%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM436+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 : n004.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 11:47:44 EDT 2023 % Result : Theorem 78.45s 11.13s % Output : Proof 78.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM436+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 11:00:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.96/1.13 Prover 4: Preprocessing ... % 2.96/1.13 Prover 1: Preprocessing ... % 3.21/1.17 Prover 6: Preprocessing ... % 3.21/1.17 Prover 5: Preprocessing ... % 3.21/1.17 Prover 3: Preprocessing ... % 3.21/1.17 Prover 0: Preprocessing ... % 3.21/1.17 Prover 2: Preprocessing ... % 6.61/1.71 Prover 3: Constructing countermodel ... % 6.61/1.72 Prover 1: Constructing countermodel ... % 7.11/1.76 Prover 6: Proving ... % 7.25/1.78 Prover 5: Constructing countermodel ... % 7.90/1.85 Prover 4: Constructing countermodel ... % 7.90/1.87 Prover 2: Proving ... % 7.90/1.98 Prover 0: Proving ... % 10.49/2.23 Prover 3: gave up % 10.49/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.74/2.30 Prover 7: Preprocessing ... % 12.82/2.52 Prover 7: Constructing countermodel ... % 12.82/2.63 Prover 1: gave up % 12.82/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.42/2.68 Prover 8: Preprocessing ... % 14.95/2.84 Prover 8: Warning: ignoring some quantifiers % 15.21/2.85 Prover 8: Constructing countermodel ... % 18.95/3.46 Prover 8: gave up % 18.95/3.46 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 20.00/3.49 Prover 9: Preprocessing ... % 21.55/3.71 Prover 9: Constructing countermodel ... % 70.61/10.13 Prover 2: stopped % 70.61/10.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 70.96/10.17 Prover 10: Preprocessing ... % 71.40/10.24 Prover 10: Constructing countermodel ... % 77.93/11.11 Prover 10: Found proof (size 53) % 77.93/11.11 Prover 10: proved (980ms) % 77.93/11.11 Prover 6: stopped % 77.93/11.11 Prover 0: stopped % 77.93/11.11 Prover 7: stopped % 77.93/11.11 Prover 4: stopped % 77.93/11.11 Prover 5: stopped % 78.45/11.13 Prover 9: stopped % 78.45/11.13 % 78.45/11.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 78.45/11.13 % 78.45/11.14 % SZS output start Proof for theBenchmark % 78.45/11.14 Assumptions after simplification: % 78.45/11.14 --------------------------------- % 78.45/11.14 % 78.45/11.14 (mDivisor) % 78.45/11.17 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 78.45/11.17 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.45/11.17 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) & % 78.45/11.17 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) | % 78.45/11.17 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 78.45/11.18 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] : % 78.45/11.18 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0) % 78.45/11.18 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0)) % 78.45/11.18 % 78.45/11.18 (mEquMod) % 78.45/11.18 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 78.45/11.18 : (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | % 78.45/11.18 ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~ % 78.45/11.18 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v2, v4)) & % 78.45/11.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = % 78.45/11.18 sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ % 78.45/11.18 $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ aInteger0(v2) | ~ % 78.45/11.18 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2)) % 78.45/11.18 % 78.45/11.18 (mEquModRef) % 78.45/11.18 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 78.45/11.18 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 78.45/11.18 % 78.45/11.18 (mIntMult) % 78.45/11.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 78.45/11.18 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2)) % 78.45/11.18 % 78.45/11.18 (mIntZero) % 78.45/11.18 $i(sz00) & aInteger0(sz00) % 78.45/11.18 % 78.45/11.18 (mMulComm) % 78.45/11.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 78.45/11.18 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtasdt0(v1, v0) % 78.45/11.18 = v2 & $i(v2))) % 78.45/11.18 % 78.45/11.18 (m__) % 78.45/11.19 $i(xq) & $i(xp) & $i(xb) & $i(xa) & ( ~ sdteqdtlpzmzozddtrp0(xa, xb, xq) | ~ % 78.45/11.19 sdteqdtlpzmzozddtrp0(xa, xb, xp)) % 78.45/11.19 % 78.45/11.19 (m__1032) % 78.45/11.19 $i(xm) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? % 78.45/11.19 [v2: $i] : (sdtasdt0(v0, xm) = v1 & sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v2) = % 78.45/11.19 v1 & smndt0(xb) = v2 & $i(v2) & $i(v1) & $i(v0) & aInteger0(xm)) % 78.45/11.19 % 78.45/11.19 (m__1071) % 78.45/11.19 $i(xm) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? % 78.45/11.19 [v2: $i] : ? [v3: $i] : (sdtasdt0(xq, v3) = v1 & sdtasdt0(xq, xm) = v0 & % 78.45/11.19 sdtasdt0(xp, v0) = v1 & sdtasdt0(xp, xm) = v3 & sdtpldt0(xa, v2) = v1 & % 78.45/11.19 smndt0(xb) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 78.45/11.19 % 78.45/11.19 (m__979) % 78.45/11.19 ~ (xq = sz00) & ~ (xp = sz00) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & $i(sz00) % 78.45/11.19 & aInteger0(xq) & aInteger0(xp) & aInteger0(xb) & aInteger0(xa) % 78.45/11.19 % 78.45/11.19 (function-axioms) % 78.45/11.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.45/11.19 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 78.45/11.19 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 78.45/11.19 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 78.45/11.19 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 78.45/11.19 % 78.45/11.19 Further assumptions not needed in the proof: % 78.45/11.19 -------------------------------------------- % 78.45/11.19 mAddAsso, mAddComm, mAddNeg, mAddZero, mDistrib, mEquModSym, mEquModTrn, % 78.45/11.19 mIntNeg, mIntOne, mIntPlus, mIntegers, mMulAsso, mMulMinOne, mMulOne, mMulZero, % 78.45/11.19 mZeroDiv, m__1003 % 78.45/11.19 % 78.45/11.19 Those formulas are unsatisfiable: % 78.45/11.19 --------------------------------- % 78.45/11.19 % 78.45/11.19 Begin of proof % 78.45/11.19 | % 78.45/11.19 | ALPHA: (mIntZero) implies: % 78.45/11.19 | (1) aInteger0(sz00) % 78.45/11.19 | % 78.45/11.19 | ALPHA: (mDivisor) implies: % 78.45/11.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (sdtasdt0(v1, % 78.45/11.20 | v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) % 78.45/11.20 | | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (mEquMod) implies: % 78.45/11.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.45/11.20 | (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ % 78.45/11.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ % 78.45/11.20 | aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 78.45/11.20 | sdteqdtlpzmzozddtrp0(v0, v1, v2)) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (mEquModRef) implies: % 78.45/11.20 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 78.45/11.20 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (m__979) implies: % 78.45/11.20 | (5) ~ (xp = sz00) % 78.45/11.20 | (6) ~ (xq = sz00) % 78.45/11.20 | (7) aInteger0(xa) % 78.45/11.20 | (8) aInteger0(xb) % 78.45/11.20 | (9) aInteger0(xp) % 78.45/11.20 | (10) aInteger0(xq) % 78.45/11.20 | (11) $i(sz00) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (m__1032) implies: % 78.45/11.20 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(v0, xm) = v1 & % 78.45/11.20 | sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v2) = v1 & smndt0(xb) = v2 & % 78.45/11.20 | $i(v2) & $i(v1) & $i(v0) & aInteger0(xm)) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (m__1071) implies: % 78.45/11.20 | (13) $i(xm) % 78.45/11.20 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xq, % 78.45/11.20 | v3) = v1 & sdtasdt0(xq, xm) = v0 & sdtasdt0(xp, v0) = v1 & % 78.45/11.20 | sdtasdt0(xp, xm) = v3 & sdtpldt0(xa, v2) = v1 & smndt0(xb) = v2 & % 78.45/11.20 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (m__) implies: % 78.45/11.20 | (15) $i(xa) % 78.45/11.20 | (16) $i(xb) % 78.45/11.20 | (17) $i(xp) % 78.45/11.20 | (18) $i(xq) % 78.45/11.20 | (19) ~ sdteqdtlpzmzozddtrp0(xa, xb, xq) | ~ sdteqdtlpzmzozddtrp0(xa, xb, % 78.45/11.20 | xp) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (function-axioms) implies: % 78.45/11.20 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 78.45/11.20 | v1) | ~ (smndt0(v2) = v0)) % 78.45/11.20 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.45/11.20 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 78.45/11.20 | % 78.45/11.20 | DELTA: instantiating (12) with fresh symbols all_27_0, all_27_1, all_27_2 % 78.45/11.20 | gives: % 78.45/11.20 | (22) sdtasdt0(all_27_2, xm) = all_27_1 & sdtasdt0(xp, xq) = all_27_2 & % 78.45/11.20 | sdtpldt0(xa, all_27_0) = all_27_1 & smndt0(xb) = all_27_0 & % 78.45/11.20 | $i(all_27_0) & $i(all_27_1) & $i(all_27_2) & aInteger0(xm) % 78.45/11.20 | % 78.45/11.20 | ALPHA: (22) implies: % 78.45/11.21 | (23) aInteger0(xm) % 78.45/11.21 | (24) smndt0(xb) = all_27_0 % 78.45/11.21 | (25) sdtpldt0(xa, all_27_0) = all_27_1 % 78.45/11.21 | % 78.45/11.21 | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1, all_29_2, % 78.45/11.21 | all_29_3 gives: % 78.45/11.21 | (26) sdtasdt0(xq, all_29_0) = all_29_2 & sdtasdt0(xq, xm) = all_29_3 & % 78.45/11.21 | sdtasdt0(xp, all_29_3) = all_29_2 & sdtasdt0(xp, xm) = all_29_0 & % 78.45/11.21 | sdtpldt0(xa, all_29_1) = all_29_2 & smndt0(xb) = all_29_1 & % 78.45/11.21 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) % 78.45/11.21 | % 78.45/11.21 | ALPHA: (26) implies: % 78.45/11.21 | (27) smndt0(xb) = all_29_1 % 78.45/11.21 | (28) sdtpldt0(xa, all_29_1) = all_29_2 % 78.45/11.21 | (29) sdtasdt0(xp, xm) = all_29_0 % 78.45/11.21 | (30) sdtasdt0(xp, all_29_3) = all_29_2 % 78.45/11.21 | (31) sdtasdt0(xq, xm) = all_29_3 % 78.45/11.21 | (32) sdtasdt0(xq, all_29_0) = all_29_2 % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (20) with all_27_0, all_29_1, xb, simplifying with % 78.45/11.21 | (24), (27) gives: % 78.45/11.21 | (33) all_29_1 = all_27_0 % 78.45/11.21 | % 78.45/11.21 | REDUCE: (28), (33) imply: % 78.45/11.21 | (34) sdtpldt0(xa, all_27_0) = all_29_2 % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (21) with all_27_1, all_29_2, all_27_0, xa, % 78.45/11.21 | simplifying with (25), (34) gives: % 78.45/11.21 | (35) all_29_2 = all_27_1 % 78.45/11.21 | % 78.45/11.21 | REDUCE: (32), (35) imply: % 78.45/11.21 | (36) sdtasdt0(xq, all_29_0) = all_27_1 % 78.45/11.21 | % 78.45/11.21 | REDUCE: (30), (35) imply: % 78.45/11.21 | (37) sdtasdt0(xp, all_29_3) = all_27_1 % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (4) with sz00, xp, simplifying with (1), (9), (11), % 78.45/11.21 | (17) gives: % 78.45/11.21 | (38) xp = sz00 | sdteqdtlpzmzozddtrp0(sz00, sz00, xp) % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (mIntMult) with xp, xm, all_29_0, simplifying with % 78.45/11.21 | (9), (13), (17), (23), (29) gives: % 78.45/11.21 | (39) aInteger0(all_29_0) % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (mMulComm) with xp, xm, all_29_0, simplifying with % 78.45/11.21 | (9), (13), (17), (23), (29) gives: % 78.45/11.21 | (40) sdtasdt0(xm, xp) = all_29_0 & $i(all_29_0) % 78.45/11.21 | % 78.45/11.21 | ALPHA: (40) implies: % 78.45/11.21 | (41) $i(all_29_0) % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (mIntMult) with xq, xm, all_29_3, simplifying with % 78.45/11.21 | (10), (13), (18), (23), (31) gives: % 78.45/11.21 | (42) aInteger0(all_29_3) % 78.45/11.21 | % 78.45/11.21 | GROUND_INST: instantiating (mMulComm) with xq, xm, all_29_3, simplifying with % 78.45/11.21 | (10), (13), (18), (23), (31) gives: % 78.45/11.21 | (43) sdtasdt0(xm, xq) = all_29_3 & $i(all_29_3) % 78.45/11.21 | % 78.45/11.21 | ALPHA: (43) implies: % 78.45/11.21 | (44) $i(all_29_3) % 78.45/11.21 | % 78.45/11.21 | BETA: splitting (38) gives: % 78.45/11.21 | % 78.45/11.21 | Case 1: % 78.45/11.21 | | % 78.45/11.21 | | % 78.45/11.21 | | GROUND_INST: instantiating (mIntMult) with xq, all_29_0, all_27_1, % 78.45/11.21 | | simplifying with (10), (18), (36), (39), (41) gives: % 78.45/11.22 | | (45) aInteger0(all_27_1) % 78.45/11.22 | | % 78.45/11.22 | | GROUND_INST: instantiating (mMulComm) with xq, all_29_0, all_27_1, % 78.45/11.22 | | simplifying with (10), (18), (36), (39), (41) gives: % 78.45/11.22 | | (46) sdtasdt0(all_29_0, xq) = all_27_1 & $i(all_27_1) % 78.45/11.22 | | % 78.45/11.22 | | ALPHA: (46) implies: % 78.45/11.22 | | (47) $i(all_27_1) % 78.45/11.22 | | % 78.45/11.22 | | BETA: splitting (19) gives: % 78.45/11.22 | | % 78.45/11.22 | | Case 1: % 78.45/11.22 | | | % 78.45/11.22 | | | (48) ~ sdteqdtlpzmzozddtrp0(xa, xb, xq) % 78.45/11.22 | | | % 78.90/11.22 | | | GROUND_INST: instantiating (2) with all_27_1, xq, all_29_0, simplifying % 78.90/11.22 | | | with (10), (18), (36), (39), (41), (45), (47) gives: % 78.90/11.22 | | | (49) xq = sz00 | aDivisorOf0(xq, all_27_1) % 78.90/11.22 | | | % 78.90/11.22 | | | BETA: splitting (49) gives: % 78.90/11.22 | | | % 78.90/11.22 | | | Case 1: % 78.90/11.22 | | | | % 78.90/11.22 | | | | (50) aDivisorOf0(xq, all_27_1) % 78.90/11.22 | | | | % 78.90/11.22 | | | | GROUND_INST: instantiating (3) with xa, xb, xq, all_27_0, all_27_1, % 78.90/11.22 | | | | simplifying with (7), (8), (10), (15), (16), (18), (24), % 78.90/11.22 | | | | (25), (48), (50) gives: % 78.90/11.22 | | | | (51) xq = sz00 % 78.90/11.22 | | | | % 78.90/11.22 | | | | REDUCE: (6), (51) imply: % 78.90/11.22 | | | | (52) $false % 78.90/11.22 | | | | % 78.90/11.22 | | | | CLOSE: (52) is inconsistent. % 78.90/11.22 | | | | % 78.90/11.22 | | | Case 2: % 78.90/11.22 | | | | % 78.90/11.22 | | | | (53) xq = sz00 % 78.90/11.22 | | | | % 78.90/11.22 | | | | REDUCE: (6), (53) imply: % 78.90/11.22 | | | | (54) $false % 78.90/11.22 | | | | % 78.90/11.22 | | | | CLOSE: (54) is inconsistent. % 78.90/11.22 | | | | % 78.90/11.22 | | | End of split % 78.90/11.22 | | | % 78.90/11.22 | | Case 2: % 78.90/11.22 | | | % 78.90/11.22 | | | (55) ~ sdteqdtlpzmzozddtrp0(xa, xb, xp) % 78.90/11.22 | | | % 78.90/11.22 | | | GROUND_INST: instantiating (2) with all_27_1, xp, all_29_3, simplifying % 78.90/11.22 | | | with (9), (17), (37), (42), (44), (45), (47) gives: % 78.90/11.22 | | | (56) xp = sz00 | aDivisorOf0(xp, all_27_1) % 78.90/11.22 | | | % 78.90/11.22 | | | BETA: splitting (56) gives: % 78.90/11.22 | | | % 78.90/11.22 | | | Case 1: % 78.90/11.22 | | | | % 78.90/11.22 | | | | (57) aDivisorOf0(xp, all_27_1) % 78.90/11.22 | | | | % 78.90/11.22 | | | | GROUND_INST: instantiating (3) with xa, xb, xp, all_27_0, all_27_1, % 78.90/11.22 | | | | simplifying with (7), (8), (9), (15), (16), (17), (24), % 78.90/11.22 | | | | (25), (55), (57) gives: % 78.90/11.22 | | | | (58) xp = sz00 % 78.90/11.22 | | | | % 78.90/11.22 | | | | REDUCE: (5), (58) imply: % 78.90/11.22 | | | | (59) $false % 78.90/11.22 | | | | % 78.90/11.22 | | | | CLOSE: (59) is inconsistent. % 78.90/11.22 | | | | % 78.90/11.22 | | | Case 2: % 78.90/11.22 | | | | % 78.90/11.22 | | | | (60) xp = sz00 % 78.90/11.22 | | | | % 78.90/11.22 | | | | REDUCE: (5), (60) imply: % 78.90/11.22 | | | | (61) $false % 78.90/11.22 | | | | % 78.90/11.22 | | | | CLOSE: (61) is inconsistent. % 78.90/11.22 | | | | % 78.90/11.22 | | | End of split % 78.90/11.22 | | | % 78.90/11.22 | | End of split % 78.90/11.22 | | % 78.90/11.22 | Case 2: % 78.90/11.22 | | % 78.90/11.22 | | (62) xp = sz00 % 78.90/11.22 | | % 78.90/11.22 | | REDUCE: (5), (62) imply: % 78.90/11.22 | | (63) $false % 78.90/11.22 | | % 78.90/11.22 | | CLOSE: (63) is inconsistent. % 78.90/11.22 | | % 78.90/11.22 | End of split % 78.90/11.22 | % 78.90/11.22 End of proof % 78.90/11.22 % SZS output end Proof for theBenchmark % 78.90/11.22 % 78.90/11.22 10598ms %------------------------------------------------------------------------------