%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC279+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 : n023.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 20:50:37 EDT 2023 % Result : Theorem 32.90s 4.99s % Output : Proof 74.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SWC279+1 : TPTP v8.1.2. Released v2.4.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 15:06:55 EDT 2023 % 0.12/0.33 % CPUTime : % 0.66/0.63 ________ _____ % 0.66/0.63 ___ __ \_________(_)________________________________ % 0.66/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.63 (2023-06-19) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2023 % 0.66/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.63 Amanda Stjerna. % 0.66/0.63 Free software under BSD-3-Clause. % 0.66/0.63 % 0.66/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.63 % 0.66/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.65 Running up to 7 provers in parallel. % 0.66/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.66/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 5.45/1.44 Prover 4: Preprocessing ... % 5.45/1.44 Prover 1: Preprocessing ... % 5.65/1.48 Prover 6: Preprocessing ... % 5.65/1.48 Prover 0: Preprocessing ... % 5.65/1.48 Prover 2: Preprocessing ... % 5.65/1.48 Prover 5: Preprocessing ... % 5.65/1.48 Prover 3: Preprocessing ... % 14.76/2.68 Prover 2: Proving ... % 14.76/2.70 Prover 5: Constructing countermodel ... % 15.30/2.77 Prover 1: Constructing countermodel ... % 15.73/2.78 Prover 3: Constructing countermodel ... % 15.73/2.81 Prover 6: Proving ... % 22.27/3.62 Prover 4: Constructing countermodel ... % 22.80/3.74 Prover 0: Proving ... % 32.90/4.99 Prover 0: proved (4324ms) % 32.90/4.99 % 32.90/4.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 32.90/4.99 % 32.90/4.99 Prover 3: stopped % 32.90/4.99 Prover 5: stopped % 32.90/5.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 32.90/5.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.90/5.00 Prover 6: stopped % 32.90/5.01 Prover 2: stopped % 32.90/5.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.90/5.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 32.90/5.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 34.25/5.18 Prover 7: Preprocessing ... % 34.25/5.20 Prover 10: Preprocessing ... % 34.93/5.24 Prover 8: Preprocessing ... % 35.24/5.29 Prover 13: Preprocessing ... % 35.24/5.31 Prover 11: Preprocessing ... % 35.79/5.38 Prover 10: Constructing countermodel ... % 36.25/5.42 Prover 7: Constructing countermodel ... % 37.69/5.62 Prover 8: Warning: ignoring some quantifiers % 38.04/5.64 Prover 8: Constructing countermodel ... % 38.07/5.64 Prover 13: Constructing countermodel ... % 46.98/6.81 Prover 11: Constructing countermodel ... % 72.68/10.10 Prover 13: stopped % 72.95/10.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 73.15/10.17 Prover 1: Found proof (size 259) % 73.15/10.17 Prover 1: proved (9515ms) % 73.15/10.17 Prover 4: stopped % 73.15/10.17 Prover 7: stopped % 73.15/10.17 Prover 8: stopped % 73.15/10.17 Prover 11: stopped % 73.15/10.17 Prover 10: stopped % 73.15/10.21 Prover 16: Preprocessing ... % 73.69/10.24 Prover 16: stopped % 73.69/10.24 % 73.69/10.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 73.69/10.24 % 73.69/10.28 % SZS output start Proof for theBenchmark % 73.69/10.29 Assumptions after simplification: % 73.69/10.29 --------------------------------- % 73.69/10.29 % 73.69/10.29 (ax16) % 73.97/10.31 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 73.97/10.32 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 73.97/10.32 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 73.97/10.32 % 73.97/10.32 (ax17) % 73.97/10.32 ssList(nil) = 0 & $i(nil) % 73.97/10.32 % 73.97/10.32 (ax2) % 73.97/10.32 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 73.97/10.32 ssItem(v1) = 0 & $i(v1))) % 73.97/10.32 % 73.97/10.32 (ax23) % 73.97/10.32 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 73.97/10.32 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 73.97/10.32 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 73.97/10.32 % 73.97/10.32 (ax25) % 73.97/10.32 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 73.97/10.32 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 73.97/10.32 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 73.97/10.32 % 73.97/10.32 (ax44) % 73.97/10.32 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) % 73.97/10.33 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) | % 73.97/10.33 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] % 73.97/10.33 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~ % 73.97/10.33 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : % 73.97/10.33 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = % 73.97/10.33 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = % 73.97/10.33 v0))))))))) % 73.97/10.33 % 73.97/10.33 (ax59) % 73.97/10.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.33 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 73.97/10.33 (v2 = 0) | v3 = 0))) % 73.97/10.33 % 73.97/10.33 (ax60) % 73.97/10.33 cyclefreeP(nil) = 0 & $i(nil) % 73.97/10.33 % 73.97/10.33 (ax61) % 73.97/10.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.33 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 73.97/10.33 (v2 = 0) | v3 = 0))) % 73.97/10.33 % 73.97/10.33 (ax62) % 73.97/10.33 totalorderP(nil) = 0 & $i(nil) % 73.97/10.33 % 73.97/10.33 (ax63) % 73.97/10.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.33 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 73.97/10.33 (v2 = 0) | v3 = 0))) % 73.97/10.33 % 73.97/10.33 (ax65) % 73.97/10.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.33 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 73.97/10.33 (v2 = 0) | v3 = 0))) % 73.97/10.33 % 73.97/10.33 (ax68) % 73.97/10.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.33 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 73.97/10.33 ~ (v2 = 0) | v3 = 0))) % 73.97/10.33 % 73.97/10.33 (ax71) % 73.97/10.34 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.34 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 73.97/10.34 ~ (v2 = 0) | v3 = 0))) % 73.97/10.34 % 73.97/10.34 (ax73) % 73.97/10.34 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 73.97/10.34 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 73.97/10.34 (v2 = 0) | v3 = 0))) % 73.97/10.34 % 73.97/10.34 (ax8) % 73.97/10.34 ! [v0: $i] : ! [v1: any] : ( ~ (cyclefreeP(v0) = v1) | ~ $i(v0) | ? [v2: % 73.97/10.34 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~ % 73.97/10.34 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 73.97/10.34 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 73.97/10.34 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 73.97/10.34 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] : % 73.97/10.34 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10) % 73.97/10.34 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) = % 73.97/10.34 v11) | ! [v11: $i] : ! [v12: $i] : ( ~ (v6 = 0) | ~ (v4 % 73.97/10.34 = 0) | ~ (cons(v3, v11) = v12) | ~ (app(v10, v12) = % 73.97/10.34 v0) | ~ $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & % 73.97/10.34 ssList(v11) = v13))))))))) & (v1 = 0 | ? [v2: $i] : % 73.97/10.34 (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 73.97/10.34 (leq(v3, v2) = v5 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? % 73.97/10.34 [v6: $i] : (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? % 73.97/10.34 [v9: $i] : (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 % 73.97/10.34 & $i(v9) & $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : (v5 = % 73.97/10.34 0 & v4 = 0 & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9, % 73.97/10.35 v11) = v0 & $i(v11) & $i(v10))))))))) % 73.97/10.35 % 73.97/10.35 (ax9) % 73.97/10.35 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderP(v0) = v1) | ~ $i(v0) | ? [v2: % 73.97/10.35 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~ % 73.97/10.35 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 73.97/10.35 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 73.97/10.35 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 73.97/10.35 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] : % 73.97/10.35 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10) % 73.97/10.35 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) = % 73.97/10.35 v11) | ! [v11: $i] : ! [v12: $i] : (v6 = 0 | v4 = 0 | ~ % 73.97/10.35 (cons(v3, v11) = v12) | ~ (app(v10, v12) = v0) | ~ % 73.97/10.35 $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & ssList(v11) = % 73.97/10.35 v13))))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 73.97/10.35 $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5 % 73.97/10.35 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? [v6: $i] : % 73.97/10.35 (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 73.97/10.35 (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 & $i(v9) & % 73.97/10.35 $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : ( ~ (v5 = 0) & % 73.97/10.35 ~ (v4 = 0) & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9, % 73.97/10.35 v11) = v0 & $i(v11) & $i(v10))))))))) % 73.97/10.35 % 73.97/10.35 (co1) % 73.97/10.36 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 73.97/10.36 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ % 73.97/10.36 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : % 73.97/10.36 ! [v5: $i] : ( ~ (app(v4, v3) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 % 73.97/10.36 = 0) & ssList(v4) = v6) | ! [v6: $i] : ( ~ (app(v5, v6) = v0) | % 73.97/10.36 ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v6) = v7) | ! [v7: % 73.97/10.36 $i] : ! [v8: any] : ( ~ (memberP(v4, v7) = v8) | ~ $i(v7) | ? % 73.97/10.36 [v9: any] : ? [v10: any] : ? [v11: any] : ? [v12: any] : % 73.97/10.36 (leq(v7, v2) = v12 & leq(v2, v7) = v10 & memberP(v6, v7) = v11 & % 73.97/10.36 ssItem(v7) = v9 & ( ~ (v9 = 0) | (( ~ (v11 = 0) | v10 = 0) & ( ~ % 73.97/10.36 (v8 = 0) | v12 = 0)))))))) & ? [v2: $i] : ? [v3: $i] : % 73.97/10.36 (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? % 73.97/10.36 [v5: $i] : (ssList(v4) = 0 & app(v4, v3) = v5 & $i(v5) & $i(v4) & ? % 73.97/10.36 [v6: $i] : (ssList(v6) = 0 & app(v5, v6) = v0 & $i(v6) & ? [v7: $i] : % 73.97/10.36 ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: any] : % 73.97/10.36 (leq(v7, v2) = v9 & leq(v2, v7) = v11 & memberP(v6, v7) = v10 & % 73.97/10.36 memberP(v4, v7) = v8 & ssItem(v7) = 0 & $i(v7) & ((v10 = 0 & ~ % 73.97/10.36 (v11 = 0)) | (v8 = 0 & ~ (v9 = 0))))))))) % 73.97/10.36 % 73.97/10.36 (function-axioms) % 74.33/10.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.33/10.37 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 74.33/10.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.33/10.37 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 74.33/10.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.33/10.37 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 74.33/10.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.33/10.37 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 74.33/10.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.33/10.37 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 74.33/10.37 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 74.33/10.37 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 74.33/10.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 74.33/10.37 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 74.33/10.37 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.33/10.37 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 74.33/10.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.33/10.37 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 74.33/10.37 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 74.33/10.37 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 74.33/10.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 74.33/10.37 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 74.33/10.37 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.33/10.37 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 74.33/10.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 74.33/10.37 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 74.33/10.37 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 74.33/10.37 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 74.33/10.37 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 74.33/10.37 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 74.33/10.37 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 74.33/10.37 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 74.33/10.37 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.33/10.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 74.33/10.37 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 74.33/10.37 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 74.33/10.37 % 74.33/10.37 Further assumptions not needed in the proof: % 74.33/10.37 -------------------------------------------- % 74.37/10.37 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax18, ax19, ax20, ax21, ax22, ax24, % 74.37/10.37 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, % 74.37/10.37 ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49, ax5, % 74.37/10.37 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax64, ax66, ax67, % 74.37/10.37 ax69, ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax80, ax81, ax82, % 74.37/10.37 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax90, ax91, ax92, ax93, ax94, ax95 % 74.37/10.37 % 74.37/10.37 Those formulas are unsatisfiable: % 74.37/10.37 --------------------------------- % 74.37/10.37 % 74.37/10.37 Begin of proof % 74.37/10.37 | % 74.37/10.37 | ALPHA: (ax17) implies: % 74.37/10.37 | (1) ssList(nil) = 0 % 74.37/10.37 | % 74.37/10.37 | ALPHA: (ax59) implies: % 74.37/10.37 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.37 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 74.37/10.37 | ~ (v2 = 0) | v3 = 0))) % 74.37/10.37 | % 74.37/10.37 | ALPHA: (ax60) implies: % 74.37/10.37 | (3) cyclefreeP(nil) = 0 % 74.37/10.37 | % 74.37/10.37 | ALPHA: (ax61) implies: % 74.37/10.37 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.37 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 74.37/10.37 | ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax62) implies: % 74.37/10.38 | (5) totalorderP(nil) = 0 % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax63) implies: % 74.37/10.38 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.38 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 74.37/10.38 | ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax65) implies: % 74.37/10.38 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.38 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 74.37/10.38 | & ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax68) implies: % 74.37/10.38 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.38 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 74.37/10.38 | & ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax71) implies: % 74.37/10.38 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.38 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 74.37/10.38 | & ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (ax73) implies: % 74.37/10.38 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.38 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 74.37/10.38 | ( ~ (v2 = 0) | v3 = 0))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (co1) implies: % 74.37/10.38 | (11) $i(nil) % 74.37/10.38 | (12) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 74.37/10.38 | & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | % 74.37/10.38 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! % 74.37/10.38 | [v4: $i] : ! [v5: $i] : ( ~ (app(v4, v3) = v5) | ~ $i(v4) | ? % 74.37/10.38 | [v6: int] : ( ~ (v6 = 0) & ssList(v4) = v6) | ! [v6: $i] : ( % 74.37/10.38 | ~ (app(v5, v6) = v0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = % 74.37/10.38 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: any] : ( ~ % 74.37/10.38 | (memberP(v4, v7) = v8) | ~ $i(v7) | ? [v9: any] : ? % 74.37/10.38 | [v10: any] : ? [v11: any] : ? [v12: any] : (leq(v7, v2) % 74.37/10.38 | = v12 & leq(v2, v7) = v10 & memberP(v6, v7) = v11 & % 74.37/10.38 | ssItem(v7) = v9 & ( ~ (v9 = 0) | (( ~ (v11 = 0) | v10 = % 74.37/10.38 | 0) & ( ~ (v8 = 0) | v12 = 0)))))))) & ? [v2: $i] % 74.37/10.38 | : ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & % 74.37/10.38 | $i(v2) & ? [v4: $i] : ? [v5: $i] : (ssList(v4) = 0 & app(v4, % 74.37/10.38 | v3) = v5 & $i(v5) & $i(v4) & ? [v6: $i] : (ssList(v6) = 0 & % 74.37/10.38 | app(v5, v6) = v0 & $i(v6) & ? [v7: $i] : ? [v8: any] : ? % 74.37/10.38 | [v9: any] : ? [v10: any] : ? [v11: any] : (leq(v7, v2) = % 74.37/10.38 | v9 & leq(v2, v7) = v11 & memberP(v6, v7) = v10 & % 74.37/10.38 | memberP(v4, v7) = v8 & ssItem(v7) = 0 & $i(v7) & ((v10 = 0 % 74.37/10.38 | & ~ (v11 = 0)) | (v8 = 0 & ~ (v9 = 0))))))))) % 74.37/10.38 | % 74.37/10.38 | ALPHA: (function-axioms) implies: % 74.37/10.38 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.37/10.38 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 74.37/10.38 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.37/10.38 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 74.37/10.39 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.37/10.39 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, % 74.37/10.39 | v2) = v0)) % 74.37/10.39 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.37/10.39 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 74.37/10.39 | v0)) % 74.37/10.39 | % 74.37/10.39 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives: % 74.37/10.39 | (17) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 = % 74.37/10.39 | all_91_0) & ssItem(v0) = 0 & $i(v0)) % 74.37/10.39 | % 74.37/10.39 | ALPHA: (17) implies: % 74.37/10.39 | (18) $i(all_91_0) % 74.37/10.39 | (19) ssItem(all_91_0) = 0 % 74.37/10.39 | % 74.37/10.39 | DELTA: instantiating (12) with fresh symbol all_93_0 gives: % 74.37/10.39 | (20) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 74.37/10.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ % 74.37/10.39 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: % 74.37/10.39 | $i] : ! [v4: $i] : ( ~ (app(v3, v2) = v4) | ~ $i(v3) | ? [v5: % 74.37/10.39 | int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 74.37/10.39 | (app(v4, v5) = all_93_0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 % 74.37/10.39 | = 0) & ssList(v5) = v6) | ! [v6: $i] : ! [v7: any] : ( ~ % 74.37/10.39 | (memberP(v3, v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 74.37/10.39 | any] : ? [v10: any] : ? [v11: any] : (leq(v6, v1) = v11 % 74.37/10.39 | & leq(v1, v6) = v9 & memberP(v5, v6) = v10 & ssItem(v6) = % 74.37/10.39 | v8 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v9 = 0) & ( ~ (v7 = % 74.37/10.39 | 0) | v11 = 0)))))))) & ? [v1: $i] : ? [v2: $i] : % 74.37/10.39 | (cons(v1, nil) = v2 & ssItem(v1) = 0 & $i(v2) & $i(v1) & ? [v3: $i] % 74.37/10.39 | : ? [v4: $i] : (ssList(v3) = 0 & app(v3, v2) = v4 & $i(v4) & % 74.37/10.39 | $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & app(v4, v5) = all_93_0 % 74.37/10.39 | & $i(v5) & ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: % 74.37/10.39 | any] : ? [v10: any] : (leq(v6, v1) = v8 & leq(v1, v6) = v10 % 74.37/10.39 | & memberP(v5, v6) = v9 & memberP(v3, v6) = v7 & ssItem(v6) = % 74.37/10.39 | 0 & $i(v6) & ((v9 = 0 & ~ (v10 = 0)) | (v7 = 0 & ~ (v8 = % 74.37/10.39 | 0)))))))) % 74.37/10.39 | % 74.37/10.39 | ALPHA: (20) implies: % 74.37/10.39 | (21) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 74.37/10.39 | ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 74.37/10.39 | ssItem(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ (app(v3, v2) % 74.37/10.39 | = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = % 74.37/10.39 | v5) | ! [v5: $i] : ( ~ (app(v4, v5) = all_93_0) | ~ $i(v5) | % 74.37/10.39 | ? [v6: int] : ( ~ (v6 = 0) & ssList(v5) = v6) | ! [v6: $i] : % 74.37/10.39 | ! [v7: any] : ( ~ (memberP(v3, v6) = v7) | ~ $i(v6) | ? % 74.37/10.39 | [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: any] : % 74.37/10.39 | (leq(v6, v1) = v11 & leq(v1, v6) = v9 & memberP(v5, v6) = % 74.37/10.39 | v10 & ssItem(v6) = v8 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v9 % 74.37/10.39 | = 0) & ( ~ (v7 = 0) | v11 = 0)))))))) & ? [v1: $i] % 74.37/10.39 | : ? [v2: $i] : (cons(v1, nil) = v2 & ssItem(v1) = 0 & $i(v2) & % 74.37/10.39 | $i(v1) & ? [v3: $i] : ? [v4: $i] : (ssList(v3) = 0 & app(v3, v2) % 74.37/10.39 | = v4 & $i(v4) & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & app(v4, % 74.37/10.39 | v5) = all_93_0 & $i(v5) & ? [v6: $i] : ? [v7: any] : ? % 74.37/10.39 | [v8: any] : ? [v9: any] : ? [v10: any] : (leq(v6, v1) = v8 & % 74.37/10.39 | leq(v1, v6) = v10 & memberP(v5, v6) = v9 & memberP(v3, v6) = % 74.37/10.39 | v7 & ssItem(v6) = 0 & $i(v6) & ((v9 = 0 & ~ (v10 = 0)) | % 74.37/10.39 | (v7 = 0 & ~ (v8 = 0)))))))) % 74.37/10.39 | % 74.37/10.39 | DELTA: instantiating (21) with fresh symbol all_97_0 gives: % 74.37/10.40 | (22) ssList(all_97_0) = 0 & $i(all_97_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 74.37/10.40 | (cons(v0, nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 74.37/10.40 | ssItem(v0) = v2) | ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v1) = % 74.37/10.40 | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) % 74.37/10.40 | | ! [v4: $i] : ( ~ (app(v3, v4) = all_93_0) | ~ $i(v4) | ? [v5: % 74.37/10.40 | int] : ( ~ (v5 = 0) & ssList(v4) = v5) | ! [v5: $i] : ! [v6: % 74.37/10.40 | any] : ( ~ (memberP(v2, v5) = v6) | ~ $i(v5) | ? [v7: any] : % 74.37/10.40 | ? [v8: any] : ? [v9: any] : ? [v10: any] : (leq(v5, v0) = % 74.37/10.40 | v10 & leq(v0, v5) = v8 & memberP(v4, v5) = v9 & ssItem(v5) = % 74.37/10.40 | v7 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v6 = 0) | % 74.37/10.40 | v10 = 0)))))))) & ? [v0: $i] : ? [v1: $i] : % 74.37/10.40 | (cons(v0, nil) = v1 & ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : % 74.37/10.40 | ? [v3: $i] : (ssList(v2) = 0 & app(v2, v1) = v3 & $i(v3) & $i(v2) & % 74.37/10.40 | ? [v4: $i] : (ssList(v4) = 0 & app(v3, v4) = all_93_0 & $i(v4) & % 74.37/10.40 | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 74.37/10.40 | [v9: any] : (leq(v5, v0) = v7 & leq(v0, v5) = v9 & memberP(v4, % 74.37/10.40 | v5) = v8 & memberP(v2, v5) = v6 & ssItem(v5) = 0 & $i(v5) & % 74.37/10.40 | ((v8 = 0 & ~ (v9 = 0)) | (v6 = 0 & ~ (v7 = 0))))))) % 74.37/10.40 | % 74.37/10.40 | ALPHA: (22) implies: % 74.37/10.40 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.37/10.40 | [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! [v2: $i] : ! [v3: % 74.37/10.40 | $i] : ( ~ (app(v2, v1) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 % 74.37/10.40 | = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) = % 74.37/10.40 | all_93_0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 74.37/10.40 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: any] : ( ~ % 74.37/10.40 | (memberP(v2, v5) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: % 74.37/10.40 | any] : ? [v9: any] : ? [v10: any] : (leq(v5, v0) = v10 & % 74.37/10.40 | leq(v0, v5) = v8 & memberP(v4, v5) = v9 & ssItem(v5) = v7 & % 74.37/10.40 | ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v6 = 0) | v10 % 74.37/10.40 | = 0)))))))) % 74.37/10.40 | (24) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 74.37/10.40 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & % 74.37/10.40 | app(v2, v1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 % 74.37/10.40 | & app(v3, v4) = all_93_0 & $i(v4) & ? [v5: $i] : ? [v6: any] : % 74.37/10.40 | ? [v7: any] : ? [v8: any] : ? [v9: any] : (leq(v5, v0) = v7 & % 74.37/10.40 | leq(v0, v5) = v9 & memberP(v4, v5) = v8 & memberP(v2, v5) = v6 % 74.37/10.40 | & ssItem(v5) = 0 & $i(v5) & ((v8 = 0 & ~ (v9 = 0)) | (v6 = 0 % 74.37/10.40 | & ~ (v7 = 0))))))) % 74.37/10.40 | % 74.37/10.40 | DELTA: instantiating (24) with fresh symbols all_100_0, all_100_1 gives: % 74.37/10.40 | (25) cons(all_100_1, nil) = all_100_0 & ssItem(all_100_1) = 0 & % 74.37/10.40 | $i(all_100_0) & $i(all_100_1) & ? [v0: $i] : ? [v1: $i] : % 74.37/10.40 | (ssList(v0) = 0 & app(v0, all_100_0) = v1 & $i(v1) & $i(v0) & ? [v2: % 74.37/10.40 | $i] : (ssList(v2) = 0 & app(v1, v2) = all_93_0 & $i(v2) & ? [v3: % 74.37/10.40 | $i] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] % 74.37/10.40 | : (leq(v3, all_100_1) = v5 & leq(all_100_1, v3) = v7 & memberP(v2, % 74.37/10.40 | v3) = v6 & memberP(v0, v3) = v4 & ssItem(v3) = 0 & $i(v3) & % 74.37/10.40 | ((v6 = 0 & ~ (v7 = 0)) | (v4 = 0 & ~ (v5 = 0)))))) % 74.37/10.40 | % 74.37/10.40 | ALPHA: (25) implies: % 74.37/10.40 | (26) $i(all_100_1) % 74.37/10.40 | (27) ssItem(all_100_1) = 0 % 74.37/10.40 | (28) cons(all_100_1, nil) = all_100_0 % 74.37/10.41 | (29) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_100_0) = v1 % 74.37/10.41 | & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, v2) = % 74.37/10.41 | all_93_0 & $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? % 74.37/10.41 | [v6: any] : ? [v7: any] : (leq(v3, all_100_1) = v5 & % 74.37/10.41 | leq(all_100_1, v3) = v7 & memberP(v2, v3) = v6 & memberP(v0, v3) % 74.37/10.41 | = v4 & ssItem(v3) = 0 & $i(v3) & ((v6 = 0 & ~ (v7 = 0)) | (v4 = % 74.37/10.41 | 0 & ~ (v5 = 0)))))) % 74.37/10.41 | % 74.37/10.41 | DELTA: instantiating (29) with fresh symbols all_102_0, all_102_1 gives: % 74.37/10.41 | (30) ssList(all_102_1) = 0 & app(all_102_1, all_100_0) = all_102_0 & % 74.37/10.41 | $i(all_102_0) & $i(all_102_1) & ? [v0: $i] : (ssList(v0) = 0 & % 74.37/10.41 | app(all_102_0, v0) = all_93_0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 74.37/10.41 | : ? [v3: any] : ? [v4: any] : ? [v5: any] : (leq(v1, all_100_1) = % 74.37/10.41 | v3 & leq(all_100_1, v1) = v5 & memberP(v0, v1) = v4 & % 74.37/10.41 | memberP(all_102_1, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ((v4 = 0 & % 74.37/10.41 | ~ (v5 = 0)) | (v2 = 0 & ~ (v3 = 0))))) % 74.37/10.41 | % 74.37/10.41 | ALPHA: (30) implies: % 74.37/10.41 | (31) $i(all_102_1) % 74.37/10.41 | (32) app(all_102_1, all_100_0) = all_102_0 % 74.37/10.41 | (33) ssList(all_102_1) = 0 % 74.37/10.41 | (34) ? [v0: $i] : (ssList(v0) = 0 & app(all_102_0, v0) = all_93_0 & $i(v0) % 74.37/10.41 | & ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: % 74.37/10.41 | any] : (leq(v1, all_100_1) = v3 & leq(all_100_1, v1) = v5 & % 74.37/10.41 | memberP(v0, v1) = v4 & memberP(all_102_1, v1) = v2 & ssItem(v1) = % 74.37/10.41 | 0 & $i(v1) & ((v4 = 0 & ~ (v5 = 0)) | (v2 = 0 & ~ (v3 = 0))))) % 74.37/10.41 | % 74.37/10.41 | DELTA: instantiating (34) with fresh symbol all_104_0 gives: % 74.37/10.41 | (35) ssList(all_104_0) = 0 & app(all_102_0, all_104_0) = all_93_0 & % 74.37/10.41 | $i(all_104_0) & ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: % 74.37/10.41 | any] : ? [v4: any] : (leq(v0, all_100_1) = v2 & leq(all_100_1, v0) % 74.37/10.41 | = v4 & memberP(all_104_0, v0) = v3 & memberP(all_102_1, v0) = v1 & % 74.37/10.41 | ssItem(v0) = 0 & $i(v0) & ((v3 = 0 & ~ (v4 = 0)) | (v1 = 0 & ~ (v2 % 74.37/10.41 | = 0)))) % 74.37/10.41 | % 74.37/10.41 | ALPHA: (35) implies: % 74.37/10.41 | (36) $i(all_104_0) % 74.37/10.41 | (37) app(all_102_0, all_104_0) = all_93_0 % 74.37/10.41 | (38) ssList(all_104_0) = 0 % 74.37/10.41 | (39) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 74.37/10.41 | any] : (leq(v0, all_100_1) = v2 & leq(all_100_1, v0) = v4 & % 74.37/10.41 | memberP(all_104_0, v0) = v3 & memberP(all_102_1, v0) = v1 & % 74.37/10.41 | ssItem(v0) = 0 & $i(v0) & ((v3 = 0 & ~ (v4 = 0)) | (v1 = 0 & ~ (v2 % 74.37/10.41 | = 0)))) % 74.37/10.41 | % 74.37/10.41 | DELTA: instantiating (39) with fresh symbols all_106_0, all_106_1, all_106_2, % 74.37/10.41 | all_106_3, all_106_4 gives: % 74.37/10.41 | (40) leq(all_106_4, all_100_1) = all_106_2 & leq(all_100_1, all_106_4) = % 74.37/10.41 | all_106_0 & memberP(all_104_0, all_106_4) = all_106_1 & % 74.37/10.41 | memberP(all_102_1, all_106_4) = all_106_3 & ssItem(all_106_4) = 0 & % 74.37/10.41 | $i(all_106_4) & ((all_106_1 = 0 & ~ (all_106_0 = 0)) | (all_106_3 = 0 % 74.37/10.41 | & ~ (all_106_2 = 0))) % 74.37/10.41 | % 74.37/10.41 | ALPHA: (40) implies: % 74.57/10.41 | (41) $i(all_106_4) % 74.57/10.41 | (42) ssItem(all_106_4) = 0 % 74.57/10.41 | (43) memberP(all_102_1, all_106_4) = all_106_3 % 74.57/10.41 | (44) memberP(all_104_0, all_106_4) = all_106_1 % 74.57/10.41 | (45) leq(all_100_1, all_106_4) = all_106_0 % 74.57/10.41 | (46) leq(all_106_4, all_100_1) = all_106_2 % 74.57/10.41 | (47) (all_106_1 = 0 & ~ (all_106_0 = 0)) | (all_106_3 = 0 & ~ (all_106_2 % 74.57/10.41 | = 0)) % 74.57/10.41 | % 74.57/10.42 | GROUND_INST: instantiating (ax44) with all_100_1, simplifying with (26), (27) % 74.57/10.42 | gives: % 74.57/10.42 | (48) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 74.57/10.42 | $i] : ( ~ (cons(all_100_1, v1) = v2) | ~ $i(v1) | ? [v3: int] : % 74.57/10.42 | ( ~ (v3 = 0) & ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ! % 74.57/10.42 | [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) % 74.57/10.42 | | ~ $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1, v3) = % 74.57/10.42 | v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | ~ (v0 = % 74.57/10.42 | all_100_1) | v5 = 0) & ( ~ (v5 = 0) | (v7 = 0 & v0 = % 74.57/10.42 | all_100_1)))))))) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (10) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (49) ? [v0: any] : ? [v1: any] : (equalelemsP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (9) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (50) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (8) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (51) ? [v0: any] : ? [v1: any] : (strictorderedP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (7) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (52) ? [v0: any] : ? [v1: any] : (totalorderedP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (6) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (53) ? [v0: any] : ? [v1: any] : (strictorderP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (4) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (54) ? [v0: any] : ? [v1: any] : (totalorderP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (2) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (55) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_100_0) = v1 & % 74.57/10.42 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (23) with all_100_1, all_100_0, simplifying with % 74.57/10.42 | (26), (28) gives: % 74.57/10.42 | (56) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_100_1) = v0) | ! [v0: $i] : % 74.57/10.42 | ! [v1: $i] : ( ~ (app(v0, all_100_0) = v1) | ~ $i(v0) | ? [v2: int] % 74.57/10.42 | : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = % 74.57/10.42 | all_93_0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) % 74.57/10.42 | = v3) | ! [v3: $i] : ! [v4: any] : ( ~ (memberP(v0, v3) = v4) % 74.57/10.42 | | ~ $i(v3) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? % 74.57/10.42 | [v8: any] : (leq(v3, all_100_1) = v8 & leq(all_100_1, v3) = v6 & % 74.57/10.42 | memberP(v2, v3) = v7 & ssItem(v3) = v5 & ( ~ (v5 = 0) | (( ~ % 74.57/10.42 | (v7 = 0) | v6 = 0) & ( ~ (v4 = 0) | v8 = 0))))))) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (11) gives: % 74.57/10.42 | (57) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.57/10.42 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 74.57/10.42 | ( ~ (v2 = 0) | v3 = nil))) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (11) gives: % 74.57/10.42 | (58) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.57/10.42 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 74.57/10.42 | ( ~ (v2 = 0) | v3 = v0))) % 74.57/10.42 | % 74.57/10.42 | GROUND_INST: instantiating (ax16) with nil, simplifying with (1), (11) gives: % 74.57/10.43 | (59) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.57/10.43 | [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.57/10.43 | (v2 = 0) | v3 = 0))) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (ax8) with nil, 0, simplifying with (3), (11) % 74.57/10.43 | gives: % 74.57/10.43 | (60) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 74.57/10.43 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ % 74.57/10.43 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 74.57/10.43 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] : % 74.57/10.43 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] : % 74.57/10.43 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = % 74.57/10.43 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & % 74.57/10.43 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : ( ~ (v4 % 74.57/10.43 | = 0) | ~ (v2 = 0) | ~ (cons(v1, v9) = v10) | ~ % 74.57/10.43 | (app(v8, v10) = nil) | ~ $i(v9) | ? [v11: int] : ( ~ % 74.57/10.43 | (v11 = 0) & ssList(v9) = v11)))))))) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (ax9) with nil, 0, simplifying with (5), (11) % 74.57/10.43 | gives: % 74.57/10.43 | (61) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 74.57/10.43 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ % 74.57/10.43 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 74.57/10.43 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] : % 74.57/10.43 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] : % 74.57/10.43 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = % 74.57/10.43 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & % 74.57/10.43 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 = 0 % 74.57/10.43 | | v2 = 0 | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) = % 74.57/10.43 | nil) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & % 74.57/10.43 | ssList(v9) = v11)))))))) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (48) with all_91_0, simplifying with (18), (19) % 74.57/10.43 | gives: % 74.57/10.43 | (62) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_100_1, v0) = v1) | ~ $i(v0) % 74.57/10.43 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! % 74.57/10.43 | [v3: $i] : ! [v4: any] : ( ~ (frontsegP(v1, v3) = v4) | ~ % 74.57/10.43 | (cons(all_91_0, v2) = v3) | ~ $i(v2) | ? [v5: any] : ? [v6: % 74.57/10.43 | any] : (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) % 74.57/10.43 | | (( ~ (v6 = 0) | ~ (all_100_1 = all_91_0) | v4 = 0) & ( ~ % 74.57/10.43 | (v4 = 0) | (v6 = 0 & all_100_1 = all_91_0))))))) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (58) with all_100_1, all_100_0, simplifying with % 74.57/10.43 | (26), (28) gives: % 74.57/10.43 | (63) ? [v0: any] : ? [v1: $i] : (hd(all_100_0) = v1 & ssItem(all_100_1) = % 74.57/10.43 | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_100_1)) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (57) with all_100_1, all_100_0, simplifying with % 74.57/10.43 | (26), (28) gives: % 74.57/10.43 | (64) ? [v0: any] : ? [v1: $i] : (tl(all_100_0) = v1 & ssItem(all_100_1) = % 74.57/10.43 | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (59) with all_100_1, all_100_0, simplifying with % 74.57/10.43 | (26), (28) gives: % 74.57/10.43 | (65) ? [v0: any] : ? [v1: any] : (ssList(all_100_0) = v1 & % 74.57/10.43 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.57/10.43 | % 74.57/10.43 | GROUND_INST: instantiating (62) with nil, all_100_0, simplifying with (11), % 74.57/10.43 | (28) gives: % 74.57/10.43 | (66) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ! % 74.57/10.43 | [v1: $i] : ! [v2: any] : ( ~ (frontsegP(all_100_0, v1) = v2) | ~ % 74.57/10.43 | (cons(all_91_0, v0) = v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 74.57/10.43 | : (frontsegP(nil, v0) = v4 & ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ % 74.57/10.43 | (v4 = 0) | ~ (all_100_1 = all_91_0) | v2 = 0) & ( ~ (v2 = % 74.57/10.43 | 0) | (v4 = 0 & all_100_1 = all_91_0)))))) % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (55) with fresh symbols all_380_0, all_380_1 gives: % 74.57/10.43 | (67) cyclefreeP(all_100_0) = all_380_0 & ssItem(all_100_1) = all_380_1 & ( % 74.57/10.43 | ~ (all_380_1 = 0) | all_380_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (67) implies: % 74.57/10.43 | (68) ssItem(all_100_1) = all_380_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (53) with fresh symbols all_382_0, all_382_1 gives: % 74.57/10.43 | (69) strictorderP(all_100_0) = all_382_0 & ssItem(all_100_1) = all_382_1 & % 74.57/10.43 | ( ~ (all_382_1 = 0) | all_382_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (69) implies: % 74.57/10.43 | (70) ssItem(all_100_1) = all_382_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (49) with fresh symbols all_384_0, all_384_1 gives: % 74.57/10.43 | (71) equalelemsP(all_100_0) = all_384_0 & ssItem(all_100_1) = all_384_1 & ( % 74.57/10.43 | ~ (all_384_1 = 0) | all_384_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (71) implies: % 74.57/10.43 | (72) ssItem(all_100_1) = all_384_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (51) with fresh symbols all_386_0, all_386_1 gives: % 74.57/10.43 | (73) strictorderedP(all_100_0) = all_386_0 & ssItem(all_100_1) = all_386_1 % 74.57/10.43 | & ( ~ (all_386_1 = 0) | all_386_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (73) implies: % 74.57/10.43 | (74) ssItem(all_100_1) = all_386_1 % 74.57/10.43 | (75) ~ (all_386_1 = 0) | all_386_0 = 0 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (52) with fresh symbols all_388_0, all_388_1 gives: % 74.57/10.43 | (76) totalorderedP(all_100_0) = all_388_0 & ssItem(all_100_1) = all_388_1 & % 74.57/10.43 | ( ~ (all_388_1 = 0) | all_388_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (76) implies: % 74.57/10.43 | (77) ssItem(all_100_1) = all_388_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (54) with fresh symbols all_390_0, all_390_1 gives: % 74.57/10.43 | (78) totalorderP(all_100_0) = all_390_0 & ssItem(all_100_1) = all_390_1 & ( % 74.57/10.43 | ~ (all_390_1 = 0) | all_390_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (78) implies: % 74.57/10.43 | (79) ssItem(all_100_1) = all_390_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (50) with fresh symbols all_392_0, all_392_1 gives: % 74.57/10.43 | (80) duplicatefreeP(all_100_0) = all_392_0 & ssItem(all_100_1) = all_392_1 % 74.57/10.43 | & ( ~ (all_392_1 = 0) | all_392_0 = 0) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (80) implies: % 74.57/10.43 | (81) ssItem(all_100_1) = all_392_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (63) with fresh symbols all_396_0, all_396_1 gives: % 74.57/10.43 | (82) hd(all_100_0) = all_396_0 & ssItem(all_100_1) = all_396_1 & % 74.57/10.43 | $i(all_396_0) & ( ~ (all_396_1 = 0) | all_396_0 = all_100_1) % 74.57/10.43 | % 74.57/10.43 | ALPHA: (82) implies: % 74.57/10.43 | (83) ssItem(all_100_1) = all_396_1 % 74.57/10.43 | % 74.57/10.43 | DELTA: instantiating (64) with fresh symbols all_398_0, all_398_1 gives: % 74.57/10.43 | (84) tl(all_100_0) = all_398_0 & ssItem(all_100_1) = all_398_1 & % 74.57/10.43 | $i(all_398_0) & ( ~ (all_398_1 = 0) | all_398_0 = nil) % 74.57/10.44 | % 74.57/10.44 | ALPHA: (84) implies: % 74.57/10.44 | (85) ssItem(all_100_1) = all_398_1 % 74.57/10.44 | % 74.57/10.44 | DELTA: instantiating (65) with fresh symbols all_400_0, all_400_1 gives: % 74.57/10.44 | (86) ssList(all_100_0) = all_400_0 & ssItem(all_100_1) = all_400_1 & ( ~ % 74.57/10.44 | (all_400_1 = 0) | all_400_0 = 0) % 74.57/10.44 | % 74.57/10.44 | ALPHA: (86) implies: % 74.57/10.44 | (87) ssItem(all_100_1) = all_400_1 % 74.57/10.44 | % 74.57/10.44 | BETA: splitting (61) gives: % 74.57/10.44 | % 74.57/10.44 | Case 1: % 74.57/10.44 | | % 74.57/10.44 | | (88) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_599_0 gives: % 74.57/10.44 | | (89) ~ (all_599_0 = 0) & ssList(nil) = all_599_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (89) implies: % 74.57/10.44 | | (90) ~ (all_599_0 = 0) % 74.57/10.44 | | (91) ssList(nil) = all_599_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_601_0 gives: % 74.57/10.44 | | (92) ~ (all_601_0 = 0) & ssList(nil) = all_601_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (92) implies: % 74.57/10.44 | | (93) ssList(nil) = all_601_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_603_0 gives: % 74.57/10.44 | | (94) ~ (all_603_0 = 0) & ssList(nil) = all_603_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (94) implies: % 74.57/10.44 | | (95) ssList(nil) = all_603_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_607_0 gives: % 74.57/10.44 | | (96) ~ (all_607_0 = 0) & ssList(nil) = all_607_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (96) implies: % 74.57/10.44 | | (97) ssList(nil) = all_607_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_609_0 gives: % 74.57/10.44 | | (98) ~ (all_609_0 = 0) & ssList(nil) = all_609_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (98) implies: % 74.57/10.44 | | (99) ssList(nil) = all_609_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_611_0 gives: % 74.57/10.44 | | (100) ~ (all_611_0 = 0) & ssList(nil) = all_611_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (100) implies: % 74.57/10.44 | | (101) ssList(nil) = all_611_0 % 74.57/10.44 | | % 74.57/10.44 | | DELTA: instantiating (88) with fresh symbol all_613_0 gives: % 74.57/10.44 | | (102) ~ (all_613_0 = 0) & ssList(nil) = all_613_0 % 74.57/10.44 | | % 74.57/10.44 | | ALPHA: (102) implies: % 74.57/10.44 | | (103) ssList(nil) = all_613_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with 0, all_603_0, nil, simplifying with % 74.57/10.44 | | (1), (95) gives: % 74.57/10.44 | | (104) all_603_0 = 0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_599_0, all_603_0, nil, simplifying % 74.57/10.44 | | with (91), (95) gives: % 74.57/10.44 | | (105) all_603_0 = all_599_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_603_0, all_607_0, nil, simplifying % 74.57/10.44 | | with (95), (97) gives: % 74.57/10.44 | | (106) all_607_0 = all_603_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_607_0, all_609_0, nil, simplifying % 74.57/10.44 | | with (97), (99) gives: % 74.57/10.44 | | (107) all_609_0 = all_607_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_609_0, all_611_0, nil, simplifying % 74.57/10.44 | | with (99), (101) gives: % 74.57/10.44 | | (108) all_611_0 = all_609_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_611_0, all_613_0, nil, simplifying % 74.57/10.44 | | with (101), (103) gives: % 74.57/10.44 | | (109) all_613_0 = all_611_0 % 74.57/10.44 | | % 74.57/10.44 | | GROUND_INST: instantiating (14) with all_601_0, all_613_0, nil, simplifying % 74.57/10.44 | | with (93), (103) gives: % 74.57/10.44 | | (110) all_613_0 = all_601_0 % 74.57/10.44 | | % 74.57/10.44 | | COMBINE_EQS: (109), (110) imply: % 74.57/10.44 | | (111) all_611_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | SIMP: (111) implies: % 74.70/10.44 | | (112) all_611_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (108), (112) imply: % 74.70/10.44 | | (113) all_609_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | SIMP: (113) implies: % 74.70/10.44 | | (114) all_609_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (107), (114) imply: % 74.70/10.44 | | (115) all_607_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | SIMP: (115) implies: % 74.70/10.44 | | (116) all_607_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (106), (116) imply: % 74.70/10.44 | | (117) all_603_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | SIMP: (117) implies: % 74.70/10.44 | | (118) all_603_0 = all_601_0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (104), (118) imply: % 74.70/10.44 | | (119) all_601_0 = 0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (105), (118) imply: % 74.70/10.44 | | (120) all_601_0 = all_599_0 % 74.70/10.44 | | % 74.70/10.44 | | COMBINE_EQS: (119), (120) imply: % 74.70/10.44 | | (121) all_599_0 = 0 % 74.70/10.44 | | % 74.70/10.44 | | SIMP: (121) implies: % 74.70/10.44 | | (122) all_599_0 = 0 % 74.70/10.44 | | % 74.70/10.44 | | REDUCE: (90), (122) imply: % 74.70/10.44 | | (123) $false % 74.70/10.44 | | % 74.70/10.44 | | CLOSE: (123) is inconsistent. % 74.70/10.44 | | % 74.70/10.44 | Case 2: % 74.70/10.44 | | % 74.70/10.44 | | (124) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 74.70/10.44 | | [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : % 74.70/10.44 | | ? [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = % 74.70/10.44 | | 0) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! % 74.70/10.44 | | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v0, v6) % 74.70/10.44 | | = v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: % 74.70/10.44 | | int] : ( ~ (v9 = 0) & ssList(v6) = v9) | ! [v9: $i] % 74.70/10.44 | | : ! [v10: $i] : (v4 = 0 | v2 = 0 | ~ (cons(v1, v9) = % 74.70/10.44 | | v10) | ~ (app(v8, v10) = nil) | ~ $i(v9) | ? % 74.70/10.44 | | [v11: int] : ( ~ (v11 = 0) & ssList(v9) = v11)))))))) % 74.70/10.44 | | % 74.70/10.44 | | GROUND_INST: instantiating (124) with all_100_1, simplifying with (26), (27) % 74.70/10.44 | | gives: % 74.70/10.45 | | (125) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_100_1, v0) = v1) | ~ % 74.70/10.45 | | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, all_100_1) = v3 & % 74.70/10.45 | | ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : ( ~ (ssList(v4) % 74.70/10.45 | | = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: $i] : ! [v7: % 74.70/10.45 | | $i] : ( ~ (cons(all_100_1, v5) = v6) | ~ (app(v4, v6) = % 74.70/10.45 | | v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 74.70/10.45 | | ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : (v3 = 0 % 74.70/10.45 | | | v1 = 0 | ~ (cons(v0, v8) = v9) | ~ (app(v7, v9) = % 74.70/10.45 | | nil) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & % 74.70/10.45 | | ssList(v8) = v10))))))) % 74.70/10.45 | | % 74.70/10.45 | | GROUND_INST: instantiating (124) with all_106_4, simplifying with (41), (42) % 74.70/10.45 | | gives: % 74.70/10.45 | | (126) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_106_4, v0) = v1) | ~ % 74.70/10.45 | | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, all_106_4) = v3 & % 74.70/10.45 | | ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : ( ~ (ssList(v4) % 74.70/10.45 | | = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: $i] : ! [v7: % 74.70/10.45 | | $i] : ( ~ (cons(all_106_4, v5) = v6) | ~ (app(v4, v6) = % 74.70/10.45 | | v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 74.70/10.45 | | ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : (v3 = 0 % 74.70/10.45 | | | v1 = 0 | ~ (cons(v0, v8) = v9) | ~ (app(v7, v9) = % 74.70/10.45 | | nil) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & % 74.70/10.45 | | ssList(v8) = v10))))))) % 74.70/10.45 | | % 74.70/10.45 | | GROUND_INST: instantiating (126) with all_100_1, all_106_2, simplifying with % 74.70/10.45 | | (26), (46) gives: % 74.70/10.45 | | (127) ? [v0: any] : ? [v1: any] : (leq(all_100_1, all_106_4) = v1 & % 74.70/10.45 | | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | ! [v2: $i] : ( ~ % 74.70/10.45 | | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! % 74.70/10.45 | | [v5: $i] : ( ~ (cons(all_106_4, v3) = v4) | ~ (app(v2, v4) = % 74.70/10.45 | | v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) & % 74.70/10.45 | | ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : (v1 = 0 | % 74.70/10.45 | | all_106_2 = 0 | ~ (cons(all_100_1, v6) = v7) | ~ % 74.70/10.45 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 % 74.70/10.45 | | = 0) & ssList(v6) = v8)))))) % 74.70/10.45 | | % 74.70/10.45 | | GROUND_INST: instantiating (125) with all_106_4, all_106_0, simplifying with % 74.70/10.45 | | (41), (45) gives: % 74.70/10.45 | | (128) ? [v0: any] : ? [v1: any] : (leq(all_106_4, all_100_1) = v1 & % 74.70/10.45 | | ssItem(all_106_4) = v0 & ( ~ (v0 = 0) | ! [v2: $i] : ( ~ % 74.70/10.45 | | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! % 74.70/10.45 | | [v5: $i] : ( ~ (cons(all_100_1, v3) = v4) | ~ (app(v2, v4) = % 74.70/10.45 | | v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) & % 74.70/10.45 | | ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : (v1 = 0 | % 74.70/10.45 | | all_106_0 = 0 | ~ (cons(all_106_4, v6) = v7) | ~ % 74.70/10.45 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 % 74.70/10.45 | | = 0) & ssList(v6) = v8)))))) % 74.70/10.45 | | % 74.70/10.45 | | BETA: splitting (60) gives: % 74.70/10.45 | | % 74.70/10.45 | | Case 1: % 74.70/10.45 | | | % 74.70/10.45 | | | (129) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 74.70/10.45 | | | % 74.70/10.45 | | | DELTA: instantiating (129) with fresh symbol all_611_0 gives: % 74.70/10.45 | | | (130) ~ (all_611_0 = 0) & ssList(nil) = all_611_0 % 74.70/10.45 | | | % 74.70/10.45 | | | ALPHA: (130) implies: % 74.70/10.45 | | | (131) ~ (all_611_0 = 0) % 74.70/10.45 | | | (132) ssList(nil) = all_611_0 % 74.70/10.45 | | | % 74.70/10.45 | | | DELTA: instantiating (129) with fresh symbol all_619_0 gives: % 74.70/10.45 | | | (133) ~ (all_619_0 = 0) & ssList(nil) = all_619_0 % 74.70/10.45 | | | % 74.70/10.45 | | | ALPHA: (133) implies: % 74.70/10.45 | | | (134) ssList(nil) = all_619_0 % 74.70/10.45 | | | % 74.70/10.45 | | | DELTA: instantiating (129) with fresh symbol all_621_0 gives: % 74.70/10.45 | | | (135) ~ (all_621_0 = 0) & ssList(nil) = all_621_0 % 74.70/10.45 | | | % 74.70/10.45 | | | ALPHA: (135) implies: % 74.70/10.45 | | | (136) ssList(nil) = all_621_0 % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (14) with 0, all_619_0, nil, simplifying with % 74.70/10.45 | | | (1), (134) gives: % 74.70/10.45 | | | (137) all_619_0 = 0 % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (14) with all_619_0, all_621_0, nil, % 74.70/10.45 | | | simplifying with (134), (136) gives: % 74.70/10.45 | | | (138) all_621_0 = all_619_0 % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (14) with all_611_0, all_621_0, nil, % 74.70/10.45 | | | simplifying with (132), (136) gives: % 74.70/10.45 | | | (139) all_621_0 = all_611_0 % 74.70/10.45 | | | % 74.70/10.45 | | | COMBINE_EQS: (138), (139) imply: % 74.70/10.45 | | | (140) all_619_0 = all_611_0 % 74.70/10.45 | | | % 74.70/10.45 | | | SIMP: (140) implies: % 74.70/10.45 | | | (141) all_619_0 = all_611_0 % 74.70/10.45 | | | % 74.70/10.45 | | | COMBINE_EQS: (137), (141) imply: % 74.70/10.45 | | | (142) all_611_0 = 0 % 74.70/10.45 | | | % 74.70/10.45 | | | REDUCE: (131), (142) imply: % 74.70/10.45 | | | (143) $false % 74.70/10.45 | | | % 74.70/10.45 | | | CLOSE: (143) is inconsistent. % 74.70/10.45 | | | % 74.70/10.45 | | Case 2: % 74.70/10.45 | | | % 74.70/10.45 | | | (144) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 74.70/10.45 | | | [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : % 74.70/10.45 | | | ? [v4: any] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 % 74.70/10.45 | | | = 0) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) | % 74.70/10.45 | | | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v0, % 74.70/10.45 | | | v6) = v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | % 74.70/10.45 | | | ? [v9: int] : ( ~ (v9 = 0) & ssList(v6) = v9) | ! % 74.70/10.45 | | | [v9: $i] : ! [v10: $i] : ( ~ (v4 = 0) | ~ (v2 = 0) % 74.70/10.45 | | | | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) = nil) % 74.70/10.45 | | | | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & % 74.70/10.45 | | | ssList(v9) = v11)))))))) % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (144) with all_100_1, simplifying with (26), % 74.70/10.45 | | | (27) gives: % 74.70/10.45 | | | (145) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_100_1, v0) = v1) | ~ % 74.70/10.45 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, all_100_1) = v3 % 74.70/10.45 | | | & ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : ( ~ % 74.70/10.45 | | | (ssList(v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: $i] % 74.70/10.45 | | | : ! [v7: $i] : ( ~ (cons(all_100_1, v5) = v6) | ~ % 74.70/10.45 | | | (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 % 74.70/10.45 | | | = 0) & ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] % 74.70/10.45 | | | : ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (cons(v0, v8) = v9) | % 74.70/10.45 | | | ~ (app(v7, v9) = nil) | ~ $i(v8) | ? [v10: int] : % 74.70/10.45 | | | ( ~ (v10 = 0) & ssList(v8) = v10))))))) % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (144) with all_106_4, simplifying with (41), % 74.70/10.45 | | | (42) gives: % 74.70/10.45 | | | (146) ! [v0: $i] : ! [v1: any] : ( ~ (leq(all_106_4, v0) = v1) | ~ % 74.70/10.45 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, all_106_4) = v3 % 74.70/10.45 | | | & ssItem(v0) = v2 & ( ~ (v2 = 0) | ! [v4: $i] : ( ~ % 74.70/10.45 | | | (ssList(v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: $i] % 74.70/10.45 | | | : ! [v7: $i] : ( ~ (cons(all_106_4, v5) = v6) | ~ % 74.70/10.45 | | | (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 % 74.70/10.45 | | | = 0) & ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] % 74.70/10.45 | | | : ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (cons(v0, v8) = v9) | % 74.70/10.45 | | | ~ (app(v7, v9) = nil) | ~ $i(v8) | ? [v10: int] : % 74.70/10.45 | | | ( ~ (v10 = 0) & ssList(v8) = v10))))))) % 74.70/10.45 | | | % 74.70/10.45 | | | GROUND_INST: instantiating (146) with all_100_1, all_106_2, simplifying % 74.70/10.45 | | | with (26), (46) gives: % 74.70/10.46 | | | (147) ? [v0: any] : ? [v1: any] : (leq(all_100_1, all_106_4) = v1 & % 74.70/10.46 | | | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | ! [v2: $i] : ( ~ % 74.70/10.46 | | | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : % 74.70/10.46 | | | ! [v5: $i] : ( ~ (cons(all_106_4, v3) = v4) | ~ (app(v2, % 74.70/10.46 | | | v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) & % 74.70/10.46 | | | ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ (v1 % 74.70/10.46 | | | = 0) | ~ (all_106_2 = 0) | ~ (cons(all_100_1, v6) = % 74.70/10.46 | | | v7) | ~ (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: % 74.70/10.46 | | | int] : ( ~ (v8 = 0) & ssList(v6) = v8)))))) % 74.70/10.46 | | | % 74.70/10.46 | | | GROUND_INST: instantiating (145) with all_106_4, all_106_0, simplifying % 74.70/10.46 | | | with (41), (45) gives: % 74.70/10.46 | | | (148) ? [v0: any] : ? [v1: any] : (leq(all_106_4, all_100_1) = v1 & % 74.70/10.46 | | | ssItem(all_106_4) = v0 & ( ~ (v0 = 0) | ! [v2: $i] : ( ~ % 74.70/10.46 | | | (ssList(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : % 74.70/10.46 | | | ! [v5: $i] : ( ~ (cons(all_100_1, v3) = v4) | ~ (app(v2, % 74.70/10.46 | | | v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) & % 74.70/10.46 | | | ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ (v1 % 74.70/10.46 | | | = 0) | ~ (all_106_0 = 0) | ~ (cons(all_106_4, v6) = % 74.70/10.46 | | | v7) | ~ (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: % 74.70/10.46 | | | int] : ( ~ (v8 = 0) & ssList(v6) = v8)))))) % 74.70/10.46 | | | % 74.70/10.46 | | | BETA: splitting (66) gives: % 74.70/10.46 | | | % 74.70/10.46 | | | Case 1: % 74.70/10.46 | | | | % 74.70/10.46 | | | | (149) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 74.70/10.46 | | | | % 74.70/10.46 | | | | DELTA: instantiating (149) with fresh symbol all_626_0 gives: % 74.70/10.46 | | | | (150) ~ (all_626_0 = 0) & ssList(nil) = all_626_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | ALPHA: (150) implies: % 74.70/10.46 | | | | (151) ~ (all_626_0 = 0) % 74.70/10.46 | | | | (152) ssList(nil) = all_626_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (14) with 0, all_626_0, nil, simplifying with % 74.70/10.46 | | | | (1), (152) gives: % 74.70/10.46 | | | | (153) all_626_0 = 0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | REDUCE: (151), (153) imply: % 74.70/10.46 | | | | (154) $false % 74.70/10.46 | | | | % 74.70/10.46 | | | | CLOSE: (154) is inconsistent. % 74.70/10.46 | | | | % 74.70/10.46 | | | Case 2: % 74.70/10.46 | | | | % 74.70/10.46 | | | | % 74.70/10.46 | | | | DELTA: instantiating (127) with fresh symbols all_619_0, all_619_1 % 74.70/10.46 | | | | gives: % 74.70/10.46 | | | | (155) leq(all_100_1, all_106_4) = all_619_0 & ssItem(all_100_1) = % 74.70/10.46 | | | | all_619_1 & ( ~ (all_619_1 = 0) | ! [v0: $i] : ( ~ (ssList(v0) % 74.70/10.46 | | | | = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: % 74.70/10.46 | | | | $i] : ( ~ (cons(all_106_4, v1) = v2) | ~ (app(v0, v2) = % 74.70/10.46 | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 74.70/10.46 | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : % 74.70/10.46 | | | | (all_619_0 = 0 | all_106_2 = 0 | ~ (cons(all_100_1, v4) % 74.70/10.46 | | | | = v5) | ~ (app(v3, v5) = nil) | ~ $i(v4) | ? [v6: % 74.70/10.46 | | | | int] : ( ~ (v6 = 0) & ssList(v4) = v6))))) % 74.70/10.46 | | | | % 74.70/10.46 | | | | ALPHA: (155) implies: % 74.70/10.46 | | | | (156) ssItem(all_100_1) = all_619_1 % 74.70/10.46 | | | | (157) leq(all_100_1, all_106_4) = all_619_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | DELTA: instantiating (128) with fresh symbols all_621_0, all_621_1 % 74.70/10.46 | | | | gives: % 74.70/10.46 | | | | (158) leq(all_106_4, all_100_1) = all_621_0 & ssItem(all_106_4) = % 74.70/10.46 | | | | all_621_1 & ( ~ (all_621_1 = 0) | ! [v0: $i] : ( ~ (ssList(v0) % 74.70/10.46 | | | | = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: % 74.70/10.46 | | | | $i] : ( ~ (cons(all_100_1, v1) = v2) | ~ (app(v0, v2) = % 74.70/10.46 | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 74.70/10.46 | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : % 74.70/10.46 | | | | (all_621_0 = 0 | all_106_0 = 0 | ~ (cons(all_106_4, v4) % 74.70/10.46 | | | | = v5) | ~ (app(v3, v5) = nil) | ~ $i(v4) | ? [v6: % 74.70/10.46 | | | | int] : ( ~ (v6 = 0) & ssList(v4) = v6))))) % 74.70/10.46 | | | | % 74.70/10.46 | | | | ALPHA: (158) implies: % 74.70/10.46 | | | | (159) ssItem(all_106_4) = all_621_1 % 74.70/10.46 | | | | (160) leq(all_106_4, all_100_1) = all_621_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | DELTA: instantiating (147) with fresh symbols all_623_0, all_623_1 % 74.70/10.46 | | | | gives: % 74.70/10.46 | | | | (161) leq(all_100_1, all_106_4) = all_623_0 & ssItem(all_100_1) = % 74.70/10.46 | | | | all_623_1 & ( ~ (all_623_1 = 0) | ! [v0: $i] : ( ~ (ssList(v0) % 74.70/10.46 | | | | = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: % 74.70/10.46 | | | | $i] : ( ~ (cons(all_106_4, v1) = v2) | ~ (app(v0, v2) = % 74.70/10.46 | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 74.70/10.46 | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 74.70/10.46 | | | | (all_623_0 = 0) | ~ (all_106_2 = 0) | ~ % 74.70/10.46 | | | | (cons(all_100_1, v4) = v5) | ~ (app(v3, v5) = nil) | % 74.70/10.46 | | | | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) = % 74.70/10.46 | | | | v6))))) % 74.70/10.46 | | | | % 74.70/10.46 | | | | ALPHA: (161) implies: % 74.70/10.46 | | | | (162) ssItem(all_100_1) = all_623_1 % 74.70/10.46 | | | | (163) leq(all_100_1, all_106_4) = all_623_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | DELTA: instantiating (148) with fresh symbols all_625_0, all_625_1 % 74.70/10.46 | | | | gives: % 74.70/10.46 | | | | (164) leq(all_106_4, all_100_1) = all_625_0 & ssItem(all_106_4) = % 74.70/10.46 | | | | all_625_1 & ( ~ (all_625_1 = 0) | ! [v0: $i] : ( ~ (ssList(v0) % 74.70/10.46 | | | | = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: % 74.70/10.46 | | | | $i] : ( ~ (cons(all_100_1, v1) = v2) | ~ (app(v0, v2) = % 74.70/10.46 | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 74.70/10.46 | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 74.70/10.46 | | | | (all_625_0 = 0) | ~ (all_106_0 = 0) | ~ % 74.70/10.46 | | | | (cons(all_106_4, v4) = v5) | ~ (app(v3, v5) = nil) | % 74.70/10.46 | | | | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) = % 74.70/10.46 | | | | v6))))) % 74.70/10.46 | | | | % 74.70/10.46 | | | | ALPHA: (164) implies: % 74.70/10.46 | | | | (165) ssItem(all_106_4) = all_625_1 % 74.70/10.46 | | | | (166) leq(all_106_4, all_100_1) = all_625_0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with 0, all_384_1, all_100_1, % 74.70/10.46 | | | | simplifying with (27), (72) gives: % 74.70/10.46 | | | | (167) all_384_1 = 0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_380_1, all_384_1, all_100_1, % 74.70/10.46 | | | | simplifying with (68), (72) gives: % 74.70/10.46 | | | | (168) all_384_1 = all_380_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_388_1, all_390_1, all_100_1, % 74.70/10.46 | | | | simplifying with (77), (79) gives: % 74.70/10.46 | | | | (169) all_390_1 = all_388_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_384_1, all_390_1, all_100_1, % 74.70/10.46 | | | | simplifying with (72), (79) gives: % 74.70/10.46 | | | | (170) all_390_1 = all_384_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_390_1, all_396_1, all_100_1, % 74.70/10.46 | | | | simplifying with (79), (83) gives: % 74.70/10.46 | | | | (171) all_396_1 = all_390_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_392_1, all_398_1, all_100_1, % 74.70/10.46 | | | | simplifying with (81), (85) gives: % 74.70/10.46 | | | | (172) all_398_1 = all_392_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_388_1, all_398_1, all_100_1, % 74.70/10.46 | | | | simplifying with (77), (85) gives: % 74.70/10.46 | | | | (173) all_398_1 = all_388_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_396_1, all_619_1, all_100_1, % 74.70/10.46 | | | | simplifying with (83), (156) gives: % 74.70/10.46 | | | | (174) all_619_1 = all_396_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_386_1, all_619_1, all_100_1, % 74.70/10.46 | | | | simplifying with (74), (156) gives: % 74.70/10.46 | | | | (175) all_619_1 = all_386_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_400_1, all_623_1, all_100_1, % 74.70/10.46 | | | | simplifying with (87), (162) gives: % 74.70/10.46 | | | | (176) all_623_1 = all_400_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_398_1, all_623_1, all_100_1, % 74.70/10.46 | | | | simplifying with (85), (162) gives: % 74.70/10.46 | | | | (177) all_623_1 = all_398_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_382_1, all_623_1, all_100_1, % 74.70/10.46 | | | | simplifying with (70), (162) gives: % 74.70/10.46 | | | | (178) all_623_1 = all_382_1 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with 0, all_625_1, all_106_4, % 74.70/10.46 | | | | simplifying with (42), (165) gives: % 74.70/10.46 | | | | (179) all_625_1 = 0 % 74.70/10.46 | | | | % 74.70/10.46 | | | | GROUND_INST: instantiating (13) with all_621_1, all_625_1, all_106_4, % 74.70/10.46 | | | | simplifying with (159), (165) gives: % 74.70/10.46 | | | | (180) all_625_1 = all_621_1 % 74.70/10.46 | | | | % 74.70/10.47 | | | | GROUND_INST: instantiating (16) with all_106_0, all_623_0, all_106_4, % 74.70/10.47 | | | | all_100_1, simplifying with (45), (163) gives: % 74.70/10.47 | | | | (181) all_623_0 = all_106_0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | GROUND_INST: instantiating (16) with all_619_0, all_623_0, all_106_4, % 74.70/10.47 | | | | all_100_1, simplifying with (157), (163) gives: % 74.70/10.47 | | | | (182) all_623_0 = all_619_0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | GROUND_INST: instantiating (16) with all_106_2, all_625_0, all_100_1, % 74.70/10.47 | | | | all_106_4, simplifying with (46), (166) gives: % 74.70/10.47 | | | | (183) all_625_0 = all_106_2 % 74.70/10.47 | | | | % 74.70/10.47 | | | | GROUND_INST: instantiating (16) with all_621_0, all_625_0, all_100_1, % 74.70/10.47 | | | | all_106_4, simplifying with (160), (166) gives: % 74.70/10.47 | | | | (184) all_625_0 = all_621_0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (183), (184) imply: % 74.70/10.47 | | | | (185) all_621_0 = all_106_2 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (179), (180) imply: % 74.70/10.47 | | | | (186) all_621_1 = 0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (181), (182) imply: % 74.70/10.47 | | | | (187) all_619_0 = all_106_0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (176), (178) imply: % 74.70/10.47 | | | | (188) all_400_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (176), (177) imply: % 74.70/10.47 | | | | (189) all_400_1 = all_398_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (174), (175) imply: % 74.70/10.47 | | | | (190) all_396_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (190) implies: % 74.70/10.47 | | | | (191) all_396_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (188), (189) imply: % 74.70/10.47 | | | | (192) all_398_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (192) implies: % 74.70/10.47 | | | | (193) all_398_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (172), (193) imply: % 74.70/10.47 | | | | (194) all_392_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (172), (173) imply: % 74.70/10.47 | | | | (195) all_392_1 = all_388_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (171), (191) imply: % 74.70/10.47 | | | | (196) all_390_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (196) implies: % 74.70/10.47 | | | | (197) all_390_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (194), (195) imply: % 74.70/10.47 | | | | (198) all_388_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (198) implies: % 74.70/10.47 | | | | (199) all_388_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (169), (197) imply: % 74.70/10.47 | | | | (200) all_388_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (200) implies: % 74.70/10.47 | | | | (201) all_388_1 = all_386_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (170), (197) imply: % 74.70/10.47 | | | | (202) all_386_1 = all_384_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (199), (201) imply: % 74.70/10.47 | | | | (203) all_386_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (203) implies: % 74.70/10.47 | | | | (204) all_386_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (202), (204) imply: % 74.70/10.47 | | | | (205) all_384_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | SIMP: (205) implies: % 74.70/10.47 | | | | (206) all_384_1 = all_382_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (167), (206) imply: % 74.70/10.47 | | | | (207) all_382_1 = 0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (168), (206) imply: % 74.70/10.47 | | | | (208) all_382_1 = all_380_1 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (207), (208) imply: % 74.70/10.47 | | | | (209) all_380_1 = 0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | COMBINE_EQS: (204), (207) imply: % 74.70/10.47 | | | | (210) all_386_1 = 0 % 74.70/10.47 | | | | % 74.70/10.47 | | | | BETA: splitting (56) gives: % 74.70/10.47 | | | | % 74.70/10.47 | | | | Case 1: % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | (211) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_100_1) = v0) % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | DELTA: instantiating (211) with fresh symbol all_692_0 gives: % 74.70/10.47 | | | | | (212) ~ (all_692_0 = 0) & ssItem(all_100_1) = all_692_0 % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | ALPHA: (212) implies: % 74.70/10.47 | | | | | (213) ~ (all_692_0 = 0) % 74.70/10.47 | | | | | (214) ssItem(all_100_1) = all_692_0 % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | BETA: splitting (75) gives: % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | Case 1: % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | (215) ~ (all_386_1 = 0) % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | REDUCE: (210), (215) imply: % 74.70/10.47 | | | | | | (216) $false % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | CLOSE: (216) is inconsistent. % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | Case 2: % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | DELTA: instantiating (211) with fresh symbol all_706_0 gives: % 74.70/10.47 | | | | | | (217) ~ (all_706_0 = 0) & ssItem(all_100_1) = all_706_0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | ALPHA: (217) implies: % 74.70/10.47 | | | | | | (218) ssItem(all_100_1) = all_706_0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | GROUND_INST: instantiating (13) with 0, all_706_0, all_100_1, % 74.70/10.47 | | | | | | simplifying with (27), (218) gives: % 74.70/10.47 | | | | | | (219) all_706_0 = 0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | GROUND_INST: instantiating (13) with all_692_0, all_706_0, % 74.70/10.47 | | | | | | all_100_1, simplifying with (214), (218) gives: % 74.70/10.47 | | | | | | (220) all_706_0 = all_692_0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | COMBINE_EQS: (219), (220) imply: % 74.70/10.47 | | | | | | (221) all_692_0 = 0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | REDUCE: (213), (221) imply: % 74.70/10.47 | | | | | | (222) $false % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | CLOSE: (222) is inconsistent. % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | End of split % 74.70/10.47 | | | | | % 74.70/10.47 | | | | Case 2: % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | (223) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_100_0) = v1) | % 74.70/10.47 | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | % 74.70/10.47 | | | | | ! [v2: $i] : ( ~ (app(v1, v2) = all_93_0) | ~ $i(v2) | ? % 74.70/10.47 | | | | | [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | ! [v3: $i] % 74.70/10.47 | | | | | : ! [v4: any] : ( ~ (memberP(v0, v3) = v4) | ~ $i(v3) | % 74.70/10.47 | | | | | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 74.70/10.47 | | | | | any] : (leq(v3, all_100_1) = v8 & leq(all_100_1, v3) % 74.70/10.47 | | | | | = v6 & memberP(v2, v3) = v7 & ssItem(v3) = v5 & ( ~ % 74.70/10.47 | | | | | (v5 = 0) | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v4 = 0) | % 74.70/10.47 | | | | | v8 = 0))))))) % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | GROUND_INST: instantiating (223) with all_102_1, all_102_0, % 74.70/10.47 | | | | | simplifying with (31), (32) gives: % 74.70/10.47 | | | | | (224) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_102_1) = v0) | ! % 74.70/10.47 | | | | | [v0: $i] : ( ~ (app(all_102_0, v0) = all_93_0) | ~ $i(v0) | % 74.70/10.47 | | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1) | ! [v1: $i] % 74.70/10.47 | | | | | : ! [v2: any] : ( ~ (memberP(all_102_1, v1) = v2) | ~ % 74.70/10.47 | | | | | $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? % 74.70/10.47 | | | | | [v6: any] : (leq(v1, all_100_1) = v6 & leq(all_100_1, v1) % 74.70/10.47 | | | | | = v4 & memberP(v0, v1) = v5 & ssItem(v1) = v3 & ( ~ (v3 % 74.70/10.47 | | | | | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v2 = 0) | v6 % 74.70/10.47 | | | | | = 0)))))) % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | BETA: splitting (224) gives: % 74.70/10.47 | | | | | % 74.70/10.47 | | | | | Case 1: % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | (225) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_102_1) = v0) % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | DELTA: instantiating (225) with fresh symbol all_774_0 gives: % 74.70/10.47 | | | | | | (226) ~ (all_774_0 = 0) & ssList(all_102_1) = all_774_0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | ALPHA: (226) implies: % 74.70/10.47 | | | | | | (227) ~ (all_774_0 = 0) % 74.70/10.47 | | | | | | (228) ssList(all_102_1) = all_774_0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | GROUND_INST: instantiating (14) with 0, all_774_0, all_102_1, % 74.70/10.47 | | | | | | simplifying with (33), (228) gives: % 74.70/10.47 | | | | | | (229) all_774_0 = 0 % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | REDUCE: (227), (229) imply: % 74.70/10.47 | | | | | | (230) $false % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | CLOSE: (230) is inconsistent. % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | Case 2: % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | (231) ! [v0: $i] : ( ~ (app(all_102_0, v0) = all_93_0) | ~ % 74.70/10.47 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1) | % 74.70/10.47 | | | | | | ! [v1: $i] : ! [v2: any] : ( ~ (memberP(all_102_1, v1) % 74.70/10.47 | | | | | | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? % 74.70/10.47 | | | | | | [v5: any] : ? [v6: any] : (leq(v1, all_100_1) = v6 & % 74.70/10.47 | | | | | | leq(all_100_1, v1) = v4 & memberP(v0, v1) = v5 & % 74.70/10.47 | | | | | | ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = % 74.70/10.47 | | | | | | 0) & ( ~ (v2 = 0) | v6 = 0)))))) % 74.70/10.47 | | | | | | % 74.70/10.47 | | | | | | GROUND_INST: instantiating (231) with all_104_0, simplifying with % 74.70/10.47 | | | | | | (36), (37) gives: % 74.70/10.48 | | | | | | (232) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_104_0) = v0) | ! % 74.70/10.48 | | | | | | [v0: $i] : ! [v1: any] : ( ~ (memberP(all_102_1, v0) = v1) % 74.70/10.48 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] % 74.70/10.48 | | | | | | : ? [v5: any] : (leq(v0, all_100_1) = v5 & % 74.70/10.48 | | | | | | leq(all_100_1, v0) = v3 & memberP(all_104_0, v0) = v4 & % 74.70/10.48 | | | | | | ssItem(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 = % 74.70/10.48 | | | | | | 0) & ( ~ (v1 = 0) | v5 = 0))))) % 74.70/10.48 | | | | | | % 74.70/10.48 | | | | | | BETA: splitting (232) gives: % 74.70/10.48 | | | | | | % 74.70/10.48 | | | | | | Case 1: % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | (233) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_104_0) = v0) % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | DELTA: instantiating (233) with fresh symbol all_785_0 gives: % 74.70/10.48 | | | | | | | (234) ~ (all_785_0 = 0) & ssList(all_104_0) = all_785_0 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | ALPHA: (234) implies: % 74.70/10.48 | | | | | | | (235) ~ (all_785_0 = 0) % 74.70/10.48 | | | | | | | (236) ssList(all_104_0) = all_785_0 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (14) with 0, all_785_0, all_104_0, % 74.70/10.48 | | | | | | | simplifying with (38), (236) gives: % 74.70/10.48 | | | | | | | (237) all_785_0 = 0 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | REDUCE: (235), (237) imply: % 74.70/10.48 | | | | | | | (238) $false % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | CLOSE: (238) is inconsistent. % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | Case 2: % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | (239) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_102_1, v0) % 74.70/10.48 | | | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 74.70/10.48 | | | | | | | [v4: any] : ? [v5: any] : (leq(v0, all_100_1) = v5 & % 74.70/10.48 | | | | | | | leq(all_100_1, v0) = v3 & memberP(all_104_0, v0) = v4 % 74.70/10.48 | | | | | | | & ssItem(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 % 74.70/10.48 | | | | | | | = 0) & ( ~ (v1 = 0) | v5 = 0))))) % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (239) with all_106_4, all_106_3, % 74.70/10.48 | | | | | | | simplifying with (41), (43) gives: % 74.70/10.48 | | | | | | | (240) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] % 74.70/10.48 | | | | | | | : (leq(all_106_4, all_100_1) = v3 & leq(all_100_1, % 74.70/10.48 | | | | | | | all_106_4) = v1 & memberP(all_104_0, all_106_4) = v2 % 74.70/10.48 | | | | | | | & ssItem(all_106_4) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) % 74.70/10.48 | | | | | | | | v1 = 0) & ( ~ (all_106_3 = 0) | v3 = 0)))) % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | DELTA: instantiating (240) with fresh symbols all_786_0, % 74.70/10.48 | | | | | | | all_786_1, all_786_2, all_786_3 gives: % 74.70/10.48 | | | | | | | (241) leq(all_106_4, all_100_1) = all_786_0 & leq(all_100_1, % 74.70/10.48 | | | | | | | all_106_4) = all_786_2 & memberP(all_104_0, all_106_4) % 74.70/10.48 | | | | | | | = all_786_1 & ssItem(all_106_4) = all_786_3 & ( ~ % 74.70/10.48 | | | | | | | (all_786_3 = 0) | (( ~ (all_786_1 = 0) | all_786_2 = 0) % 74.70/10.48 | | | | | | | & ( ~ (all_106_3 = 0) | all_786_0 = 0))) % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | ALPHA: (241) implies: % 74.70/10.48 | | | | | | | (242) ssItem(all_106_4) = all_786_3 % 74.70/10.48 | | | | | | | (243) memberP(all_104_0, all_106_4) = all_786_1 % 74.70/10.48 | | | | | | | (244) leq(all_100_1, all_106_4) = all_786_2 % 74.70/10.48 | | | | | | | (245) leq(all_106_4, all_100_1) = all_786_0 % 74.70/10.48 | | | | | | | (246) ~ (all_786_3 = 0) | (( ~ (all_786_1 = 0) | all_786_2 = % 74.70/10.48 | | | | | | | 0) & ( ~ (all_106_3 = 0) | all_786_0 = 0)) % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (13) with 0, all_786_3, all_106_4, % 74.70/10.48 | | | | | | | simplifying with (42), (242) gives: % 74.70/10.48 | | | | | | | (247) all_786_3 = 0 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (15) with all_106_1, all_786_1, % 74.70/10.48 | | | | | | | all_106_4, all_104_0, simplifying with (44), (243) % 74.70/10.48 | | | | | | | gives: % 74.70/10.48 | | | | | | | (248) all_786_1 = all_106_1 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (16) with all_106_0, all_786_2, % 74.70/10.48 | | | | | | | all_106_4, all_100_1, simplifying with (45), (244) % 74.70/10.48 | | | | | | | gives: % 74.70/10.48 | | | | | | | (249) all_786_2 = all_106_0 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | GROUND_INST: instantiating (16) with all_106_2, all_786_0, % 74.70/10.48 | | | | | | | all_100_1, all_106_4, simplifying with (46), (245) % 74.70/10.48 | | | | | | | gives: % 74.70/10.48 | | | | | | | (250) all_786_0 = all_106_2 % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | BETA: splitting (47) gives: % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | | Case 1: % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | (251) all_106_1 = 0 & ~ (all_106_0 = 0) % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | ALPHA: (251) implies: % 74.70/10.48 | | | | | | | | (252) all_106_1 = 0 % 74.70/10.48 | | | | | | | | (253) ~ (all_106_0 = 0) % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | COMBINE_EQS: (248), (252) imply: % 74.70/10.48 | | | | | | | | (254) all_786_1 = 0 % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | BETA: splitting (246) gives: % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | Case 1: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | (255) ~ (all_786_3 = 0) % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | REDUCE: (247), (255) imply: % 74.70/10.48 | | | | | | | | | (256) $false % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | CLOSE: (256) is inconsistent. % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | Case 2: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | (257) ( ~ (all_786_1 = 0) | all_786_2 = 0) & ( ~ (all_106_3 % 74.70/10.48 | | | | | | | | | = 0) | all_786_0 = 0) % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | ALPHA: (257) implies: % 74.70/10.48 | | | | | | | | | (258) ~ (all_786_1 = 0) | all_786_2 = 0 % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | BETA: splitting (258) gives: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | Case 1: % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | (259) ~ (all_786_1 = 0) % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | REDUCE: (254), (259) imply: % 74.70/10.48 | | | | | | | | | | (260) $false % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | CLOSE: (260) is inconsistent. % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | Case 2: % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | (261) all_786_2 = 0 % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | COMBINE_EQS: (249), (261) imply: % 74.70/10.48 | | | | | | | | | | (262) all_106_0 = 0 % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | SIMP: (262) implies: % 74.70/10.48 | | | | | | | | | | (263) all_106_0 = 0 % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | REDUCE: (253), (263) imply: % 74.70/10.48 | | | | | | | | | | (264) $false % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | CLOSE: (264) is inconsistent. % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | End of split % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | End of split % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | Case 2: % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | (265) all_106_3 = 0 & ~ (all_106_2 = 0) % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | ALPHA: (265) implies: % 74.70/10.48 | | | | | | | | (266) all_106_3 = 0 % 74.70/10.48 | | | | | | | | (267) ~ (all_106_2 = 0) % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | BETA: splitting (246) gives: % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | | Case 1: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | (268) ~ (all_786_3 = 0) % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | REDUCE: (247), (268) imply: % 74.70/10.48 | | | | | | | | | (269) $false % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | CLOSE: (269) is inconsistent. % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | Case 2: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | (270) ( ~ (all_786_1 = 0) | all_786_2 = 0) & ( ~ (all_106_3 % 74.70/10.48 | | | | | | | | | = 0) | all_786_0 = 0) % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | ALPHA: (270) implies: % 74.70/10.48 | | | | | | | | | (271) ~ (all_106_3 = 0) | all_786_0 = 0 % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | BETA: splitting (271) gives: % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | | Case 1: % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | (272) ~ (all_106_3 = 0) % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | REDUCE: (266), (272) imply: % 74.70/10.48 | | | | | | | | | | (273) $false % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | CLOSE: (273) is inconsistent. % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | Case 2: % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | (274) all_786_0 = 0 % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | COMBINE_EQS: (250), (274) imply: % 74.70/10.48 | | | | | | | | | | (275) all_106_2 = 0 % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | REDUCE: (267), (275) imply: % 74.70/10.48 | | | | | | | | | | (276) $false % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | | CLOSE: (276) is inconsistent. % 74.70/10.48 | | | | | | | | | | % 74.70/10.48 | | | | | | | | | End of split % 74.70/10.48 | | | | | | | | | % 74.70/10.48 | | | | | | | | End of split % 74.70/10.48 | | | | | | | | % 74.70/10.48 | | | | | | | End of split % 74.70/10.48 | | | | | | | % 74.70/10.48 | | | | | | End of split % 74.70/10.48 | | | | | | % 74.70/10.48 | | | | | End of split % 74.70/10.48 | | | | | % 74.70/10.48 | | | | End of split % 74.70/10.48 | | | | % 74.70/10.48 | | | End of split % 74.70/10.48 | | | % 74.70/10.48 | | End of split % 74.70/10.48 | | % 74.70/10.48 | End of split % 74.70/10.48 | % 74.70/10.48 End of proof % 74.70/10.48 % SZS output end Proof for theBenchmark % 74.70/10.48 % 74.70/10.48 9848ms %------------------------------------------------------------------------------