%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM432+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 : n023.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 11:47:43 EDT 2023 % Result : Theorem 8.60s 1.90s % Output : Proof 14.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM432+3 : TPTP v8.1.2. Released v4.0.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n023.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 11:35:27 EDT 2023 % 0.13/0.34 % CPUTime : % 0.60/0.60 ________ _____ % 0.60/0.60 ___ __ \_________(_)________________________________ % 0.60/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.60/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.60/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.60/0.60 % 0.60/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.60/0.60 (2023-06-19) % 0.60/0.60 % 0.60/0.60 (c) Philipp Rümmer, 2009-2023 % 0.60/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.60/0.60 Amanda Stjerna. % 0.60/0.60 Free software under BSD-3-Clause. % 0.60/0.60 % 0.60/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.60/0.60 % 0.60/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.60/0.62 Running up to 7 provers in parallel. % 0.60/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.60/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.60/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.60/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.60/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.60/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.60/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.74/1.11 Prover 1: Preprocessing ... % 2.74/1.11 Prover 4: Preprocessing ... % 2.74/1.15 Prover 6: Preprocessing ... % 2.74/1.15 Prover 5: Preprocessing ... % 2.74/1.15 Prover 0: Preprocessing ... % 2.74/1.15 Prover 3: Preprocessing ... % 2.74/1.15 Prover 2: Preprocessing ... % 5.54/1.56 Prover 1: Constructing countermodel ... % 6.33/1.56 Prover 3: Constructing countermodel ... % 6.59/1.62 Prover 6: Proving ... % 6.82/1.65 Prover 4: Constructing countermodel ... % 6.82/1.67 Prover 5: Constructing countermodel ... % 6.82/1.72 Prover 2: Proving ... % 7.53/1.76 Prover 0: Proving ... % 8.60/1.89 Prover 3: proved (1268ms) % 8.60/1.90 % 8.60/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.60/1.90 % 8.60/1.90 Prover 5: stopped % 8.60/1.91 Prover 2: stopped % 8.60/1.91 Prover 6: stopped % 8.60/1.91 Prover 0: stopped % 8.60/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.60/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.60/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.60/1.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.60/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.33/1.99 Prover 7: Preprocessing ... % 9.33/1.99 Prover 8: Preprocessing ... % 9.51/2.00 Prover 10: Preprocessing ... % 9.51/2.00 Prover 11: Preprocessing ... % 9.51/2.02 Prover 13: Preprocessing ... % 9.70/2.11 Prover 8: Warning: ignoring some quantifiers % 9.70/2.12 Prover 8: Constructing countermodel ... % 10.47/2.13 Prover 10: Constructing countermodel ... % 10.47/2.18 Prover 7: Constructing countermodel ... % 11.05/2.21 Prover 11: Constructing countermodel ... % 11.05/2.22 Prover 13: Constructing countermodel ... % 14.70/2.69 Prover 10: Found proof (size 47) % 14.70/2.69 Prover 10: proved (778ms) % 14.82/2.69 Prover 11: stopped % 14.82/2.69 Prover 8: stopped % 14.82/2.69 Prover 4: stopped % 14.82/2.69 Prover 1: stopped % 14.82/2.69 Prover 7: stopped % 14.82/2.69 Prover 13: stopped % 14.82/2.69 % 14.82/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.82/2.69 % 14.82/2.70 % SZS output start Proof for theBenchmark % 14.82/2.70 Assumptions after simplification: % 14.82/2.70 --------------------------------- % 14.82/2.70 % 14.82/2.70 (mAddComm) % 14.99/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 14.99/2.73 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v1, v0) % 14.99/2.73 = v2 & $i(v2))) % 14.99/2.73 % 14.99/2.73 (mDivisor) % 14.99/2.73 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 14.99/2.73 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 14.99/2.73 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) & % 14.99/2.73 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) | % 14.99/2.73 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 14.99/2.73 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] : % 14.99/2.73 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0) % 14.99/2.73 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0)) % 14.99/2.73 % 14.99/2.73 (mEquModRef) % 14.99/2.73 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 14.99/2.73 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 14.99/2.73 % 14.99/2.73 (mIntMult) % 14.99/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 14.99/2.73 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2)) % 14.99/2.73 % 14.99/2.73 (mIntOne) % 14.99/2.74 $i(sz10) & aInteger0(sz10) % 14.99/2.74 % 14.99/2.74 (mIntPlus) % 14.99/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 14.99/2.74 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2)) % 14.99/2.74 % 14.99/2.74 (mMulComm) % 14.99/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 14.99/2.74 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtasdt0(v1, v0) % 14.99/2.74 = v2 & $i(v2))) % 14.99/2.74 % 14.99/2.74 (mMulMinOne) % 14.99/2.74 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.99/2.74 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) | % 14.99/2.74 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))) % 14.99/2.74 % 14.99/2.74 (m__) % 14.99/2.74 $i(xc) & $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 % 14.99/2.74 & smndt0(xc) = v0 & $i(v1) & $i(v0) & ~ sdteqdtlpzmzozddtrp0(xa, xc, xq) & % 14.99/2.74 ~ aDivisorOf0(xq, v1) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~ % 14.99/2.74 $i(v2) | ~ aInteger0(v2))) % 14.99/2.74 % 14.99/2.74 (m__818) % 14.99/2.74 ~ (xq = sz00) & $i(xc) & $i(xq) & $i(xb) & $i(xa) & $i(sz00) & aInteger0(xc) % 14.99/2.74 & aInteger0(xq) & aInteger0(xb) & aInteger0(xa) % 14.99/2.74 % 14.99/2.74 (m__853) % 14.99/2.75 $i(xc) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 14.99/2.75 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(xq, v5) = v1 & sdtasdt0(xq, % 14.99/2.75 v4) = v3 & sdtpldt0(xb, v2) = v3 & sdtpldt0(xa, v0) = v1 & smndt0(xc) = v2 % 14.99/2.75 & smndt0(xb) = v0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 14.99/2.75 sdteqdtlpzmzozddtrp0(xb, xc, xq) & sdteqdtlpzmzozddtrp0(xa, xb, xq) & % 14.99/2.75 aDivisorOf0(xq, v3) & aDivisorOf0(xq, v1) & aInteger0(v5) & aInteger0(v4)) % 14.99/2.75 % 14.99/2.75 (m__876) % 14.99/2.75 $i(xn) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, % 14.99/2.75 xn) = v0 & sdtpldt0(xa, v1) = v0 & smndt0(xb) = v1 & $i(v1) & $i(v0) & % 14.99/2.75 aInteger0(xn)) % 14.99/2.75 % 14.99/2.75 (m__899) % 14.99/2.75 $i(xm) & $i(xc) & $i(xq) & $i(xb) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, % 14.99/2.75 xm) = v0 & sdtpldt0(xb, v1) = v0 & smndt0(xc) = v1 & $i(v1) & $i(v0) & % 14.99/2.75 aInteger0(xm)) % 14.99/2.75 % 14.99/2.75 (m__924) % 14.99/2.75 $i(xm) & $i(xn) & $i(xc) & $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? % 14.99/2.75 [v2: $i] : (sdtasdt0(xq, v0) = v1 & sdtpldt0(xn, xm) = v0 & sdtpldt0(xa, v2) = % 14.99/2.75 v1 & smndt0(xc) = v2 & $i(v2) & $i(v1) & $i(v0)) % 14.99/2.75 % 14.99/2.75 (function-axioms) % 14.99/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.99/2.75 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 14.99/2.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 14.99/2.75 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 14.99/2.75 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 14.99/2.75 % 14.99/2.75 Further assumptions not needed in the proof: % 14.99/2.75 -------------------------------------------- % 14.99/2.75 mAddAsso, mAddNeg, mAddZero, mDistrib, mEquMod, mEquModSym, mIntNeg, mIntZero, % 14.99/2.75 mIntegers, mMulAsso, mMulOne, mMulZero, mZeroDiv % 14.99/2.75 % 14.99/2.75 Those formulas are unsatisfiable: % 14.99/2.75 --------------------------------- % 14.99/2.75 % 14.99/2.75 Begin of proof % 14.99/2.75 | % 14.99/2.75 | ALPHA: (mIntOne) implies: % 14.99/2.75 | (1) aInteger0(sz10) % 14.99/2.75 | % 14.99/2.75 | ALPHA: (mMulMinOne) implies: % 14.99/2.76 | (2) $i(sz10) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (mDivisor) implies: % 14.99/2.76 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (sdtasdt0(v1, % 14.99/2.76 | v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2) % 14.99/2.76 | | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (mEquModRef) implies: % 14.99/2.76 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 14.99/2.76 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__818) implies: % 14.99/2.76 | (5) ~ (xq = sz00) % 14.99/2.76 | (6) aInteger0(xq) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__853) implies: % 14.99/2.76 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.99/2.76 | ? [v5: $i] : (sdtasdt0(xq, v5) = v1 & sdtasdt0(xq, v4) = v3 & % 14.99/2.76 | sdtpldt0(xb, v2) = v3 & sdtpldt0(xa, v0) = v1 & smndt0(xc) = v2 & % 14.99/2.76 | smndt0(xb) = v0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 14.99/2.76 | & sdteqdtlpzmzozddtrp0(xb, xc, xq) & sdteqdtlpzmzozddtrp0(xa, xb, xq) % 14.99/2.76 | & aDivisorOf0(xq, v3) & aDivisorOf0(xq, v1) & aInteger0(v5) & % 14.99/2.76 | aInteger0(v4)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__876) implies: % 14.99/2.76 | (8) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xn) = v0 & sdtpldt0(xa, v1) = % 14.99/2.76 | v0 & smndt0(xb) = v1 & $i(v1) & $i(v0) & aInteger0(xn)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__899) implies: % 14.99/2.76 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xm) = v0 & sdtpldt0(xb, v1) = % 14.99/2.76 | v0 & smndt0(xc) = v1 & $i(v1) & $i(v0) & aInteger0(xm)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__924) implies: % 14.99/2.76 | (10) $i(xn) % 14.99/2.76 | (11) $i(xm) % 14.99/2.76 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xq, v0) = v1 & % 14.99/2.76 | sdtpldt0(xn, xm) = v0 & sdtpldt0(xa, v2) = v1 & smndt0(xc) = v2 & % 14.99/2.76 | $i(v2) & $i(v1) & $i(v0)) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (m__) implies: % 14.99/2.76 | (13) $i(xq) % 14.99/2.76 | (14) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 & smndt0(xc) = v0 & % 14.99/2.76 | $i(v1) & $i(v0) & ~ sdteqdtlpzmzozddtrp0(xa, xc, xq) & ~ % 14.99/2.76 | aDivisorOf0(xq, v1) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~ % 14.99/2.76 | $i(v2) | ~ aInteger0(v2))) % 14.99/2.76 | % 14.99/2.76 | ALPHA: (function-axioms) implies: % 14.99/2.76 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 14.99/2.76 | v1) | ~ (smndt0(v2) = v0)) % 14.99/2.77 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.99/2.77 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.99/2.77 | % 14.99/2.77 | DELTA: instantiating (9) with fresh symbols all_21_0, all_21_1 gives: % 14.99/2.77 | (17) sdtasdt0(xq, xm) = all_21_1 & sdtpldt0(xb, all_21_0) = all_21_1 & % 14.99/2.77 | smndt0(xc) = all_21_0 & $i(all_21_0) & $i(all_21_1) & aInteger0(xm) % 14.99/2.77 | % 14.99/2.77 | ALPHA: (17) implies: % 14.99/2.77 | (18) aInteger0(xm) % 14.99/2.77 | (19) smndt0(xc) = all_21_0 % 14.99/2.77 | % 14.99/2.77 | DELTA: instantiating (8) with fresh symbols all_23_0, all_23_1 gives: % 14.99/2.77 | (20) sdtasdt0(xq, xn) = all_23_1 & sdtpldt0(xa, all_23_0) = all_23_1 & % 14.99/2.77 | smndt0(xb) = all_23_0 & $i(all_23_0) & $i(all_23_1) & aInteger0(xn) % 14.99/2.77 | % 14.99/2.77 | ALPHA: (20) implies: % 14.99/2.77 | (21) aInteger0(xn) % 14.99/2.77 | % 14.99/2.77 | DELTA: instantiating (12) with fresh symbols all_25_0, all_25_1, all_25_2 % 14.99/2.77 | gives: % 14.99/2.77 | (22) sdtasdt0(xq, all_25_2) = all_25_1 & sdtpldt0(xn, xm) = all_25_2 & % 14.99/2.77 | sdtpldt0(xa, all_25_0) = all_25_1 & smndt0(xc) = all_25_0 & % 14.99/2.77 | $i(all_25_0) & $i(all_25_1) & $i(all_25_2) % 14.99/2.77 | % 14.99/2.77 | ALPHA: (22) implies: % 14.99/2.77 | (23) smndt0(xc) = all_25_0 % 14.99/2.77 | (24) sdtpldt0(xa, all_25_0) = all_25_1 % 14.99/2.77 | (25) sdtpldt0(xn, xm) = all_25_2 % 14.99/2.77 | (26) sdtasdt0(xq, all_25_2) = all_25_1 % 14.99/2.77 | % 14.99/2.77 | DELTA: instantiating (14) with fresh symbols all_30_0, all_30_1 gives: % 14.99/2.77 | (27) sdtpldt0(xa, all_30_1) = all_30_0 & smndt0(xc) = all_30_1 & % 14.99/2.77 | $i(all_30_0) & $i(all_30_1) & ~ sdteqdtlpzmzozddtrp0(xa, xc, xq) & ~ % 14.99/2.77 | aDivisorOf0(xq, all_30_0) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = % 14.99/2.77 | all_30_0) | ~ $i(v0) | ~ aInteger0(v0)) % 14.99/2.77 | % 14.99/2.77 | ALPHA: (27) implies: % 14.99/2.77 | (28) ~ aDivisorOf0(xq, all_30_0) % 14.99/2.77 | (29) smndt0(xc) = all_30_1 % 14.99/2.77 | (30) sdtpldt0(xa, all_30_1) = all_30_0 % 14.99/2.77 | % 14.99/2.77 | DELTA: instantiating (7) with fresh symbols all_33_0, all_33_1, all_33_2, % 14.99/2.77 | all_33_3, all_33_4, all_33_5 gives: % 14.99/2.77 | (31) sdtasdt0(xq, all_33_0) = all_33_4 & sdtasdt0(xq, all_33_1) = all_33_2 % 14.99/2.77 | & sdtpldt0(xb, all_33_3) = all_33_2 & sdtpldt0(xa, all_33_5) = % 14.99/2.77 | all_33_4 & smndt0(xc) = all_33_3 & smndt0(xb) = all_33_5 & % 14.99/2.77 | $i(all_33_0) & $i(all_33_1) & $i(all_33_2) & $i(all_33_3) & % 14.99/2.77 | $i(all_33_4) & $i(all_33_5) & sdteqdtlpzmzozddtrp0(xb, xc, xq) & % 14.99/2.77 | sdteqdtlpzmzozddtrp0(xa, xb, xq) & aDivisorOf0(xq, all_33_2) & % 14.99/2.77 | aDivisorOf0(xq, all_33_4) & aInteger0(all_33_0) & aInteger0(all_33_1) % 14.99/2.77 | % 14.99/2.77 | ALPHA: (31) implies: % 14.99/2.77 | (32) smndt0(xc) = all_33_3 % 14.99/2.77 | % 14.99/2.77 | GROUND_INST: instantiating (15) with all_25_0, all_30_1, xc, simplifying with % 14.99/2.77 | (23), (29) gives: % 14.99/2.77 | (33) all_30_1 = all_25_0 % 14.99/2.77 | % 14.99/2.77 | GROUND_INST: instantiating (15) with all_30_1, all_33_3, xc, simplifying with % 14.99/2.77 | (29), (32) gives: % 14.99/2.77 | (34) all_33_3 = all_30_1 % 14.99/2.77 | % 14.99/2.77 | GROUND_INST: instantiating (15) with all_21_0, all_33_3, xc, simplifying with % 14.99/2.77 | (19), (32) gives: % 14.99/2.77 | (35) all_33_3 = all_21_0 % 14.99/2.77 | % 14.99/2.77 | COMBINE_EQS: (34), (35) imply: % 14.99/2.77 | (36) all_30_1 = all_21_0 % 14.99/2.77 | % 14.99/2.77 | SIMP: (36) implies: % 14.99/2.77 | (37) all_30_1 = all_21_0 % 14.99/2.77 | % 14.99/2.77 | COMBINE_EQS: (33), (37) imply: % 14.99/2.77 | (38) all_25_0 = all_21_0 % 14.99/2.77 | % 14.99/2.77 | SIMP: (38) implies: % 14.99/2.77 | (39) all_25_0 = all_21_0 % 14.99/2.77 | % 14.99/2.77 | REDUCE: (30), (37) imply: % 14.99/2.77 | (40) sdtpldt0(xa, all_21_0) = all_30_0 % 14.99/2.77 | % 14.99/2.77 | REDUCE: (24), (39) imply: % 14.99/2.77 | (41) sdtpldt0(xa, all_21_0) = all_25_1 % 14.99/2.77 | % 14.99/2.77 | GROUND_INST: instantiating (16) with all_25_1, all_30_0, all_21_0, xa, % 14.99/2.78 | simplifying with (40), (41) gives: % 14.99/2.78 | (42) all_30_0 = all_25_1 % 14.99/2.78 | % 14.99/2.78 | REDUCE: (28), (42) imply: % 14.99/2.78 | (43) ~ aDivisorOf0(xq, all_25_1) % 14.99/2.78 | % 14.99/2.78 | GROUND_INST: instantiating (4) with sz10, xq, simplifying with (1), (2), (6), % 14.99/2.78 | (13) gives: % 14.99/2.78 | (44) xq = sz00 | sdteqdtlpzmzozddtrp0(sz10, sz10, xq) % 14.99/2.78 | % 14.99/2.78 | GROUND_INST: instantiating (mIntPlus) with xn, xm, all_25_2, simplifying with % 14.99/2.78 | (10), (11), (18), (21), (25) gives: % 14.99/2.78 | (45) aInteger0(all_25_2) % 14.99/2.78 | % 14.99/2.78 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_25_2, simplifying with % 14.99/2.78 | (10), (11), (18), (21), (25) gives: % 14.99/2.78 | (46) sdtpldt0(xm, xn) = all_25_2 & $i(all_25_2) % 14.99/2.78 | % 14.99/2.78 | ALPHA: (46) implies: % 14.99/2.78 | (47) $i(all_25_2) % 14.99/2.78 | % 14.99/2.78 | BETA: splitting (44) gives: % 14.99/2.78 | % 14.99/2.78 | Case 1: % 14.99/2.78 | | % 14.99/2.78 | | % 14.99/2.78 | | GROUND_INST: instantiating (mIntMult) with xq, all_25_2, all_25_1, % 14.99/2.78 | | simplifying with (6), (13), (26), (45), (47) gives: % 14.99/2.78 | | (48) aInteger0(all_25_1) % 14.99/2.78 | | % 14.99/2.78 | | GROUND_INST: instantiating (mMulComm) with xq, all_25_2, all_25_1, % 14.99/2.78 | | simplifying with (6), (13), (26), (45), (47) gives: % 14.99/2.78 | | (49) sdtasdt0(all_25_2, xq) = all_25_1 & $i(all_25_1) % 14.99/2.78 | | % 14.99/2.78 | | ALPHA: (49) implies: % 14.99/2.78 | | (50) $i(all_25_1) % 14.99/2.78 | | % 14.99/2.78 | | GROUND_INST: instantiating (3) with all_25_1, xq, all_25_2, simplifying with % 14.99/2.78 | | (6), (13), (26), (43), (45), (47), (48), (50) gives: % 14.99/2.78 | | (51) xq = sz00 % 14.99/2.78 | | % 14.99/2.78 | | REDUCE: (5), (51) imply: % 14.99/2.78 | | (52) $false % 14.99/2.78 | | % 14.99/2.78 | | CLOSE: (52) is inconsistent. % 14.99/2.78 | | % 14.99/2.78 | Case 2: % 14.99/2.78 | | % 14.99/2.78 | | (53) xq = sz00 % 14.99/2.78 | | % 14.99/2.78 | | REDUCE: (5), (53) imply: % 14.99/2.78 | | (54) $false % 14.99/2.78 | | % 14.99/2.78 | | CLOSE: (54) is inconsistent. % 14.99/2.78 | | % 14.99/2.78 | End of split % 14.99/2.78 | % 14.99/2.78 End of proof % 14.99/2.78 % SZS output end Proof for theBenchmark % 14.99/2.78 % 14.99/2.78 2178ms %------------------------------------------------------------------------------