%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM233_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Tue May 5 06:21:37 PM UTC 2026 % Result : Theorem 19.40s 3.38s % Output : Proof 33.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM233_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.33 % Computer : n020.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Mon May 4 19:16:34 EDT 2026 % 0.15/0.34 % CPUTime : % 0.52/0.60 ________ _____ % 0.52/0.60 ___ __ \_________(_)________________________________ % 0.52/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.60 (2023-06-19) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2023 % 0.52/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.60 Amanda Stjerna. % 0.52/0.60 Free software under BSD-3-Clause. % 0.52/0.60 % 0.52/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.61 Running up to 7 provers in parallel. % 0.52/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.06/1.46 Prover 4: Preprocessing ... % 5.06/1.47 Prover 1: Preprocessing ... % 5.06/1.50 Prover 2: Preprocessing ... % 5.06/1.50 Prover 0: Preprocessing ... % 5.06/1.50 Prover 6: Preprocessing ... % 5.06/1.50 Prover 3: Preprocessing ... % 5.06/1.50 Prover 5: Preprocessing ... % 11.77/2.36 Prover 1: Warning: ignoring some quantifiers % 12.52/2.44 Prover 1: Constructing countermodel ... % 12.52/2.45 Prover 6: Proving ... % 12.52/2.46 Prover 3: Warning: ignoring some quantifiers % 12.52/2.49 Prover 3: Constructing countermodel ... % 13.26/2.51 Prover 4: Warning: ignoring some quantifiers % 13.26/2.58 Prover 5: Proving ... % 13.96/2.60 Prover 4: Constructing countermodel ... % 14.77/2.72 Prover 0: Proving ... % 14.77/2.78 Prover 2: Proving ... % 19.40/3.37 Prover 5: proved (2746ms) % 19.40/3.37 % 19.40/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.40/3.38 % 19.40/3.38 Prover 6: stopped % 19.40/3.38 Prover 2: stopped % 19.40/3.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.40/3.39 Prover 3: stopped % 20.10/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.10/3.40 Prover 0: stopped % 20.10/3.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.10/3.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.10/3.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.65/3.67 Prover 13: Preprocessing ... % 21.65/3.67 Prover 7: Preprocessing ... % 22.36/3.70 Prover 10: Preprocessing ... % 22.36/3.70 Prover 8: Preprocessing ... % 22.36/3.73 Prover 11: Preprocessing ... % 23.92/3.96 Prover 8: Warning: ignoring some quantifiers % 23.92/3.98 Prover 8: Constructing countermodel ... % 24.80/4.09 Prover 7: Warning: ignoring some quantifiers % 24.80/4.09 Prover 10: Warning: ignoring some quantifiers % 24.80/4.10 Prover 10: Constructing countermodel ... % 25.56/4.13 Prover 7: Constructing countermodel ... % 26.22/4.21 Prover 13: Warning: ignoring some quantifiers % 26.22/4.22 Prover 13: Constructing countermodel ... % 27.00/4.33 Prover 11: Warning: ignoring some quantifiers % 27.00/4.35 Prover 11: Constructing countermodel ... % 32.54/5.09 Prover 4: Found proof (size 75) % 32.54/5.10 Prover 4: proved (4476ms) % 32.54/5.11 Prover 1: stopped % 32.54/5.11 Prover 8: stopped % 32.54/5.11 Prover 11: stopped % 32.54/5.11 Prover 7: stopped % 33.30/5.12 Prover 13: stopped % 33.30/5.13 Prover 10: stopped % 33.30/5.13 % 33.30/5.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.30/5.13 % 33.30/5.14 % SZS output start Proof for theBenchmark % 33.30/5.14 Assumptions after simplification: % 33.30/5.14 --------------------------------- % 33.30/5.15 % 33.30/5.15 (DIFF-noTerm-someTerm) % 33.30/5.17 vOptTerm(vnoTerm) & ! [v0: vTerm] : ( ~ (vsomeTerm(v0) = vnoTerm) | ~ % 33.30/5.17 vTerm(v0)) % 33.30/5.17 % 33.30/5.17 (Progress-Plus-IH0) % 33.30/5.17 vOptTerm(vnoTerm) & vTerm(vt1) & ? [v0: any] : ? [v1: vOptTerm] : % 33.30/5.17 (vreduce(vt1) = v1 & visValue(vt1) = v0 & vOptTerm(v1) & ! [v2: vTy] : ( ~ % 33.30/5.17 (v1 = vnoTerm) | v0 = 0 | ~ (vptchecksimple(vt1, v2) = 0) | ~ vTy(v2))) % 33.30/5.17 % 33.30/5.17 (Progress-Plus-isNV-False-isSomeTerm-True) % 33.30/5.17 vOptTerm(vnoTerm) & vTerm(vt1) & vTerm(vt2) & ? [v0: vOptTerm] : ? [v1: int] % 33.30/5.17 : ? [v2: vTerm] : ? [v3: int] : ? [v4: vTy] : ( ~ (v3 = 0) & ~ (v1 = 0) & % 33.30/5.17 vptchecksimple(v2, v4) = 0 & vreduce(v2) = vnoTerm & vreduce(vt1) = v0 & % 33.30/5.17 visSomeTerm(v0) = 0 & visValue(v2) = v3 & visNV(vt1) = v1 & vPlus(vt1, vt2) % 33.30/5.17 = v2 & vTy(v4) & vOptTerm(v0) & vTerm(v2)) % 33.30/5.17 % 33.30/5.17 (reduce-18) % 33.30/5.18 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vplusop(v0, v1) = v2) % 33.30/5.18 | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : ? [v5: vTerm] % 33.30/5.18 : ? [v6: vOptTerm] : ? [v7: vOptTerm] : (vreduce(v5) = v6 & visNV(v1) = v4 % 33.30/5.18 & visNV(v0) = v3 & vsomeTerm(v2) = v7 & vPlus(v0, v1) = v5 & vOptTerm(v7) % 33.30/5.18 & vOptTerm(v6) & vTerm(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = v6))) & ! % 33.30/5.18 [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = v2) | ~ % 33.30/5.18 vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : ? [v5: vOptTerm] : % 33.30/5.18 ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v2) = v5 & vplusop(v0, v1) = % 33.30/5.18 v6 & visNV(v1) = v4 & visNV(v0) = v3 & vsomeTerm(v6) = v7 & vOptTerm(v7) & % 33.30/5.18 vOptTerm(v5) & vTerm(v6) & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = v5))) % 33.30/5.18 % 33.30/5.18 (reduce-19) % 33.30/5.18 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : ! [v3: vTerm] : ! [v4: % 33.30/5.18 vTerm] : ( ~ (vreduce(v1) = v2) | ~ (vgetTerm(v2) = v3) | ~ (vPlus(v0, v3) % 33.30/5.18 = v4) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v5: any] : ? [v6: any] : ? % 33.30/5.18 [v7: any] : ? [v8: vTerm] : ? [v9: vOptTerm] : ? [v10: vOptTerm] : % 33.30/5.18 (vreduce(v8) = v9 & visSomeTerm(v2) = v7 & visNV(v1) = v6 & visNV(v0) = v5 & % 33.30/5.18 vsomeTerm(v4) = v10 & vPlus(v0, v1) = v8 & vOptTerm(v10) & vOptTerm(v9) & % 33.30/5.18 vTerm(v8) & ( ~ (v7 = 0) | ~ (v5 = 0) | v10 = v9 | v6 = 0))) & ! [v0: % 33.30/5.18 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = v2) | ~ % 33.30/5.18 vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : ? [v5: vOptTerm] : % 33.30/5.18 ? [v6: any] : ? [v7: vOptTerm] : ? [v8: vTerm] : ? [v9: vTerm] : ? % 33.30/5.18 [v10: vOptTerm] : (vreduce(v2) = v7 & vreduce(v1) = v5 & visSomeTerm(v5) = % 33.30/5.18 v6 & visNV(v1) = v4 & visNV(v0) = v3 & vgetTerm(v5) = v8 & vsomeTerm(v9) = % 33.30/5.18 v10 & vPlus(v0, v8) = v9 & vOptTerm(v10) & vOptTerm(v7) & vOptTerm(v5) & % 33.30/5.18 vTerm(v9) & vTerm(v8) & ( ~ (v6 = 0) | ~ (v3 = 0) | v10 = v7 | v4 = 0))) % 33.30/5.18 % 33.30/5.18 (reduce-20) % 33.30/5.18 vOptTerm(vnoTerm) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ % 33.30/5.18 (vPlus(v0, v1) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: % 33.30/5.18 any] : ? [v5: vOptTerm] : ? [v6: any] : ? [v7: vOptTerm] : (vreduce(v2) % 33.30/5.18 = v7 & vreduce(v1) = v5 & visSomeTerm(v5) = v6 & visNV(v1) = v4 & % 33.30/5.18 visNV(v0) = v3 & vOptTerm(v7) & vOptTerm(v5) & ( ~ (v3 = 0) | v7 = vnoTerm % 33.30/5.18 | v6 = 0 | v4 = 0))) % 33.30/5.18 % 33.30/5.18 (reduce-21) % 33.30/5.18 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : ! [v3: vTerm] : ! [v4: % 33.30/5.18 vTerm] : ( ~ (vreduce(v0) = v2) | ~ (vgetTerm(v2) = v3) | ~ (vPlus(v3, v1) % 33.30/5.18 = v4) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v5: any] : ? [v6: any] : ? % 33.30/5.18 [v7: vTerm] : ? [v8: vOptTerm] : ? [v9: vOptTerm] : (vreduce(v7) = v8 & % 33.30/5.18 visSomeTerm(v2) = v6 & visNV(v0) = v5 & vsomeTerm(v4) = v9 & vPlus(v0, v1) % 33.30/5.18 = v7 & vOptTerm(v9) & vOptTerm(v8) & vTerm(v7) & ( ~ (v6 = 0) | v9 = v8 | % 33.30/5.18 v5 = 0))) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ % 33.30/5.18 (vPlus(v0, v1) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: % 33.30/5.18 vOptTerm] : ? [v5: any] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: % 33.30/5.18 vTerm] : ? [v9: vOptTerm] : (vreduce(v2) = v6 & vreduce(v0) = v4 & % 33.30/5.18 visSomeTerm(v4) = v5 & visNV(v0) = v3 & vgetTerm(v4) = v7 & vsomeTerm(v8) % 33.30/5.18 = v9 & vPlus(v7, v1) = v8 & vOptTerm(v9) & vOptTerm(v6) & vOptTerm(v4) & % 33.30/5.18 vTerm(v8) & vTerm(v7) & ( ~ (v5 = 0) | v9 = v6 | v3 = 0))) % 33.30/5.18 % 33.30/5.18 (reduce-4) % 33.30/5.19 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vreduce(v0) = v1) | ~ vTerm(v0) | % 33.30/5.19 ? [v2: any] : ? [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: % 33.30/5.19 vTerm] : ? [v7: vOptTerm] : (vreduce(v3) = v4 & visSomeTerm(v1) = v2 & % 33.30/5.19 vgetTerm(v1) = v5 & vsomeTerm(v6) = v7 & vSucc(v5) = v6 & vSucc(v0) = v3 & % 33.30/5.19 vOptTerm(v7) & vOptTerm(v4) & vTerm(v6) & vTerm(v5) & vTerm(v3) & ( ~ (v2 % 33.30/5.19 = 0) | v7 = v4))) & ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = % 33.30/5.19 v1) | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: any] : ? [v4: vOptTerm] % 33.30/5.19 : ? [v5: vTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v1) = v4 & % 33.30/5.19 vreduce(v0) = v2 & visSomeTerm(v2) = v3 & vgetTerm(v2) = v5 & % 33.30/5.19 vsomeTerm(v6) = v7 & vSucc(v5) = v6 & vOptTerm(v7) & vOptTerm(v4) & % 33.30/5.19 vOptTerm(v2) & vTerm(v6) & vTerm(v5) & ( ~ (v3 = 0) | v7 = v4))) % 33.30/5.19 % 33.30/5.19 (reduce-5) % 33.30/5.19 vOptTerm(vnoTerm) & ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vreduce(v0) = % 33.30/5.19 v1) | ~ vTerm(v0) | ? [v2: any] : ? [v3: vTerm] : ? [v4: vOptTerm] : % 33.30/5.19 (vreduce(v3) = v4 & visSomeTerm(v1) = v2 & vSucc(v0) = v3 & vOptTerm(v4) & % 33.30/5.19 vTerm(v3) & (v4 = vnoTerm | v2 = 0))) & ! [v0: vTerm] : ! [v1: vTerm] : % 33.30/5.19 ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: any] : ? % 33.30/5.19 [v4: vOptTerm] : (vreduce(v1) = v4 & vreduce(v0) = v2 & visSomeTerm(v2) = v3 % 33.30/5.19 & vOptTerm(v4) & vOptTerm(v2) & (v4 = vnoTerm | v3 = 0))) % 33.30/5.19 % 33.30/5.19 (reduce-8) % 33.30/5.19 ! [v0: vTerm] : ! [v1: int] : (v1 = 0 | ~ (visNV(v0) = v1) | ~ vTerm(v0) | % 33.30/5.19 ? [v2: vTerm] : ? [v3: vOptTerm] : ? [v4: any] : ? [v5: vTerm] : ? [v6: % 33.30/5.19 vOptTerm] : ? [v7: vTerm] : ? [v8: vTerm] : ? [v9: vOptTerm] : % 33.30/5.19 (vreduce(v5) = v6 & vreduce(v2) = v3 & visSomeTerm(v3) = v4 & vgetTerm(v3) = % 33.30/5.19 v7 & vsomeTerm(v8) = v9 & vPred(v7) = v8 & vPred(v2) = v5 & vSucc(v0) = v2 % 33.30/5.19 & vOptTerm(v9) & vOptTerm(v6) & vOptTerm(v3) & vTerm(v8) & vTerm(v7) & % 33.30/5.19 vTerm(v5) & vTerm(v2) & ( ~ (v4 = 0) | v9 = v6))) & ! [v0: vTerm] : ! % 33.30/5.19 [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | ? [v2: any] : ? [v3: % 33.30/5.19 vOptTerm] : ? [v4: any] : ? [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: % 33.30/5.19 vTerm] : ? [v8: vTerm] : ? [v9: vOptTerm] : (vreduce(v5) = v6 & % 33.30/5.19 vreduce(v1) = v3 & visSomeTerm(v3) = v4 & visNV(v0) = v2 & vgetTerm(v3) = % 33.30/5.19 v7 & vsomeTerm(v8) = v9 & vPred(v7) = v8 & vPred(v1) = v5 & vOptTerm(v9) & % 33.30/5.19 vOptTerm(v6) & vOptTerm(v3) & vTerm(v8) & vTerm(v7) & vTerm(v5) & ( ~ (v4 % 33.30/5.19 = 0) | v9 = v6 | v2 = 0))) % 33.30/5.19 % 33.30/5.19 (function-axioms) % 33.30/5.20 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 33.30/5.20 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 33.30/5.20 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 33.30/5.20 vTy] : ! [v3: vTerm] : (v1 = v0 | ~ (vptchecksimple(v3, v2) = v1) | ~ % 33.30/5.20 (vptchecksimple(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: % 33.30/5.20 vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ % 33.30/5.20 (vplusop(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : % 33.30/5.20 ! [v3: vTerm] : (v1 = v0 | ~ (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) % 33.30/5.20 & ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 33.30/5.20 (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: MultipleValueBool] : % 33.30/5.20 ! [v1: MultipleValueBool] : ! [v2: vOptTerm] : (v1 = v0 | ~ (visSomeTerm(v2) % 33.30/5.20 = v1) | ~ (visSomeTerm(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.30/5.20 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 33.30/5.20 (visValue(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.30/5.20 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visNV(v2) = v1) | ~ % 33.30/5.20 (visNV(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 33.30/5.20 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 33.30/5.20 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 33.30/5.20 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 33.30/5.20 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 33.30/5.20 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 33.30/5.20 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 33.30/5.20 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 33.30/5.20 % 33.30/5.20 Further assumptions not needed in the proof: % 33.30/5.20 -------------------------------------------- % 33.70/5.20 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 33.70/5.20 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 33.70/5.20 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 33.70/5.20 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 33.70/5.20 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 33.70/5.20 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 33.70/5.20 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 33.70/5.20 DIFF-Zero-Succ, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, EQ-Succ, EQ-someTerm, % 33.70/5.20 Progress-Plus-IH1, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, TPred_inv1, % 33.70/5.20 TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, Tif, % 33.70/5.20 Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 33.70/5.20 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 33.70/5.20 isNV-false-INV, isNV-true-INV, isNVisNat, isSomeTerm-0, isSomeTerm-1, % 33.70/5.20 isSomeTerm-false-INV, isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, % 33.70/5.20 isValue-false-INV, isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, % 33.70/5.20 reduce-0, reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, % 33.70/5.20 reduce-15, reduce-16, reduce-17, reduce-2, reduce-22, reduce-23, reduce-3, % 33.70/5.20 reduce-6, reduce-7, reduce-9, reduce-INV % 33.70/5.20 % 33.70/5.20 Those formulas are unsatisfiable: % 33.70/5.20 --------------------------------- % 33.70/5.20 % 33.70/5.20 Begin of proof % 33.70/5.20 | % 33.70/5.20 | ALPHA: (DIFF-noTerm-someTerm) implies: % 33.70/5.20 | (1) ! [v0: vTerm] : ( ~ (vsomeTerm(v0) = vnoTerm) | ~ vTerm(v0)) % 33.70/5.20 | % 33.70/5.20 | ALPHA: (reduce-4) implies: % 33.70/5.20 | (2) ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vreduce(v0) = v1) | ~ % 33.70/5.20 | vTerm(v0) | ? [v2: any] : ? [v3: vTerm] : ? [v4: vOptTerm] : ? % 33.70/5.20 | [v5: vTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v3) = v4 % 33.70/5.20 | & visSomeTerm(v1) = v2 & vgetTerm(v1) = v5 & vsomeTerm(v6) = v7 & % 33.70/5.20 | vSucc(v5) = v6 & vSucc(v0) = v3 & vOptTerm(v7) & vOptTerm(v4) & % 33.70/5.20 | vTerm(v6) & vTerm(v5) & vTerm(v3) & ( ~ (v2 = 0) | v7 = v4))) % 33.70/5.20 | % 33.70/5.20 | ALPHA: (reduce-5) implies: % 33.70/5.20 | (3) ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vreduce(v0) = v1) | ~ % 33.70/5.20 | vTerm(v0) | ? [v2: any] : ? [v3: vTerm] : ? [v4: vOptTerm] : % 33.70/5.20 | (vreduce(v3) = v4 & visSomeTerm(v1) = v2 & vSucc(v0) = v3 & % 33.70/5.20 | vOptTerm(v4) & vTerm(v3) & (v4 = vnoTerm | v2 = 0))) % 33.70/5.20 | % 33.70/5.20 | ALPHA: (reduce-8) implies: % 33.70/5.20 | (4) ! [v0: vTerm] : ! [v1: int] : (v1 = 0 | ~ (visNV(v0) = v1) | ~ % 33.70/5.20 | vTerm(v0) | ? [v2: vTerm] : ? [v3: vOptTerm] : ? [v4: any] : ? % 33.70/5.20 | [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: vTerm] : % 33.70/5.20 | ? [v9: vOptTerm] : (vreduce(v5) = v6 & vreduce(v2) = v3 & % 33.70/5.20 | visSomeTerm(v3) = v4 & vgetTerm(v3) = v7 & vsomeTerm(v8) = v9 & % 33.70/5.20 | vPred(v7) = v8 & vPred(v2) = v5 & vSucc(v0) = v2 & vOptTerm(v9) & % 33.70/5.20 | vOptTerm(v6) & vOptTerm(v3) & vTerm(v8) & vTerm(v7) & vTerm(v5) & % 33.70/5.20 | vTerm(v2) & ( ~ (v4 = 0) | v9 = v6))) % 33.70/5.20 | % 33.70/5.20 | ALPHA: (reduce-18) implies: % 33.70/5.21 | (5) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = % 33.70/5.21 | v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : % 33.70/5.21 | ? [v5: vOptTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v2) % 33.70/5.21 | = v5 & vplusop(v0, v1) = v6 & visNV(v1) = v4 & visNV(v0) = v3 & % 33.70/5.21 | vsomeTerm(v6) = v7 & vOptTerm(v7) & vOptTerm(v5) & vTerm(v6) & ( ~ % 33.70/5.21 | (v4 = 0) | ~ (v3 = 0) | v7 = v5))) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (reduce-19) implies: % 33.70/5.21 | (6) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = % 33.70/5.21 | v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : % 33.70/5.21 | ? [v5: vOptTerm] : ? [v6: any] : ? [v7: vOptTerm] : ? [v8: vTerm] % 33.70/5.21 | : ? [v9: vTerm] : ? [v10: vOptTerm] : (vreduce(v2) = v7 & % 33.70/5.21 | vreduce(v1) = v5 & visSomeTerm(v5) = v6 & visNV(v1) = v4 & % 33.70/5.21 | visNV(v0) = v3 & vgetTerm(v5) = v8 & vsomeTerm(v9) = v10 & % 33.70/5.21 | vPlus(v0, v8) = v9 & vOptTerm(v10) & vOptTerm(v7) & vOptTerm(v5) & % 33.70/5.21 | vTerm(v9) & vTerm(v8) & ( ~ (v6 = 0) | ~ (v3 = 0) | v10 = v7 | v4 % 33.70/5.21 | = 0))) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (reduce-20) implies: % 33.70/5.21 | (7) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = % 33.70/5.21 | v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: any] : % 33.70/5.21 | ? [v5: vOptTerm] : ? [v6: any] : ? [v7: vOptTerm] : (vreduce(v2) = % 33.70/5.21 | v7 & vreduce(v1) = v5 & visSomeTerm(v5) = v6 & visNV(v1) = v4 & % 33.70/5.21 | visNV(v0) = v3 & vOptTerm(v7) & vOptTerm(v5) & ( ~ (v3 = 0) | v7 = % 33.70/5.21 | vnoTerm | v6 = 0 | v4 = 0))) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (reduce-21) implies: % 33.70/5.21 | (8) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPlus(v0, v1) = % 33.70/5.21 | v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? [v3: any] : ? [v4: % 33.70/5.21 | vOptTerm] : ? [v5: any] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? % 33.70/5.21 | [v8: vTerm] : ? [v9: vOptTerm] : (vreduce(v2) = v6 & vreduce(v0) = % 33.70/5.21 | v4 & visSomeTerm(v4) = v5 & visNV(v0) = v3 & vgetTerm(v4) = v7 & % 33.70/5.21 | vsomeTerm(v8) = v9 & vPlus(v7, v1) = v8 & vOptTerm(v9) & % 33.70/5.21 | vOptTerm(v6) & vOptTerm(v4) & vTerm(v8) & vTerm(v7) & ( ~ (v5 = 0) % 33.70/5.21 | | v9 = v6 | v3 = 0))) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (Progress-Plus-IH0) implies: % 33.70/5.21 | (9) ? [v0: any] : ? [v1: vOptTerm] : (vreduce(vt1) = v1 & visValue(vt1) = % 33.70/5.21 | v0 & vOptTerm(v1) & ! [v2: vTy] : ( ~ (v1 = vnoTerm) | v0 = 0 | ~ % 33.70/5.21 | (vptchecksimple(vt1, v2) = 0) | ~ vTy(v2))) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (Progress-Plus-isNV-False-isSomeTerm-True) implies: % 33.70/5.21 | (10) vTerm(vt2) % 33.70/5.21 | (11) vTerm(vt1) % 33.70/5.21 | (12) ? [v0: vOptTerm] : ? [v1: int] : ? [v2: vTerm] : ? [v3: int] : ? % 33.70/5.21 | [v4: vTy] : ( ~ (v3 = 0) & ~ (v1 = 0) & vptchecksimple(v2, v4) = 0 & % 33.70/5.21 | vreduce(v2) = vnoTerm & vreduce(vt1) = v0 & visSomeTerm(v0) = 0 & % 33.70/5.21 | visValue(v2) = v3 & visNV(vt1) = v1 & vPlus(vt1, vt2) = v2 & vTy(v4) % 33.70/5.21 | & vOptTerm(v0) & vTerm(v2)) % 33.70/5.21 | % 33.70/5.21 | ALPHA: (function-axioms) implies: % 33.70/5.22 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 33.70/5.22 | vTerm] : (v1 = v0 | ~ (visNV(v2) = v1) | ~ (visNV(v2) = v0)) % 33.70/5.22 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 33.70/5.22 | vOptTerm] : (v1 = v0 | ~ (visSomeTerm(v2) = v1) | ~ % 33.70/5.22 | (visSomeTerm(v2) = v0)) % 33.70/5.22 | (15) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 33.70/5.22 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 33.70/5.22 | % 33.70/5.22 | DELTA: instantiating (9) with fresh symbols all_107_0, all_107_1 gives: % 33.70/5.22 | (16) vreduce(vt1) = all_107_0 & visValue(vt1) = all_107_1 & % 33.70/5.22 | vOptTerm(all_107_0) & ! [v0: vTy] : ( ~ (all_107_0 = vnoTerm) | % 33.70/5.22 | all_107_1 = 0 | ~ (vptchecksimple(vt1, v0) = 0) | ~ vTy(v0)) % 33.70/5.22 | % 33.70/5.22 | ALPHA: (16) implies: % 33.70/5.22 | (17) vreduce(vt1) = all_107_0 % 33.70/5.22 | % 33.70/5.22 | DELTA: instantiating (12) with fresh symbols all_110_0, all_110_1, all_110_2, % 33.70/5.22 | all_110_3, all_110_4 gives: % 33.70/5.22 | (18) ~ (all_110_1 = 0) & ~ (all_110_3 = 0) & vptchecksimple(all_110_2, % 33.70/5.22 | all_110_0) = 0 & vreduce(all_110_2) = vnoTerm & vreduce(vt1) = % 33.70/5.22 | all_110_4 & visSomeTerm(all_110_4) = 0 & visValue(all_110_2) = % 33.70/5.22 | all_110_1 & visNV(vt1) = all_110_3 & vPlus(vt1, vt2) = all_110_2 & % 33.70/5.22 | vTy(all_110_0) & vOptTerm(all_110_4) & vTerm(all_110_2) % 33.70/5.22 | % 33.70/5.22 | ALPHA: (18) implies: % 33.70/5.22 | (19) ~ (all_110_3 = 0) % 33.70/5.22 | (20) vPlus(vt1, vt2) = all_110_2 % 33.70/5.22 | (21) visNV(vt1) = all_110_3 % 33.70/5.22 | (22) visSomeTerm(all_110_4) = 0 % 33.70/5.22 | (23) vreduce(vt1) = all_110_4 % 33.70/5.22 | (24) vreduce(all_110_2) = vnoTerm % 33.70/5.22 | % 33.70/5.22 | GROUND_INST: instantiating (15) with all_107_0, all_110_4, vt1, simplifying % 33.70/5.22 | with (17), (23) gives: % 33.70/5.22 | (25) all_110_4 = all_107_0 % 33.70/5.22 | % 33.70/5.22 | REDUCE: (22), (25) imply: % 33.70/5.22 | (26) visSomeTerm(all_107_0) = 0 % 33.70/5.22 | % 33.70/5.22 | GROUND_INST: instantiating (6) with vt1, vt2, all_110_2, simplifying with % 33.70/5.22 | (10), (11), (20) gives: % 33.70/5.22 | (27) ? [v0: any] : ? [v1: any] : ? [v2: vOptTerm] : ? [v3: any] : ? % 33.70/5.22 | [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : % 33.70/5.22 | (vreduce(all_110_2) = v4 & vreduce(vt2) = v2 & visSomeTerm(v2) = v3 & % 33.70/5.22 | visNV(vt1) = v0 & visNV(vt2) = v1 & vgetTerm(v2) = v5 & % 33.70/5.22 | vsomeTerm(v6) = v7 & vPlus(vt1, v5) = v6 & vOptTerm(v7) & % 33.70/5.22 | vOptTerm(v4) & vOptTerm(v2) & vTerm(v6) & vTerm(v5) & ( ~ (v3 = 0) | % 33.70/5.22 | ~ (v0 = 0) | v7 = v4 | v1 = 0)) % 33.70/5.22 | % 33.70/5.22 | GROUND_INST: instantiating (8) with vt1, vt2, all_110_2, simplifying with % 33.70/5.22 | (10), (11), (20) gives: % 33.70/5.23 | (28) ? [v0: any] : ? [v1: vOptTerm] : ? [v2: any] : ? [v3: vOptTerm] : % 33.70/5.23 | ? [v4: vTerm] : ? [v5: vTerm] : ? [v6: vOptTerm] : % 33.70/5.23 | (vreduce(all_110_2) = v3 & vreduce(vt1) = v1 & visSomeTerm(v1) = v2 & % 33.70/5.23 | visNV(vt1) = v0 & vgetTerm(v1) = v4 & vsomeTerm(v5) = v6 & vPlus(v4, % 33.70/5.23 | vt2) = v5 & vOptTerm(v6) & vOptTerm(v3) & vOptTerm(v1) & vTerm(v5) % 33.70/5.23 | & vTerm(v4) & ( ~ (v2 = 0) | v6 = v3 | v0 = 0)) % 33.70/5.23 | % 33.70/5.23 | GROUND_INST: instantiating (7) with vt1, vt2, all_110_2, simplifying with % 33.70/5.23 | (10), (11), (20) gives: % 33.70/5.23 | (29) ? [v0: any] : ? [v1: any] : ? [v2: vOptTerm] : ? [v3: any] : ? % 33.70/5.23 | [v4: vOptTerm] : (vreduce(all_110_2) = v4 & vreduce(vt2) = v2 & % 33.70/5.23 | visSomeTerm(v2) = v3 & visNV(vt1) = v0 & visNV(vt2) = v1 & % 33.70/5.23 | vOptTerm(v4) & vOptTerm(v2) & ( ~ (v0 = 0) | v4 = vnoTerm | v3 = 0 | % 33.70/5.23 | v1 = 0)) % 33.70/5.23 | % 33.70/5.23 | GROUND_INST: instantiating (5) with vt1, vt2, all_110_2, simplifying with % 33.70/5.23 | (10), (11), (20) gives: % 33.70/5.23 | (30) ? [v0: any] : ? [v1: any] : ? [v2: vOptTerm] : ? [v3: vTerm] : ? % 33.70/5.23 | [v4: vOptTerm] : (vreduce(all_110_2) = v2 & vplusop(vt1, vt2) = v3 & % 33.70/5.23 | visNV(vt1) = v0 & visNV(vt2) = v1 & vsomeTerm(v3) = v4 & % 33.70/5.23 | vOptTerm(v4) & vOptTerm(v2) & vTerm(v3) & ( ~ (v1 = 0) | ~ (v0 = 0) % 33.70/5.23 | | v4 = v2)) % 33.70/5.23 | % 33.70/5.23 | GROUND_INST: instantiating (4) with vt1, all_110_3, simplifying with (11), % 33.70/5.23 | (21) gives: % 33.70/5.23 | (31) all_110_3 = 0 | ? [v0: vTerm] : ? [v1: vOptTerm] : ? [v2: any] : ? % 33.70/5.23 | [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: vTerm] : ? % 33.70/5.23 | [v7: vOptTerm] : (vreduce(v3) = v4 & vreduce(v0) = v1 & % 33.70/5.23 | visSomeTerm(v1) = v2 & vgetTerm(v1) = v5 & vsomeTerm(v6) = v7 & % 33.70/5.23 | vPred(v5) = v6 & vPred(v0) = v3 & vSucc(vt1) = v0 & vOptTerm(v7) & % 33.70/5.23 | vOptTerm(v4) & vOptTerm(v1) & vTerm(v6) & vTerm(v5) & vTerm(v3) & % 33.70/5.23 | vTerm(v0) & ( ~ (v2 = 0) | v7 = v4)) % 33.70/5.23 | % 33.70/5.23 | GROUND_INST: instantiating (2) with vt1, all_107_0, simplifying with (11), % 33.70/5.23 | (17) gives: % 33.70/5.23 | (32) ? [v0: any] : ? [v1: vTerm] : ? [v2: vOptTerm] : ? [v3: vTerm] : % 33.70/5.23 | ? [v4: vTerm] : ? [v5: vOptTerm] : (vreduce(v1) = v2 & % 33.70/5.23 | visSomeTerm(all_107_0) = v0 & vgetTerm(all_107_0) = v3 & % 33.70/5.23 | vsomeTerm(v4) = v5 & vSucc(v3) = v4 & vSucc(vt1) = v1 & vOptTerm(v5) % 33.70/5.23 | & vOptTerm(v2) & vTerm(v4) & vTerm(v3) & vTerm(v1) & ( ~ (v0 = 0) | % 33.70/5.23 | v5 = v2)) % 33.70/5.23 | % 33.70/5.23 | GROUND_INST: instantiating (3) with vt1, all_107_0, simplifying with (11), % 33.70/5.23 | (17) gives: % 33.70/5.23 | (33) ? [v0: any] : ? [v1: vTerm] : ? [v2: vOptTerm] : (vreduce(v1) = v2 % 33.70/5.23 | & visSomeTerm(all_107_0) = v0 & vSucc(vt1) = v1 & vOptTerm(v2) & % 33.70/5.23 | vTerm(v1) & (v2 = vnoTerm | v0 = 0)) % 33.70/5.23 | % 33.70/5.23 | DELTA: instantiating (33) with fresh symbols all_158_0, all_158_1, all_158_2 % 33.70/5.23 | gives: % 33.70/5.23 | (34) vreduce(all_158_1) = all_158_0 & visSomeTerm(all_107_0) = all_158_2 & % 33.70/5.23 | vSucc(vt1) = all_158_1 & vOptTerm(all_158_0) & vTerm(all_158_1) & % 33.70/5.23 | (all_158_0 = vnoTerm | all_158_2 = 0) % 33.70/5.23 | % 33.70/5.23 | ALPHA: (34) implies: % 33.70/5.23 | (35) visSomeTerm(all_107_0) = all_158_2 % 33.70/5.23 | % 33.70/5.23 | DELTA: instantiating (30) with fresh symbols all_176_0, all_176_1, all_176_2, % 33.70/5.23 | all_176_3, all_176_4 gives: % 33.70/5.23 | (36) vreduce(all_110_2) = all_176_2 & vplusop(vt1, vt2) = all_176_1 & % 33.70/5.23 | visNV(vt1) = all_176_4 & visNV(vt2) = all_176_3 & vsomeTerm(all_176_1) % 33.70/5.23 | = all_176_0 & vOptTerm(all_176_0) & vOptTerm(all_176_2) & % 33.70/5.23 | vTerm(all_176_1) & ( ~ (all_176_3 = 0) | ~ (all_176_4 = 0) | % 33.70/5.23 | all_176_0 = all_176_2) % 33.70/5.23 | % 33.70/5.23 | ALPHA: (36) implies: % 33.70/5.23 | (37) vreduce(all_110_2) = all_176_2 % 33.70/5.23 | % 33.70/5.23 | DELTA: instantiating (29) with fresh symbols all_178_0, all_178_1, all_178_2, % 33.70/5.23 | all_178_3, all_178_4 gives: % 33.70/5.24 | (38) vreduce(all_110_2) = all_178_0 & vreduce(vt2) = all_178_2 & % 33.70/5.24 | visSomeTerm(all_178_2) = all_178_1 & visNV(vt1) = all_178_4 & % 33.70/5.24 | visNV(vt2) = all_178_3 & vOptTerm(all_178_0) & vOptTerm(all_178_2) & ( % 33.70/5.24 | ~ (all_178_4 = 0) | all_178_0 = vnoTerm | all_178_1 = 0 | all_178_3 % 33.70/5.24 | = 0) % 33.70/5.24 | % 33.70/5.24 | ALPHA: (38) implies: % 33.70/5.24 | (39) vreduce(all_110_2) = all_178_0 % 33.70/5.24 | % 33.70/5.24 | DELTA: instantiating (32) with fresh symbols all_180_0, all_180_1, all_180_2, % 33.70/5.24 | all_180_3, all_180_4, all_180_5 gives: % 33.70/5.24 | (40) vreduce(all_180_4) = all_180_3 & visSomeTerm(all_107_0) = all_180_5 & % 33.70/5.24 | vgetTerm(all_107_0) = all_180_2 & vsomeTerm(all_180_1) = all_180_0 & % 33.70/5.24 | vSucc(all_180_2) = all_180_1 & vSucc(vt1) = all_180_4 & % 33.70/5.24 | vOptTerm(all_180_0) & vOptTerm(all_180_3) & vTerm(all_180_1) & % 33.70/5.24 | vTerm(all_180_2) & vTerm(all_180_4) & ( ~ (all_180_5 = 0) | all_180_0 % 33.70/5.24 | = all_180_3) % 33.70/5.24 | % 33.70/5.24 | ALPHA: (40) implies: % 33.70/5.24 | (41) visSomeTerm(all_107_0) = all_180_5 % 33.70/5.24 | % 33.70/5.24 | DELTA: instantiating (28) with fresh symbols all_190_0, all_190_1, all_190_2, % 33.70/5.24 | all_190_3, all_190_4, all_190_5, all_190_6 gives: % 33.70/5.24 | (42) vreduce(all_110_2) = all_190_3 & vreduce(vt1) = all_190_5 & % 33.70/5.24 | visSomeTerm(all_190_5) = all_190_4 & visNV(vt1) = all_190_6 & % 33.70/5.24 | vgetTerm(all_190_5) = all_190_2 & vsomeTerm(all_190_1) = all_190_0 & % 33.70/5.24 | vPlus(all_190_2, vt2) = all_190_1 & vOptTerm(all_190_0) & % 33.70/5.24 | vOptTerm(all_190_3) & vOptTerm(all_190_5) & vTerm(all_190_1) & % 33.70/5.24 | vTerm(all_190_2) & ( ~ (all_190_4 = 0) | all_190_0 = all_190_3 | % 33.70/5.24 | all_190_6 = 0) % 33.70/5.24 | % 33.70/5.24 | ALPHA: (42) implies: % 33.70/5.24 | (43) vTerm(all_190_1) % 33.70/5.24 | (44) vsomeTerm(all_190_1) = all_190_0 % 33.70/5.24 | (45) visNV(vt1) = all_190_6 % 33.70/5.24 | (46) visSomeTerm(all_190_5) = all_190_4 % 33.70/5.24 | (47) vreduce(vt1) = all_190_5 % 33.70/5.24 | (48) vreduce(all_110_2) = all_190_3 % 33.70/5.24 | (49) ~ (all_190_4 = 0) | all_190_0 = all_190_3 | all_190_6 = 0 % 33.70/5.24 | % 33.70/5.24 | DELTA: instantiating (27) with fresh symbols all_192_0, all_192_1, all_192_2, % 33.70/5.24 | all_192_3, all_192_4, all_192_5, all_192_6, all_192_7 gives: % 33.70/5.24 | (50) vreduce(all_110_2) = all_192_3 & vreduce(vt2) = all_192_5 & % 33.70/5.24 | visSomeTerm(all_192_5) = all_192_4 & visNV(vt1) = all_192_7 & % 33.70/5.24 | visNV(vt2) = all_192_6 & vgetTerm(all_192_5) = all_192_2 & % 33.70/5.24 | vsomeTerm(all_192_1) = all_192_0 & vPlus(vt1, all_192_2) = all_192_1 & % 33.70/5.24 | vOptTerm(all_192_0) & vOptTerm(all_192_3) & vOptTerm(all_192_5) & % 33.70/5.24 | vTerm(all_192_1) & vTerm(all_192_2) & ( ~ (all_192_4 = 0) | ~ % 33.70/5.24 | (all_192_7 = 0) | all_192_0 = all_192_3 | all_192_6 = 0) % 33.70/5.24 | % 33.70/5.24 | ALPHA: (50) implies: % 33.70/5.24 | (51) visNV(vt1) = all_192_7 % 33.70/5.24 | (52) vreduce(all_110_2) = all_192_3 % 33.70/5.24 | % 33.70/5.24 | BETA: splitting (31) gives: % 33.70/5.24 | % 33.70/5.24 | Case 1: % 33.70/5.24 | | % 33.70/5.24 | | (53) all_110_3 = 0 % 33.70/5.24 | | % 33.70/5.24 | | REDUCE: (19), (53) imply: % 33.70/5.24 | | (54) $false % 33.70/5.24 | | % 33.70/5.24 | | CLOSE: (54) is inconsistent. % 33.70/5.24 | | % 33.70/5.24 | Case 2: % 33.70/5.24 | | % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (13) with all_110_3, all_192_7, vt1, simplifying % 33.70/5.24 | | with (21), (51) gives: % 33.70/5.24 | | (55) all_192_7 = all_110_3 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (13) with all_190_6, all_192_7, vt1, simplifying % 33.70/5.24 | | with (45), (51) gives: % 33.70/5.24 | | (56) all_192_7 = all_190_6 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (14) with 0, all_180_5, all_107_0, simplifying % 33.70/5.24 | | with (26), (41) gives: % 33.70/5.24 | | (57) all_180_5 = 0 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (14) with all_158_2, all_180_5, all_107_0, % 33.70/5.24 | | simplifying with (35), (41) gives: % 33.70/5.24 | | (58) all_180_5 = all_158_2 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (15) with all_107_0, all_190_5, vt1, simplifying % 33.70/5.24 | | with (17), (47) gives: % 33.70/5.24 | | (59) all_190_5 = all_107_0 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (15) with vnoTerm, all_190_3, all_110_2, % 33.70/5.24 | | simplifying with (24), (48) gives: % 33.70/5.24 | | (60) all_190_3 = vnoTerm % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (15) with all_176_2, all_190_3, all_110_2, % 33.70/5.24 | | simplifying with (37), (48) gives: % 33.70/5.24 | | (61) all_190_3 = all_176_2 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (15) with all_190_3, all_192_3, all_110_2, % 33.70/5.24 | | simplifying with (48), (52) gives: % 33.70/5.24 | | (62) all_192_3 = all_190_3 % 33.70/5.24 | | % 33.70/5.24 | | GROUND_INST: instantiating (15) with all_178_0, all_192_3, all_110_2, % 33.70/5.24 | | simplifying with (39), (52) gives: % 33.70/5.24 | | (63) all_192_3 = all_178_0 % 33.70/5.24 | | % 33.70/5.24 | | COMBINE_EQS: (62), (63) imply: % 33.70/5.24 | | (64) all_190_3 = all_178_0 % 33.70/5.24 | | % 33.70/5.24 | | SIMP: (64) implies: % 33.70/5.24 | | (65) all_190_3 = all_178_0 % 33.70/5.24 | | % 33.70/5.24 | | COMBINE_EQS: (55), (56) imply: % 33.70/5.24 | | (66) all_190_6 = all_110_3 % 33.70/5.24 | | % 33.70/5.24 | | COMBINE_EQS: (60), (65) imply: % 33.70/5.24 | | (67) all_178_0 = vnoTerm % 33.70/5.24 | | % 33.70/5.24 | | COMBINE_EQS: (61), (65) imply: % 33.70/5.24 | | (68) all_178_0 = all_176_2 % 33.70/5.24 | | % 33.70/5.24 | | COMBINE_EQS: (57), (58) imply: % 33.70/5.24 | | (69) all_158_2 = 0 % 33.70/5.24 | | % 33.70/5.24 | | SIMP: (69) implies: % 33.70/5.25 | | (70) all_158_2 = 0 % 33.70/5.25 | | % 33.70/5.25 | | COMBINE_EQS: (67), (68) imply: % 33.70/5.25 | | (71) all_176_2 = vnoTerm % 33.70/5.25 | | % 33.70/5.25 | | REDUCE: (46), (59) imply: % 33.70/5.25 | | (72) visSomeTerm(all_107_0) = all_190_4 % 33.70/5.25 | | % 33.70/5.25 | | GROUND_INST: instantiating (14) with 0, all_190_4, all_107_0, simplifying % 33.70/5.25 | | with (26), (72) gives: % 33.70/5.25 | | (73) all_190_4 = 0 % 33.70/5.25 | | % 33.70/5.25 | | BETA: splitting (49) gives: % 33.70/5.25 | | % 33.70/5.25 | | Case 1: % 33.70/5.25 | | | % 33.70/5.25 | | | (74) ~ (all_190_4 = 0) % 33.70/5.25 | | | % 33.70/5.25 | | | REDUCE: (73), (74) imply: % 33.70/5.25 | | | (75) $false % 33.70/5.25 | | | % 33.70/5.25 | | | CLOSE: (75) is inconsistent. % 33.70/5.25 | | | % 33.70/5.25 | | Case 2: % 33.70/5.25 | | | % 33.70/5.25 | | | (76) all_190_0 = all_190_3 | all_190_6 = 0 % 33.70/5.25 | | | % 33.70/5.25 | | | BETA: splitting (76) gives: % 33.70/5.25 | | | % 33.70/5.25 | | | Case 1: % 33.70/5.25 | | | | % 33.70/5.25 | | | | (77) all_190_6 = 0 % 33.70/5.25 | | | | % 33.70/5.25 | | | | COMBINE_EQS: (66), (77) imply: % 33.70/5.25 | | | | (78) all_110_3 = 0 % 33.70/5.25 | | | | % 33.70/5.25 | | | | REDUCE: (19), (78) imply: % 33.70/5.25 | | | | (79) $false % 33.70/5.25 | | | | % 33.70/5.25 | | | | CLOSE: (79) is inconsistent. % 33.70/5.25 | | | | % 33.70/5.25 | | | Case 2: % 33.70/5.25 | | | | % 33.70/5.25 | | | | (80) all_190_0 = all_190_3 % 33.70/5.25 | | | | % 33.70/5.25 | | | | COMBINE_EQS: (60), (80) imply: % 33.70/5.25 | | | | (81) all_190_0 = vnoTerm % 33.70/5.25 | | | | % 33.70/5.25 | | | | REDUCE: (44), (81) imply: % 33.70/5.25 | | | | (82) vsomeTerm(all_190_1) = vnoTerm % 33.70/5.25 | | | | % 33.70/5.25 | | | | GROUND_INST: instantiating (1) with all_190_1, simplifying with (43), % 33.70/5.25 | | | | (82) gives: % 33.70/5.25 | | | | (83) $false % 33.70/5.25 | | | | % 33.70/5.25 | | | | CLOSE: (83) is inconsistent. % 33.70/5.25 | | | | % 33.70/5.25 | | | End of split % 33.70/5.25 | | | % 33.70/5.25 | | End of split % 33.70/5.25 | | % 33.70/5.25 | End of split % 33.70/5.25 | % 33.70/5.25 End of proof % 33.70/5.25 % SZS output end Proof for theBenchmark % 33.70/5.25 % 33.70/5.25 4650ms %------------------------------------------------------------------------------