%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 13:58:01 EDT 2023 % Result : Theorem 30.89s 5.06s % Output : Proof 36.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.18 % Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0. % 0.09/0.19 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.41 % Computer : n010.cluster.edu % 0.17/0.41 % Model : x86_64 x86_64 % 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.41 % Memory : 8042.1875MB % 0.17/0.41 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.41 % CPULimit : 300 % 0.17/0.41 % WCLimit : 300 % 0.17/0.41 % DateTime : Sun Aug 27 01:57:05 EDT 2023 % 0.17/0.41 % CPUTime : % 0.24/0.70 ________ _____ % 0.24/0.70 ___ __ \_________(_)________________________________ % 0.24/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.24/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.24/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.24/0.70 % 0.24/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.24/0.70 (2023-06-19) % 0.24/0.70 % 0.24/0.70 (c) Philipp Rümmer, 2009-2023 % 0.24/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.24/0.70 Amanda Stjerna. % 0.24/0.70 Free software under BSD-3-Clause. % 0.24/0.70 % 0.24/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.24/0.70 % 0.24/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.24/0.72 Running up to 7 provers in parallel. % 0.24/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.24/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.24/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.24/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.24/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.24/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.24/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.56/1.48 Prover 1: Preprocessing ... % 3.56/1.48 Prover 4: Preprocessing ... % 4.79/1.53 Prover 6: Preprocessing ... % 4.79/1.53 Prover 0: Preprocessing ... % 4.79/1.53 Prover 3: Preprocessing ... % 4.79/1.54 Prover 5: Preprocessing ... % 4.79/1.55 Prover 2: Preprocessing ... % 12.32/2.57 Prover 3: Constructing countermodel ... % 12.32/2.57 Prover 1: Constructing countermodel ... % 12.32/2.59 Prover 6: Proving ... % 12.32/2.60 Prover 5: Proving ... % 12.92/2.66 Prover 2: Proving ... % 13.78/2.82 Prover 4: Constructing countermodel ... % 13.78/2.90 Prover 0: Proving ... % 30.89/5.05 Prover 3: proved (4323ms) % 30.89/5.06 % 30.89/5.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.89/5.06 % 30.89/5.06 Prover 2: stopped % 30.89/5.06 Prover 5: stopped % 30.89/5.06 Prover 0: stopped % 30.89/5.06 Prover 6: stopped % 30.89/5.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 30.89/5.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 30.89/5.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 30.89/5.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 30.89/5.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 33.05/5.30 Prover 13: Preprocessing ... % 33.05/5.33 Prover 11: Preprocessing ... % 33.05/5.35 Prover 7: Preprocessing ... % 33.05/5.35 Prover 8: Preprocessing ... % 33.05/5.36 Prover 10: Preprocessing ... % 34.10/5.56 Prover 7: Constructing countermodel ... % 35.40/5.61 Prover 10: Constructing countermodel ... % 35.40/5.62 Prover 8: Warning: ignoring some quantifiers % 35.40/5.63 Prover 8: Constructing countermodel ... % 35.40/5.63 Prover 13: Warning: ignoring some quantifiers % 35.40/5.67 Prover 13: Constructing countermodel ... % 36.00/5.72 Prover 1: Found proof (size 76) % 36.00/5.72 Prover 1: proved (4993ms) % 36.00/5.72 Prover 10: stopped % 36.00/5.72 Prover 4: stopped % 36.00/5.72 Prover 8: stopped % 36.00/5.72 Prover 13: stopped % 36.00/5.72 Prover 7: stopped % 36.00/5.75 Prover 11: Constructing countermodel ... % 36.00/5.76 Prover 11: stopped % 36.00/5.76 % 36.00/5.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.00/5.76 % 36.51/5.77 % SZS output start Proof for theBenchmark % 36.51/5.77 Assumptions after simplification: % 36.51/5.77 --------------------------------- % 36.51/5.77 % 36.51/5.77 (mDefIdeal) % 36.58/5.80 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ? % 36.58/5.80 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2, % 36.58/5.80 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 36.58/5.80 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 & % 36.58/5.80 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : % 36.58/5.80 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, % 36.58/5.80 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : ( % 36.58/5.80 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~ % 36.58/5.80 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : ! % 36.58/5.80 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2, % 36.58/5.80 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & % 36.58/5.80 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 36.58/5.80 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | % 36.58/5.80 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = % 36.58/5.80 v5)))))) % 36.58/5.80 % 36.58/5.80 (m__) % 36.58/5.80 $i(xr) & $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 36.58/5.80 ( ~ (v2 = 0) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & aElementOf0(xr, xI) = % 36.58/5.80 v2 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (aElementOf0(v4, v1) % 36.58/5.80 = 0) | ~ (aElementOf0(v3, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: % 36.58/5.80 $i] : ( ~ (v5 = xr) & sdtpldt0(v3, v4) = v5 & $i(v5)))) % 36.58/5.80 % 36.58/5.80 (m__2174) % 36.58/5.81 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 36.58/5.81 slsdtgt0(xa) = v0 & aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0 % 36.58/5.81 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 36.58/5.81 (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xb, % 36.58/5.81 v4) = v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) % 36.58/5.81 = v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 36.58/5.81 v0) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xa, v4) = v2) | ~ % 36.58/5.81 $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = v5))) & ! [v2: % 36.58/5.81 $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ $i(v2) | % 36.58/5.81 ! [v4: $i] : ! [v5: $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ % 36.58/5.81 (aElementOf0(v4, v0) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: $i] : ( ~ % 36.58/5.81 (v6 = v2) & sdtpldt0(v4, v5) = v6 & $i(v6)))) & ! [v2: $i] : ( ~ % 36.58/5.81 (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xb, v3) = % 36.58/5.81 v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ (aElementOf0(v2, % 36.58/5.81 v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & % 36.58/5.81 aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ (aElementOf0(v2, xI) = % 36.58/5.81 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (aElementOf0(v4, v1) = 0 & % 36.58/5.81 aElementOf0(v3, v0) = 0 & sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3))) & ! % 36.58/5.81 [v2: $i] : ( ~ (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ( ! [v3: $i] : ! % 36.58/5.81 [v4: $i] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? % 36.58/5.81 [v6: any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( ~ (v5 = % 36.58/5.81 0) | v6 = 0))) & ! [v3: $i] : ( ~ (aElementOf0(v3, xI) = 0) | % 36.58/5.81 ~ $i(v3) | ? [v4: $i] : (aElementOf0(v4, xI) = 0 & sdtpldt0(v2, v3) = % 36.58/5.81 v4 & $i(v4)))))) % 36.58/5.81 % 36.58/5.81 (m__2203) % 36.58/5.81 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 36.58/5.81 slsdtgt0(xa) = v0 & aElementOf0(xb, v1) = 0 & aElementOf0(xa, v0) = 0 & % 36.58/5.81 aElementOf0(sz00, v1) = 0 & aElementOf0(sz00, v0) = 0 & $i(v1) & $i(v0) & ? % 36.58/5.81 [v2: $i] : (sdtasdt0(xb, v2) = xb & aElement0(v2) = 0 & $i(v2)) & ? [v2: % 36.58/5.81 $i] : (sdtasdt0(xb, v2) = sz00 & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] % 36.58/5.81 : (sdtasdt0(xa, v2) = xa & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] : % 36.58/5.81 (sdtasdt0(xa, v2) = sz00 & aElement0(v2) = 0 & $i(v2))) % 36.58/5.81 % 36.58/5.81 (m__2228) % 36.72/5.81 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 36.72/5.81 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & % 36.72/5.81 $i(v1) & $i(v0) & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & % 36.72/5.81 $i(v3) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = % 36.72/5.81 v5) | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xb, v6) = v4) | ~ % 36.72/5.81 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & ! [v4: % 36.72/5.81 $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v0) = v5) | ~ $i(v4) % 36.72/5.81 | ! [v6: $i] : ( ~ (sdtasdt0(xa, v6) = v4) | ~ $i(v6) | ? [v7: int] : % 36.72/5.81 ( ~ (v7 = 0) & aElement0(v6) = v7))) & ! [v4: $i] : ( ~ % 36.72/5.81 (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: $i] : (sdtasdt0(xb, v5) % 36.72/5.81 = v4 & aElement0(v5) = 0 & $i(v5))) & ! [v4: $i] : ( ~ % 36.72/5.81 (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ? [v5: $i] : (sdtasdt0(xa, v5) % 36.72/5.81 = v4 & aElement0(v5) = 0 & $i(v5))) & ? [v4: $i] : ? [v5: $i] : % 36.72/5.81 (aElementOf0(v5, v1) = 0 & aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 % 36.72/5.81 & $i(v5) & $i(v4)))) % 36.72/5.81 % 36.72/5.81 (m__2273) % 36.72/5.82 $i(xu) & $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 36.72/5.82 [v2: $i] : ( ~ (xu = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 36.72/5.82 sbrdtbr0(xu) = v2 & aElementOf0(xu, xI) = 0 & $i(v2) & $i(v1) & $i(v0) & ! % 36.72/5.82 [v3: $i] : ! [v4: any] : (v3 = sz00 | ~ (aElementOf0(v3, xI) = v4) | ~ % 36.72/5.82 $i(v3) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & iLess0(v5, v2) = v6 & % 36.72/5.82 sbrdtbr0(v3) = v5 & $i(v5)) | ( ~ (v4 = 0) & ! [v5: $i] : ! [v6: $i] : % 36.72/5.82 ( ~ (aElementOf0(v6, v1) = 0) | ~ (aElementOf0(v5, v0) = 0) | ~ $i(v6) % 36.72/5.82 | ~ $i(v5) | ? [v7: $i] : ( ~ (v7 = v3) & sdtpldt0(v5, v6) = v7 & % 36.72/5.82 $i(v7))))) & ? [v3: $i] : ? [v4: $i] : (aElementOf0(v4, v1) = 0 & % 36.72/5.82 aElementOf0(v3, v0) = 0 & sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3))) % 36.72/5.82 % 36.72/5.82 (m__2666) % 36.72/5.82 $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 36.72/5.82 [v2: $i] : ? [v3: any] : (iLess0(v1, v2) = v3 & sbrdtbr0(xr) = v1 & % 36.72/5.82 sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb & % 36.72/5.82 aElement0(xr) = 0 & aElement0(xq) = 0 & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | % 36.72/5.82 xr = sz00)) % 36.72/5.82 % 36.72/5.82 (m__2690) % 36.72/5.82 $i(xq) & $i(xu) & $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? % 36.72/5.82 [v2: $i] : ? [v3: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 36.72/5.82 aElementOf0(v3, xI) = 0 & sdtasdt0(xq, xu) = v2 & smndt0(v2) = v3 & $i(v3) & % 36.72/5.82 $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] : ? [v5: $i] : (aElementOf0(v5, v1) % 36.72/5.82 = 0 & aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4))) % 36.72/5.82 % 36.72/5.82 (m__2699) % 36.72/5.82 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 36.72/5.82 slsdtgt0(xa) = v0 & aElementOf0(xb, xI) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 36.72/5.82 : ? [v3: $i] : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 & % 36.72/5.82 sdtpldt0(v2, v3) = xb & $i(v3) & $i(v2))) % 36.72/5.82 % 36.72/5.82 (m__2718) % 36.72/5.82 $i(xr) & $i(xq) & $i(xu) & $i(xb) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, % 36.72/5.82 xu) = v0 & sdtpldt0(v1, xb) = xr & smndt0(v0) = v1 & $i(v1) & $i(v0)) % 36.72/5.82 % 36.72/5.82 (function-axioms) % 36.72/5.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 36.72/5.82 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~ % 36.72/5.82 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.72/5.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 36.72/5.82 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, % 36.72/5.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 36.72/5.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) | % 36.72/5.82 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.72/5.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.72/5.82 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: % 36.72/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 36.72/5.82 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 36.72/5.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 36.72/5.82 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 36.72/5.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.72/5.82 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 36.72/5.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 36.72/5.82 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.72/5.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.72/5.82 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 36.72/5.82 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 36.72/5.82 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 36.72/5.82 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 36.72/5.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) % 36.72/5.82 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 36.72/5.82 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: % 36.72/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 36.72/5.82 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0: % 36.72/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 36.72/5.82 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : % 36.72/5.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 36.72/5.82 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 36.72/5.82 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 36.72/5.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 36.72/5.82 ~ (aElement0(v2) = v0)) % 36.72/5.82 % 36.72/5.82 Further assumptions not needed in the proof: % 36.72/5.82 -------------------------------------------- % 36.72/5.82 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 36.72/5.82 mDefDiv, mDefDvs, mDefGCD, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, mDefSSum, % 36.72/5.82 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm, % 36.72/5.82 mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, % 36.72/5.82 mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2091, m__2110, % 36.72/5.82 m__2129, m__2383, m__2416, m__2479, m__2612, m__2673 % 36.72/5.82 % 36.72/5.82 Those formulas are unsatisfiable: % 36.72/5.82 --------------------------------- % 36.72/5.82 % 36.72/5.82 Begin of proof % 36.79/5.83 | % 36.79/5.83 | ALPHA: (mDefIdeal) implies: % 36.79/5.83 | (1) ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! % 36.79/5.83 | [v1: $i] : ( ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] % 36.79/5.83 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 36.79/5.83 | v0) = v4) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ? % 36.79/5.83 | [v5: int] : ( ~ (v5 = 0) & aElement0(v2) = v5)) & ! [v2: $i] % 36.79/5.83 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 36.79/5.83 | v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ? % 36.79/5.83 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = v5)))))) % 36.79/5.83 | % 36.79/5.83 | ALPHA: (m__2174) implies: % 36.79/5.83 | (2) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 36.79/5.83 | aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0 & $i(v1) & % 36.79/5.83 | $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 36.79/5.83 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xb, v4) = % 36.79/5.83 | v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = % 36.79/5.83 | v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 36.79/5.83 | (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ % 36.79/5.83 | (sdtasdt0(xa, v4) = v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) % 36.79/5.83 | & aElement0(v4) = v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 % 36.79/5.83 | | ~ (aElementOf0(v2, xI) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: % 36.79/5.83 | $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ (aElementOf0(v4, v0) = % 36.79/5.83 | 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: $i] : ( ~ (v6 = v2) & % 36.79/5.83 | sdtpldt0(v4, v5) = v6 & $i(v6)))) & ! [v2: $i] : ( ~ % 36.79/5.83 | (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xb, % 36.79/5.83 | v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ % 36.79/5.83 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xa, % 36.79/5.83 | v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ % 36.79/5.83 | (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : % 36.79/5.83 | (aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 & sdtpldt0(v3, % 36.79/5.83 | v4) = v2 & $i(v4) & $i(v3))) & ! [v2: $i] : ( ~ % 36.79/5.83 | (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ( ! [v3: $i] : ! [v4: $i] % 36.79/5.83 | : ( ~ (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? % 36.79/5.83 | [v6: any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( % 36.79/5.83 | ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] : ( ~ (aElementOf0(v3, % 36.79/5.83 | xI) = 0) | ~ $i(v3) | ? [v4: $i] : (aElementOf0(v4, xI) = % 36.79/5.83 | 0 & sdtpldt0(v2, v3) = v4 & $i(v4)))))) % 36.79/5.83 | % 36.79/5.83 | ALPHA: (m__2203) implies: % 36.79/5.83 | (3) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 36.79/5.83 | aElementOf0(xb, v1) = 0 & aElementOf0(xa, v0) = 0 & aElementOf0(sz00, % 36.79/5.83 | v1) = 0 & aElementOf0(sz00, v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 36.79/5.83 | : (sdtasdt0(xb, v2) = xb & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] % 36.79/5.83 | : (sdtasdt0(xb, v2) = sz00 & aElement0(v2) = 0 & $i(v2)) & ? [v2: % 36.79/5.83 | $i] : (sdtasdt0(xa, v2) = xa & aElement0(v2) = 0 & $i(v2)) & ? % 36.79/5.83 | [v2: $i] : (sdtasdt0(xa, v2) = sz00 & aElement0(v2) = 0 & $i(v2))) % 36.79/5.83 | % 36.79/5.83 | ALPHA: (m__2228) implies: % 36.79/5.84 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xb) = v1 & % 36.79/5.84 | slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 36.79/5.84 | & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & $i(v3) & % 36.79/5.84 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = v5) % 36.79/5.84 | | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xb, v6) = v4) | ~ % 36.79/5.84 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & % 36.79/5.84 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v0) = v5) % 36.79/5.84 | | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xa, v6) = v4) | ~ % 36.79/5.84 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & % 36.79/5.84 | ! [v4: $i] : ( ~ (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: % 36.79/5.84 | $i] : (sdtasdt0(xb, v5) = v4 & aElement0(v5) = 0 & $i(v5))) & % 36.79/5.84 | ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ? [v5: % 36.79/5.84 | $i] : (sdtasdt0(xa, v5) = v4 & aElement0(v5) = 0 & $i(v5))) & % 36.79/5.84 | ? [v4: $i] : ? [v5: $i] : (aElementOf0(v5, v1) = 0 & % 36.79/5.84 | aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & % 36.79/5.84 | $i(v4)))) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__2273) implies: % 36.79/5.84 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (xu = sz00) & % 36.79/5.84 | slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sbrdtbr0(xu) = v2 & % 36.79/5.84 | aElementOf0(xu, xI) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 36.79/5.84 | [v4: any] : (v3 = sz00 | ~ (aElementOf0(v3, xI) = v4) | ~ $i(v3) | % 36.79/5.84 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & iLess0(v5, v2) = v6 & % 36.79/5.84 | sbrdtbr0(v3) = v5 & $i(v5)) | ( ~ (v4 = 0) & ! [v5: $i] : ! % 36.79/5.84 | [v6: $i] : ( ~ (aElementOf0(v6, v1) = 0) | ~ (aElementOf0(v5, % 36.79/5.84 | v0) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ( ~ (v7 = % 36.79/5.84 | v3) & sdtpldt0(v5, v6) = v7 & $i(v7))))) & ? [v3: $i] : ? % 36.79/5.84 | [v4: $i] : (aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 & % 36.79/5.84 | sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3))) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__2666) implies: % 36.79/5.84 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (iLess0(v1, % 36.79/5.84 | v2) = v3 & sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) % 36.79/5.84 | = v0 & sdtpldt0(v0, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 % 36.79/5.84 | & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | xr = sz00)) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__2690) implies: % 36.79/5.84 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (slsdtgt0(xb) = % 36.79/5.84 | v1 & slsdtgt0(xa) = v0 & aElementOf0(v3, xI) = 0 & sdtasdt0(xq, xu) = % 36.79/5.84 | v2 & smndt0(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: % 36.79/5.84 | $i] : ? [v5: $i] : (aElementOf0(v5, v1) = 0 & aElementOf0(v4, v0) % 36.79/5.84 | = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4))) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__2699) implies: % 36.79/5.84 | (8) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 36.79/5.84 | aElementOf0(xb, xI) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] % 36.79/5.84 | : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 & sdtpldt0(v2, % 36.79/5.84 | v3) = xb & $i(v3) & $i(v2))) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__2718) implies: % 36.79/5.84 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xu) = v0 & sdtpldt0(v1, xb) = % 36.79/5.84 | xr & smndt0(v0) = v1 & $i(v1) & $i(v0)) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (m__) implies: % 36.79/5.84 | (10) $i(xb) % 36.79/5.84 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & slsdtgt0(xb) % 36.79/5.84 | = v1 & slsdtgt0(xa) = v0 & aElementOf0(xr, xI) = v2 & $i(v1) & % 36.79/5.84 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (aElementOf0(v4, v1) = 0) | % 36.79/5.84 | ~ (aElementOf0(v3, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: $i] % 36.79/5.84 | : ( ~ (v5 = xr) & sdtpldt0(v3, v4) = v5 & $i(v5)))) % 36.79/5.84 | % 36.79/5.84 | ALPHA: (function-axioms) implies: % 36.79/5.85 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 36.79/5.85 | v1) | ~ (smndt0(v2) = v0)) % 36.79/5.85 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 36.79/5.85 | = v1) | ~ (slsdtgt0(v2) = v0)) % 36.79/5.85 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.79/5.85 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 36.79/5.85 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 36.79/5.85 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 36.79/5.85 | (aElementOf0(v3, v2) = v0)) % 36.79/5.85 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.79/5.85 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (9) with fresh symbols all_41_0, all_41_1 gives: % 36.79/5.85 | (17) sdtasdt0(xq, xu) = all_41_1 & sdtpldt0(all_41_0, xb) = xr & % 36.79/5.85 | smndt0(all_41_1) = all_41_0 & $i(all_41_0) & $i(all_41_1) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (17) implies: % 36.79/5.85 | (18) smndt0(all_41_1) = all_41_0 % 36.79/5.85 | (19) sdtpldt0(all_41_0, xb) = xr % 36.79/5.85 | (20) sdtasdt0(xq, xu) = all_41_1 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (8) with fresh symbols all_48_0, all_48_1 gives: % 36.79/5.85 | (21) slsdtgt0(xb) = all_48_0 & slsdtgt0(xa) = all_48_1 & aElementOf0(xb, % 36.79/5.85 | xI) = 0 & $i(all_48_0) & $i(all_48_1) & ? [v0: $i] : ? [v1: $i] : % 36.79/5.85 | (aElementOf0(v1, all_48_0) = 0 & aElementOf0(v0, all_48_1) = 0 & % 36.79/5.85 | sdtpldt0(v0, v1) = xb & $i(v1) & $i(v0)) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (21) implies: % 36.79/5.85 | (22) aElementOf0(xb, xI) = 0 % 36.79/5.85 | (23) slsdtgt0(xa) = all_48_1 % 36.79/5.85 | (24) slsdtgt0(xb) = all_48_0 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (6) with fresh symbols all_50_0, all_50_1, all_50_2, % 36.79/5.85 | all_50_3 gives: % 36.79/5.85 | (25) iLess0(all_50_2, all_50_1) = all_50_0 & sbrdtbr0(xr) = all_50_2 & % 36.79/5.85 | sbrdtbr0(xu) = all_50_1 & sdtasdt0(xq, xu) = all_50_3 & % 36.79/5.85 | sdtpldt0(all_50_3, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 & % 36.79/5.85 | $i(all_50_1) & $i(all_50_2) & $i(all_50_3) & (all_50_0 = 0 | xr = % 36.79/5.85 | sz00) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (25) implies: % 36.79/5.85 | (26) sdtasdt0(xq, xu) = all_50_3 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (11) with fresh symbols all_55_0, all_55_1, all_55_2 % 36.79/5.85 | gives: % 36.79/5.85 | (27) ~ (all_55_0 = 0) & slsdtgt0(xb) = all_55_1 & slsdtgt0(xa) = all_55_2 % 36.79/5.85 | & aElementOf0(xr, xI) = all_55_0 & $i(all_55_1) & $i(all_55_2) & ! % 36.79/5.85 | [v0: $i] : ! [v1: $i] : ( ~ (aElementOf0(v1, all_55_1) = 0) | ~ % 36.79/5.85 | (aElementOf0(v0, all_55_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 36.79/5.85 | $i] : ( ~ (v2 = xr) & sdtpldt0(v0, v1) = v2 & $i(v2))) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (27) implies: % 36.79/5.85 | (28) ~ (all_55_0 = 0) % 36.79/5.85 | (29) aElementOf0(xr, xI) = all_55_0 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (7) with fresh symbols all_58_0, all_58_1, all_58_2, % 36.79/5.85 | all_58_3 gives: % 36.79/5.85 | (30) slsdtgt0(xb) = all_58_2 & slsdtgt0(xa) = all_58_3 & % 36.79/5.85 | aElementOf0(all_58_0, xI) = 0 & sdtasdt0(xq, xu) = all_58_1 & % 36.79/5.85 | smndt0(all_58_1) = all_58_0 & $i(all_58_0) & $i(all_58_1) & % 36.79/5.85 | $i(all_58_2) & $i(all_58_3) & ? [v0: $i] : ? [v1: $i] : % 36.79/5.85 | (aElementOf0(v1, all_58_2) = 0 & aElementOf0(v0, all_58_3) = 0 & % 36.79/5.85 | sdtpldt0(v0, v1) = all_58_0 & $i(v1) & $i(v0)) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (30) implies: % 36.79/5.85 | (31) $i(all_58_0) % 36.79/5.85 | (32) smndt0(all_58_1) = all_58_0 % 36.79/5.85 | (33) sdtasdt0(xq, xu) = all_58_1 % 36.79/5.85 | (34) aElementOf0(all_58_0, xI) = 0 % 36.79/5.85 | (35) slsdtgt0(xb) = all_58_2 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (3) with fresh symbols all_62_0, all_62_1 gives: % 36.79/5.85 | (36) slsdtgt0(xb) = all_62_0 & slsdtgt0(xa) = all_62_1 & aElementOf0(xb, % 36.79/5.85 | all_62_0) = 0 & aElementOf0(xa, all_62_1) = 0 & aElementOf0(sz00, % 36.79/5.85 | all_62_0) = 0 & aElementOf0(sz00, all_62_1) = 0 & $i(all_62_0) & % 36.79/5.85 | $i(all_62_1) & ? [v0: $i] : (sdtasdt0(xb, v0) = xb & aElement0(v0) = % 36.79/5.85 | 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xb, v0) = sz00 & aElement0(v0) % 36.79/5.85 | = 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xa, v0) = xa & aElement0(v0) % 36.79/5.85 | = 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xa, v0) = sz00 & % 36.79/5.85 | aElement0(v0) = 0 & $i(v0)) % 36.79/5.85 | % 36.79/5.85 | ALPHA: (36) implies: % 36.79/5.85 | (37) slsdtgt0(xa) = all_62_1 % 36.79/5.85 | (38) slsdtgt0(xb) = all_62_0 % 36.79/5.85 | % 36.79/5.85 | DELTA: instantiating (5) with fresh symbols all_64_0, all_64_1, all_64_2 % 36.79/5.85 | gives: % 36.79/5.86 | (39) ~ (xu = sz00) & slsdtgt0(xb) = all_64_1 & slsdtgt0(xa) = all_64_2 & % 36.79/5.86 | sbrdtbr0(xu) = all_64_0 & aElementOf0(xu, xI) = 0 & $i(all_64_0) & % 36.79/5.86 | $i(all_64_1) & $i(all_64_2) & ! [v0: $i] : ! [v1: any] : (v0 = sz00 % 36.79/5.86 | | ~ (aElementOf0(v0, xI) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 36.79/5.86 | int] : ( ~ (v3 = 0) & iLess0(v2, all_64_0) = v3 & sbrdtbr0(v0) = % 36.79/5.86 | v2 & $i(v2)) | ( ~ (v1 = 0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 36.79/5.86 | (aElementOf0(v3, all_64_1) = 0) | ~ (aElementOf0(v2, all_64_2) % 36.79/5.86 | = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v0) & % 36.79/5.86 | sdtpldt0(v2, v3) = v4 & $i(v4))))) & ? [v0: $i] : ? [v1: $i] % 36.79/5.86 | : (aElementOf0(v1, all_64_1) = 0 & aElementOf0(v0, all_64_2) = 0 & % 36.79/5.86 | sdtpldt0(v0, v1) = xu & $i(v1) & $i(v0)) % 36.79/5.86 | % 36.79/5.86 | ALPHA: (39) implies: % 36.79/5.86 | (40) slsdtgt0(xb) = all_64_1 % 36.79/5.86 | % 36.79/5.86 | DELTA: instantiating (4) with fresh symbols all_67_0, all_67_1, all_67_2 % 36.79/5.86 | gives: % 36.79/5.86 | (41) slsdtgt0(xb) = all_67_1 & slsdtgt0(xa) = all_67_2 & sdtpldt1(all_67_2, % 36.79/5.86 | all_67_1) = all_67_0 & $i(all_67_0) & $i(all_67_1) & $i(all_67_2) & % 36.79/5.86 | ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_67_0) = 0 & $i(v0) % 36.79/5.86 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 36.79/5.86 | all_67_1) = v2) | ~ $i(v1) | ! [v3: $i] : ( ~ (sdtasdt0(xb, % 36.79/5.86 | v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 36.79/5.86 | aElement0(v3) = v4))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 36.79/5.86 | ~ (aElementOf0(v1, all_67_2) = v2) | ~ $i(v1) | ! [v3: $i] : ( % 36.79/5.86 | ~ (sdtasdt0(xa, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 36.79/5.86 | 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 36.79/5.86 | (aElementOf0(v1, all_67_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 36.79/5.86 | (sdtasdt0(xb, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ! [v1: % 36.79/5.86 | $i] : ( ~ (aElementOf0(v1, all_67_2) = 0) | ~ $i(v1) | ? [v2: % 36.79/5.86 | $i] : (sdtasdt0(xa, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ? % 36.79/5.86 | [v1: $i] : ? [v2: $i] : (aElementOf0(v2, all_67_1) = 0 & % 36.79/5.86 | aElementOf0(v1, all_67_2) = 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & % 36.79/5.86 | $i(v1))) % 36.79/5.86 | % 36.79/5.86 | ALPHA: (41) implies: % 36.79/5.86 | (42) $i(all_67_0) % 36.79/5.86 | (43) sdtpldt1(all_67_2, all_67_1) = all_67_0 % 36.79/5.86 | (44) slsdtgt0(xa) = all_67_2 % 36.79/5.86 | (45) slsdtgt0(xb) = all_67_1 % 36.79/5.86 | % 36.79/5.86 | DELTA: instantiating (2) with fresh symbols all_71_0, all_71_1 gives: % 36.79/5.86 | (46) slsdtgt0(xb) = all_71_0 & slsdtgt0(xa) = all_71_1 & aIdeal0(xI) = 0 & % 36.79/5.86 | sdtpldt1(all_71_1, all_71_0) = xI & aSet0(xI) = 0 & $i(all_71_0) & % 36.79/5.86 | $i(all_71_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 36.79/5.86 | (aElementOf0(v0, all_71_0) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 36.79/5.86 | (sdtasdt0(xb, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 36.79/5.86 | & aElement0(v2) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 36.79/5.86 | ~ (aElementOf0(v0, all_71_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 36.79/5.86 | (sdtasdt0(xa, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 36.79/5.86 | & aElement0(v2) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 36.79/5.86 | ~ (aElementOf0(v0, xI) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 36.79/5.86 | $i] : ( ~ (aElementOf0(v3, all_71_0) = 0) | ~ (aElementOf0(v2, % 36.79/5.86 | all_71_1) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 % 36.79/5.86 | = v0) & sdtpldt0(v2, v3) = v4 & $i(v4)))) & ! [v0: $i] : ( ~ % 36.79/5.86 | (aElementOf0(v0, all_71_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 36.79/5.86 | (sdtasdt0(xb, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i] % 36.79/5.86 | : ( ~ (aElementOf0(v0, all_71_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 36.79/5.86 | (sdtasdt0(xa, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i] % 36.79/5.86 | : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 36.79/5.86 | $i] : (aElementOf0(v2, all_71_0) = 0 & aElementOf0(v1, all_71_1) = % 36.79/5.86 | 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1))) & ! [v0: $i] : ( ~ % 36.79/5.86 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : % 36.79/5.86 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 36.79/5.86 | any] : (aElementOf0(v2, xI) = v4 & aElement0(v1) = v3 & ( ~ % 36.79/5.86 | (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, % 36.79/5.86 | xI) = 0) | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, xI) = % 36.79/5.86 | 0 & sdtpldt0(v0, v1) = v2 & $i(v2))))) % 36.79/5.86 | % 36.79/5.86 | ALPHA: (46) implies: % 36.79/5.86 | (47) sdtpldt1(all_71_1, all_71_0) = xI % 36.79/5.86 | (48) aIdeal0(xI) = 0 % 36.79/5.86 | (49) slsdtgt0(xa) = all_71_1 % 36.79/5.86 | (50) slsdtgt0(xb) = all_71_0 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (14) with all_50_3, all_58_1, xu, xq, simplifying % 36.79/5.86 | with (26), (33) gives: % 36.79/5.86 | (51) all_58_1 = all_50_3 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (14) with all_41_1, all_58_1, xu, xq, simplifying % 36.79/5.86 | with (20), (33) gives: % 36.79/5.86 | (52) all_58_1 = all_41_1 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_62_1, all_67_2, xa, simplifying with % 36.79/5.86 | (37), (44) gives: % 36.79/5.86 | (53) all_67_2 = all_62_1 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_67_2, all_71_1, xa, simplifying with % 36.79/5.86 | (44), (49) gives: % 36.79/5.86 | (54) all_71_1 = all_67_2 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_48_1, all_71_1, xa, simplifying with % 36.79/5.86 | (23), (49) gives: % 36.79/5.86 | (55) all_71_1 = all_48_1 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_62_0, all_64_1, xb, simplifying with % 36.79/5.86 | (38), (40) gives: % 36.79/5.86 | (56) all_64_1 = all_62_0 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_62_0, all_67_1, xb, simplifying with % 36.79/5.86 | (38), (45) gives: % 36.79/5.86 | (57) all_67_1 = all_62_0 % 36.79/5.86 | % 36.79/5.86 | GROUND_INST: instantiating (13) with all_58_2, all_67_1, xb, simplifying with % 36.79/5.87 | (35), (45) gives: % 36.79/5.87 | (58) all_67_1 = all_58_2 % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (13) with all_64_1, all_71_0, xb, simplifying with % 36.79/5.87 | (40), (50) gives: % 36.79/5.87 | (59) all_71_0 = all_64_1 % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (13) with all_48_0, all_71_0, xb, simplifying with % 36.79/5.87 | (24), (50) gives: % 36.79/5.87 | (60) all_71_0 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (59), (60) imply: % 36.79/5.87 | (61) all_64_1 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | SIMP: (61) implies: % 36.79/5.87 | (62) all_64_1 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (54), (55) imply: % 36.79/5.87 | (63) all_67_2 = all_48_1 % 36.79/5.87 | % 36.79/5.87 | SIMP: (63) implies: % 36.79/5.87 | (64) all_67_2 = all_48_1 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (57), (58) imply: % 36.79/5.87 | (65) all_62_0 = all_58_2 % 36.79/5.87 | % 36.79/5.87 | SIMP: (65) implies: % 36.79/5.87 | (66) all_62_0 = all_58_2 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (53), (64) imply: % 36.79/5.87 | (67) all_62_1 = all_48_1 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (56), (62) imply: % 36.79/5.87 | (68) all_62_0 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | SIMP: (68) implies: % 36.79/5.87 | (69) all_62_0 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (66), (69) imply: % 36.79/5.87 | (70) all_58_2 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (51), (52) imply: % 36.79/5.87 | (71) all_50_3 = all_41_1 % 36.79/5.87 | % 36.79/5.87 | COMBINE_EQS: (58), (70) imply: % 36.79/5.87 | (72) all_67_1 = all_48_0 % 36.79/5.87 | % 36.79/5.87 | REDUCE: (47), (55), (60) imply: % 36.79/5.87 | (73) sdtpldt1(all_48_1, all_48_0) = xI % 36.79/5.87 | % 36.79/5.87 | REDUCE: (43), (64), (72) imply: % 36.79/5.87 | (74) sdtpldt1(all_48_1, all_48_0) = all_67_0 % 36.79/5.87 | % 36.79/5.87 | REDUCE: (32), (52) imply: % 36.79/5.87 | (75) smndt0(all_41_1) = all_58_0 % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (12) with all_41_0, all_58_0, all_41_1, simplifying % 36.79/5.87 | with (18), (75) gives: % 36.79/5.87 | (76) all_58_0 = all_41_0 % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (16) with xI, all_67_0, all_48_0, all_48_1, % 36.79/5.87 | simplifying with (73), (74) gives: % 36.79/5.87 | (77) all_67_0 = xI % 36.79/5.87 | % 36.79/5.87 | REDUCE: (34), (76) imply: % 36.79/5.87 | (78) aElementOf0(all_41_0, xI) = 0 % 36.79/5.87 | % 36.79/5.87 | REDUCE: (42), (77) imply: % 36.79/5.87 | (79) $i(xI) % 36.79/5.87 | % 36.79/5.87 | REDUCE: (31), (76) imply: % 36.79/5.87 | (80) $i(all_41_0) % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (1) with xI, simplifying with (48), (79) gives: % 36.79/5.87 | (81) aSet0(xI) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ % 36.79/5.87 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 36.79/5.87 | (aElementOf0(v2, xI) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 36.79/5.87 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! % 36.79/5.87 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 36.79/5.87 | (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~ % 36.79/5.87 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xI) = % 36.79/5.87 | v4)))) % 36.79/5.87 | % 36.79/5.87 | ALPHA: (81) implies: % 36.79/5.87 | (82) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] % 36.79/5.87 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = % 36.79/5.87 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] : % 36.79/5.87 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i] % 36.79/5.87 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ % 36.79/5.87 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 36.79/5.87 | 0) & aElementOf0(v1, xI) = v4)))) % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (82) with all_41_0, simplifying with (78), (80) % 36.79/5.87 | gives: % 36.79/5.87 | (83) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 36.79/5.87 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, all_41_0) = v1) | ~ % 36.79/5.87 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! % 36.79/5.87 | [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 36.79/5.87 | xI) = v2) | ~ (sdtpldt0(all_41_0, v0) = v1) | ~ $i(v0) | ? % 36.79/5.87 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3)) % 36.79/5.87 | % 36.79/5.87 | ALPHA: (83) implies: % 36.79/5.87 | (84) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 36.79/5.87 | (aElementOf0(v1, xI) = v2) | ~ (sdtpldt0(all_41_0, v0) = v1) | ~ % 36.79/5.87 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3)) % 36.79/5.87 | % 36.79/5.87 | GROUND_INST: instantiating (84) with xb, xr, all_55_0, simplifying with (10), % 36.79/5.87 | (19), (29) gives: % 36.79/5.87 | (85) all_55_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xI) = v0) % 36.79/5.87 | % 36.79/5.87 | BETA: splitting (85) gives: % 36.79/5.87 | % 36.79/5.87 | Case 1: % 36.79/5.87 | | % 36.79/5.87 | | (86) all_55_0 = 0 % 36.79/5.87 | | % 36.79/5.87 | | REDUCE: (28), (86) imply: % 36.79/5.87 | | (87) $false % 36.79/5.87 | | % 36.79/5.87 | | CLOSE: (87) is inconsistent. % 36.79/5.87 | | % 36.79/5.87 | Case 2: % 36.79/5.87 | | % 36.79/5.87 | | (88) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xI) = v0) % 36.79/5.87 | | % 36.79/5.87 | | DELTA: instantiating (88) with fresh symbol all_554_0 gives: % 36.79/5.87 | | (89) ~ (all_554_0 = 0) & aElementOf0(xb, xI) = all_554_0 % 36.79/5.87 | | % 36.79/5.87 | | ALPHA: (89) implies: % 36.79/5.87 | | (90) ~ (all_554_0 = 0) % 36.79/5.87 | | (91) aElementOf0(xb, xI) = all_554_0 % 36.79/5.87 | | % 36.79/5.87 | | GROUND_INST: instantiating (15) with 0, all_554_0, xI, xb, simplifying with % 36.79/5.87 | | (22), (91) gives: % 36.79/5.87 | | (92) all_554_0 = 0 % 36.79/5.87 | | % 36.79/5.87 | | REDUCE: (90), (92) imply: % 36.79/5.87 | | (93) $false % 36.79/5.87 | | % 36.79/5.88 | | CLOSE: (93) is inconsistent. % 36.79/5.88 | | % 36.79/5.88 | End of split % 36.79/5.88 | % 36.79/5.88 End of proof % 36.79/5.88 % SZS output end Proof for theBenchmark % 36.79/5.88 % 36.79/5.88 5169ms %------------------------------------------------------------------------------