%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG124+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 : n009.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 22.09s 3.60s % Output : Proof 45.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : RNG124+4 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.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 : Sun Aug 27 01:45:50 EDT 2023 % 0.12/0.33 % CPUTime : % 0.58/0.59 ________ _____ % 0.58/0.59 ___ __ \_________(_)________________________________ % 0.58/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.59 (2023-06-19) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2023 % 0.58/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.59 Amanda Stjerna. % 0.58/0.59 Free software under BSD-3-Clause. % 0.58/0.59 % 0.58/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.58/0.60 Running up to 7 provers in parallel. % 0.58/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.58/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.58/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.58/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.58/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.58/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.58/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.80/1.21 Prover 4: Preprocessing ... % 3.80/1.21 Prover 1: Preprocessing ... % 4.23/1.25 Prover 5: Preprocessing ... % 4.23/1.25 Prover 3: Preprocessing ... % 4.23/1.25 Prover 6: Preprocessing ... % 4.23/1.25 Prover 2: Preprocessing ... % 4.23/1.27 Prover 0: Preprocessing ... % 11.71/2.26 Prover 1: Constructing countermodel ... % 12.18/2.34 Prover 6: Proving ... % 12.73/2.36 Prover 5: Proving ... % 12.73/2.37 Prover 3: Constructing countermodel ... % 13.18/2.43 Prover 2: Proving ... % 14.41/2.60 Prover 4: Constructing countermodel ... % 15.05/2.67 Prover 0: Proving ... % 22.09/3.60 Prover 3: proved (2992ms) % 22.09/3.60 % 22.09/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.09/3.60 % 22.09/3.61 Prover 6: stopped % 22.09/3.61 Prover 0: stopped % 22.09/3.61 Prover 5: stopped % 22.09/3.62 Prover 2: stopped % 22.09/3.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.09/3.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.09/3.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.09/3.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.09/3.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.29/3.75 Prover 10: Preprocessing ... % 23.29/3.76 Prover 8: Preprocessing ... % 23.63/3.80 Prover 7: Preprocessing ... % 23.63/3.80 Prover 11: Preprocessing ... % 24.23/3.85 Prover 13: Preprocessing ... % 25.56/4.02 Prover 8: Warning: ignoring some quantifiers % 25.56/4.06 Prover 8: Constructing countermodel ... % 25.88/4.09 Prover 7: Constructing countermodel ... % 25.88/4.09 Prover 10: Constructing countermodel ... % 27.93/4.34 Prover 13: Warning: ignoring some quantifiers % 28.33/4.37 Prover 13: Constructing countermodel ... % 28.33/4.41 Prover 11: Constructing countermodel ... % 43.90/6.43 Prover 1: Found proof (size 76) % 43.90/6.43 Prover 1: proved (5819ms) % 44.55/6.43 Prover 11: stopped % 44.55/6.43 Prover 7: stopped % 44.55/6.43 Prover 13: stopped % 44.55/6.43 Prover 10: stopped % 44.55/6.43 Prover 8: stopped % 44.55/6.43 Prover 4: stopped % 44.55/6.43 % 44.55/6.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 44.55/6.43 % 44.55/6.44 % SZS output start Proof for theBenchmark % 44.55/6.44 Assumptions after simplification: % 44.55/6.44 --------------------------------- % 44.55/6.44 % 44.55/6.44 (m__2174) % 44.55/6.48 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 44.55/6.48 slsdtgt0(xa) = v0 & aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0 % 44.55/6.48 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 44.55/6.48 (aElementOf0(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xb, % 44.55/6.48 v4) = v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) % 44.55/6.48 = v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 44.55/6.48 v0) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xa, v4) = v2) | ~ % 44.55/6.48 $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = v5))) & ! [v2: % 44.55/6.48 $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ $i(v2) | % 44.55/6.48 ! [v4: $i] : ! [v5: $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ % 44.55/6.48 (aElementOf0(v4, v0) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: $i] : ( ~ % 44.55/6.48 (v6 = v2) & sdtpldt0(v4, v5) = v6 & $i(v6)))) & ! [v2: $i] : ( ~ % 44.55/6.48 (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xb, v3) = % 44.55/6.48 v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ (aElementOf0(v2, % 44.55/6.48 v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & % 44.55/6.48 aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ (aElementOf0(v2, xI) = % 44.55/6.48 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (aElementOf0(v4, v1) = 0 & % 44.55/6.48 aElementOf0(v3, v0) = 0 & sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3))) & ! % 44.55/6.48 [v2: $i] : ( ~ (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ( ! [v3: $i] : ! % 44.55/6.48 [v4: $i] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? % 44.55/6.48 [v6: any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( ~ (v5 = % 44.55/6.48 0) | v6 = 0))) & ! [v3: $i] : ( ~ (aElementOf0(v3, xI) = 0) | % 44.55/6.48 ~ $i(v3) | ? [v4: $i] : (aElementOf0(v4, xI) = 0 & sdtpldt0(v2, v3) = % 44.55/6.48 v4 & $i(v4)))))) % 44.55/6.48 % 44.55/6.48 (m__2203) % 44.78/6.48 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 44.78/6.48 slsdtgt0(xa) = v0 & aElementOf0(xb, v1) = 0 & aElementOf0(xa, v0) = 0 & % 44.78/6.48 aElementOf0(sz00, v1) = 0 & aElementOf0(sz00, v0) = 0 & $i(v1) & $i(v0) & ? % 44.78/6.48 [v2: $i] : (sdtasdt0(xb, v2) = xb & aElement0(v2) = 0 & $i(v2)) & ? [v2: % 44.78/6.48 $i] : (sdtasdt0(xb, v2) = sz00 & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] % 44.78/6.48 : (sdtasdt0(xa, v2) = xa & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] : % 44.78/6.48 (sdtasdt0(xa, v2) = sz00 & aElement0(v2) = 0 & $i(v2))) % 44.78/6.48 % 44.78/6.48 (m__2228) % 44.78/6.48 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 44.78/6.48 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & % 44.78/6.48 $i(v1) & $i(v0) & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & % 44.78/6.48 $i(v3) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = % 44.78/6.48 v5) | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xb, v6) = v4) | ~ % 44.78/6.48 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & ! [v4: % 44.78/6.48 $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v0) = v5) | ~ $i(v4) % 44.78/6.48 | ! [v6: $i] : ( ~ (sdtasdt0(xa, v6) = v4) | ~ $i(v6) | ? [v7: int] : % 44.78/6.48 ( ~ (v7 = 0) & aElement0(v6) = v7))) & ! [v4: $i] : ( ~ % 44.78/6.48 (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: $i] : (sdtasdt0(xb, v5) % 44.78/6.48 = v4 & aElement0(v5) = 0 & $i(v5))) & ! [v4: $i] : ( ~ % 44.78/6.48 (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ? [v5: $i] : (sdtasdt0(xa, v5) % 44.78/6.48 = v4 & aElement0(v5) = 0 & $i(v5))) & ? [v4: $i] : ? [v5: $i] : % 44.78/6.48 (aElementOf0(v5, v1) = 0 & aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 % 44.78/6.48 & $i(v5) & $i(v4)))) % 44.78/6.48 % 44.78/6.48 (m__2273) % 44.78/6.49 $i(xu) & $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 44.78/6.49 [v2: $i] : ( ~ (xu = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.49 sbrdtbr0(xu) = v2 & aElementOf0(xu, xI) = 0 & $i(v2) & $i(v1) & $i(v0) & ! % 44.78/6.49 [v3: $i] : ! [v4: any] : (v3 = sz00 | ~ (aElementOf0(v3, xI) = v4) | ~ % 44.78/6.49 $i(v3) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & iLess0(v5, v2) = v6 & % 44.78/6.49 sbrdtbr0(v3) = v5 & $i(v5)) | ( ~ (v4 = 0) & ! [v5: $i] : ! [v6: $i] : % 44.78/6.49 ( ~ (aElementOf0(v6, v1) = 0) | ~ (aElementOf0(v5, v0) = 0) | ~ $i(v6) % 44.78/6.49 | ~ $i(v5) | ? [v7: $i] : ( ~ (v7 = v3) & sdtpldt0(v5, v6) = v7 & % 44.78/6.49 $i(v7))))) & ? [v3: $i] : ? [v4: $i] : (aElementOf0(v4, v1) = 0 & % 44.78/6.49 aElementOf0(v3, v0) = 0 & sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3))) % 44.78/6.49 % 44.78/6.49 (m__2666) % 44.78/6.49 $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 44.78/6.49 [v2: $i] : ? [v3: any] : (iLess0(v1, v2) = v3 & sbrdtbr0(xr) = v1 & % 44.78/6.49 sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb & % 44.78/6.49 aElement0(xr) = 0 & aElement0(xq) = 0 & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | % 44.78/6.49 xr = sz00)) % 44.78/6.49 % 44.78/6.49 (m__2673) % 44.78/6.49 ~ (xr = sz00) & $i(xr) & $i(sz00) % 44.78/6.49 % 44.78/6.49 (m__2690) % 44.78/6.49 $i(xq) & $i(xu) & $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? % 44.78/6.49 [v2: $i] : ? [v3: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.49 aElementOf0(v3, xI) = 0 & sdtasdt0(xq, xu) = v2 & smndt0(v2) = v3 & $i(v3) & % 44.78/6.49 $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] : ? [v5: $i] : (aElementOf0(v5, v1) % 44.78/6.49 = 0 & aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4))) % 44.78/6.49 % 44.78/6.49 (m__2699) % 44.78/6.49 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 44.78/6.49 slsdtgt0(xa) = v0 & aElementOf0(xb, xI) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 44.78/6.49 : ? [v3: $i] : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 & % 44.78/6.49 sdtpldt0(v2, v3) = xb & $i(v3) & $i(v2))) % 44.78/6.49 % 44.78/6.49 (m__2729) % 44.78/6.49 $i(xr) & $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) % 44.78/6.49 = v1 & slsdtgt0(xa) = v0 & aElementOf0(xr, xI) = 0 & $i(v1) & $i(v0) & ? % 44.78/6.49 [v2: $i] : ? [v3: $i] : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 % 44.78/6.49 & sdtpldt0(v2, v3) = xr & $i(v3) & $i(v2))) % 44.78/6.49 % 44.78/6.49 (function-axioms) % 44.78/6.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 44.78/6.50 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~ % 44.78/6.50 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 44.78/6.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 44.78/6.50 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, % 44.78/6.50 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 44.78/6.50 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) | % 44.78/6.50 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 44.78/6.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 44.78/6.50 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: % 44.78/6.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 44.78/6.50 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 44.78/6.50 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 44.78/6.50 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 44.78/6.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 44.78/6.50 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 44.78/6.50 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 44.78/6.50 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 44.78/6.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 44.78/6.50 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 44.78/6.50 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 44.78/6.50 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 44.78/6.50 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 44.78/6.50 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) % 44.78/6.50 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 44.78/6.50 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: % 44.78/6.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 44.78/6.50 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0: % 44.78/6.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 44.78/6.50 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : % 44.78/6.50 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 44.78/6.50 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 44.78/6.50 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 44.78/6.50 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 44.78/6.50 ~ (aElement0(v2) = v0)) % 44.78/6.50 % 44.78/6.50 Further assumptions not needed in the proof: % 44.78/6.50 -------------------------------------------- % 44.78/6.50 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 44.78/6.50 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, % 44.78/6.50 mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, % 44.78/6.50 mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, % 44.78/6.50 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__, % 44.78/6.50 m__2091, m__2110, m__2129, m__2383, m__2416, m__2479, m__2612, m__2718 % 44.78/6.50 % 44.78/6.50 Those formulas are unsatisfiable: % 44.78/6.50 --------------------------------- % 44.78/6.50 % 44.78/6.50 Begin of proof % 44.78/6.50 | % 44.78/6.50 | ALPHA: (m__2174) implies: % 44.78/6.51 | (1) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.51 | aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0 & $i(v1) & % 44.78/6.51 | $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, % 44.78/6.51 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (sdtasdt0(xb, v4) = % 44.78/6.51 | v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = % 44.78/6.51 | v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 44.78/6.51 | (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ % 44.78/6.51 | (sdtasdt0(xa, v4) = v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) % 44.78/6.51 | & aElement0(v4) = v5))) & ! [v2: $i] : ! [v3: int] : (v3 = 0 % 44.78/6.51 | | ~ (aElementOf0(v2, xI) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: % 44.78/6.51 | $i] : ( ~ (aElementOf0(v5, v1) = 0) | ~ (aElementOf0(v4, v0) = % 44.78/6.51 | 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: $i] : ( ~ (v6 = v2) & % 44.78/6.51 | sdtpldt0(v4, v5) = v6 & $i(v6)))) & ! [v2: $i] : ( ~ % 44.78/6.51 | (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xb, % 44.78/6.51 | v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ % 44.78/6.51 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xa, % 44.78/6.51 | v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ % 44.78/6.51 | (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : % 44.78/6.51 | (aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 & sdtpldt0(v3, % 44.78/6.51 | v4) = v2 & $i(v4) & $i(v3))) & ! [v2: $i] : ( ~ % 44.78/6.51 | (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ( ! [v3: $i] : ! [v4: $i] % 44.78/6.51 | : ( ~ (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ? [v5: any] : ? % 44.78/6.51 | [v6: any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( % 44.78/6.51 | ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] : ( ~ (aElementOf0(v3, % 44.78/6.51 | xI) = 0) | ~ $i(v3) | ? [v4: $i] : (aElementOf0(v4, xI) = % 44.78/6.51 | 0 & sdtpldt0(v2, v3) = v4 & $i(v4)))))) % 44.78/6.51 | % 44.78/6.51 | ALPHA: (m__2203) implies: % 44.78/6.51 | (2) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.51 | aElementOf0(xb, v1) = 0 & aElementOf0(xa, v0) = 0 & aElementOf0(sz00, % 44.78/6.51 | v1) = 0 & aElementOf0(sz00, v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 44.78/6.51 | : (sdtasdt0(xb, v2) = xb & aElement0(v2) = 0 & $i(v2)) & ? [v2: $i] % 44.78/6.51 | : (sdtasdt0(xb, v2) = sz00 & aElement0(v2) = 0 & $i(v2)) & ? [v2: % 44.78/6.51 | $i] : (sdtasdt0(xa, v2) = xa & aElement0(v2) = 0 & $i(v2)) & ? % 44.78/6.51 | [v2: $i] : (sdtasdt0(xa, v2) = sz00 & aElement0(v2) = 0 & $i(v2))) % 44.78/6.51 | % 44.78/6.51 | ALPHA: (m__2228) implies: % 44.78/6.51 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xb) = v1 & % 44.78/6.51 | slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 44.78/6.51 | & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & $i(v3) & % 44.78/6.51 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = v5) % 44.78/6.51 | | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xb, v6) = v4) | ~ % 44.78/6.51 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & % 44.78/6.51 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v0) = v5) % 44.78/6.51 | | ~ $i(v4) | ! [v6: $i] : ( ~ (sdtasdt0(xa, v6) = v4) | ~ % 44.78/6.51 | $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & aElement0(v6) = v7))) & % 44.78/6.51 | ! [v4: $i] : ( ~ (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: % 44.78/6.51 | $i] : (sdtasdt0(xb, v5) = v4 & aElement0(v5) = 0 & $i(v5))) & % 44.78/6.51 | ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ? [v5: % 44.78/6.51 | $i] : (sdtasdt0(xa, v5) = v4 & aElement0(v5) = 0 & $i(v5))) & % 44.78/6.51 | ? [v4: $i] : ? [v5: $i] : (aElementOf0(v5, v1) = 0 & % 44.78/6.51 | aElementOf0(v4, v0) = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & % 44.78/6.51 | $i(v4)))) % 44.78/6.51 | % 44.78/6.51 | ALPHA: (m__2273) implies: % 44.78/6.52 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (xu = sz00) & % 44.78/6.52 | slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sbrdtbr0(xu) = v2 & % 44.78/6.52 | aElementOf0(xu, xI) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 44.78/6.52 | [v4: any] : (v3 = sz00 | ~ (aElementOf0(v3, xI) = v4) | ~ $i(v3) | % 44.78/6.52 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & iLess0(v5, v2) = v6 & % 44.78/6.52 | sbrdtbr0(v3) = v5 & $i(v5)) | ( ~ (v4 = 0) & ! [v5: $i] : ! % 44.78/6.52 | [v6: $i] : ( ~ (aElementOf0(v6, v1) = 0) | ~ (aElementOf0(v5, % 44.78/6.52 | v0) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ( ~ (v7 = % 44.78/6.52 | v3) & sdtpldt0(v5, v6) = v7 & $i(v7))))) & ? [v3: $i] : ? % 44.78/6.52 | [v4: $i] : (aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 & % 44.78/6.52 | sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3))) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (m__2666) implies: % 44.78/6.52 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (iLess0(v1, % 44.78/6.52 | v2) = v3 & sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) % 44.78/6.52 | = v0 & sdtpldt0(v0, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 % 44.78/6.52 | & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | xr = sz00)) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (m__2673) implies: % 44.78/6.52 | (6) ~ (xr = sz00) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (m__2690) implies: % 44.78/6.52 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (slsdtgt0(xb) = % 44.78/6.52 | v1 & slsdtgt0(xa) = v0 & aElementOf0(v3, xI) = 0 & sdtasdt0(xq, xu) = % 44.78/6.52 | v2 & smndt0(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: % 44.78/6.52 | $i] : ? [v5: $i] : (aElementOf0(v5, v1) = 0 & aElementOf0(v4, v0) % 44.78/6.52 | = 0 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4))) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (m__2699) implies: % 44.78/6.52 | (8) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.52 | aElementOf0(xb, xI) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] % 44.78/6.52 | : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 & sdtpldt0(v2, % 44.78/6.52 | v3) = xb & $i(v3) & $i(v2))) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (m__2729) implies: % 44.78/6.52 | (9) $i(xr) % 44.78/6.52 | (10) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 44.78/6.52 | aElementOf0(xr, xI) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: % 44.78/6.52 | $i] : (aElementOf0(v3, v1) = 0 & aElementOf0(v2, v0) = 0 & % 44.78/6.52 | sdtpldt0(v2, v3) = xr & $i(v3) & $i(v2))) % 44.78/6.52 | % 44.78/6.52 | ALPHA: (function-axioms) implies: % 44.78/6.52 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 44.78/6.52 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 44.78/6.53 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 44.78/6.53 | = v1) | ~ (slsdtgt0(v2) = v0)) % 44.78/6.53 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 44.78/6.53 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 44.78/6.53 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 44.78/6.53 | : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, % 44.78/6.53 | v2) = v0)) % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (8) with fresh symbols all_48_0, all_48_1 gives: % 44.78/6.53 | (15) slsdtgt0(xb) = all_48_0 & slsdtgt0(xa) = all_48_1 & aElementOf0(xb, % 44.78/6.53 | xI) = 0 & $i(all_48_0) & $i(all_48_1) & ? [v0: $i] : ? [v1: $i] : % 44.78/6.53 | (aElementOf0(v1, all_48_0) = 0 & aElementOf0(v0, all_48_1) = 0 & % 44.78/6.53 | sdtpldt0(v0, v1) = xb & $i(v1) & $i(v0)) % 44.78/6.53 | % 44.78/6.53 | ALPHA: (15) implies: % 44.78/6.53 | (16) slsdtgt0(xa) = all_48_1 % 44.78/6.53 | (17) slsdtgt0(xb) = all_48_0 % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (10) with fresh symbols all_50_0, all_50_1 gives: % 44.78/6.53 | (18) slsdtgt0(xb) = all_50_0 & slsdtgt0(xa) = all_50_1 & aElementOf0(xr, % 44.78/6.53 | xI) = 0 & $i(all_50_0) & $i(all_50_1) & ? [v0: $i] : ? [v1: $i] : % 44.78/6.53 | (aElementOf0(v1, all_50_0) = 0 & aElementOf0(v0, all_50_1) = 0 & % 44.78/6.53 | sdtpldt0(v0, v1) = xr & $i(v1) & $i(v0)) % 44.78/6.53 | % 44.78/6.53 | ALPHA: (18) implies: % 44.78/6.53 | (19) aElementOf0(xr, xI) = 0 % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (5) with fresh symbols all_52_0, all_52_1, all_52_2, % 44.78/6.53 | all_52_3 gives: % 44.78/6.53 | (20) iLess0(all_52_2, all_52_1) = all_52_0 & sbrdtbr0(xr) = all_52_2 & % 44.78/6.53 | sbrdtbr0(xu) = all_52_1 & sdtasdt0(xq, xu) = all_52_3 & % 44.78/6.53 | sdtpldt0(all_52_3, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 & % 44.78/6.53 | $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & (all_52_0 = 0 | xr = % 44.78/6.53 | sz00) % 44.78/6.53 | % 44.78/6.53 | ALPHA: (20) implies: % 44.78/6.53 | (21) sbrdtbr0(xu) = all_52_1 % 44.78/6.53 | (22) sbrdtbr0(xr) = all_52_2 % 44.78/6.53 | (23) iLess0(all_52_2, all_52_1) = all_52_0 % 44.78/6.53 | (24) all_52_0 = 0 | xr = sz00 % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (7) with fresh symbols all_57_0, all_57_1, all_57_2, % 44.78/6.53 | all_57_3 gives: % 44.78/6.53 | (25) slsdtgt0(xb) = all_57_2 & slsdtgt0(xa) = all_57_3 & % 44.78/6.53 | aElementOf0(all_57_0, xI) = 0 & sdtasdt0(xq, xu) = all_57_1 & % 44.78/6.53 | smndt0(all_57_1) = all_57_0 & $i(all_57_0) & $i(all_57_1) & % 44.78/6.53 | $i(all_57_2) & $i(all_57_3) & ? [v0: $i] : ? [v1: $i] : % 44.78/6.53 | (aElementOf0(v1, all_57_2) = 0 & aElementOf0(v0, all_57_3) = 0 & % 44.78/6.53 | sdtpldt0(v0, v1) = all_57_0 & $i(v1) & $i(v0)) % 44.78/6.53 | % 44.78/6.53 | ALPHA: (25) implies: % 44.78/6.53 | (26) slsdtgt0(xb) = all_57_2 % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (2) with fresh symbols all_61_0, all_61_1 gives: % 44.78/6.53 | (27) slsdtgt0(xb) = all_61_0 & slsdtgt0(xa) = all_61_1 & aElementOf0(xb, % 44.78/6.53 | all_61_0) = 0 & aElementOf0(xa, all_61_1) = 0 & aElementOf0(sz00, % 44.78/6.53 | all_61_0) = 0 & aElementOf0(sz00, all_61_1) = 0 & $i(all_61_0) & % 44.78/6.53 | $i(all_61_1) & ? [v0: $i] : (sdtasdt0(xb, v0) = xb & aElement0(v0) = % 44.78/6.53 | 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xb, v0) = sz00 & aElement0(v0) % 44.78/6.53 | = 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xa, v0) = xa & aElement0(v0) % 44.78/6.53 | = 0 & $i(v0)) & ? [v0: $i] : (sdtasdt0(xa, v0) = sz00 & % 44.78/6.53 | aElement0(v0) = 0 & $i(v0)) % 44.78/6.53 | % 44.78/6.53 | ALPHA: (27) implies: % 44.78/6.53 | (28) slsdtgt0(xa) = all_61_1 % 44.78/6.53 | (29) slsdtgt0(xb) = all_61_0 % 44.78/6.53 | % 44.78/6.53 | DELTA: instantiating (4) with fresh symbols all_63_0, all_63_1, all_63_2 % 44.78/6.53 | gives: % 44.78/6.54 | (30) ~ (xu = sz00) & slsdtgt0(xb) = all_63_1 & slsdtgt0(xa) = all_63_2 & % 44.78/6.54 | sbrdtbr0(xu) = all_63_0 & aElementOf0(xu, xI) = 0 & $i(all_63_0) & % 44.78/6.54 | $i(all_63_1) & $i(all_63_2) & ! [v0: $i] : ! [v1: any] : (v0 = sz00 % 44.78/6.54 | | ~ (aElementOf0(v0, xI) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 44.78/6.54 | int] : ( ~ (v3 = 0) & iLess0(v2, all_63_0) = v3 & sbrdtbr0(v0) = % 44.78/6.54 | v2 & $i(v2)) | ( ~ (v1 = 0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 44.78/6.54 | (aElementOf0(v3, all_63_1) = 0) | ~ (aElementOf0(v2, all_63_2) % 44.78/6.54 | = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v0) & % 44.78/6.54 | sdtpldt0(v2, v3) = v4 & $i(v4))))) & ? [v0: $i] : ? [v1: $i] % 44.78/6.54 | : (aElementOf0(v1, all_63_1) = 0 & aElementOf0(v0, all_63_2) = 0 & % 44.78/6.54 | sdtpldt0(v0, v1) = xu & $i(v1) & $i(v0)) % 44.78/6.54 | % 44.78/6.54 | ALPHA: (30) implies: % 44.78/6.54 | (31) sbrdtbr0(xu) = all_63_0 % 44.78/6.54 | (32) slsdtgt0(xb) = all_63_1 % 44.78/6.54 | (33) ! [v0: $i] : ! [v1: any] : (v0 = sz00 | ~ (aElementOf0(v0, xI) = % 44.78/6.54 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 44.78/6.54 | iLess0(v2, all_63_0) = v3 & sbrdtbr0(v0) = v2 & $i(v2)) | ( ~ (v1 % 44.78/6.54 | = 0) & ! [v2: $i] : ! [v3: $i] : ( ~ (aElementOf0(v3, % 44.78/6.54 | all_63_1) = 0) | ~ (aElementOf0(v2, all_63_2) = 0) | ~ % 44.78/6.54 | $i(v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 = v0) & sdtpldt0(v2, % 44.78/6.54 | v3) = v4 & $i(v4))))) % 44.78/6.54 | % 44.78/6.54 | DELTA: instantiating (3) with fresh symbols all_66_0, all_66_1, all_66_2 % 44.78/6.54 | gives: % 44.78/6.54 | (34) slsdtgt0(xb) = all_66_1 & slsdtgt0(xa) = all_66_2 & sdtpldt1(all_66_2, % 44.78/6.54 | all_66_1) = all_66_0 & $i(all_66_0) & $i(all_66_1) & $i(all_66_2) & % 44.78/6.54 | ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_66_0) = 0 & $i(v0) % 44.78/6.54 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 44.78/6.54 | all_66_1) = v2) | ~ $i(v1) | ! [v3: $i] : ( ~ (sdtasdt0(xb, % 44.78/6.54 | v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 44.78/6.54 | aElement0(v3) = v4))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 44.78/6.54 | ~ (aElementOf0(v1, all_66_2) = v2) | ~ $i(v1) | ! [v3: $i] : ( % 44.78/6.54 | ~ (sdtasdt0(xa, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 44.78/6.54 | 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 44.78/6.54 | (aElementOf0(v1, all_66_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 44.78/6.54 | (sdtasdt0(xb, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ! [v1: % 44.78/6.54 | $i] : ( ~ (aElementOf0(v1, all_66_2) = 0) | ~ $i(v1) | ? [v2: % 44.78/6.54 | $i] : (sdtasdt0(xa, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ? % 44.78/6.54 | [v1: $i] : ? [v2: $i] : (aElementOf0(v2, all_66_1) = 0 & % 44.78/6.54 | aElementOf0(v1, all_66_2) = 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & % 44.78/6.54 | $i(v1))) % 44.78/6.54 | % 44.78/6.54 | ALPHA: (34) implies: % 44.78/6.54 | (35) sdtpldt1(all_66_2, all_66_1) = all_66_0 % 44.78/6.54 | (36) slsdtgt0(xa) = all_66_2 % 44.78/6.54 | (37) slsdtgt0(xb) = all_66_1 % 44.78/6.54 | (38) ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_66_0) = 0 & $i(v0) % 44.78/6.54 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 44.78/6.54 | all_66_1) = v2) | ~ $i(v1) | ! [v3: $i] : ( ~ (sdtasdt0(xb, % 44.78/6.54 | v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 44.78/6.54 | aElement0(v3) = v4))) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 44.78/6.54 | ~ (aElementOf0(v1, all_66_2) = v2) | ~ $i(v1) | ! [v3: $i] : ( % 44.78/6.54 | ~ (sdtasdt0(xa, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 44.78/6.54 | 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 44.78/6.54 | (aElementOf0(v1, all_66_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 44.78/6.54 | (sdtasdt0(xb, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ! [v1: % 44.78/6.54 | $i] : ( ~ (aElementOf0(v1, all_66_2) = 0) | ~ $i(v1) | ? [v2: % 44.78/6.54 | $i] : (sdtasdt0(xa, v2) = v1 & aElement0(v2) = 0 & $i(v2))) & ? % 44.78/6.54 | [v1: $i] : ? [v2: $i] : (aElementOf0(v2, all_66_1) = 0 & % 44.78/6.54 | aElementOf0(v1, all_66_2) = 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & % 44.78/6.54 | $i(v1))) % 44.78/6.54 | % 44.78/6.54 | DELTA: instantiating (1) with fresh symbols all_72_0, all_72_1 gives: % 44.78/6.55 | (39) slsdtgt0(xb) = all_72_0 & slsdtgt0(xa) = all_72_1 & aIdeal0(xI) = 0 & % 44.78/6.55 | sdtpldt1(all_72_1, all_72_0) = xI & aSet0(xI) = 0 & $i(all_72_0) & % 44.78/6.55 | $i(all_72_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 44.78/6.55 | (aElementOf0(v0, all_72_0) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 44.78/6.55 | (sdtasdt0(xb, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 44.78/6.55 | & aElement0(v2) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 44.78/6.55 | ~ (aElementOf0(v0, all_72_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 44.78/6.55 | (sdtasdt0(xa, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 44.78/6.55 | & aElement0(v2) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 44.78/6.55 | ~ (aElementOf0(v0, xI) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 44.78/6.55 | $i] : ( ~ (aElementOf0(v3, all_72_0) = 0) | ~ (aElementOf0(v2, % 44.78/6.55 | all_72_1) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ( ~ (v4 % 44.78/6.55 | = v0) & sdtpldt0(v2, v3) = v4 & $i(v4)))) & ! [v0: $i] : ( ~ % 44.78/6.55 | (aElementOf0(v0, all_72_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 44.78/6.55 | (sdtasdt0(xb, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i] % 44.78/6.55 | : ( ~ (aElementOf0(v0, all_72_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 44.78/6.55 | (sdtasdt0(xa, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i] % 44.78/6.55 | : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 44.78/6.55 | $i] : (aElementOf0(v2, all_72_0) = 0 & aElementOf0(v1, all_72_1) = % 44.78/6.55 | 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1))) & ! [v0: $i] : ( ~ % 44.78/6.55 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: $i] : % 44.78/6.55 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 44.78/6.55 | any] : (aElementOf0(v2, xI) = v4 & aElement0(v1) = v3 & ( ~ % 44.78/6.55 | (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, % 44.78/6.55 | xI) = 0) | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, xI) = % 44.78/6.55 | 0 & sdtpldt0(v0, v1) = v2 & $i(v2))))) % 45.13/6.55 | % 45.13/6.55 | ALPHA: (39) implies: % 45.13/6.55 | (40) sdtpldt1(all_72_1, all_72_0) = xI % 45.13/6.55 | (41) slsdtgt0(xa) = all_72_1 % 45.13/6.55 | (42) slsdtgt0(xb) = all_72_0 % 45.13/6.55 | % 45.13/6.55 | DELTA: instantiating (38) with fresh symbol all_87_0 gives: % 45.13/6.55 | (43) ~ (all_87_0 = sz00) & aElementOf0(all_87_0, all_66_0) = 0 & % 45.13/6.55 | $i(all_87_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 45.13/6.55 | (aElementOf0(v0, all_66_1) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 45.13/6.55 | (sdtasdt0(xb, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 45.13/6.55 | & aElement0(v2) = v3))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 45.13/6.55 | ~ (aElementOf0(v0, all_66_2) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ % 45.13/6.55 | (sdtasdt0(xa, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) % 45.13/6.55 | & aElement0(v2) = v3))) & ! [v0: $i] : ( ~ (aElementOf0(v0, % 45.13/6.55 | all_66_1) = 0) | ~ $i(v0) | ? [v1: $i] : (sdtasdt0(xb, v1) = % 45.13/6.55 | v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ % 45.13/6.55 | (aElementOf0(v0, all_66_2) = 0) | ~ $i(v0) | ? [v1: $i] : % 45.13/6.55 | (sdtasdt0(xa, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ? [v0: $i] % 45.13/6.55 | : ? [v1: $i] : (aElementOf0(v1, all_66_1) = 0 & aElementOf0(v0, % 45.13/6.55 | all_66_2) = 0 & sdtpldt0(v0, v1) = all_87_0 & $i(v1) & $i(v0)) % 45.13/6.55 | % 45.13/6.55 | ALPHA: (43) implies: % 45.13/6.55 | (44) ~ (all_87_0 = sz00) % 45.13/6.55 | (45) $i(all_87_0) % 45.13/6.55 | (46) aElementOf0(all_87_0, all_66_0) = 0 % 45.13/6.55 | % 45.13/6.55 | BETA: splitting (24) gives: % 45.13/6.55 | % 45.13/6.55 | Case 1: % 45.13/6.55 | | % 45.13/6.55 | | (47) xr = sz00 % 45.13/6.55 | | % 45.13/6.55 | | REDUCE: (6), (47) imply: % 45.13/6.55 | | (48) $false % 45.13/6.55 | | % 45.13/6.55 | | CLOSE: (48) is inconsistent. % 45.13/6.55 | | % 45.13/6.55 | Case 2: % 45.13/6.55 | | % 45.13/6.55 | | (49) all_52_0 = 0 % 45.13/6.55 | | % 45.13/6.55 | | REDUCE: (23), (49) imply: % 45.13/6.55 | | (50) iLess0(all_52_2, all_52_1) = 0 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (11) with all_52_1, all_63_0, xu, simplifying % 45.13/6.55 | | with (21), (31) gives: % 45.13/6.55 | | (51) all_63_0 = all_52_1 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_61_1, all_66_2, xa, simplifying % 45.13/6.55 | | with (28), (36) gives: % 45.13/6.55 | | (52) all_66_2 = all_61_1 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_66_2, all_72_1, xa, simplifying % 45.13/6.55 | | with (36), (41) gives: % 45.13/6.55 | | (53) all_72_1 = all_66_2 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_48_1, all_72_1, xa, simplifying % 45.13/6.55 | | with (16), (41) gives: % 45.13/6.55 | | (54) all_72_1 = all_48_1 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_61_0, all_63_1, xb, simplifying % 45.13/6.55 | | with (29), (32) gives: % 45.13/6.55 | | (55) all_63_1 = all_61_0 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_61_0, all_66_1, xb, simplifying % 45.13/6.55 | | with (29), (37) gives: % 45.13/6.55 | | (56) all_66_1 = all_61_0 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_57_2, all_66_1, xb, simplifying % 45.13/6.55 | | with (26), (37) gives: % 45.13/6.55 | | (57) all_66_1 = all_57_2 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_63_1, all_72_0, xb, simplifying % 45.13/6.55 | | with (32), (42) gives: % 45.13/6.55 | | (58) all_72_0 = all_63_1 % 45.13/6.55 | | % 45.13/6.55 | | GROUND_INST: instantiating (12) with all_48_0, all_72_0, xb, simplifying % 45.13/6.55 | | with (17), (42) gives: % 45.13/6.55 | | (59) all_72_0 = all_48_0 % 45.13/6.55 | | % 45.13/6.55 | | COMBINE_EQS: (58), (59) imply: % 45.13/6.55 | | (60) all_63_1 = all_48_0 % 45.13/6.55 | | % 45.13/6.56 | | SIMP: (60) implies: % 45.13/6.56 | | (61) all_63_1 = all_48_0 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (53), (54) imply: % 45.13/6.56 | | (62) all_66_2 = all_48_1 % 45.13/6.56 | | % 45.13/6.56 | | SIMP: (62) implies: % 45.13/6.56 | | (63) all_66_2 = all_48_1 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (56), (57) imply: % 45.13/6.56 | | (64) all_61_0 = all_57_2 % 45.13/6.56 | | % 45.13/6.56 | | SIMP: (64) implies: % 45.13/6.56 | | (65) all_61_0 = all_57_2 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (52), (63) imply: % 45.13/6.56 | | (66) all_61_1 = all_48_1 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (55), (61) imply: % 45.13/6.56 | | (67) all_61_0 = all_48_0 % 45.13/6.56 | | % 45.13/6.56 | | SIMP: (67) implies: % 45.13/6.56 | | (68) all_61_0 = all_48_0 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (65), (68) imply: % 45.13/6.56 | | (69) all_57_2 = all_48_0 % 45.13/6.56 | | % 45.13/6.56 | | COMBINE_EQS: (57), (69) imply: % 45.13/6.56 | | (70) all_66_1 = all_48_0 % 45.13/6.56 | | % 45.13/6.56 | | REDUCE: (40), (54), (59) imply: % 45.13/6.56 | | (71) sdtpldt1(all_48_1, all_48_0) = xI % 45.13/6.56 | | % 45.13/6.56 | | REDUCE: (35), (63), (70) imply: % 45.13/6.56 | | (72) sdtpldt1(all_48_1, all_48_0) = all_66_0 % 45.13/6.56 | | % 45.13/6.56 | | GROUND_INST: instantiating (13) with xI, all_66_0, all_48_0, all_48_1, % 45.13/6.56 | | simplifying with (71), (72) gives: % 45.13/6.56 | | (73) all_66_0 = xI % 45.13/6.56 | | % 45.13/6.56 | | REDUCE: (46), (73) imply: % 45.13/6.56 | | (74) aElementOf0(all_87_0, xI) = 0 % 45.13/6.56 | | % 45.13/6.56 | | GROUND_INST: instantiating (33) with xr, 0, simplifying with (9), (19) % 45.13/6.56 | | gives: % 45.13/6.56 | | (75) xr = sz00 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & iLess0(v0, % 45.13/6.56 | | all_63_0) = v1 & sbrdtbr0(xr) = v0 & $i(v0)) % 45.13/6.56 | | % 45.13/6.56 | | GROUND_INST: instantiating (33) with all_87_0, 0, simplifying with (45), % 45.13/6.56 | | (74) gives: % 45.13/6.56 | | (76) all_87_0 = sz00 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 45.13/6.56 | | iLess0(v0, all_63_0) = v1 & sbrdtbr0(all_87_0) = v0 & $i(v0)) % 45.13/6.56 | | % 45.13/6.56 | | BETA: splitting (75) gives: % 45.13/6.56 | | % 45.13/6.56 | | Case 1: % 45.13/6.56 | | | % 45.13/6.56 | | | (77) xr = sz00 % 45.13/6.56 | | | % 45.13/6.56 | | | REDUCE: (6), (77) imply: % 45.13/6.56 | | | (78) $false % 45.13/6.56 | | | % 45.13/6.56 | | | CLOSE: (78) is inconsistent. % 45.13/6.56 | | | % 45.13/6.56 | | Case 2: % 45.13/6.56 | | | % 45.13/6.56 | | | (79) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & iLess0(v0, all_63_0) = % 45.13/6.56 | | | v1 & sbrdtbr0(xr) = v0 & $i(v0)) % 45.13/6.56 | | | % 45.13/6.56 | | | DELTA: instantiating (79) with fresh symbols all_572_0, all_572_1 gives: % 45.13/6.56 | | | (80) ~ (all_572_0 = 0) & iLess0(all_572_1, all_63_0) = all_572_0 & % 45.13/6.56 | | | sbrdtbr0(xr) = all_572_1 & $i(all_572_1) % 45.13/6.56 | | | % 45.13/6.56 | | | ALPHA: (80) implies: % 45.13/6.56 | | | (81) ~ (all_572_0 = 0) % 45.13/6.56 | | | (82) sbrdtbr0(xr) = all_572_1 % 45.13/6.56 | | | (83) iLess0(all_572_1, all_63_0) = all_572_0 % 45.13/6.56 | | | % 45.13/6.56 | | | REDUCE: (51), (83) imply: % 45.13/6.56 | | | (84) iLess0(all_572_1, all_52_1) = all_572_0 % 45.13/6.56 | | | % 45.13/6.56 | | | BETA: splitting (76) gives: % 45.13/6.56 | | | % 45.13/6.56 | | | Case 1: % 45.13/6.56 | | | | % 45.13/6.56 | | | | (85) all_87_0 = sz00 % 45.13/6.56 | | | | % 45.13/6.56 | | | | REDUCE: (44), (85) imply: % 45.13/6.56 | | | | (86) $false % 45.13/6.56 | | | | % 45.13/6.56 | | | | CLOSE: (86) is inconsistent. % 45.13/6.56 | | | | % 45.13/6.56 | | | Case 2: % 45.13/6.56 | | | | % 45.13/6.56 | | | | % 45.13/6.56 | | | | GROUND_INST: instantiating (11) with all_52_2, all_572_1, xr, % 45.13/6.56 | | | | simplifying with (22), (82) gives: % 45.13/6.56 | | | | (87) all_572_1 = all_52_2 % 45.13/6.56 | | | | % 45.13/6.56 | | | | REDUCE: (84), (87) imply: % 45.13/6.56 | | | | (88) iLess0(all_52_2, all_52_1) = all_572_0 % 45.13/6.56 | | | | % 45.13/6.56 | | | | GROUND_INST: instantiating (14) with 0, all_572_0, all_52_1, all_52_2, % 45.13/6.56 | | | | simplifying with (50), (88) gives: % 45.13/6.56 | | | | (89) all_572_0 = 0 % 45.13/6.56 | | | | % 45.13/6.56 | | | | REDUCE: (81), (89) imply: % 45.13/6.56 | | | | (90) $false % 45.13/6.56 | | | | % 45.13/6.56 | | | | CLOSE: (90) is inconsistent. % 45.13/6.56 | | | | % 45.13/6.56 | | | End of split % 45.13/6.56 | | | % 45.13/6.56 | | End of split % 45.13/6.56 | | % 45.13/6.56 | End of split % 45.13/6.56 | % 45.13/6.56 End of proof % 45.13/6.56 % SZS output end Proof for theBenchmark % 45.13/6.56 % 45.13/6.56 5973ms %------------------------------------------------------------------------------