93/15.25 | | | | | | | | | ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : % 108.93/15.25 | | | | | | | | | ! [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ % 108.93/15.25 | | | | | | | | | (cons(v0, v3) = v4) | ~ $i(v3) | ? [v6: any] : % 108.93/15.25 | | | | | | | | | ? [v7: any] : (frontsegP(v1, v3) = v7 & % 108.93/15.25 | | | | | | | | | ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) % 108.93/15.25 | | | | | | | | | | ~ (v0 = all_367_0) | v5 = 0) & ( ~ % 108.93/15.25 | | | | | | | | | (v5 = 0) | (v7 = 0 & v0 = % 108.93/15.25 | | | | | | | | | all_367_0)))))))) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | GROUND_INST: instantiating (ax44) with all_380_0, simplifying % 108.93/15.25 | | | | | | | | | with (74), (75) gives: % 108.93/15.25 | | | | | | | | | (78) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! % 108.93/15.25 | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (cons(all_380_0, v1) = % 108.93/15.25 | | | | | | | | | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 108.93/15.25 | | | | | | | | | ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : % 108.93/15.25 | | | | | | | | | ! [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ % 108.93/15.25 | | | | | | | | | (cons(v0, v3) = v4) | ~ $i(v3) | ? [v6: any] : % 108.93/15.25 | | | | | | | | | ? [v7: any] : (frontsegP(v1, v3) = v7 & % 108.93/15.25 | | | | | | | | | ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) % 108.93/15.25 | | | | | | | | | | ~ (v0 = all_380_0) | v5 = 0) & ( ~ % 108.93/15.25 | | | | | | | | | (v5 = 0) | (v7 = 0 & v0 = % 108.93/15.25 | | | | | | | | | all_380_0)))))))) % 108.93/15.25 | | | | | | | | | % 108.93/15.25 | | | | | | | | | GROUND_INST: instantiating (41) with all_139_0, simplifying % 108.93/15.25 | | | | | | | | | with (31), (50) gives: % 108.93/15.26 | | | | | | | | | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 108.93/15.26 | | | | | | | | | (frontsegP(all_143_1, all_139_0) = v1 & % 108.93/15.26 | | | | | | | | | frontsegP(all_139_0, all_139_0) = v2 & % 108.93/15.26 | | | | | | | | | ssList(all_139_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) % 108.93/15.26 | | | | | | | | | | ~ (v0 = 0))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (ax25) with all_365_0, simplifying % 108.93/15.26 | | | | | | | | | with (58), (59) gives: % 108.93/15.26 | | | | | | | | | (80) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_365_0) = % 108.93/15.26 | | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 108.93/15.26 | | | | | | | | | (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = % 108.93/15.26 | | | | | | | | | 0) | v3 = all_365_0))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (ax23) with all_365_0, simplifying % 108.93/15.26 | | | | | | | | | with (58), (59) gives: % 108.93/15.26 | | | | | | | | | (81) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_365_0) = % 108.93/15.26 | | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 108.93/15.26 | | | | | | | | | (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = % 108.93/15.26 | | | | | | | | | 0) | v3 = v0))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (77) with all_380_0, simplifying % 108.93/15.26 | | | | | | | | | with (74), (75) gives: % 108.93/15.26 | | | | | | | | | (82) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_367_0, v0) = % 108.93/15.26 | | | | | | | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 108.93/15.26 | | | | | | | | | ssList(v0) = v2) | ! [v2: $i] : ! [v3: $i] : ! % 108.93/15.26 | | | | | | | | | [v4: any] : ( ~ (frontsegP(v1, v3) = v4) | ~ % 108.93/15.26 | | | | | | | | | (cons(all_380_0, v2) = v3) | ~ $i(v2) | ? [v5: % 108.93/15.26 | | | | | | | | | any] : ? [v6: any] : (frontsegP(v0, v2) = v6 & % 108.93/15.26 | | | | | | | | | ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) | % 108.93/15.26 | | | | | | | | | ~ (all_380_0 = all_367_0) | v4 = 0) & ( ~ % 108.93/15.26 | | | | | | | | | (v4 = 0) | (v6 = 0 & all_380_0 = % 108.93/15.26 | | | | | | | | | all_367_0))))))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (78) with all_137_0, simplifying % 108.93/15.26 | | | | | | | | | with (10), (11) gives: % 108.93/15.26 | | | | | | | | | (83) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_380_0, v0) = % 108.93/15.26 | | | | | | | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 108.93/15.26 | | | | | | | | | ssList(v0) = v2) | ! [v2: $i] : ! [v3: $i] : ! % 108.93/15.26 | | | | | | | | | [v4: any] : ( ~ (frontsegP(v1, v3) = v4) | ~ % 108.93/15.26 | | | | | | | | | (cons(all_137_0, v2) = v3) | ~ $i(v2) | ? [v5: % 108.93/15.26 | | | | | | | | | any] : ? [v6: any] : (frontsegP(v0, v2) = v6 & % 108.93/15.26 | | | | | | | | | ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) | % 108.93/15.26 | | | | | | | | | ~ (all_380_0 = all_137_0) | v4 = 0) & ( ~ % 108.93/15.26 | | | | | | | | | (v4 = 0) | (v6 = 0 & all_380_0 = % 108.93/15.26 | | | | | | | | | all_137_0))))))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (81) with all_367_0, all_143_1, % 108.93/15.26 | | | | | | | | | simplifying with (62), (64) gives: % 108.93/15.26 | | | | | | | | | (84) ? [v0: any] : ? [v1: $i] : (hd(all_143_1) = v1 & % 108.93/15.26 | | | | | | | | | ssItem(all_367_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 108.93/15.26 | | | | | | | | | = all_367_0)) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (80) with all_367_0, all_143_1, % 108.93/15.26 | | | | | | | | | simplifying with (62), (64) gives: % 108.93/15.26 | | | | | | | | | (85) ? [v0: any] : ? [v1: $i] : (tl(all_143_1) = v1 & % 108.93/15.26 | | | | | | | | | ssItem(all_367_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 108.93/15.26 | | | | | | | | | = all_365_0)) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (82) with all_365_0, all_143_1, % 108.93/15.26 | | | | | | | | | simplifying with (58), (64) gives: % 108.93/15.26 | | | | | | | | | (86) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_365_0) = v0) % 108.93/15.26 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 108.93/15.26 | | | | | | | | | (frontsegP(all_143_1, v1) = v2) | ~ % 108.93/15.26 | | | | | | | | | (cons(all_380_0, v0) = v1) | ~ $i(v0) | ? [v3: % 108.93/15.26 | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_365_0, v0) = % 108.93/15.26 | | | | | | | | | v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = % 108.93/15.26 | | | | | | | | | 0) | ~ (all_380_0 = all_367_0) | v2 = 0) % 108.93/15.26 | | | | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & all_380_0 = % 108.93/15.26 | | | | | | | | | all_367_0)))))) % 108.93/15.26 | | | | | | | | | % 108.93/15.26 | | | | | | | | | GROUND_INST: instantiating (83) with all_378_0, all_139_0, % 108.93/15.26 | | | | | | | | | simplifying with (70), (76) gives: % 109.25/15.26 | | | | | | | | | (87) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_378_0) = v0) % 109.25/15.26 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 109.25/15.26 | | | | | | | | | (frontsegP(all_139_0, v1) = v2) | ~ % 109.25/15.26 | | | | | | | | | (cons(all_137_0, v0) = v1) | ~ $i(v0) | ? [v3: % 109.25/15.26 | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_378_0, v0) = % 109.25/15.26 | | | | | | | | | v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = % 109.25/15.26 | | | | | | | | | 0) | ~ (all_380_0 = all_137_0) | v2 = 0) % 109.25/15.26 | | | | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & all_380_0 = % 109.25/15.26 | | | | | | | | | all_137_0)))))) % 109.25/15.26 | | | | | | | | | % 109.25/15.26 | | | | | | | | | DELTA: instantiating (79) with fresh symbols all_756_0, % 109.25/15.26 | | | | | | | | | all_756_1, all_756_2 gives: % 109.25/15.26 | | | | | | | | | (88) frontsegP(all_143_1, all_139_0) = all_756_1 & % 109.25/15.26 | | | | | | | | | frontsegP(all_139_0, all_139_0) = all_756_0 & % 109.25/15.26 | | | | | | | | | ssList(all_139_0) = all_756_2 & ( ~ (all_756_0 = 0) | % 109.25/15.26 | | | | | | | | | ~ (all_756_1 = 0) | ~ (all_756_2 = 0)) % 109.25/15.26 | | | | | | | | | % 109.25/15.26 | | | | | | | | | ALPHA: (88) implies: % 109.25/15.26 | | | | | | | | | (89) ssList(all_139_0) = all_756_2 % 109.25/15.27 | | | | | | | | | (90) frontsegP(all_139_0, all_139_0) = all_756_0 % 109.25/15.27 | | | | | | | | | (91) frontsegP(all_143_1, all_139_0) = all_756_1 % 109.25/15.27 | | | | | | | | | (92) ~ (all_756_0 = 0) | ~ (all_756_1 = 0) | ~ % 109.25/15.27 | | | | | | | | | (all_756_2 = 0) % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | DELTA: instantiating (84) with fresh symbols all_762_0, % 109.25/15.27 | | | | | | | | | all_762_1 gives: % 109.25/15.27 | | | | | | | | | (93) hd(all_143_1) = all_762_0 & ssItem(all_367_0) = % 109.25/15.27 | | | | | | | | | all_762_1 & $i(all_762_0) & ( ~ (all_762_1 = 0) | % 109.25/15.27 | | | | | | | | | all_762_0 = all_367_0) % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | ALPHA: (93) implies: % 109.25/15.27 | | | | | | | | | (94) ssItem(all_367_0) = all_762_1 % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | DELTA: instantiating (85) with fresh symbols all_764_0, % 109.25/15.27 | | | | | | | | | all_764_1 gives: % 109.25/15.27 | | | | | | | | | (95) tl(all_143_1) = all_764_0 & ssItem(all_367_0) = % 109.25/15.27 | | | | | | | | | all_764_1 & $i(all_764_0) & ( ~ (all_764_1 = 0) | % 109.25/15.27 | | | | | | | | | all_764_0 = all_365_0) % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | ALPHA: (95) implies: % 109.25/15.27 | | | | | | | | | (96) ssItem(all_367_0) = all_764_1 % 109.25/15.27 | | | | | | | | | (97) ~ (all_764_1 = 0) | all_764_0 = all_365_0 % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | BETA: splitting (86) gives: % 109.25/15.27 | | | | | | | | | % 109.25/15.27 | | | | | | | | | Case 1: % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | (98) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_365_0) = % 109.25/15.27 | | | | | | | | | | v0) % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | DELTA: instantiating (98) with fresh symbol all_783_0 gives: % 109.25/15.27 | | | | | | | | | | (99) ~ (all_783_0 = 0) & ssList(all_365_0) = all_783_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | ALPHA: (99) implies: % 109.25/15.27 | | | | | | | | | | (100) ~ (all_783_0 = 0) % 109.25/15.27 | | | | | | | | | | (101) ssList(all_365_0) = all_783_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | DELTA: instantiating (98) with fresh symbol all_785_0 gives: % 109.25/15.27 | | | | | | | | | | (102) ~ (all_785_0 = 0) & ssList(all_365_0) = all_785_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | ALPHA: (102) implies: % 109.25/15.27 | | | | | | | | | | (103) ssList(all_365_0) = all_785_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | DELTA: instantiating (98) with fresh symbol all_787_0 gives: % 109.25/15.27 | | | | | | | | | | (104) ~ (all_787_0 = 0) & ssList(all_365_0) = all_787_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | ALPHA: (104) implies: % 109.25/15.27 | | | | | | | | | | (105) ssList(all_365_0) = all_787_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | GROUND_INST: instantiating (7) with all_783_0, all_785_0, % 109.25/15.27 | | | | | | | | | | all_365_0, simplifying with (101), (103) gives: % 109.25/15.27 | | | | | | | | | | (106) all_785_0 = all_783_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_787_0, all_365_0, % 109.25/15.27 | | | | | | | | | | simplifying with (59), (105) gives: % 109.25/15.27 | | | | | | | | | | (107) all_787_0 = 0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | GROUND_INST: instantiating (7) with all_785_0, all_787_0, % 109.25/15.27 | | | | | | | | | | all_365_0, simplifying with (103), (105) gives: % 109.25/15.27 | | | | | | | | | | (108) all_787_0 = all_785_0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | COMBINE_EQS: (107), (108) imply: % 109.25/15.27 | | | | | | | | | | (109) all_785_0 = 0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | SIMP: (109) implies: % 109.25/15.27 | | | | | | | | | | (110) all_785_0 = 0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | COMBINE_EQS: (106), (110) imply: % 109.25/15.27 | | | | | | | | | | (111) all_783_0 = 0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | SIMP: (111) implies: % 109.25/15.27 | | | | | | | | | | (112) all_783_0 = 0 % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | REDUCE: (100), (112) imply: % 109.25/15.27 | | | | | | | | | | (113) $false % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | CLOSE: (113) is inconsistent. % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | Case 2: % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | (114) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 109.25/15.27 | | | | | | | | | | (frontsegP(all_143_1, v1) = v2) | ~ % 109.25/15.27 | | | | | | | | | | (cons(all_380_0, v0) = v1) | ~ $i(v0) | ? [v3: % 109.25/15.27 | | | | | | | | | | any] : ? [v4: any] : (frontsegP(all_365_0, v0) % 109.25/15.27 | | | | | | | | | | = v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ % 109.25/15.27 | | | | | | | | | | (v4 = 0) | ~ (all_380_0 = all_367_0) | % 109.25/15.27 | | | | | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & % 109.25/15.27 | | | | | | | | | | all_380_0 = all_367_0)))))) % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | GROUND_INST: instantiating (114) with all_378_0, all_139_0, 0, % 109.25/15.27 | | | | | | | | | | simplifying with (49), (70), (76) gives: % 109.25/15.27 | | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : (frontsegP(all_365_0, % 109.25/15.27 | | | | | | | | | | all_378_0) = v1 & ssList(all_378_0) = v0 & ( ~ % 109.25/15.27 | | | | | | | | | | (v0 = 0) | (v1 = 0 & all_380_0 = all_367_0))) % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | BETA: splitting (87) gives: % 109.25/15.27 | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | Case 1: % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | (116) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_378_0) = % 109.25/15.27 | | | | | | | | | | | v0) % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_786_0, % 109.25/15.27 | | | | | | | | | | | all_786_1 gives: % 109.25/15.27 | | | | | | | | | | | (117) frontsegP(all_365_0, all_378_0) = all_786_0 & % 109.25/15.27 | | | | | | | | | | | ssList(all_378_0) = all_786_1 & ( ~ (all_786_1 = % 109.25/15.27 | | | | | | | | | | | 0) | (all_786_0 = 0 & all_380_0 = all_367_0)) % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | ALPHA: (117) implies: % 109.25/15.27 | | | | | | | | | | | (118) ssList(all_378_0) = all_786_1 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | DELTA: instantiating (116) with fresh symbol all_788_0 % 109.25/15.27 | | | | | | | | | | | gives: % 109.25/15.27 | | | | | | | | | | | (119) ~ (all_788_0 = 0) & ssList(all_378_0) = all_788_0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | ALPHA: (119) implies: % 109.25/15.27 | | | | | | | | | | | (120) ~ (all_788_0 = 0) % 109.25/15.27 | | | | | | | | | | | (121) ssList(all_378_0) = all_788_0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | DELTA: instantiating (116) with fresh symbol all_790_0 % 109.25/15.27 | | | | | | | | | | | gives: % 109.25/15.27 | | | | | | | | | | | (122) ~ (all_790_0 = 0) & ssList(all_378_0) = all_790_0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | ALPHA: (122) implies: % 109.25/15.27 | | | | | | | | | | | (123) ssList(all_378_0) = all_790_0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_786_1, all_788_0, % 109.25/15.27 | | | | | | | | | | | all_378_0, simplifying with (118), (121) gives: % 109.25/15.27 | | | | | | | | | | | (124) all_788_0 = all_786_1 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_790_0, all_378_0, % 109.25/15.27 | | | | | | | | | | | simplifying with (71), (123) gives: % 109.25/15.27 | | | | | | | | | | | (125) all_790_0 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_788_0, all_790_0, % 109.25/15.27 | | | | | | | | | | | all_378_0, simplifying with (121), (123) gives: % 109.25/15.27 | | | | | | | | | | | (126) all_790_0 = all_788_0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | COMBINE_EQS: (125), (126) imply: % 109.25/15.27 | | | | | | | | | | | (127) all_788_0 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | SIMP: (127) implies: % 109.25/15.27 | | | | | | | | | | | (128) all_788_0 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | COMBINE_EQS: (124), (128) imply: % 109.25/15.27 | | | | | | | | | | | (129) all_786_1 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | REDUCE: (120), (128) imply: % 109.25/15.27 | | | | | | | | | | | (130) $false % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | CLOSE: (130) is inconsistent. % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | Case 2: % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_764_1, all_367_0, % 109.25/15.27 | | | | | | | | | | | simplifying with (63), (96) gives: % 109.25/15.27 | | | | | | | | | | | (131) all_764_1 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_762_1, all_764_1, % 109.25/15.27 | | | | | | | | | | | all_367_0, simplifying with (94), (96) gives: % 109.25/15.27 | | | | | | | | | | | (132) all_764_1 = all_762_1 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.27 | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_756_2, all_139_0, % 109.25/15.27 | | | | | | | | | | | simplifying with (29), (89) gives: % 109.25/15.27 | | | | | | | | | | | (133) all_756_2 = 0 % 109.25/15.27 | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_756_1, all_139_0, % 109.25/15.28 | | | | | | | | | | | all_143_1, simplifying with (49), (91) gives: % 109.25/15.28 | | | | | | | | | | | (134) all_756_1 = 0 % 109.25/15.28 | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | COMBINE_EQS: (131), (132) imply: % 109.25/15.28 | | | | | | | | | | | (135) all_762_1 = 0 % 109.25/15.28 | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | BETA: splitting (92) gives: % 109.25/15.28 | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | Case 1: % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | (136) ~ (all_756_0 = 0) % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | GROUND_INST: instantiating (ax42) with all_139_0, all_756_0, % 109.25/15.28 | | | | | | | | | | | | simplifying with (31), (90) gives: % 109.25/15.28 | | | | | | | | | | | | (137) all_756_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 109.25/15.28 | | | | | | | | | | | | ssList(all_139_0) = v0) % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | BETA: splitting (137) gives: % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | Case 1: % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | (138) all_756_0 = 0 % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | REDUCE: (136), (138) imply: % 109.25/15.28 | | | | | | | | | | | | | (139) $false % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | CLOSE: (139) is inconsistent. % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | Case 2: % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | (140) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = % 109.25/15.28 | | | | | | | | | | | | | v0) % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | DELTA: instantiating (140) with fresh symbol all_822_0 % 109.25/15.28 | | | | | | | | | | | | | gives: % 109.25/15.28 | | | | | | | | | | | | | (141) ~ (all_822_0 = 0) & ssList(all_139_0) = all_822_0 % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | ALPHA: (141) implies: % 109.25/15.28 | | | | | | | | | | | | | (142) ~ (all_822_0 = 0) % 109.25/15.28 | | | | | | | | | | | | | (143) ssList(all_139_0) = all_822_0 % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | DELTA: instantiating (140) with fresh symbol all_824_0 % 109.25/15.28 | | | | | | | | | | | | | gives: % 109.25/15.28 | | | | | | | | | | | | | (144) ~ (all_824_0 = 0) & ssList(all_139_0) = all_824_0 % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | ALPHA: (144) implies: % 109.25/15.28 | | | | | | | | | | | | | (145) ssList(all_139_0) = all_824_0 % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | BETA: splitting (97) gives: % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | Case 1: % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | (146) ~ (all_764_1 = 0) % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | REDUCE: (131), (146) imply: % 109.25/15.28 | | | | | | | | | | | | | | (147) $false % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | Case 2: % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | DELTA: instantiating (140) with fresh symbol all_842_0 % 109.25/15.28 | | | | | | | | | | | | | | gives: % 109.25/15.28 | | | | | | | | | | | | | | (148) ~ (all_842_0 = 0) & ssList(all_139_0) = all_842_0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | ALPHA: (148) implies: % 109.25/15.28 | | | | | | | | | | | | | | (149) ssList(all_139_0) = all_842_0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_842_0, all_139_0, % 109.25/15.28 | | | | | | | | | | | | | | simplifying with (29), (149) gives: % 109.25/15.28 | | | | | | | | | | | | | | (150) all_842_0 = 0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_824_0, all_842_0, % 109.25/15.28 | | | | | | | | | | | | | | all_139_0, simplifying with (145), (149) gives: % 109.25/15.28 | | | | | | | | | | | | | | (151) all_842_0 = all_824_0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_822_0, all_842_0, % 109.25/15.28 | | | | | | | | | | | | | | all_139_0, simplifying with (143), (149) gives: % 109.25/15.28 | | | | | | | | | | | | | | (152) all_842_0 = all_822_0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | COMBINE_EQS: (151), (152) imply: % 109.25/15.28 | | | | | | | | | | | | | | (153) all_824_0 = all_822_0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | COMBINE_EQS: (150), (151) imply: % 109.25/15.28 | | | | | | | | | | | | | | (154) all_824_0 = 0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | COMBINE_EQS: (153), (154) imply: % 109.25/15.28 | | | | | | | | | | | | | | (155) all_822_0 = 0 % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | REDUCE: (142), (155) imply: % 109.25/15.28 | | | | | | | | | | | | | | (156) $false % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 109.25/15.28 | | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | Case 2: % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | (157) ~ (all_756_1 = 0) | ~ (all_756_2 = 0) % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | BETA: splitting (157) gives: % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | Case 1: % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | (158) ~ (all_756_1 = 0) % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | REDUCE: (134), (158) imply: % 109.25/15.28 | | | | | | | | | | | | | (159) $false % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | Case 2: % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | (160) ~ (all_756_2 = 0) % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | REDUCE: (133), (160) imply: % 109.25/15.28 | | | | | | | | | | | | | (161) $false % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 109.25/15.28 | | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | | | % 109.25/15.28 | | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | | % 109.25/15.28 | | | | | | | | | End of split % 109.25/15.28 | | | | | | | | | % 109.25/15.28 | | | | | | | | End of split % 109.25/15.28 | | | | | | | | % 109.25/15.28 | | | | | | | Case 2: % 109.25/15.28 | | | | | | | | % 109.25/15.28 | | | | | | | | (162) ~ (all_145_0 = 0) % 109.25/15.28 | | | | | | | | % 109.25/15.28 | | | | | | | | REDUCE: (47), (162) imply: % 109.25/15.28 | | | | | | | | (163) $false % 109.25/15.28 | | | | | | | | % 109.25/15.28 | | | | | | | | CLOSE: (163) is inconsistent. % 109.25/15.28 | | | | | | | | % 109.25/15.28 | | | | | | | End of split % 109.25/15.28 | | | | | | | % 109.25/15.28 | | | | | | End of split % 109.25/15.28 | | | | | | % 109.25/15.28 | | | | | End of split % 109.25/15.28 | | | | | % 109.25/15.28 | | | | Case 2: % 109.25/15.28 | | | | | % 109.25/15.28 | | | | | (164) all_143_1 = nil & all_139_0 = nil % 109.25/15.28 | | | | | % 109.25/15.28 | | | | | ALPHA: (164) implies: % 109.25/15.28 | | | | | (165) all_143_1 = nil % 109.25/15.28 | | | | | % 109.25/15.28 | | | | | REDUCE: (45), (165) imply: % 109.25/15.28 | | | | | (166) $false % 109.25/15.28 | | | | | % 109.25/15.28 | | | | | CLOSE: (166) is inconsistent. % 109.25/15.28 | | | | | % 109.25/15.28 | | | | End of split % 109.25/15.28 | | | | % 109.25/15.28 | | | Case 2: % 109.25/15.28 | | | | % 109.25/15.28 | | | | (167) ~ (all_143_0 = 0) % 109.25/15.28 | | | | % 109.25/15.28 | | | | REDUCE: (40), (167) imply: % 109.25/15.28 | | | | (168) $false % 109.25/15.28 | | | | % 109.25/15.28 | | | | CLOSE: (168) is inconsistent. % 109.25/15.28 | | | | % 109.25/15.28 | | | End of split % 109.25/15.28 | | | % 109.25/15.28 | | End of split % 109.25/15.28 | | % 109.25/15.28 | Case 2: % 109.25/15.28 | | % 109.25/15.28 | | (169) all_143_1 = nil & ~ (all_139_0 = nil) % 109.25/15.28 | | % 109.25/15.28 | | ALPHA: (169) implies: % 109.25/15.28 | | (170) all_143_1 = nil % 109.25/15.28 | | (171) ~ (all_139_0 = nil) % 109.25/15.28 | | % 109.25/15.28 | | REDUCE: (26), (170) imply: % 109.25/15.28 | | (172) frontsegP(nil, all_139_0) = all_147_0 % 109.25/15.28 | | % 109.25/15.28 | | BETA: splitting (28) gives: % 109.25/15.28 | | % 109.25/15.28 | | Case 1: % 109.25/15.28 | | | % 109.25/15.28 | | | (173) all_147_0 = 0 & all_145_0 = 0 % 109.25/15.28 | | | % 109.25/15.28 | | | ALPHA: (173) implies: % 109.25/15.28 | | | (174) all_147_0 = 0 % 109.25/15.28 | | | % 109.25/15.28 | | | REDUCE: (172), (174) imply: % 109.25/15.28 | | | (175) frontsegP(nil, all_139_0) = 0 % 109.25/15.28 | | | % 109.25/15.28 | | | GROUND_INST: instantiating (32) with all_139_0, simplifying with (31), % 109.25/15.28 | | | (175) gives: % 109.25/15.28 | | | (176) all_139_0 = nil | ? [v0: any] : ? [v1: any] : % 109.25/15.28 | | | (frontsegP(all_139_0, nil) = v1 & ssList(all_139_0) = v0 & ( ~ % 109.25/15.28 | | | (v1 = 0) | ~ (v0 = 0))) % 109.25/15.28 | | | % 109.25/15.28 | | | GROUND_INST: instantiating (3) with all_139_0, 0, simplifying with (31), % 109.25/15.28 | | | (175) gives: % 109.25/15.28 | | | (177) all_139_0 = nil | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) % 109.25/15.28 | | | = v0) % 109.25/15.28 | | | % 109.25/15.28 | | | BETA: splitting (177) gives: % 109.25/15.28 | | | % 109.25/15.28 | | | Case 1: % 109.25/15.28 | | | | % 109.25/15.28 | | | | (178) all_139_0 = nil % 109.25/15.28 | | | | % 109.25/15.28 | | | | REDUCE: (171), (178) imply: % 109.25/15.28 | | | | (179) $false % 109.25/15.28 | | | | % 109.25/15.28 | | | | CLOSE: (179) is inconsistent. % 109.25/15.28 | | | | % 109.25/15.28 | | | Case 2: % 109.25/15.28 | | | | % 109.25/15.28 | | | | (180) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) % 109.25/15.28 | | | | % 109.25/15.28 | | | | DELTA: instantiating (180) with fresh symbol all_588_0 gives: % 109.25/15.28 | | | | (181) ~ (all_588_0 = 0) & ssList(all_139_0) = all_588_0 % 109.25/15.28 | | | | % 109.25/15.28 | | | | ALPHA: (181) implies: % 109.25/15.28 | | | | (182) ~ (all_588_0 = 0) % 109.25/15.28 | | | | (183) ssList(all_139_0) = all_588_0 % 109.25/15.28 | | | | % 109.25/15.28 | | | | DELTA: instantiating (180) with fresh symbol all_590_0 gives: % 109.25/15.28 | | | | (184) ~ (all_590_0 = 0) & ssList(all_139_0) = all_590_0 % 109.25/15.28 | | | | % 109.25/15.28 | | | | ALPHA: (184) implies: % 109.25/15.29 | | | | (185) ssList(all_139_0) = all_590_0 % 109.25/15.29 | | | | % 109.25/15.29 | | | | DELTA: instantiating (180) with fresh symbol all_594_0 gives: % 109.25/15.29 | | | | (186) ~ (all_594_0 = 0) & ssList(all_139_0) = all_594_0 % 109.25/15.29 | | | | % 109.25/15.29 | | | | ALPHA: (186) implies: % 109.25/15.29 | | | | (187) ssList(all_139_0) = all_594_0 % 109.25/15.29 | | | | % 109.25/15.29 | | | | BETA: splitting (176) gives: % 109.25/15.29 | | | | % 109.25/15.29 | | | | Case 1: % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | (188) all_139_0 = nil % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | REDUCE: (171), (188) imply: % 109.25/15.29 | | | | | (189) $false % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | CLOSE: (189) is inconsistent. % 109.25/15.29 | | | | | % 109.25/15.29 | | | | Case 2: % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | (190) ? [v0: any] : ? [v1: any] : (frontsegP(all_139_0, nil) = v1 % 109.25/15.29 | | | | | & ssList(all_139_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | DELTA: instantiating (190) with fresh symbols all_603_0, all_603_1 % 109.25/15.29 | | | | | gives: % 109.25/15.29 | | | | | (191) frontsegP(all_139_0, nil) = all_603_0 & ssList(all_139_0) = % 109.25/15.29 | | | | | all_603_1 & ( ~ (all_603_0 = 0) | ~ (all_603_1 = 0)) % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | ALPHA: (191) implies: % 109.25/15.29 | | | | | (192) ssList(all_139_0) = all_603_1 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | GROUND_INST: instantiating (7) with 0, all_590_0, all_139_0, % 109.25/15.29 | | | | | simplifying with (29), (185) gives: % 109.25/15.29 | | | | | (193) all_590_0 = 0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | GROUND_INST: instantiating (7) with all_590_0, all_594_0, all_139_0, % 109.25/15.29 | | | | | simplifying with (185), (187) gives: % 109.25/15.29 | | | | | (194) all_594_0 = all_590_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | GROUND_INST: instantiating (7) with all_594_0, all_603_1, all_139_0, % 109.25/15.29 | | | | | simplifying with (187), (192) gives: % 109.25/15.29 | | | | | (195) all_603_1 = all_594_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | GROUND_INST: instantiating (7) with all_588_0, all_603_1, all_139_0, % 109.25/15.29 | | | | | simplifying with (183), (192) gives: % 109.25/15.29 | | | | | (196) all_603_1 = all_588_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | COMBINE_EQS: (195), (196) imply: % 109.25/15.29 | | | | | (197) all_594_0 = all_588_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | SIMP: (197) implies: % 109.25/15.29 | | | | | (198) all_594_0 = all_588_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | COMBINE_EQS: (194), (198) imply: % 109.25/15.29 | | | | | (199) all_590_0 = all_588_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | SIMP: (199) implies: % 109.25/15.29 | | | | | (200) all_590_0 = all_588_0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | COMBINE_EQS: (193), (200) imply: % 109.25/15.29 | | | | | (201) all_588_0 = 0 % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | REDUCE: (182), (201) imply: % 109.25/15.29 | | | | | (202) $false % 109.25/15.29 | | | | | % 109.25/15.29 | | | | | CLOSE: (202) is inconsistent. % 109.25/15.29 | | | | | % 109.25/15.29 | | | | End of split % 109.25/15.29 | | | | % 109.25/15.29 | | | End of split % 109.25/15.29 | | | % 109.25/15.29 | | Case 2: % 109.25/15.29 | | | % 109.25/15.29 | | | (203) all_143_1 = nil & all_139_0 = nil % 109.25/15.29 | | | % 109.25/15.29 | | | ALPHA: (203) implies: % 109.25/15.29 | | | (204) all_139_0 = nil % 109.25/15.29 | | | % 109.25/15.29 | | | REDUCE: (171), (204) imply: % 109.25/15.29 | | | (205) $false % 109.25/15.29 | | | % 109.25/15.29 | | | CLOSE: (205) is inconsistent. % 109.25/15.29 | | | % 109.25/15.29 | | End of split % 109.25/15.29 | | % 109.25/15.29 | End of split % 109.25/15.29 | % 109.25/15.29 End of proof % 109.25/15.29 % 109.25/15.29 Sub-proof #1 shows that the following formulas are inconsistent: % 109.25/15.29 ---------------------------------------------------------------- % 109.25/15.29 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 109.25/15.29 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 109.25/15.29 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 109.25/15.29 (3) ssList(nil) = 0 % 109.25/15.29 % 109.25/15.29 Begin of proof % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_304_0 gives: % 109.25/15.29 | (4) ~ (all_304_0 = 0) & ssList(nil) = all_304_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (4) implies: % 109.25/15.29 | (5) ~ (all_304_0 = 0) % 109.25/15.29 | (6) ssList(nil) = all_304_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_306_0 gives: % 109.25/15.29 | (7) ~ (all_306_0 = 0) & ssList(nil) = all_306_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (7) implies: % 109.25/15.29 | (8) ssList(nil) = all_306_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_308_0 gives: % 109.25/15.29 | (9) ~ (all_308_0 = 0) & ssList(nil) = all_308_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (9) implies: % 109.25/15.29 | (10) ssList(nil) = all_308_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_310_0 gives: % 109.25/15.29 | (11) ~ (all_310_0 = 0) & ssList(nil) = all_310_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (11) implies: % 109.25/15.29 | (12) ssList(nil) = all_310_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_312_0 gives: % 109.25/15.29 | (13) ~ (all_312_0 = 0) & ssList(nil) = all_312_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (13) implies: % 109.25/15.29 | (14) ssList(nil) = all_312_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_314_0 gives: % 109.25/15.29 | (15) ~ (all_314_0 = 0) & ssList(nil) = all_314_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (15) implies: % 109.25/15.29 | (16) ssList(nil) = all_314_0 % 109.25/15.29 | % 109.25/15.29 | DELTA: instantiating (1) with fresh symbol all_316_0 gives: % 109.25/15.29 | (17) ~ (all_316_0 = 0) & ssList(nil) = all_316_0 % 109.25/15.29 | % 109.25/15.29 | ALPHA: (17) implies: % 109.25/15.29 | (18) ssList(nil) = all_316_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with 0, all_312_0, nil, simplifying with (3), % 109.25/15.29 | (14) gives: % 109.25/15.29 | (19) all_312_0 = 0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_308_0, all_312_0, nil, simplifying % 109.25/15.29 | with (10), (14) gives: % 109.25/15.29 | (20) all_312_0 = all_308_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_310_0, all_314_0, nil, simplifying % 109.25/15.29 | with (12), (16) gives: % 109.25/15.29 | (21) all_314_0 = all_310_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_308_0, all_314_0, nil, simplifying % 109.25/15.29 | with (10), (16) gives: % 109.25/15.29 | (22) all_314_0 = all_308_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_306_0, all_314_0, nil, simplifying % 109.25/15.29 | with (8), (16) gives: % 109.25/15.29 | (23) all_314_0 = all_306_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_310_0, all_316_0, nil, simplifying % 109.25/15.29 | with (12), (18) gives: % 109.25/15.29 | (24) all_316_0 = all_310_0 % 109.25/15.29 | % 109.25/15.29 | GROUND_INST: instantiating (2) with all_304_0, all_316_0, nil, simplifying % 109.25/15.29 | with (6), (18) gives: % 109.25/15.29 | (25) all_316_0 = all_304_0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (24), (25) imply: % 109.25/15.29 | (26) all_310_0 = all_304_0 % 109.25/15.29 | % 109.25/15.29 | SIMP: (26) implies: % 109.25/15.29 | (27) all_310_0 = all_304_0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (22), (23) imply: % 109.25/15.29 | (28) all_308_0 = all_306_0 % 109.25/15.29 | % 109.25/15.29 | SIMP: (28) implies: % 109.25/15.29 | (29) all_308_0 = all_306_0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (21), (23) imply: % 109.25/15.29 | (30) all_310_0 = all_306_0 % 109.25/15.29 | % 109.25/15.29 | SIMP: (30) implies: % 109.25/15.29 | (31) all_310_0 = all_306_0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (19), (20) imply: % 109.25/15.29 | (32) all_308_0 = 0 % 109.25/15.29 | % 109.25/15.29 | SIMP: (32) implies: % 109.25/15.29 | (33) all_308_0 = 0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (27), (31) imply: % 109.25/15.29 | (34) all_306_0 = all_304_0 % 109.25/15.29 | % 109.25/15.29 | SIMP: (34) implies: % 109.25/15.29 | (35) all_306_0 = all_304_0 % 109.25/15.29 | % 109.25/15.29 | COMBINE_EQS: (29), (33) imply: % 109.25/15.29 | (36) all_306_0 = 0 % 109.25/15.30 | % 109.25/15.30 | SIMP: (36) implies: % 109.25/15.30 | (37) all_306_0 = 0 % 109.25/15.30 | % 109.25/15.30 | COMBINE_EQS: (35), (37) imply: % 109.25/15.30 | (38) all_304_0 = 0 % 109.25/15.30 | % 109.25/15.30 | SIMP: (38) implies: % 109.25/15.30 | (39) all_304_0 = 0 % 109.25/15.30 | % 109.25/15.30 | REDUCE: (5), (39) imply: % 109.25/15.30 | (40) $false % 109.25/15.30 | % 109.25/15.30 | CLOSE: (40) is inconsistent. % 109.25/15.30 | % 109.25/15.30 End of proof % 109.25/15.30 % SZS output end Proof for theBenchmark % 109.25/15.30 % 109.25/15.30 14691ms %------------------------------------------------------------------------------