%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC256+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 : n029.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 20:50:29 EDT 2023 % Result : Theorem 22.65s 3.78s % Output : Proof 66.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC256+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 18:02:41 EDT 2023 % 0.12/0.33 % CPUTime : % 0.56/0.59 ________ _____ % 0.56/0.59 ___ __ \_________(_)________________________________ % 0.56/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.56/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.56/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.56/0.59 (2023-06-19) % 0.56/0.59 % 0.56/0.59 (c) Philipp Rümmer, 2009-2023 % 0.56/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.56/0.59 Amanda Stjerna. % 0.56/0.59 Free software under BSD-3-Clause. % 0.56/0.59 % 0.56/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.56/0.59 % 0.56/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.62/0.61 Running up to 7 provers in parallel. % 0.62/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.01/1.55 Prover 1: Preprocessing ... % 6.01/1.58 Prover 4: Preprocessing ... % 6.01/1.60 Prover 3: Preprocessing ... % 6.01/1.60 Prover 5: Preprocessing ... % 6.01/1.60 Prover 0: Preprocessing ... % 6.01/1.60 Prover 6: Preprocessing ... % 6.01/1.60 Prover 2: Preprocessing ... % 14.61/2.76 Prover 2: Proving ... % 15.34/2.79 Prover 5: Constructing countermodel ... % 15.76/2.84 Prover 6: Proving ... % 15.76/2.87 Prover 1: Constructing countermodel ... % 16.37/2.91 Prover 3: Constructing countermodel ... % 21.30/3.64 Prover 0: Proving ... % 21.96/3.66 Prover 4: Constructing countermodel ... % 22.65/3.78 Prover 3: proved (3155ms) % 22.65/3.78 % 22.65/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.65/3.78 % 22.65/3.78 Prover 5: stopped % 22.65/3.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.65/3.78 Prover 6: stopped % 22.65/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.65/3.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.65/3.78 Prover 0: stopped % 22.65/3.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.65/3.79 Prover 2: stopped % 22.65/3.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.96/4.07 Prover 10: Preprocessing ... % 24.96/4.08 Prover 8: Preprocessing ... % 25.41/4.11 Prover 11: Preprocessing ... % 25.41/4.13 Prover 13: Preprocessing ... % 25.84/4.16 Prover 7: Preprocessing ... % 27.28/4.36 Prover 7: Constructing countermodel ... % 27.28/4.37 Prover 10: Constructing countermodel ... % 27.28/4.38 Prover 13: Constructing countermodel ... % 27.74/4.45 Prover 8: Warning: ignoring some quantifiers % 28.22/4.47 Prover 8: Constructing countermodel ... % 34.24/5.30 Prover 11: Constructing countermodel ... % 65.34/9.22 Prover 1: Found proof (size 149) % 65.34/9.22 Prover 1: proved (8605ms) % 65.54/9.22 Prover 7: stopped % 65.54/9.22 Prover 4: stopped % 65.54/9.22 Prover 8: stopped % 65.54/9.22 Prover 11: stopped % 65.58/9.22 Prover 10: stopped % 65.58/9.22 Prover 13: stopped % 65.58/9.22 % 65.58/9.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 65.58/9.22 % 65.58/9.24 % SZS output start Proof for theBenchmark % 65.58/9.24 Assumptions after simplification: % 65.58/9.24 --------------------------------- % 65.58/9.24 % 65.58/9.24 (ax15) % 65.58/9.27 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 65.58/9.27 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 65.58/9.27 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 65.58/9.27 % 65.58/9.27 (ax17) % 65.58/9.27 ssList(nil) = 0 & $i(nil) % 65.58/9.27 % 65.58/9.27 (ax18) % 65.58/9.27 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1, % 65.58/9.27 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) = % 65.58/9.27 v2))) % 65.58/9.27 % 65.58/9.27 (ax20) % 65.58/9.27 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 65.58/9.27 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 65.58/9.27 ssItem(v2) = 0 & $i(v2)))) % 65.58/9.27 % 65.58/9.27 (ax23) % 65.58/9.28 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 65.58/9.28 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 65.58/9.28 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 65.58/9.28 % 65.58/9.28 (ax25) % 65.58/9.28 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 65.58/9.28 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 65.58/9.28 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 65.58/9.28 % 65.58/9.28 (ax4) % 65.58/9.28 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | % 65.58/9.28 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i] % 65.58/9.28 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2: % 65.58/9.28 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 65.58/9.28 0) & ssItem(v2) = v3))))) % 65.58/9.28 % 65.58/9.28 (ax59) % 65.58/9.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.28 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 65.58/9.28 (v2 = 0) | v3 = 0))) % 65.58/9.28 % 65.58/9.28 (ax61) % 65.58/9.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.28 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 65.58/9.28 (v2 = 0) | v3 = 0))) % 65.58/9.28 % 65.58/9.28 (ax62) % 65.58/9.28 totalorderP(nil) = 0 & $i(nil) % 65.58/9.28 % 65.58/9.28 (ax63) % 65.58/9.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.28 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 65.58/9.28 (v2 = 0) | v3 = 0))) % 65.58/9.28 % 65.58/9.28 (ax65) % 65.58/9.28 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.28 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 65.58/9.28 (v2 = 0) | v3 = 0))) % 65.58/9.28 % 65.58/9.28 (ax68) % 65.58/9.29 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.29 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 65.58/9.29 ~ (v2 = 0) | v3 = 0))) % 65.58/9.29 % 65.58/9.29 (ax71) % 65.58/9.29 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.29 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 65.58/9.29 ~ (v2 = 0) | v3 = 0))) % 65.58/9.29 % 65.58/9.29 (ax73) % 65.58/9.29 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 65.58/9.29 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 65.58/9.29 (v2 = 0) | v3 = 0))) % 65.58/9.29 % 65.58/9.29 (ax9) % 65.58/9.29 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderP(v0) = v1) | ~ $i(v0) | ? [v2: % 65.58/9.29 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : ( ~ % 65.58/9.29 (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 65.58/9.29 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : % 65.58/9.29 (leq(v3, v2) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 65.58/9.29 ~ (ssList(v7) = 0) | ~ $i(v7) | ! [v8: $i] : ! [v9: $i] : % 65.58/9.29 ! [v10: $i] : ( ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v10) % 65.58/9.29 | ~ $i(v8) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v8) = % 65.58/9.29 v11) | ! [v11: $i] : ! [v12: $i] : (v6 = 0 | v4 = 0 | ~ % 65.58/9.29 (cons(v3, v11) = v12) | ~ (app(v10, v12) = v0) | ~ % 65.58/9.29 $i(v11) | ? [v13: int] : ( ~ (v13 = 0) & ssList(v11) = % 65.58/9.29 v13))))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 65.58/9.29 $i(v2) & ? [v3: $i] : ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5 % 65.58/9.29 & leq(v2, v3) = v4 & ssItem(v3) = 0 & $i(v3) & ? [v6: $i] : % 65.58/9.29 (ssList(v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 65.58/9.29 (ssList(v7) = 0 & cons(v2, v7) = v8 & app(v6, v8) = v9 & $i(v9) & % 65.58/9.29 $i(v8) & $i(v7) & ? [v10: $i] : ? [v11: $i] : ( ~ (v5 = 0) & % 65.58/9.29 ~ (v4 = 0) & ssList(v10) = 0 & cons(v3, v10) = v11 & app(v9, % 65.58/9.29 v11) = v0 & $i(v11) & $i(v10))))))))) % 65.58/9.29 % 65.58/9.29 (co1) % 65.58/9.30 $i(nil) & ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 65.58/9.30 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = 0 & % 65.58/9.30 $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) = v0 & % 65.58/9.30 ssItem(v3) = 0 & $i(v3)) | (v2 = nil & v0 = nil)))) % 65.58/9.30 % 65.58/9.30 (function-axioms) % 65.94/9.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 65.94/9.30 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 65.94/9.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 65.94/9.30 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 65.94/9.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 65.94/9.30 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 65.94/9.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 65.94/9.30 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 65.94/9.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 65.94/9.30 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 65.94/9.30 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 65.94/9.30 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 65.94/9.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 65.94/9.30 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 65.94/9.30 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 65.94/9.30 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 65.94/9.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 65.94/9.30 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 65.94/9.30 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 65.94/9.30 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 65.94/9.30 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 65.94/9.30 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 65.94/9.30 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 65.94/9.30 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 65.94/9.30 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 65.94/9.30 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 65.94/9.30 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 65.94/9.30 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 65.94/9.30 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 65.94/9.30 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 65.94/9.30 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 65.94/9.30 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 65.94/9.30 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.94/9.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 65.94/9.30 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 65.94/9.30 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 65.94/9.30 % 65.94/9.30 Further assumptions not needed in the proof: % 65.94/9.30 -------------------------------------------- % 65.94/9.31 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax2, ax21, ax22, ax24, ax26, % 65.94/9.31 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 65.94/9.31 ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, % 65.94/9.31 ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax64, ax66, ax67, % 65.94/9.31 ax69, ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 65.94/9.31 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax90, ax91, ax92, ax93, ax94, % 65.94/9.31 ax95 % 65.94/9.31 % 65.94/9.31 Those formulas are unsatisfiable: % 65.94/9.31 --------------------------------- % 65.94/9.31 % 65.94/9.31 Begin of proof % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax4) implies: % 65.94/9.31 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ? % 65.94/9.31 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: % 65.94/9.31 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 % 65.94/9.31 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: % 65.94/9.31 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3))))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax17) implies: % 65.94/9.31 | (2) ssList(nil) = 0 % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax20) implies: % 65.94/9.31 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 65.94/9.31 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 65.94/9.31 | ssItem(v2) = 0 & $i(v2)))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax59) implies: % 65.94/9.31 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.31 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 65.94/9.31 | ~ (v2 = 0) | v3 = 0))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax61) implies: % 65.94/9.31 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.31 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 65.94/9.31 | ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax62) implies: % 65.94/9.31 | (6) totalorderP(nil) = 0 % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax63) implies: % 65.94/9.31 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.31 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 65.94/9.31 | ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax65) implies: % 65.94/9.31 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.31 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 65.94/9.31 | & ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.31 | % 65.94/9.31 | ALPHA: (ax68) implies: % 65.94/9.32 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.32 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 65.94/9.32 | & ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.32 | % 65.94/9.32 | ALPHA: (ax71) implies: % 65.94/9.32 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.32 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = % 65.94/9.32 | v2 & ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.32 | % 65.94/9.32 | ALPHA: (ax73) implies: % 65.94/9.32 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.32 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 65.94/9.32 | ( ~ (v2 = 0) | v3 = 0))) % 65.94/9.32 | % 65.94/9.32 | ALPHA: (co1) implies: % 65.94/9.32 | (12) $i(nil) % 65.94/9.32 | (13) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 65.94/9.32 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) % 65.94/9.32 | = 0 & $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) % 65.94/9.32 | = v0 & ssItem(v3) = 0 & $i(v3)) | (v2 = nil & v0 = nil)))) % 65.94/9.32 | % 65.94/9.32 | ALPHA: (function-axioms) implies: % 65.94/9.32 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 65.94/9.32 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 65.94/9.32 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 65.94/9.32 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 65.94/9.32 | % 65.94/9.32 | DELTA: instantiating (13) with fresh symbols all_93_0, all_93_1 gives: % 65.94/9.32 | (16) singletonP(all_93_1) = all_93_0 & ssList(all_93_1) = 0 & $i(all_93_1) % 65.94/9.32 | & ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 % 65.94/9.32 | & $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) = % 65.94/9.32 | all_93_1 & ssItem(v1) = 0 & $i(v1)) | (v0 = nil & all_93_1 = % 65.94/9.32 | nil))) % 65.94/9.32 | % 65.94/9.32 | ALPHA: (16) implies: % 65.94/9.32 | (17) $i(all_93_1) % 65.94/9.32 | (18) ssList(all_93_1) = 0 % 65.94/9.32 | (19) singletonP(all_93_1) = all_93_0 % 65.94/9.32 | (20) ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 & % 65.94/9.32 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) = % 65.94/9.32 | all_93_1 & ssItem(v1) = 0 & $i(v1)) | (v0 = nil & all_93_1 = % 65.94/9.32 | nil))) % 65.94/9.32 | % 65.94/9.32 | DELTA: instantiating (20) with fresh symbol all_97_0 gives: % 65.94/9.33 | (21) ~ (all_93_0 = 0) & ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 & % 65.94/9.33 | $i(all_97_0) & ( ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, % 65.94/9.33 | nil) = all_93_1 & ssItem(v0) = 0 & $i(v0)) | (all_97_0 = nil & % 65.94/9.33 | all_93_1 = nil)) % 65.94/9.33 | % 65.94/9.33 | ALPHA: (21) implies: % 65.94/9.33 | (22) ~ (all_93_0 = 0) % 65.94/9.33 | (23) $i(all_97_0) % 65.94/9.33 | (24) neq(all_97_0, nil) = 0 % 65.94/9.33 | (25) ssList(all_97_0) = 0 % 65.94/9.33 | (26) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_1 & % 65.94/9.33 | ssItem(v0) = 0 & $i(v0)) | (all_97_0 = nil & all_93_1 = nil) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (12) gives: % 65.94/9.33 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.33 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 65.94/9.33 | ( ~ (v2 = 0) | v3 = nil))) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (12) gives: % 65.94/9.33 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 65.94/9.33 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 65.94/9.33 | ( ~ (v2 = 0) | v3 = v0))) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (ax18) with nil, simplifying with (2), (12) gives: % 65.94/9.33 | (29) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : ( % 65.94/9.33 | ~ (v1 = 0) & ssItem(v0) = v1)) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (3) with all_93_1, simplifying with (17), (18) % 65.94/9.33 | gives: % 65.94/9.33 | (30) all_93_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 65.94/9.33 | : (cons(v1, v0) = all_93_1 & ssItem(v1) = 0 & $i(v1))) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (23), (25) % 65.94/9.33 | gives: % 65.94/9.33 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0) % 65.94/9.33 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 65.94/9.33 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0))) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (1) with all_93_1, all_93_0, simplifying with (17), % 65.94/9.33 | (19) gives: % 65.94/9.33 | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_93_0 % 65.94/9.33 | = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & ssItem(v0) = 0 % 65.94/9.33 | & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = % 65.94/9.33 | all_93_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.94/9.33 | ssItem(v0) = v1)))) % 65.94/9.33 | % 65.94/9.33 | GROUND_INST: instantiating (ax9) with nil, 0, simplifying with (6), (12) % 65.94/9.33 | gives: % 65.94/9.34 | (33) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 65.94/9.34 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ % 65.94/9.34 | (leq(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 65.94/9.34 | (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | ! [v5: $i] : % 65.94/9.34 | ( ~ (ssList(v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: $i] : % 65.94/9.34 | ! [v8: $i] : ( ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = % 65.94/9.34 | v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & % 65.94/9.34 | ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 = 0 % 65.94/9.34 | | v2 = 0 | ~ (cons(v1, v9) = v10) | ~ (app(v8, v10) = % 65.94/9.34 | nil) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & % 65.94/9.34 | ssList(v9) = v11)))))))) % 65.94/9.34 | % 65.94/9.34 | GROUND_INST: instantiating (31) with nil, 0, simplifying with (12) gives: % 65.94/9.34 | (34) ~ (all_97_0 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0 % 65.94/9.34 | = 0) & ssList(nil) = v0) % 65.94/9.34 | % 65.94/9.34 | BETA: splitting (32) gives: % 65.94/9.34 | % 65.94/9.34 | Case 1: % 65.94/9.34 | | % 65.94/9.34 | | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 65.94/9.34 | | % 65.94/9.34 | | BETA: splitting (33) gives: % 65.94/9.34 | | % 65.94/9.34 | | Case 1: % 65.94/9.34 | | | % 65.94/9.34 | | | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 65.94/9.34 | | | % 65.94/9.34 | | | DELTA: instantiating (36) with fresh symbol all_308_0 gives: % 65.94/9.34 | | | (37) ~ (all_308_0 = 0) & ssList(nil) = all_308_0 % 65.94/9.34 | | | % 65.94/9.34 | | | REF_CLOSE: (2), (15), (37) are inconsistent by sub-proof #1. % 65.94/9.34 | | | % 65.94/9.34 | | Case 2: % 65.94/9.34 | | | % 65.94/9.34 | | | % 65.94/9.34 | | | DELTA: instantiating (35) with fresh symbol all_286_0 gives: % 65.94/9.34 | | | (38) ~ (all_286_0 = 0) & ssList(all_93_1) = all_286_0 % 65.94/9.34 | | | % 65.94/9.34 | | | ALPHA: (38) implies: % 65.94/9.34 | | | (39) ~ (all_286_0 = 0) % 65.94/9.34 | | | (40) ssList(all_93_1) = all_286_0 % 65.94/9.34 | | | % 65.94/9.34 | | | GROUND_INST: instantiating (15) with 0, all_286_0, all_93_1, simplifying % 65.94/9.34 | | | with (18), (40) gives: % 65.94/9.34 | | | (41) all_286_0 = 0 % 65.94/9.34 | | | % 65.94/9.34 | | | REDUCE: (39), (41) imply: % 65.94/9.34 | | | (42) $false % 65.94/9.34 | | | % 65.94/9.34 | | | CLOSE: (42) is inconsistent. % 65.94/9.34 | | | % 65.94/9.34 | | End of split % 65.94/9.34 | | % 65.94/9.34 | Case 2: % 65.94/9.34 | | % 65.94/9.35 | | (43) ( ~ (all_93_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & % 65.94/9.35 | | ssItem(v0) = 0 & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( ~ % 65.94/9.35 | | (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 65.94/9.35 | | = 0) & ssItem(v0) = v1))) % 65.94/9.35 | | % 65.94/9.35 | | ALPHA: (43) implies: % 65.94/9.35 | | (44) all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ % 65.94/9.35 | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 65.94/9.35 | | % 65.94/9.35 | | BETA: splitting (44) gives: % 65.94/9.35 | | % 65.94/9.35 | | Case 1: % 65.94/9.35 | | | % 65.94/9.35 | | | (45) all_93_0 = 0 % 65.94/9.35 | | | % 65.94/9.35 | | | REDUCE: (22), (45) imply: % 65.94/9.35 | | | (46) $false % 65.94/9.35 | | | % 65.94/9.35 | | | CLOSE: (46) is inconsistent. % 65.94/9.35 | | | % 65.94/9.35 | | Case 2: % 65.94/9.35 | | | % 65.94/9.35 | | | (47) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? [v1: % 65.94/9.35 | | | int] : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 65.94/9.35 | | | % 65.94/9.35 | | | BETA: splitting (26) gives: % 65.94/9.35 | | | % 65.94/9.35 | | | Case 1: % 65.94/9.35 | | | | % 65.94/9.35 | | | | (48) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = % 65.94/9.35 | | | | all_93_1 & ssItem(v0) = 0 & $i(v0)) % 65.94/9.35 | | | | % 65.94/9.35 | | | | DELTA: instantiating (48) with fresh symbol all_299_0 gives: % 65.94/9.35 | | | | (49) memberP(all_97_0, all_299_0) = 0 & cons(all_299_0, nil) = % 65.94/9.35 | | | | all_93_1 & ssItem(all_299_0) = 0 & $i(all_299_0) % 65.94/9.35 | | | | % 65.94/9.35 | | | | ALPHA: (49) implies: % 65.94/9.35 | | | | (50) $i(all_299_0) % 65.94/9.35 | | | | (51) ssItem(all_299_0) = 0 % 65.94/9.35 | | | | (52) cons(all_299_0, nil) = all_93_1 % 65.94/9.35 | | | | % 65.94/9.35 | | | | BETA: splitting (30) gives: % 65.94/9.35 | | | | % 65.94/9.35 | | | | Case 1: % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | (53) all_93_1 = nil % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | REDUCE: (52), (53) imply: % 65.94/9.35 | | | | | (54) cons(all_299_0, nil) = nil % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | GROUND_INST: instantiating (29) with all_299_0, simplifying with (50), % 65.94/9.35 | | | | | (54) gives: % 65.94/9.35 | | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_0) = v0) % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | GROUND_INST: instantiating (27) with all_299_0, nil, simplifying with % 65.94/9.35 | | | | | (50), (54) gives: % 65.94/9.35 | | | | | (56) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & ssItem(all_299_0) % 65.94/9.35 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | GROUND_INST: instantiating (28) with all_299_0, nil, simplifying with % 65.94/9.35 | | | | | (50), (54) gives: % 65.94/9.35 | | | | | (57) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & ssItem(all_299_0) % 65.94/9.35 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_299_0)) % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | DELTA: instantiating (55) with fresh symbol all_527_0 gives: % 65.94/9.35 | | | | | (58) ~ (all_527_0 = 0) & ssItem(all_299_0) = all_527_0 % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | ALPHA: (58) implies: % 65.94/9.35 | | | | | (59) ~ (all_527_0 = 0) % 65.94/9.35 | | | | | (60) ssItem(all_299_0) = all_527_0 % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | DELTA: instantiating (56) with fresh symbols all_529_0, all_529_1 % 65.94/9.35 | | | | | gives: % 65.94/9.35 | | | | | (61) tl(nil) = all_529_0 & ssItem(all_299_0) = all_529_1 & % 65.94/9.35 | | | | | $i(all_529_0) & ( ~ (all_529_1 = 0) | all_529_0 = nil) % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | ALPHA: (61) implies: % 65.94/9.35 | | | | | (62) ssItem(all_299_0) = all_529_1 % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | DELTA: instantiating (57) with fresh symbols all_531_0, all_531_1 % 65.94/9.35 | | | | | gives: % 65.94/9.35 | | | | | (63) hd(nil) = all_531_0 & ssItem(all_299_0) = all_531_1 & % 65.94/9.35 | | | | | $i(all_531_0) & ( ~ (all_531_1 = 0) | all_531_0 = all_299_0) % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | ALPHA: (63) implies: % 65.94/9.35 | | | | | (64) ssItem(all_299_0) = all_531_1 % 65.94/9.35 | | | | | % 65.94/9.35 | | | | | GROUND_INST: instantiating (14) with all_527_0, all_529_1, all_299_0, % 65.94/9.35 | | | | | simplifying with (60), (62) gives: % 65.94/9.35 | | | | | (65) all_529_1 = all_527_0 % 65.94/9.35 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (14) with 0, all_531_1, all_299_0, % 65.94/9.36 | | | | | simplifying with (51), (64) gives: % 65.94/9.36 | | | | | (66) all_531_1 = 0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (14) with all_529_1, all_531_1, all_299_0, % 65.94/9.36 | | | | | simplifying with (62), (64) gives: % 65.94/9.36 | | | | | (67) all_531_1 = all_529_1 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | COMBINE_EQS: (66), (67) imply: % 65.94/9.36 | | | | | (68) all_529_1 = 0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | SIMP: (68) implies: % 65.94/9.36 | | | | | (69) all_529_1 = 0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | COMBINE_EQS: (65), (69) imply: % 65.94/9.36 | | | | | (70) all_527_0 = 0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | SIMP: (70) implies: % 65.94/9.36 | | | | | (71) all_527_0 = 0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | REDUCE: (59), (71) imply: % 65.94/9.36 | | | | | (72) $false % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | CLOSE: (72) is inconsistent. % 65.94/9.36 | | | | | % 65.94/9.36 | | | | Case 2: % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (47) with all_299_0, simplifying with (50), % 65.94/9.36 | | | | | (52) gives: % 65.94/9.36 | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_0) = v0) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (27) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (74) ? [v0: any] : ? [v1: $i] : (tl(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (28) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (75) ? [v0: any] : ? [v1: $i] : (hd(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 65.94/9.36 | | | | | all_299_0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (11) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (76) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (10) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (77) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (9) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (78) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (8) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (79) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (7) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (80) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (5) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (81) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | GROUND_INST: instantiating (4) with all_299_0, all_93_1, simplifying % 65.94/9.36 | | | | | with (50), (52) gives: % 65.94/9.36 | | | | | (82) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_1) = v1 & % 65.94/9.36 | | | | | ssItem(all_299_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | DELTA: instantiating (73) with fresh symbol all_758_0 gives: % 65.94/9.36 | | | | | (83) ~ (all_758_0 = 0) & ssItem(all_299_0) = all_758_0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | ALPHA: (83) implies: % 65.94/9.36 | | | | | (84) ~ (all_758_0 = 0) % 65.94/9.36 | | | | | (85) ssItem(all_299_0) = all_758_0 % 65.94/9.36 | | | | | % 65.94/9.36 | | | | | DELTA: instantiating (82) with fresh symbols all_760_0, all_760_1 % 65.94/9.36 | | | | | gives: % 65.94/9.36 | | | | | (86) cyclefreeP(all_93_1) = all_760_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_760_1 & ( ~ (all_760_1 = 0) | all_760_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (86) implies: % 65.94/9.37 | | | | | (87) ssItem(all_299_0) = all_760_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (80) with fresh symbols all_762_0, all_762_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (88) strictorderP(all_93_1) = all_762_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_762_1 & ( ~ (all_762_1 = 0) | all_762_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (88) implies: % 65.94/9.37 | | | | | (89) ssItem(all_299_0) = all_762_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (81) with fresh symbols all_764_0, all_764_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (90) totalorderP(all_93_1) = all_764_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_764_1 & ( ~ (all_764_1 = 0) | all_764_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (90) implies: % 65.94/9.37 | | | | | (91) ssItem(all_299_0) = all_764_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (79) with fresh symbols all_766_0, all_766_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (92) totalorderedP(all_93_1) = all_766_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_766_1 & ( ~ (all_766_1 = 0) | all_766_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (92) implies: % 65.94/9.37 | | | | | (93) ssItem(all_299_0) = all_766_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (78) with fresh symbols all_768_0, all_768_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (94) strictorderedP(all_93_1) = all_768_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_768_1 & ( ~ (all_768_1 = 0) | all_768_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (94) implies: % 65.94/9.37 | | | | | (95) ssItem(all_299_0) = all_768_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (77) with fresh symbols all_770_0, all_770_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (96) duplicatefreeP(all_93_1) = all_770_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_770_1 & ( ~ (all_770_1 = 0) | all_770_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (96) implies: % 65.94/9.37 | | | | | (97) ssItem(all_299_0) = all_770_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (76) with fresh symbols all_772_0, all_772_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (98) equalelemsP(all_93_1) = all_772_0 & ssItem(all_299_0) = % 65.94/9.37 | | | | | all_772_1 & ( ~ (all_772_1 = 0) | all_772_0 = 0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (98) implies: % 65.94/9.37 | | | | | (99) ssItem(all_299_0) = all_772_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (75) with fresh symbols all_774_0, all_774_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (100) hd(all_93_1) = all_774_0 & ssItem(all_299_0) = all_774_1 & % 65.94/9.37 | | | | | $i(all_774_0) & ( ~ (all_774_1 = 0) | all_774_0 = all_299_0) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (100) implies: % 65.94/9.37 | | | | | (101) ssItem(all_299_0) = all_774_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | DELTA: instantiating (74) with fresh symbols all_776_0, all_776_1 % 65.94/9.37 | | | | | gives: % 65.94/9.37 | | | | | (102) tl(all_93_1) = all_776_0 & ssItem(all_299_0) = all_776_1 & % 65.94/9.37 | | | | | $i(all_776_0) & ( ~ (all_776_1 = 0) | all_776_0 = nil) % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | ALPHA: (102) implies: % 65.94/9.37 | | | | | (103) ssItem(all_299_0) = all_776_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_762_1, all_764_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (89), (91) gives: % 65.94/9.37 | | | | | (104) all_764_1 = all_762_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with 0, all_772_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (51), (99) gives: % 65.94/9.37 | | | | | (105) all_772_1 = 0 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_766_1, all_772_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (93), (99) gives: % 65.94/9.37 | | | | | (106) all_772_1 = all_766_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_762_1, all_772_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (89), (99) gives: % 65.94/9.37 | | | | | (107) all_772_1 = all_762_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_760_1, all_772_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (87), (99) gives: % 65.94/9.37 | | | | | (108) all_772_1 = all_760_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_768_1, all_774_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (95), (101) gives: % 65.94/9.37 | | | | | (109) all_774_1 = all_768_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_764_1, all_774_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (91), (101) gives: % 65.94/9.37 | | | | | (110) all_774_1 = all_764_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_758_0, all_774_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (85), (101) gives: % 65.94/9.37 | | | | | (111) all_774_1 = all_758_0 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_774_1, all_776_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (101), (103) gives: % 65.94/9.37 | | | | | (112) all_776_1 = all_774_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | GROUND_INST: instantiating (14) with all_770_1, all_776_1, all_299_0, % 65.94/9.37 | | | | | simplifying with (97), (103) gives: % 65.94/9.37 | | | | | (113) all_776_1 = all_770_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (112), (113) imply: % 65.94/9.37 | | | | | (114) all_774_1 = all_770_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | SIMP: (114) implies: % 65.94/9.37 | | | | | (115) all_774_1 = all_770_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (110), (115) imply: % 65.94/9.37 | | | | | (116) all_770_1 = all_764_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (111), (115) imply: % 65.94/9.37 | | | | | (117) all_770_1 = all_758_0 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (109), (115) imply: % 65.94/9.37 | | | | | (118) all_770_1 = all_768_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (105), (106) imply: % 65.94/9.37 | | | | | (119) all_766_1 = 0 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (106), (107) imply: % 65.94/9.37 | | | | | (120) all_766_1 = all_762_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (106), (108) imply: % 65.94/9.37 | | | | | (121) all_766_1 = all_760_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (116), (118) imply: % 65.94/9.37 | | | | | (122) all_768_1 = all_764_1 % 65.94/9.37 | | | | | % 65.94/9.37 | | | | | COMBINE_EQS: (117), (118) imply: % 65.94/9.38 | | | | | (123) all_768_1 = all_758_0 % 65.94/9.38 | | | | | % 65.94/9.38 | | | | | COMBINE_EQS: (122), (123) imply: % 66.30/9.38 | | | | | (124) all_764_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | SIMP: (124) implies: % 66.30/9.38 | | | | | (125) all_764_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | COMBINE_EQS: (119), (121) imply: % 66.30/9.38 | | | | | (126) all_760_1 = 0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | COMBINE_EQS: (120), (121) imply: % 66.30/9.38 | | | | | (127) all_762_1 = all_760_1 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | SIMP: (127) implies: % 66.30/9.38 | | | | | (128) all_762_1 = all_760_1 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | COMBINE_EQS: (104), (125) imply: % 66.30/9.38 | | | | | (129) all_762_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | SIMP: (129) implies: % 66.30/9.38 | | | | | (130) all_762_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | COMBINE_EQS: (128), (130) imply: % 66.30/9.38 | | | | | (131) all_760_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | SIMP: (131) implies: % 66.30/9.38 | | | | | (132) all_760_1 = all_758_0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | COMBINE_EQS: (126), (132) imply: % 66.30/9.38 | | | | | (133) all_758_0 = 0 % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | REDUCE: (84), (133) imply: % 66.30/9.38 | | | | | (134) $false % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | CLOSE: (134) is inconsistent. % 66.30/9.38 | | | | | % 66.30/9.38 | | | | End of split % 66.30/9.38 | | | | % 66.30/9.38 | | | Case 2: % 66.30/9.38 | | | | % 66.30/9.38 | | | | (135) all_97_0 = nil & all_93_1 = nil % 66.30/9.38 | | | | % 66.30/9.38 | | | | ALPHA: (135) implies: % 66.30/9.38 | | | | (136) all_93_1 = nil % 66.30/9.38 | | | | (137) all_97_0 = nil % 66.30/9.38 | | | | % 66.30/9.38 | | | | REDUCE: (24), (137) imply: % 66.30/9.38 | | | | (138) neq(nil, nil) = 0 % 66.30/9.38 | | | | % 66.30/9.38 | | | | BETA: splitting (34) gives: % 66.30/9.38 | | | | % 66.30/9.38 | | | | Case 1: % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | (139) ~ (neq(nil, nil) = 0) % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | PRED_UNIFY: (138), (139) imply: % 66.30/9.38 | | | | | (140) $false % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | CLOSE: (140) is inconsistent. % 66.30/9.38 | | | | | % 66.30/9.38 | | | | Case 2: % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | (141) ~ (all_97_0 = nil) | ? [v0: int] : ( ~ (v0 = 0) & % 66.30/9.38 | | | | | ssList(nil) = v0) % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | BETA: splitting (141) gives: % 66.30/9.38 | | | | | % 66.30/9.38 | | | | | Case 1: % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | (142) ~ (all_97_0 = nil) % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | REDUCE: (137), (142) imply: % 66.30/9.38 | | | | | | (143) $false % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | CLOSE: (143) is inconsistent. % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | Case 2: % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | (144) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | DELTA: instantiating (144) with fresh symbol all_308_0 gives: % 66.30/9.38 | | | | | | (145) ~ (all_308_0 = 0) & ssList(nil) = all_308_0 % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | | REF_CLOSE: (2), (15), (145) are inconsistent by sub-proof #1. % 66.30/9.38 | | | | | | % 66.30/9.38 | | | | | End of split % 66.30/9.38 | | | | | % 66.30/9.38 | | | | End of split % 66.30/9.38 | | | | % 66.30/9.38 | | | End of split % 66.30/9.38 | | | % 66.30/9.38 | | End of split % 66.30/9.38 | | % 66.30/9.38 | End of split % 66.30/9.38 | % 66.30/9.38 End of proof % 66.30/9.38 % 66.30/9.38 Sub-proof #1 shows that the following formulas are inconsistent: % 66.30/9.38 ---------------------------------------------------------------- % 66.30/9.38 (1) ~ (all_308_0 = 0) & ssList(nil) = all_308_0 % 66.30/9.38 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 66.30/9.38 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 66.30/9.38 (3) ssList(nil) = 0 % 66.30/9.38 % 66.30/9.38 Begin of proof % 66.30/9.38 | % 66.30/9.38 | ALPHA: (1) implies: % 66.30/9.38 | (4) ~ (all_308_0 = 0) % 66.30/9.38 | (5) ssList(nil) = all_308_0 % 66.30/9.38 | % 66.30/9.38 | GROUND_INST: instantiating (2) with 0, all_308_0, nil, simplifying with (3), % 66.30/9.38 | (5) gives: % 66.30/9.38 | (6) all_308_0 = 0 % 66.30/9.38 | % 66.30/9.38 | REDUCE: (4), (6) imply: % 66.30/9.38 | (7) $false % 66.30/9.38 | % 66.30/9.38 | CLOSE: (7) is inconsistent. % 66.30/9.38 | % 66.30/9.38 End of proof % 66.30/9.38 % SZS output end Proof for theBenchmark % 66.30/9.38 % 66.30/9.38 8788ms %------------------------------------------------------------------------------