%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM427+3 : 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 11:47:41 EDT 2023 % Result : Theorem 10.76s 2.30s % Output : Proof 17.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM427+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n010.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Fri Aug 25 15:47:50 EDT 2023 % 0.12/0.33 % CPUTime : % 0.16/0.61 ________ _____ % 0.16/0.61 ___ __ \_________(_)________________________________ % 0.16/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.61 % 0.16/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.61 (2023-06-19) % 0.16/0.61 % 0.16/0.61 (c) Philipp Rümmer, 2009-2023 % 0.16/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.61 Amanda Stjerna. % 0.16/0.61 Free software under BSD-3-Clause. % 0.16/0.61 % 0.16/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.61 % 0.16/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.62 Running up to 7 provers in parallel. % 0.16/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.16/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 2.75/1.18 Prover 4: Preprocessing ... % 2.75/1.18 Prover 1: Preprocessing ... % 3.27/1.24 Prover 0: Preprocessing ... % 3.27/1.24 Prover 2: Preprocessing ... % 3.27/1.24 Prover 3: Preprocessing ... % 3.27/1.24 Prover 5: Preprocessing ... % 3.27/1.25 Prover 6: Preprocessing ... % 7.88/1.90 Prover 3: Constructing countermodel ... % 7.88/1.91 Prover 1: Constructing countermodel ... % 8.15/1.93 Prover 6: Proving ... % 8.85/2.03 Prover 5: Constructing countermodel ... % 8.85/2.05 Prover 4: Constructing countermodel ... % 8.85/2.15 Prover 0: Proving ... % 8.85/2.18 Prover 2: Proving ... % 10.60/2.29 Prover 3: proved (1649ms) % 10.76/2.30 % 10.76/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.76/2.30 % 10.76/2.30 Prover 5: stopped % 10.76/2.30 Prover 0: stopped % 10.76/2.30 Prover 6: stopped % 10.76/2.30 Prover 2: stopped % 10.76/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.76/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.76/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.76/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.76/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.48/2.43 Prover 13: Preprocessing ... % 11.48/2.45 Prover 7: Preprocessing ... % 11.48/2.45 Prover 10: Preprocessing ... % 11.48/2.46 Prover 11: Preprocessing ... % 11.48/2.47 Prover 8: Preprocessing ... % 12.85/2.60 Prover 8: Warning: ignoring some quantifiers % 12.85/2.61 Prover 8: Constructing countermodel ... % 13.11/2.66 Prover 10: Constructing countermodel ... % 13.11/2.69 Prover 13: Constructing countermodel ... % 13.11/2.73 Prover 7: Constructing countermodel ... % 13.11/2.78 Prover 11: Constructing countermodel ... % 15.80/3.05 Prover 1: Found proof (size 146) % 15.80/3.05 Prover 1: proved (2416ms) % 15.80/3.05 Prover 13: stopped % 15.80/3.05 Prover 10: stopped % 15.80/3.05 Prover 7: stopped % 15.80/3.05 Prover 11: stopped % 15.80/3.05 Prover 4: stopped % 15.80/3.05 Prover 8: stopped % 15.80/3.05 % 15.80/3.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.80/3.05 % 16.61/3.14 % SZS output start Proof for theBenchmark % 16.61/3.14 Assumptions after simplification: % 16.61/3.14 --------------------------------- % 16.61/3.14 % 16.61/3.14 (mDivisor) % 16.61/3.19 $i(sz00) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : % 16.61/3.19 ! [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | ~ % 16.61/3.19 $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | ! [v3: $i] % 16.61/3.19 : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) % 16.61/3.19 & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) = % 16.61/3.19 0) | ~ $i(v1) | ( ~ (v1 = sz00) & aInteger0(v1) = 0 & ? [v2: $i] : % 16.61/3.19 (sdtasdt0(v1, v2) = v0 & aInteger0(v2) = 0 & $i(v2)))))) % 16.61/3.19 % 16.61/3.19 (mIntMult) % 16.61/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 16.61/3.19 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 16.61/3.19 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 16.61/3.19 | ~ (v3 = 0) | v5 = 0))) % 16.61/3.19 % 16.61/3.19 (mIntNeg) % 16.61/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 16.61/3.20 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 % 16.61/3.20 = 0))) % 16.61/3.20 % 16.61/3.20 (mIntPlus) % 16.61/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 16.61/3.20 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 16.61/3.20 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 16.61/3.20 | ~ (v3 = 0) | v5 = 0))) % 16.61/3.20 % 16.61/3.20 (mMulComm) % 17.02/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 17.02/3.20 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 17.02/3.20 (sdtasdt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) & % 17.02/3.20 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 17.02/3.20 % 17.02/3.20 (m__) % 17.02/3.21 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: % 17.02/3.21 int] : ( ~ (v3 = 0) & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & % 17.02/3.21 aDivisorOf0(xq, v1) = v2 & sdtpldt0(xb, v0) = v1 & smndt0(xa) = v0 & $i(v1) % 17.02/3.21 & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: % 17.02/3.21 int] : ( ~ (v5 = 0) & aInteger0(v4) = v5))) % 17.02/3.21 % 17.02/3.21 (m__704) % 17.02/3.21 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xb) = 0 & aInteger0(xa) = 0 & % 17.02/3.21 $i(xq) & $i(xb) & $i(xa) & $i(sz00) % 17.02/3.21 % 17.02/3.21 (m__724) % 17.02/3.21 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : % 17.02/3.21 (sdteqdtlpzmzozddtrp0(xa, xb, xq) = 0 & aDivisorOf0(xq, v1) = 0 & sdtpldt0(xa, % 17.02/3.21 v0) = v1 & smndt0(xb) = v0 & $i(v1) & $i(v0) & ? [v2: $i] : (sdtasdt0(xq, % 17.02/3.21 v2) = v1 & aInteger0(v2) = 0 & $i(v2))) % 17.02/3.21 % 17.02/3.21 (m__747) % 17.02/3.21 $i(xn) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, % 17.02/3.21 xn) = v0 & sdtpldt0(xa, v1) = v0 & smndt0(xb) = v1 & aInteger0(xn) = 0 & % 17.02/3.21 $i(v1) & $i(v0)) % 17.02/3.21 % 17.02/3.21 (m__767) % 17.02/3.22 $i(xn) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 17.02/3.22 (sdtasdt0(xq, v0) = v1 & sdtpldt0(xb, v2) = v1 & smndt0(xn) = v0 & smndt0(xa) % 17.02/3.22 = v2 & $i(v2) & $i(v1) & $i(v0)) % 17.02/3.22 % 17.02/3.22 (function-axioms) % 17.02/3.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.02/3.22 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 17.02/3.22 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 17.02/3.22 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.02/3.22 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] : % 17.02/3.22 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 17.02/3.22 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.02/3.22 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 17.02/3.22 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | % 17.02/3.22 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.02/3.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ % 17.02/3.22 (aInteger0(v2) = v0)) % 17.02/3.22 % 17.02/3.22 Further assumptions not needed in the proof: % 17.02/3.22 -------------------------------------------- % 17.02/3.22 mAddAsso, mAddComm, mAddNeg, mAddZero, mDistrib, mEquMod, mEquModRef, mIntOne, % 17.02/3.22 mIntZero, mIntegers, mMulAsso, mMulMinOne, mMulOne, mMulZero, mZeroDiv % 17.02/3.22 % 17.02/3.22 Those formulas are unsatisfiable: % 17.02/3.22 --------------------------------- % 17.02/3.22 % 17.02/3.22 Begin of proof % 17.02/3.22 | % 17.02/3.22 | ALPHA: (mDivisor) implies: % 17.02/3.23 | (1) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! % 17.02/3.23 | [v2: int] : (v2 = 0 | v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | % 17.02/3.23 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v1) = v3) | ! % 17.02/3.23 | [v3: $i] : ( ~ (sdtasdt0(v1, v3) = v0) | ~ $i(v3) | ? [v4: int] % 17.02/3.23 | : ( ~ (v4 = 0) & aInteger0(v3) = v4))) & ! [v1: $i] : ( ~ % 17.02/3.23 | (aDivisorOf0(v1, v0) = 0) | ~ $i(v1) | ( ~ (v1 = sz00) & % 17.02/3.23 | aInteger0(v1) = 0 & ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & % 17.02/3.23 | aInteger0(v2) = 0 & $i(v2)))))) % 17.02/3.23 | % 17.02/3.23 | ALPHA: (m__704) implies: % 17.02/3.23 | (2) aInteger0(xq) = 0 % 17.02/3.23 | % 17.02/3.23 | ALPHA: (m__724) implies: % 17.02/3.23 | (3) ? [v0: $i] : ? [v1: $i] : (sdteqdtlpzmzozddtrp0(xa, xb, xq) = 0 & % 17.02/3.23 | aDivisorOf0(xq, v1) = 0 & sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 & % 17.02/3.23 | $i(v1) & $i(v0) & ? [v2: $i] : (sdtasdt0(xq, v2) = v1 & % 17.02/3.23 | aInteger0(v2) = 0 & $i(v2))) % 17.02/3.23 | % 17.02/3.23 | ALPHA: (m__747) implies: % 17.02/3.23 | (4) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xn) = v0 & sdtpldt0(xa, v1) = % 17.02/3.23 | v0 & smndt0(xb) = v1 & aInteger0(xn) = 0 & $i(v1) & $i(v0)) % 17.02/3.23 | % 17.02/3.23 | ALPHA: (m__767) implies: % 17.02/3.24 | (5) $i(xn) % 17.02/3.24 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xq, v0) = v1 & % 17.02/3.24 | sdtpldt0(xb, v2) = v1 & smndt0(xn) = v0 & smndt0(xa) = v2 & $i(v2) & % 17.02/3.24 | $i(v1) & $i(v0)) % 17.02/3.24 | % 17.02/3.24 | ALPHA: (m__) implies: % 17.02/3.24 | (7) $i(xa) % 17.02/3.24 | (8) $i(xb) % 17.02/3.24 | (9) $i(xq) % 17.02/3.24 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) % 17.02/3.24 | & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xb, xa, xq) = v3 & % 17.02/3.24 | aDivisorOf0(xq, v1) = v2 & sdtpldt0(xb, v0) = v1 & smndt0(xa) = v0 & % 17.02/3.24 | $i(v1) & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~ % 17.02/3.24 | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aInteger0(v4) = v5))) % 17.02/3.24 | % 17.02/3.24 | ALPHA: (function-axioms) implies: % 17.02/3.24 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.02/3.24 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 17.02/3.24 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 17.02/3.24 | v1) | ~ (smndt0(v2) = v0)) % 17.02/3.24 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.02/3.24 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 17.02/3.24 | % 17.02/3.24 | DELTA: instantiating (4) with fresh symbols all_20_0, all_20_1 gives: % 17.02/3.24 | (14) sdtasdt0(xq, xn) = all_20_1 & sdtpldt0(xa, all_20_0) = all_20_1 & % 17.02/3.24 | smndt0(xb) = all_20_0 & aInteger0(xn) = 0 & $i(all_20_0) & % 17.02/3.24 | $i(all_20_1) % 17.02/3.24 | % 17.02/3.24 | ALPHA: (14) implies: % 17.02/3.24 | (15) aInteger0(xn) = 0 % 17.02/3.24 | (16) smndt0(xb) = all_20_0 % 17.02/3.24 | (17) sdtpldt0(xa, all_20_0) = all_20_1 % 17.02/3.24 | (18) sdtasdt0(xq, xn) = all_20_1 % 17.02/3.24 | % 17.02/3.24 | DELTA: instantiating (6) with fresh symbols all_22_0, all_22_1, all_22_2 % 17.02/3.24 | gives: % 17.02/3.24 | (19) sdtasdt0(xq, all_22_2) = all_22_1 & sdtpldt0(xb, all_22_0) = all_22_1 % 17.02/3.24 | & smndt0(xn) = all_22_2 & smndt0(xa) = all_22_0 & $i(all_22_0) & % 17.02/3.24 | $i(all_22_1) & $i(all_22_2) % 17.02/3.24 | % 17.02/3.24 | ALPHA: (19) implies: % 17.02/3.24 | (20) $i(all_22_2) % 17.02/3.24 | (21) smndt0(xa) = all_22_0 % 17.02/3.25 | (22) smndt0(xn) = all_22_2 % 17.02/3.25 | (23) sdtpldt0(xb, all_22_0) = all_22_1 % 17.02/3.25 | (24) sdtasdt0(xq, all_22_2) = all_22_1 % 17.02/3.25 | % 17.02/3.25 | DELTA: instantiating (3) with fresh symbols all_24_0, all_24_1 gives: % 17.02/3.25 | (25) sdteqdtlpzmzozddtrp0(xa, xb, xq) = 0 & aDivisorOf0(xq, all_24_0) = 0 & % 17.02/3.25 | sdtpldt0(xa, all_24_1) = all_24_0 & smndt0(xb) = all_24_1 & % 17.02/3.25 | $i(all_24_0) & $i(all_24_1) & ? [v0: $i] : (sdtasdt0(xq, v0) = % 17.02/3.25 | all_24_0 & aInteger0(v0) = 0 & $i(v0)) % 17.02/3.25 | % 17.02/3.25 | ALPHA: (25) implies: % 17.02/3.25 | (26) $i(all_24_1) % 17.02/3.25 | (27) $i(all_24_0) % 17.02/3.25 | (28) smndt0(xb) = all_24_1 % 17.02/3.25 | (29) sdtpldt0(xa, all_24_1) = all_24_0 % 17.02/3.25 | (30) aDivisorOf0(xq, all_24_0) = 0 % 17.02/3.25 | (31) ? [v0: $i] : (sdtasdt0(xq, v0) = all_24_0 & aInteger0(v0) = 0 & % 17.02/3.25 | $i(v0)) % 17.02/3.25 | % 17.02/3.25 | DELTA: instantiating (10) with fresh symbols all_29_0, all_29_1, all_29_2, % 17.02/3.25 | all_29_3 gives: % 17.02/3.25 | (32) ~ (all_29_0 = 0) & ~ (all_29_1 = 0) & sdteqdtlpzmzozddtrp0(xb, xa, % 17.02/3.25 | xq) = all_29_0 & aDivisorOf0(xq, all_29_2) = all_29_1 & sdtpldt0(xb, % 17.02/3.25 | all_29_3) = all_29_2 & smndt0(xa) = all_29_3 & $i(all_29_2) & % 17.02/3.25 | $i(all_29_3) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_29_2) | ~ % 17.02/3.25 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)) % 17.02/3.25 | % 17.02/3.25 | ALPHA: (32) implies: % 17.02/3.25 | (33) ~ (all_29_1 = 0) % 17.02/3.25 | (34) $i(all_29_3) % 17.02/3.25 | (35) $i(all_29_2) % 17.02/3.25 | (36) smndt0(xa) = all_29_3 % 17.02/3.25 | (37) sdtpldt0(xb, all_29_3) = all_29_2 % 17.02/3.25 | (38) aDivisorOf0(xq, all_29_2) = all_29_1 % 17.02/3.25 | % 17.02/3.25 | DELTA: instantiating (31) with fresh symbol all_32_0 gives: % 17.02/3.25 | (39) sdtasdt0(xq, all_32_0) = all_24_0 & aInteger0(all_32_0) = 0 & % 17.02/3.25 | $i(all_32_0) % 17.02/3.25 | % 17.02/3.25 | ALPHA: (39) implies: % 17.02/3.25 | (40) $i(all_32_0) % 17.02/3.25 | (41) aInteger0(all_32_0) = 0 % 17.02/3.25 | (42) sdtasdt0(xq, all_32_0) = all_24_0 % 17.02/3.25 | % 17.02/3.25 | GROUND_INST: instantiating (12) with all_22_0, all_29_3, xa, simplifying with % 17.02/3.26 | (21), (36) gives: % 17.02/3.26 | (43) all_29_3 = all_22_0 % 17.02/3.26 | % 17.02/3.26 | GROUND_INST: instantiating (12) with all_20_0, all_24_1, xb, simplifying with % 17.02/3.26 | (16), (28) gives: % 17.02/3.26 | (44) all_24_1 = all_20_0 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (37), (43) imply: % 17.02/3.26 | (45) sdtpldt0(xb, all_22_0) = all_29_2 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (29), (44) imply: % 17.02/3.26 | (46) sdtpldt0(xa, all_20_0) = all_24_0 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (34), (43) imply: % 17.02/3.26 | (47) $i(all_22_0) % 17.02/3.26 | % 17.02/3.26 | REDUCE: (26), (44) imply: % 17.02/3.26 | (48) $i(all_20_0) % 17.02/3.26 | % 17.02/3.26 | GROUND_INST: instantiating (13) with all_20_1, all_24_0, all_20_0, xa, % 17.02/3.26 | simplifying with (17), (46) gives: % 17.02/3.26 | (49) all_24_0 = all_20_1 % 17.02/3.26 | % 17.02/3.26 | GROUND_INST: instantiating (13) with all_22_1, all_29_2, all_22_0, xb, % 17.02/3.26 | simplifying with (23), (45) gives: % 17.02/3.26 | (50) all_29_2 = all_22_1 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (38), (50) imply: % 17.02/3.26 | (51) aDivisorOf0(xq, all_22_1) = all_29_1 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (30), (49) imply: % 17.02/3.26 | (52) aDivisorOf0(xq, all_20_1) = 0 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (42), (49) imply: % 17.02/3.26 | (53) sdtasdt0(xq, all_32_0) = all_20_1 % 17.02/3.26 | % 17.02/3.26 | REDUCE: (35), (50) imply: % 17.02/3.26 | (54) $i(all_22_1) % 17.02/3.26 | % 17.02/3.26 | REDUCE: (27), (49) imply: % 17.02/3.26 | (55) $i(all_20_1) % 17.02/3.26 | % 17.02/3.26 | GROUND_INST: instantiating (mIntNeg) with xn, all_22_2, simplifying with (5), % 17.02/3.26 | (22) gives: % 17.02/3.26 | (56) ? [v0: any] : ? [v1: any] : (aInteger0(all_22_2) = v1 & % 17.02/3.26 | aInteger0(xn) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 17.02/3.26 | % 17.02/3.27 | GROUND_INST: instantiating (mIntPlus) with xa, all_20_0, all_20_1, simplifying % 17.02/3.27 | with (7), (17), (48) gives: % 17.02/3.27 | (57) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_20_0) = v1 % 17.02/3.27 | & aInteger0(all_20_1) = v2 & aInteger0(xa) = v0 & ( ~ (v1 = 0) | ~ % 17.02/3.27 | (v0 = 0) | v2 = 0)) % 17.02/3.27 | % 17.02/3.27 | GROUND_INST: instantiating (mIntPlus) with xb, all_22_0, all_22_1, simplifying % 17.02/3.27 | with (8), (23), (47) gives: % 17.02/3.27 | (58) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_22_0) = v1 % 17.02/3.27 | & aInteger0(all_22_1) = v2 & aInteger0(xb) = v0 & ( ~ (v1 = 0) | ~ % 17.02/3.27 | (v0 = 0) | v2 = 0)) % 17.02/3.27 | % 17.02/3.27 | GROUND_INST: instantiating (mMulComm) with xq, xn, all_20_1, simplifying with % 17.02/3.27 | (5), (9), (18) gives: % 17.02/3.27 | (59) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xn, xq) = v2 & % 17.02/3.27 | aInteger0(xn) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 17.02/3.27 | (v0 = 0) | v2 = all_20_1)) % 17.02/3.27 | % 17.02/3.27 | GROUND_INST: instantiating (mIntMult) with xq, xn, all_20_1, simplifying with % 17.02/3.27 | (5), (9), (18) gives: % 17.02/3.27 | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_20_1) = v2 % 17.02/3.27 | & aInteger0(xn) = v1 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 17.02/3.27 | 0) | v2 = 0)) % 17.02/3.27 | % 17.02/3.27 | GROUND_INST: instantiating (mMulComm) with xq, all_22_2, all_22_1, simplifying % 17.02/3.27 | with (9), (20), (24) gives: % 17.02/3.27 | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_22_2, xq) = % 17.02/3.27 | v2 & aInteger0(all_22_2) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~ % 17.02/3.27 | (v1 = 0) | ~ (v0 = 0) | v2 = all_22_1)) % 17.02/3.28 | % 17.02/3.28 | GROUND_INST: instantiating (mIntMult) with xq, all_22_2, all_22_1, simplifying % 17.02/3.28 | with (9), (20), (24) gives: % 17.02/3.28 | (62) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_22_1) = v2 % 17.02/3.28 | & aInteger0(all_22_2) = v1 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~ % 17.02/3.28 | (v0 = 0) | v2 = 0)) % 17.02/3.28 | % 17.02/3.28 | GROUND_INST: instantiating (mMulComm) with xq, all_32_0, all_20_1, simplifying % 17.02/3.28 | with (9), (40), (53) gives: % 17.02/3.28 | (63) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_32_0, xq) = % 17.02/3.28 | v2 & aInteger0(all_32_0) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~ % 17.02/3.28 | (v1 = 0) | ~ (v0 = 0) | v2 = all_20_1)) % 17.02/3.28 | % 17.02/3.28 | GROUND_INST: instantiating (mIntMult) with xq, all_32_0, all_20_1, simplifying % 17.02/3.28 | with (9), (40), (53) gives: % 17.02/3.28 | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_32_0) = v1 % 17.02/3.28 | & aInteger0(all_20_1) = v2 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~ % 17.02/3.28 | (v0 = 0) | v2 = 0)) % 17.02/3.28 | % 17.02/3.28 | DELTA: instantiating (56) with fresh symbols all_54_0, all_54_1 gives: % 17.02/3.28 | (65) aInteger0(all_22_2) = all_54_0 & aInteger0(xn) = all_54_1 & ( ~ % 17.02/3.28 | (all_54_1 = 0) | all_54_0 = 0) % 17.02/3.28 | % 17.02/3.28 | ALPHA: (65) implies: % 17.02/3.28 | (66) aInteger0(xn) = all_54_1 % 17.02/3.28 | (67) aInteger0(all_22_2) = all_54_0 % 17.02/3.28 | (68) ~ (all_54_1 = 0) | all_54_0 = 0 % 17.02/3.28 | % 17.02/3.28 | DELTA: instantiating (64) with fresh symbols all_62_0, all_62_1, all_62_2 % 17.02/3.28 | gives: % 17.02/3.28 | (69) aInteger0(all_32_0) = all_62_1 & aInteger0(all_20_1) = all_62_0 & % 17.02/3.28 | aInteger0(xq) = all_62_2 & ( ~ (all_62_1 = 0) | ~ (all_62_2 = 0) | % 17.02/3.28 | all_62_0 = 0) % 17.43/3.28 | % 17.43/3.28 | ALPHA: (69) implies: % 17.43/3.28 | (70) aInteger0(xq) = all_62_2 % 17.43/3.29 | (71) aInteger0(all_20_1) = all_62_0 % 17.43/3.29 | (72) aInteger0(all_32_0) = all_62_1 % 17.43/3.29 | (73) ~ (all_62_1 = 0) | ~ (all_62_2 = 0) | all_62_0 = 0 % 17.43/3.29 | % 17.43/3.29 | DELTA: instantiating (58) with fresh symbols all_64_0, all_64_1, all_64_2 % 17.43/3.29 | gives: % 17.43/3.29 | (74) aInteger0(all_22_0) = all_64_1 & aInteger0(all_22_1) = all_64_0 & % 17.43/3.29 | aInteger0(xb) = all_64_2 & ( ~ (all_64_1 = 0) | ~ (all_64_2 = 0) | % 17.43/3.29 | all_64_0 = 0) % 17.43/3.29 | % 17.43/3.29 | ALPHA: (74) implies: % 17.43/3.29 | (75) aInteger0(all_22_1) = all_64_0 % 17.43/3.29 | % 17.43/3.29 | DELTA: instantiating (57) with fresh symbols all_66_0, all_66_1, all_66_2 % 17.43/3.29 | gives: % 17.43/3.29 | (76) aInteger0(all_20_0) = all_66_1 & aInteger0(all_20_1) = all_66_0 & % 17.43/3.29 | aInteger0(xa) = all_66_2 & ( ~ (all_66_1 = 0) | ~ (all_66_2 = 0) | % 17.43/3.29 | all_66_0 = 0) % 17.43/3.29 | % 17.43/3.29 | ALPHA: (76) implies: % 17.43/3.29 | (77) aInteger0(all_20_1) = all_66_0 % 17.43/3.29 | % 17.43/3.29 | DELTA: instantiating (62) with fresh symbols all_68_0, all_68_1, all_68_2 % 17.43/3.29 | gives: % 17.43/3.29 | (78) aInteger0(all_22_1) = all_68_0 & aInteger0(all_22_2) = all_68_1 & % 17.43/3.29 | aInteger0(xq) = all_68_2 & ( ~ (all_68_1 = 0) | ~ (all_68_2 = 0) | % 17.43/3.29 | all_68_0 = 0) % 17.43/3.29 | % 17.43/3.29 | ALPHA: (78) implies: % 17.43/3.29 | (79) aInteger0(xq) = all_68_2 % 17.43/3.29 | (80) aInteger0(all_22_2) = all_68_1 % 17.43/3.29 | (81) aInteger0(all_22_1) = all_68_0 % 17.43/3.29 | (82) ~ (all_68_1 = 0) | ~ (all_68_2 = 0) | all_68_0 = 0 % 17.43/3.29 | % 17.43/3.29 | DELTA: instantiating (60) with fresh symbols all_70_0, all_70_1, all_70_2 % 17.43/3.29 | gives: % 17.43/3.29 | (83) aInteger0(all_20_1) = all_70_0 & aInteger0(xn) = all_70_1 & % 17.43/3.29 | aInteger0(xq) = all_70_2 & ( ~ (all_70_1 = 0) | ~ (all_70_2 = 0) | % 17.43/3.29 | all_70_0 = 0) % 17.43/3.29 | % 17.43/3.29 | ALPHA: (83) implies: % 17.43/3.29 | (84) aInteger0(xq) = all_70_2 % 17.43/3.29 | (85) aInteger0(xn) = all_70_1 % 17.43/3.30 | (86) aInteger0(all_20_1) = all_70_0 % 17.43/3.30 | % 17.43/3.30 | DELTA: instantiating (61) with fresh symbols all_72_0, all_72_1, all_72_2 % 17.43/3.30 | gives: % 17.43/3.30 | (87) sdtasdt0(all_22_2, xq) = all_72_0 & aInteger0(all_22_2) = all_72_1 & % 17.43/3.30 | aInteger0(xq) = all_72_2 & $i(all_72_0) & ( ~ (all_72_1 = 0) | ~ % 17.43/3.30 | (all_72_2 = 0) | all_72_0 = all_22_1) % 17.43/3.30 | % 17.43/3.30 | ALPHA: (87) implies: % 17.43/3.30 | (88) aInteger0(xq) = all_72_2 % 17.43/3.30 | (89) aInteger0(all_22_2) = all_72_1 % 17.43/3.30 | % 17.43/3.30 | DELTA: instantiating (59) with fresh symbols all_74_0, all_74_1, all_74_2 % 17.43/3.30 | gives: % 17.43/3.30 | (90) sdtasdt0(xn, xq) = all_74_0 & aInteger0(xn) = all_74_1 & aInteger0(xq) % 17.43/3.30 | = all_74_2 & $i(all_74_0) & ( ~ (all_74_1 = 0) | ~ (all_74_2 = 0) | % 17.43/3.30 | all_74_0 = all_20_1) % 17.43/3.30 | % 17.43/3.30 | ALPHA: (90) implies: % 17.43/3.30 | (91) aInteger0(xq) = all_74_2 % 17.43/3.30 | (92) aInteger0(xn) = all_74_1 % 17.43/3.30 | % 17.43/3.30 | DELTA: instantiating (63) with fresh symbols all_76_0, all_76_1, all_76_2 % 17.43/3.30 | gives: % 17.43/3.30 | (93) sdtasdt0(all_32_0, xq) = all_76_0 & aInteger0(all_32_0) = all_76_1 & % 17.43/3.30 | aInteger0(xq) = all_76_2 & $i(all_76_0) & ( ~ (all_76_1 = 0) | ~ % 17.43/3.30 | (all_76_2 = 0) | all_76_0 = all_20_1) % 17.43/3.30 | % 17.43/3.30 | ALPHA: (93) implies: % 17.43/3.30 | (94) aInteger0(xq) = all_76_2 % 17.43/3.30 | (95) aInteger0(all_32_0) = all_76_1 % 17.43/3.30 | % 17.43/3.30 | GROUND_INST: instantiating (11) with all_70_2, all_72_2, xq, simplifying with % 17.43/3.30 | (84), (88) gives: % 17.43/3.30 | (96) all_72_2 = all_70_2 % 17.43/3.30 | % 17.43/3.30 | GROUND_INST: instantiating (11) with 0, all_74_2, xq, simplifying with (2), % 17.43/3.30 | (91) gives: % 17.43/3.30 | (97) all_74_2 = 0 % 17.43/3.30 | % 17.43/3.30 | GROUND_INST: instantiating (11) with all_72_2, all_74_2, xq, simplifying with % 17.43/3.30 | (88), (91) gives: % 17.43/3.30 | (98) all_74_2 = all_72_2 % 17.43/3.30 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_68_2, all_74_2, xq, simplifying with % 17.43/3.31 | (79), (91) gives: % 17.43/3.31 | (99) all_74_2 = all_68_2 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_72_2, all_76_2, xq, simplifying with % 17.43/3.31 | (88), (94) gives: % 17.43/3.31 | (100) all_76_2 = all_72_2 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_62_2, all_76_2, xq, simplifying with % 17.43/3.31 | (70), (94) gives: % 17.43/3.31 | (101) all_76_2 = all_62_2 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_54_1, all_70_1, xn, simplifying with % 17.43/3.31 | (66), (85) gives: % 17.43/3.31 | (102) all_70_1 = all_54_1 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with 0, all_74_1, xn, simplifying with (15), % 17.43/3.31 | (92) gives: % 17.43/3.31 | (103) all_74_1 = 0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_70_1, all_74_1, xn, simplifying with % 17.43/3.31 | (85), (92) gives: % 17.43/3.31 | (104) all_74_1 = all_70_1 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_66_0, all_70_0, all_20_1, simplifying % 17.43/3.31 | with (77), (86) gives: % 17.43/3.31 | (105) all_70_0 = all_66_0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_62_0, all_70_0, all_20_1, simplifying % 17.43/3.31 | with (71), (86) gives: % 17.43/3.31 | (106) all_70_0 = all_62_0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_68_1, all_72_1, all_22_2, simplifying % 17.43/3.31 | with (80), (89) gives: % 17.43/3.31 | (107) all_72_1 = all_68_1 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_54_0, all_72_1, all_22_2, simplifying % 17.43/3.31 | with (67), (89) gives: % 17.43/3.31 | (108) all_72_1 = all_54_0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_64_0, all_68_0, all_22_1, simplifying % 17.43/3.31 | with (75), (81) gives: % 17.43/3.31 | (109) all_68_0 = all_64_0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with 0, all_76_1, all_32_0, simplifying with % 17.43/3.31 | (41), (95) gives: % 17.43/3.31 | (110) all_76_1 = 0 % 17.43/3.31 | % 17.43/3.31 | GROUND_INST: instantiating (11) with all_62_1, all_76_1, all_32_0, simplifying % 17.43/3.31 | with (72), (95) gives: % 17.43/3.31 | (111) all_76_1 = all_62_1 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (110), (111) imply: % 17.43/3.31 | (112) all_62_1 = 0 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (100), (101) imply: % 17.43/3.31 | (113) all_72_2 = all_62_2 % 17.43/3.31 | % 17.43/3.31 | SIMP: (113) implies: % 17.43/3.31 | (114) all_72_2 = all_62_2 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (103), (104) imply: % 17.43/3.31 | (115) all_70_1 = 0 % 17.43/3.31 | % 17.43/3.31 | SIMP: (115) implies: % 17.43/3.31 | (116) all_70_1 = 0 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (98), (99) imply: % 17.43/3.31 | (117) all_72_2 = all_68_2 % 17.43/3.31 | % 17.43/3.31 | SIMP: (117) implies: % 17.43/3.31 | (118) all_72_2 = all_68_2 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (97), (99) imply: % 17.43/3.31 | (119) all_68_2 = 0 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (107), (108) imply: % 17.43/3.31 | (120) all_68_1 = all_54_0 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (96), (118) imply: % 17.43/3.31 | (121) all_70_2 = all_68_2 % 17.43/3.31 | % 17.43/3.31 | COMBINE_EQS: (96), (114) imply: % 17.43/3.32 | (122) all_70_2 = all_62_2 % 17.43/3.32 | % 17.43/3.32 | COMBINE_EQS: (105), (106) imply: % 17.43/3.32 | (123) all_66_0 = all_62_0 % 17.43/3.32 | % 17.43/3.32 | COMBINE_EQS: (102), (116) imply: % 17.43/3.32 | (124) all_54_1 = 0 % 17.43/3.32 | % 17.43/3.32 | SIMP: (124) implies: % 17.43/3.32 | (125) all_54_1 = 0 % 17.43/3.32 | % 17.43/3.32 | COMBINE_EQS: (121), (122) imply: % 17.43/3.32 | (126) all_68_2 = all_62_2 % 17.43/3.32 | % 17.43/3.32 | SIMP: (126) implies: % 17.43/3.32 | (127) all_68_2 = all_62_2 % 17.43/3.32 | % 17.43/3.32 | COMBINE_EQS: (119), (127) imply: % 17.43/3.32 | (128) all_62_2 = 0 % 17.43/3.32 | % 17.43/3.32 | SIMP: (128) implies: % 17.43/3.32 | (129) all_62_2 = 0 % 17.43/3.32 | % 17.43/3.32 | BETA: splitting (68) gives: % 17.43/3.32 | % 17.43/3.32 | Case 1: % 17.43/3.32 | | % 17.43/3.32 | | (130) ~ (all_54_1 = 0) % 17.43/3.32 | | % 17.43/3.32 | | REDUCE: (125), (130) imply: % 17.43/3.32 | | (131) $false % 17.43/3.32 | | % 17.43/3.32 | | CLOSE: (131) is inconsistent. % 17.43/3.32 | | % 17.43/3.32 | Case 2: % 17.43/3.32 | | % 17.43/3.32 | | (132) all_54_0 = 0 % 17.43/3.32 | | % 17.43/3.32 | | COMBINE_EQS: (120), (132) imply: % 17.43/3.32 | | (133) all_68_1 = 0 % 17.43/3.32 | | % 17.43/3.32 | | REDUCE: (67), (132) imply: % 17.43/3.32 | | (134) aInteger0(all_22_2) = 0 % 17.43/3.32 | | % 17.43/3.32 | | BETA: splitting (73) gives: % 17.43/3.32 | | % 17.43/3.32 | | Case 1: % 17.43/3.32 | | | % 17.43/3.32 | | | (135) ~ (all_62_1 = 0) % 17.43/3.32 | | | % 17.43/3.32 | | | REDUCE: (112), (135) imply: % 17.43/3.32 | | | (136) $false % 17.43/3.32 | | | % 17.43/3.32 | | | CLOSE: (136) is inconsistent. % 17.43/3.32 | | | % 17.43/3.32 | | Case 2: % 17.43/3.32 | | | % 17.43/3.32 | | | (137) ~ (all_62_2 = 0) | all_62_0 = 0 % 17.43/3.32 | | | % 17.43/3.32 | | | BETA: splitting (82) gives: % 17.43/3.32 | | | % 17.43/3.32 | | | Case 1: % 17.43/3.32 | | | | % 17.43/3.32 | | | | (138) ~ (all_68_1 = 0) % 17.43/3.32 | | | | % 17.43/3.32 | | | | REDUCE: (133), (138) imply: % 17.43/3.32 | | | | (139) $false % 17.43/3.32 | | | | % 17.43/3.32 | | | | CLOSE: (139) is inconsistent. % 17.43/3.32 | | | | % 17.43/3.32 | | | Case 2: % 17.43/3.32 | | | | % 17.43/3.32 | | | | (140) ~ (all_68_2 = 0) | all_68_0 = 0 % 17.43/3.32 | | | | % 17.43/3.32 | | | | BETA: splitting (140) gives: % 17.43/3.32 | | | | % 17.43/3.32 | | | | Case 1: % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | (141) ~ (all_68_2 = 0) % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | REDUCE: (119), (141) imply: % 17.43/3.32 | | | | | (142) $false % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | CLOSE: (142) is inconsistent. % 17.43/3.32 | | | | | % 17.43/3.32 | | | | Case 2: % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | (143) all_68_0 = 0 % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | COMBINE_EQS: (109), (143) imply: % 17.43/3.32 | | | | | (144) all_64_0 = 0 % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | SIMP: (144) implies: % 17.43/3.32 | | | | | (145) all_64_0 = 0 % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | REDUCE: (75), (145) imply: % 17.43/3.32 | | | | | (146) aInteger0(all_22_1) = 0 % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | BETA: splitting (137) gives: % 17.43/3.32 | | | | | % 17.43/3.32 | | | | | Case 1: % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | | (147) ~ (all_62_2 = 0) % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | | REDUCE: (129), (147) imply: % 17.43/3.32 | | | | | | (148) $false % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | | CLOSE: (148) is inconsistent. % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | Case 2: % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | | (149) all_62_0 = 0 % 17.43/3.32 | | | | | | % 17.43/3.32 | | | | | | REDUCE: (71), (149) imply: % 17.43/3.33 | | | | | | (150) aInteger0(all_20_1) = 0 % 17.43/3.33 | | | | | | % 17.43/3.33 | | | | | | GROUND_INST: instantiating (1) with all_20_1, simplifying with (55), % 17.43/3.33 | | | | | | (150) gives: % 17.43/3.33 | | | | | | (151) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = sz00 | ~ % 17.43/3.33 | | | | | | (aDivisorOf0(v0, all_20_1) = v1) | ~ $i(v0) | ? [v2: % 17.43/3.33 | | | | | | int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! [v2: $i] % 17.43/3.33 | | | | | | : ( ~ (sdtasdt0(v0, v2) = all_20_1) | ~ $i(v2) | ? [v3: % 17.43/3.33 | | | | | | int] : ( ~ (v3 = 0) & aInteger0(v2) = v3))) & ! [v0: % 17.43/3.33 | | | | | | $i] : ( ~ (aDivisorOf0(v0, all_20_1) = 0) | ~ $i(v0) | ( % 17.43/3.33 | | | | | | ~ (v0 = sz00) & aInteger0(v0) = 0 & ? [v1: $i] : % 17.43/3.33 | | | | | | (sdtasdt0(v0, v1) = all_20_1 & aInteger0(v1) = 0 & % 17.43/3.33 | | | | | | $i(v1)))) % 17.43/3.33 | | | | | | % 17.43/3.33 | | | | | | ALPHA: (151) implies: % 17.43/3.33 | | | | | | (152) ! [v0: $i] : ( ~ (aDivisorOf0(v0, all_20_1) = 0) | ~ % 17.43/3.33 | | | | | | $i(v0) | ( ~ (v0 = sz00) & aInteger0(v0) = 0 & ? [v1: % 17.43/3.33 | | | | | | $i] : (sdtasdt0(v0, v1) = all_20_1 & aInteger0(v1) = % 17.43/3.33 | | | | | | 0 & $i(v1)))) % 17.43/3.33 | | | | | | % 17.43/3.33 | | | | | | GROUND_INST: instantiating (1) with all_22_1, simplifying with (54), % 17.43/3.33 | | | | | | (146) gives: % 17.43/3.33 | | | | | | (153) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = sz00 | ~ % 17.43/3.33 | | | | | | (aDivisorOf0(v0, all_22_1) = v1) | ~ $i(v0) | ? [v2: % 17.43/3.33 | | | | | | int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! [v2: $i] % 17.43/3.33 | | | | | | : ( ~ (sdtasdt0(v0, v2) = all_22_1) | ~ $i(v2) | ? [v3: % 17.43/3.33 | | | | | | int] : ( ~ (v3 = 0) & aInteger0(v2) = v3))) & ! [v0: % 17.43/3.33 | | | | | | $i] : ( ~ (aDivisorOf0(v0, all_22_1) = 0) | ~ $i(v0) | ( % 17.43/3.33 | | | | | | ~ (v0 = sz00) & aInteger0(v0) = 0 & ? [v1: $i] : % 17.43/3.33 | | | | | | (sdtasdt0(v0, v1) = all_22_1 & aInteger0(v1) = 0 & % 17.43/3.33 | | | | | | $i(v1)))) % 17.43/3.33 | | | | | | % 17.43/3.33 | | | | | | ALPHA: (153) implies: % 17.43/3.33 | | | | | | (154) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = sz00 | ~ % 17.43/3.33 | | | | | | (aDivisorOf0(v0, all_22_1) = v1) | ~ $i(v0) | ? [v2: % 17.43/3.33 | | | | | | int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! [v2: $i] % 17.43/3.33 | | | | | | : ( ~ (sdtasdt0(v0, v2) = all_22_1) | ~ $i(v2) | ? [v3: % 17.43/3.33 | | | | | | int] : ( ~ (v3 = 0) & aInteger0(v2) = v3))) % 17.43/3.33 | | | | | | % 17.43/3.34 | | | | | | GROUND_INST: instantiating (154) with xq, all_29_1, simplifying with % 17.43/3.34 | | | | | | (9), (51) gives: % 17.43/3.34 | | | | | | (155) all_29_1 = 0 | xq = sz00 | ? [v0: int] : ( ~ (v0 = 0) & % 17.43/3.34 | | | | | | aInteger0(xq) = v0) | ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) % 17.43/3.34 | | | | | | = all_22_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.43/3.34 | | | | | | aInteger0(v0) = v1)) % 17.43/3.34 | | | | | | % 17.43/3.34 | | | | | | GROUND_INST: instantiating (152) with xq, simplifying with (9), (52) % 17.43/3.34 | | | | | | gives: % 17.43/3.34 | | | | | | (156) ~ (xq = sz00) & aInteger0(xq) = 0 & ? [v0: $i] : % 17.43/3.34 | | | | | | (sdtasdt0(xq, v0) = all_20_1 & aInteger0(v0) = 0 & $i(v0)) % 17.43/3.34 | | | | | | % 17.43/3.34 | | | | | | ALPHA: (156) implies: % 17.43/3.34 | | | | | | (157) ~ (xq = sz00) % 17.43/3.34 | | | | | | % 17.43/3.34 | | | | | | BETA: splitting (155) gives: % 17.43/3.34 | | | | | | % 17.43/3.34 | | | | | | Case 1: % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | (158) xq = sz00 % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | REDUCE: (157), (158) imply: % 17.43/3.34 | | | | | | | (159) $false % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | CLOSE: (159) is inconsistent. % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | Case 2: % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | (160) all_29_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 17.43/3.34 | | | | | | | aInteger0(xq) = v0) | ! [v0: $i] : ( ~ (sdtasdt0(xq, % 17.43/3.34 | | | | | | | v0) = all_22_1) | ~ $i(v0) | ? [v1: int] : ( ~ % 17.43/3.34 | | | | | | | (v1 = 0) & aInteger0(v0) = v1)) % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | BETA: splitting (160) gives: % 17.43/3.34 | | | | | | | % 17.43/3.34 | | | | | | | Case 1: % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | (161) all_29_1 = 0 % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | REDUCE: (33), (161) imply: % 17.43/3.34 | | | | | | | | (162) $false % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | CLOSE: (162) is inconsistent. % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | Case 2: % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | (163) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(xq) = v0) | ! % 17.43/3.34 | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_22_1) | ~ % 17.43/3.34 | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) % 17.43/3.34 | | | | | | | | = v1)) % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | BETA: splitting (163) gives: % 17.43/3.34 | | | | | | | | % 17.43/3.34 | | | | | | | | Case 1: % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | (164) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(xq) = v0) % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | DELTA: instantiating (164) with fresh symbol all_195_0 gives: % 17.43/3.34 | | | | | | | | | (165) ~ (all_195_0 = 0) & aInteger0(xq) = all_195_0 % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | ALPHA: (165) implies: % 17.43/3.34 | | | | | | | | | (166) ~ (all_195_0 = 0) % 17.43/3.34 | | | | | | | | | (167) aInteger0(xq) = all_195_0 % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_195_0, xq, % 17.43/3.34 | | | | | | | | | simplifying with (2), (167) gives: % 17.43/3.34 | | | | | | | | | (168) all_195_0 = 0 % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | REDUCE: (166), (168) imply: % 17.43/3.34 | | | | | | | | | (169) $false % 17.43/3.34 | | | | | | | | | % 17.43/3.34 | | | | | | | | | CLOSE: (169) is inconsistent. % 17.43/3.34 | | | | | | | | | % 17.43/3.35 | | | | | | | | Case 2: % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | (170) ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_22_1) | ~ % 17.43/3.35 | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.43/3.35 | | | | | | | | | aInteger0(v0) = v1)) % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | GROUND_INST: instantiating (170) with all_22_2, simplifying % 17.43/3.35 | | | | | | | | | with (20), (24) gives: % 17.43/3.35 | | | | | | | | | (171) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_22_2) = % 17.43/3.35 | | | | | | | | | v0) % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | DELTA: instantiating (171) with fresh symbol all_196_0 gives: % 17.43/3.35 | | | | | | | | | (172) ~ (all_196_0 = 0) & aInteger0(all_22_2) = all_196_0 % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | ALPHA: (172) implies: % 17.43/3.35 | | | | | | | | | (173) ~ (all_196_0 = 0) % 17.43/3.35 | | | | | | | | | (174) aInteger0(all_22_2) = all_196_0 % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_196_0, all_22_2, % 17.43/3.35 | | | | | | | | | simplifying with (134), (174) gives: % 17.43/3.35 | | | | | | | | | (175) all_196_0 = 0 % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | REDUCE: (173), (175) imply: % 17.43/3.35 | | | | | | | | | (176) $false % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | | CLOSE: (176) is inconsistent. % 17.43/3.35 | | | | | | | | | % 17.43/3.35 | | | | | | | | End of split % 17.43/3.35 | | | | | | | | % 17.43/3.35 | | | | | | | End of split % 17.43/3.35 | | | | | | | % 17.43/3.35 | | | | | | End of split % 17.43/3.35 | | | | | | % 17.43/3.35 | | | | | End of split % 17.43/3.35 | | | | | % 17.43/3.35 | | | | End of split % 17.43/3.35 | | | | % 17.43/3.35 | | | End of split % 17.43/3.35 | | | % 17.43/3.35 | | End of split % 17.43/3.35 | | % 17.43/3.35 | End of split % 17.43/3.35 | % 17.43/3.35 End of proof % 17.43/3.35 % SZS output end Proof for theBenchmark % 17.43/3.35 % 17.43/3.35 2741ms %------------------------------------------------------------------------------