%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM429+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 36.91s 5.90s % Output : Proof 37.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM429+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 11:02:52 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.90/1.17 Prover 4: Preprocessing ... % 2.90/1.17 Prover 1: Preprocessing ... % 3.33/1.22 Prover 2: Preprocessing ... % 3.33/1.22 Prover 0: Preprocessing ... % 3.33/1.22 Prover 5: Preprocessing ... % 3.33/1.22 Prover 3: Preprocessing ... % 3.33/1.22 Prover 6: Preprocessing ... % 6.04/1.64 Prover 1: Constructing countermodel ... % 6.37/1.67 Prover 3: Constructing countermodel ... % 6.37/1.70 Prover 6: Proving ... % 7.09/1.82 Prover 4: Constructing countermodel ... % 7.67/1.86 Prover 5: Constructing countermodel ... % 7.67/1.90 Prover 2: Proving ... % 8.14/1.94 Prover 0: Proving ... % 8.46/2.03 Prover 3: gave up % 9.00/2.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.27/2.09 Prover 7: Preprocessing ... % 9.27/2.21 Prover 1: gave up % 9.27/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.27/2.25 Prover 8: Preprocessing ... % 10.84/2.30 Prover 7: Constructing countermodel ... % 10.84/2.36 Prover 8: Warning: ignoring some quantifiers % 11.37/2.39 Prover 8: Constructing countermodel ... % 14.37/2.79 Prover 8: gave up % 14.60/2.80 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 14.60/2.85 Prover 9: Preprocessing ... % 16.55/3.11 Prover 9: Constructing countermodel ... % 36.91/5.90 Prover 7: Found proof (size 32) % 36.91/5.90 Prover 7: proved (3859ms) % 36.91/5.90 Prover 5: stopped % 36.91/5.90 Prover 9: stopped % 36.91/5.90 Prover 0: stopped % 36.91/5.90 Prover 2: stopped % 36.91/5.90 Prover 4: stopped % 36.91/5.90 Prover 6: stopped % 36.91/5.90 % 36.91/5.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.91/5.90 % 36.91/5.91 % SZS output start Proof for theBenchmark % 36.91/5.91 Assumptions after simplification: % 36.91/5.91 --------------------------------- % 36.91/5.91 % 36.91/5.91 (mAddComm) % 37.47/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 37.47/5.93 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v0, v1) % 37.47/5.93 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 37.47/5.93 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ % 37.47/5.93 aInteger0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 37.47/5.93 % 37.47/5.93 (mDivisor) % 37.47/5.94 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 37.47/5.94 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 37.47/5.94 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) & % 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) | % 37.47/5.94 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 37.47/5.94 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] : % 37.47/5.94 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0) % 37.47/5.94 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0)) % 37.47/5.94 % 37.47/5.94 (mEquMod) % 37.47/5.94 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 37.47/5.94 : (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | % 37.47/5.94 ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~ % 37.47/5.94 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v2, v4)) & % 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = % 37.47/5.94 sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ % 37.47/5.94 $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ aInteger0(v2) | ~ % 37.47/5.94 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2)) % 37.47/5.94 % 37.47/5.94 (mIntNeg) % 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 37.47/5.94 aInteger0(v0) | aInteger0(v1)) % 37.47/5.94 % 37.47/5.94 (mIntPlus) % 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 37.47/5.94 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2)) % 37.47/5.94 % 37.47/5.94 (mMulMinOne) % 37.47/5.94 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 37.47/5.94 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 37.47/5.94 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 37.47/5.94 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 37.47/5.94 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 37.47/5.94 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 37.47/5.94 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2)))) % 37.47/5.94 % 37.47/5.94 (m__) % 37.47/5.94 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 % 37.47/5.94 & smndt0(xb) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = % 37.47/5.94 v1) | ~ $i(v2) | ~ aInteger0(v2))) % 37.47/5.94 % 37.47/5.94 (m__818) % 37.47/5.95 ~ (xq = sz00) & $i(xc) & $i(xq) & $i(xb) & $i(xa) & $i(sz00) & aInteger0(xc) % 37.47/5.95 & aInteger0(xq) & aInteger0(xb) & aInteger0(xa) % 37.47/5.95 % 37.47/5.95 (m__853) % 37.47/5.95 $i(xc) & $i(xq) & $i(xb) & $i(xa) & sdteqdtlpzmzozddtrp0(xb, xc, xq) & % 37.47/5.95 sdteqdtlpzmzozddtrp0(xa, xb, xq) % 37.47/5.95 % 37.47/5.95 Further assumptions not needed in the proof: % 37.47/5.95 -------------------------------------------- % 37.47/5.95 mAddAsso, mAddNeg, mAddZero, mDistrib, mEquModRef, mEquModSym, mIntMult, % 37.47/5.95 mIntOne, mIntZero, mIntegers, mMulAsso, mMulComm, mMulOne, mMulZero, mZeroDiv % 37.47/5.95 % 37.47/5.95 Those formulas are unsatisfiable: % 37.47/5.95 --------------------------------- % 37.47/5.95 % 37.47/5.95 Begin of proof % 37.47/5.95 | % 37.47/5.95 | ALPHA: (mAddComm) implies: % 37.47/5.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | % 37.47/5.95 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 37.47/5.95 | (sdtpldt0(v0, v1) = v2 & $i(v2))) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (mMulMinOne) implies: % 37.47/5.95 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 37.47/5.95 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 37.47/5.95 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : % 37.47/5.95 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ % 37.47/5.95 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) % 37.47/5.95 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ % 37.47/5.95 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & % 37.47/5.95 | $i(v2)))) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (mDivisor) implies: % 37.47/5.95 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, % 37.47/5.95 | v0) | ~ aInteger0(v0) | ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & % 37.47/5.95 | $i(v2) & aInteger0(v2))) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (mEquMod) implies: % 37.47/5.95 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 37.47/5.95 | (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ % 37.47/5.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) % 37.47/5.95 | | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 37.47/5.95 | aDivisorOf0(v2, v4)) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (m__818) implies: % 37.47/5.95 | (5) ~ (xq = sz00) % 37.47/5.95 | (6) aInteger0(xa) % 37.47/5.95 | (7) aInteger0(xb) % 37.47/5.95 | (8) aInteger0(xq) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (m__853) implies: % 37.47/5.95 | (9) sdteqdtlpzmzozddtrp0(xa, xb, xq) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (m__) implies: % 37.47/5.95 | (10) $i(xa) % 37.47/5.95 | (11) $i(xb) % 37.47/5.95 | (12) $i(xq) % 37.47/5.95 | (13) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 & % 37.47/5.95 | $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~ % 37.47/5.95 | $i(v2) | ~ aInteger0(v2))) % 37.47/5.95 | % 37.47/5.95 | DELTA: instantiating (13) with fresh symbols all_21_0, all_21_1 gives: % 37.47/5.95 | (14) sdtpldt0(xa, all_21_1) = all_21_0 & smndt0(xb) = all_21_1 & % 37.47/5.95 | $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = % 37.47/5.95 | all_21_0) | ~ $i(v0) | ~ aInteger0(v0)) % 37.47/5.95 | % 37.47/5.95 | ALPHA: (14) implies: % 37.47/5.95 | (15) smndt0(xb) = all_21_1 % 37.47/5.96 | (16) sdtpldt0(xa, all_21_1) = all_21_0 % 37.47/5.96 | (17) ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_21_0) | ~ $i(v0) | ~ % 37.47/5.96 | aInteger0(v0)) % 37.47/5.96 | % 37.47/5.96 | DELTA: instantiating (2) with fresh symbol all_24_0 gives: % 37.47/5.96 | (18) smndt0(sz10) = all_24_0 & $i(all_24_0) & ! [v0: $i] : ! [v1: $i] : ( % 37.47/5.96 | ~ (sdtasdt0(v0, all_24_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) | % 37.47/5.96 | (sdtasdt0(all_24_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0: % 37.47/5.96 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_24_0, v0) = v1) | ~ $i(v0) | % 37.47/5.96 | ~ aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 & smndt0(v0) = v1 & % 37.47/5.96 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ % 37.47/5.96 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 & % 37.47/5.96 | sdtasdt0(all_24_0, v0) = v1 & $i(v1))) % 37.47/5.96 | % 37.47/5.96 | ALPHA: (18) implies: % 37.47/5.96 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 37.47/5.96 | aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 & sdtasdt0(all_24_0, % 37.47/5.96 | v0) = v1 & $i(v1))) % 37.47/5.96 | % 37.47/5.96 | GROUND_INST: instantiating (mIntNeg) with xb, all_21_1, simplifying with (7), % 37.47/5.96 | (11), (15) gives: % 37.47/5.96 | (20) aInteger0(all_21_1) % 37.47/5.96 | % 37.47/5.96 | GROUND_INST: instantiating (19) with xb, all_21_1, simplifying with (7), (11), % 37.47/5.96 | (15) gives: % 37.47/5.96 | (21) sdtasdt0(all_24_0, xb) = all_21_1 & sdtasdt0(xb, all_24_0) = all_21_1 % 37.47/5.96 | & $i(all_21_1) % 37.47/5.96 | % 37.47/5.96 | ALPHA: (21) implies: % 37.47/5.96 | (22) $i(all_21_1) % 37.47/5.96 | % 37.47/5.96 | GROUND_INST: instantiating (4) with xa, xb, xq, all_21_1, all_21_0, % 37.47/5.96 | simplifying with (6), (7), (8), (9), (10), (11), (12), (15), (16) % 37.47/5.96 | gives: % 37.47/5.96 | (23) xq = sz00 | aDivisorOf0(xq, all_21_0) % 37.47/5.96 | % 37.47/5.96 | BETA: splitting (23) gives: % 37.47/5.96 | % 37.47/5.96 | Case 1: % 37.47/5.96 | | % 37.47/5.96 | | (24) aDivisorOf0(xq, all_21_0) % 37.47/5.96 | | % 37.47/5.96 | | GROUND_INST: instantiating (1) with all_21_1, xa, all_21_0, simplifying with % 37.47/5.96 | | (6), (10), (16), (20), (22) gives: % 37.47/5.96 | | (25) sdtpldt0(all_21_1, xa) = all_21_0 & $i(all_21_0) % 37.47/5.96 | | % 37.47/5.96 | | ALPHA: (25) implies: % 37.47/5.96 | | (26) $i(all_21_0) % 37.47/5.96 | | % 37.47/5.96 | | GROUND_INST: instantiating (mIntPlus) with xa, all_21_1, all_21_0, % 37.47/5.96 | | simplifying with (6), (10), (16), (20), (22) gives: % 37.47/5.96 | | (27) aInteger0(all_21_0) % 37.47/5.96 | | % 37.47/5.96 | | GROUND_INST: instantiating (3) with all_21_0, xq, simplifying with (12), % 37.47/5.96 | | (24), (26) gives: % 37.47/5.96 | | (28) ~ aInteger0(all_21_0) | ? [v0: $i] : (sdtasdt0(xq, v0) = all_21_0 % 37.47/5.96 | | & $i(v0) & aInteger0(v0)) % 37.47/5.96 | | % 37.47/5.96 | | BETA: splitting (28) gives: % 37.47/5.96 | | % 37.47/5.96 | | Case 1: % 37.47/5.96 | | | % 37.47/5.96 | | | (29) ~ aInteger0(all_21_0) % 37.47/5.96 | | | % 37.47/5.96 | | | PRED_UNIFY: (27), (29) imply: % 37.47/5.96 | | | (30) $false % 37.47/5.96 | | | % 37.47/5.96 | | | CLOSE: (30) is inconsistent. % 37.47/5.96 | | | % 37.47/5.96 | | Case 2: % 37.47/5.96 | | | % 37.47/5.96 | | | (31) ? [v0: $i] : (sdtasdt0(xq, v0) = all_21_0 & $i(v0) & % 37.47/5.96 | | | aInteger0(v0)) % 37.47/5.96 | | | % 37.47/5.96 | | | DELTA: instantiating (31) with fresh symbol all_102_0 gives: % 37.47/5.96 | | | (32) sdtasdt0(xq, all_102_0) = all_21_0 & $i(all_102_0) & % 37.47/5.96 | | | aInteger0(all_102_0) % 37.47/5.96 | | | % 37.47/5.96 | | | ALPHA: (32) implies: % 37.47/5.97 | | | (33) aInteger0(all_102_0) % 37.47/5.97 | | | (34) $i(all_102_0) % 37.47/5.97 | | | (35) sdtasdt0(xq, all_102_0) = all_21_0 % 37.47/5.97 | | | % 37.47/5.97 | | | GROUND_INST: instantiating (17) with all_102_0, simplifying with (33), % 37.47/5.97 | | | (34), (35) gives: % 37.47/5.97 | | | (36) $false % 37.47/5.97 | | | % 37.47/5.97 | | | CLOSE: (36) is inconsistent. % 37.47/5.97 | | | % 37.47/5.97 | | End of split % 37.47/5.97 | | % 37.47/5.97 | Case 2: % 37.47/5.97 | | % 37.47/5.97 | | (37) xq = sz00 % 37.47/5.97 | | % 37.47/5.97 | | REDUCE: (5), (37) imply: % 37.47/5.97 | | (38) $false % 37.47/5.97 | | % 37.47/5.97 | | CLOSE: (38) is inconsistent. % 37.47/5.97 | | % 37.47/5.97 | End of split % 37.47/5.97 | % 37.47/5.97 End of proof % 37.47/5.97 % SZS output end Proof for theBenchmark % 37.47/5.97 % 37.47/5.97 5354ms %------------------------------------------------------------------------------