%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM540+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 : n002.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 11:48:29 EDT 2023 % Result : Theorem 78.52s 11.04s % Output : Proof 79.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM540+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 10:45:47 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.34/1.19 Prover 1: Preprocessing ... % 3.34/1.19 Prover 4: Preprocessing ... % 3.66/1.22 Prover 0: Preprocessing ... % 3.66/1.22 Prover 6: Preprocessing ... % 3.66/1.22 Prover 3: Preprocessing ... % 3.66/1.22 Prover 2: Preprocessing ... % 3.66/1.23 Prover 5: Preprocessing ... % 8.97/2.06 Prover 1: Constructing countermodel ... % 8.97/2.07 Prover 5: Constructing countermodel ... % 8.97/2.08 Prover 3: Constructing countermodel ... % 9.52/2.13 Prover 2: Proving ... % 10.55/2.18 Prover 6: Proving ... % 12.27/2.44 Prover 4: Constructing countermodel ... % 13.53/2.61 Prover 0: Proving ... % 73.85/10.36 Prover 2: stopped % 73.85/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.25/10.45 Prover 7: Preprocessing ... % 74.80/10.56 Prover 7: Constructing countermodel ... % 78.16/10.96 Prover 7: Found proof (size 21) % 78.52/11.02 Prover 7: proved (626ms) % 78.52/11.02 Prover 0: stopped % 78.52/11.02 Prover 3: stopped % 78.52/11.02 Prover 5: stopped % 78.52/11.03 Prover 1: stopped % 78.52/11.03 Prover 4: stopped % 78.52/11.03 Prover 6: stopped % 78.52/11.03 % 78.52/11.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 78.52/11.04 % 78.52/11.04 % SZS output start Proof for theBenchmark % 78.52/11.04 Assumptions after simplification: % 78.52/11.04 --------------------------------- % 79.02/11.04 % 79.02/11.04 (mDefEmp) % 79.02/11.05 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 79.02/11.05 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 79.02/11.05 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 79.02/11.05 % 79.02/11.05 (mDefSeg) % 79.14/11.08 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 79.14/11.08 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 79.14/11.08 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 79.14/11.08 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 79.14/11.08 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 79.14/11.08 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 79.14/11.08 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 79.14/11.08 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 79.14/11.08 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 79.14/11.08 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 79.14/11.08 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 79.14/11.08 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 79.14/11.08 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 79.14/11.08 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 79.14/11.08 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 79.14/11.08 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 79.14/11.08 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 79.14/11.08 | aSet0(v1)) % 79.14/11.08 % 79.14/11.08 (mNoScLessZr) % 79.14/11.08 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 79.14/11.08 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 79.14/11.08 % 79.14/11.08 (mZeroNum) % 79.14/11.08 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 79.14/11.08 % 79.14/11.08 (m__) % 79.14/11.08 $i(sz00) & $i(slcrc0) & ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0 % 79.14/11.08 & $i(v0)) % 79.14/11.08 % 79.14/11.08 Further assumptions not needed in the proof: % 79.14/11.08 -------------------------------------------- % 79.14/11.08 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 79.14/11.08 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, % 79.14/11.08 mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin, % 79.14/11.08 mFConsSet, mFDiffSet, mFinRel, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, % 79.14/11.08 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, % 79.14/11.08 mSegFin, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, % 79.14/11.08 mSuccLess, mSuccNum, mZeroLess % 79.14/11.08 % 79.14/11.08 Those formulas are unsatisfiable: % 79.14/11.08 --------------------------------- % 79.14/11.08 % 79.14/11.08 Begin of proof % 79.14/11.08 | % 79.14/11.08 | ALPHA: (mDefEmp) implies: % 79.14/11.08 | (1) aSet0(slcrc0) % 79.14/11.08 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 79.14/11.08 | % 79.14/11.08 | ALPHA: (mZeroNum) implies: % 79.14/11.08 | (3) aElementOf0(sz00, szNzAzT0) % 79.14/11.08 | % 79.14/11.08 | ALPHA: (mNoScLessZr) implies: % 79.14/11.08 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 79.14/11.08 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 79.14/11.08 | % 79.14/11.08 | ALPHA: (mDefSeg) implies: % 79.14/11.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = % 79.14/11.09 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ % 79.14/11.09 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3, % 79.14/11.09 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 & % 79.14/11.09 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) | % 79.14/11.09 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) & % 79.14/11.09 | aElementOf0(v3, szNzAzT0))))) % 79.14/11.09 | % 79.14/11.09 | ALPHA: (m__) implies: % 79.14/11.09 | (6) $i(slcrc0) % 79.14/11.09 | (7) $i(sz00) % 79.14/11.09 | (8) ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0 & $i(v0)) % 79.14/11.09 | % 79.14/11.09 | DELTA: instantiating (8) with fresh symbol all_45_0 gives: % 79.14/11.09 | (9) ~ (all_45_0 = slcrc0) & slbdtrb0(sz00) = all_45_0 & $i(all_45_0) % 79.14/11.09 | % 79.14/11.09 | ALPHA: (9) implies: % 79.14/11.09 | (10) ~ (all_45_0 = slcrc0) % 79.14/11.09 | (11) slbdtrb0(sz00) = all_45_0 % 79.14/11.09 | % 79.14/11.09 | GROUND_INST: instantiating (5) with sz00, all_45_0, slcrc0, simplifying with % 79.14/11.09 | (1), (3), (6), (7), (11) gives: % 79.14/11.09 | (12) all_45_0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ % 79.14/11.09 | aElementOf0(v0, szNzAzT0) | ~ aElementOf0(v0, slcrc0) | % 79.14/11.09 | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) & % 79.14/11.09 | (aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 79.14/11.09 | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0)))) % 79.14/11.09 | % 79.14/11.09 | BETA: splitting (12) gives: % 79.14/11.09 | % 79.14/11.09 | Case 1: % 79.14/11.09 | | % 79.14/11.09 | | (13) all_45_0 = slcrc0 % 79.14/11.09 | | % 79.14/11.09 | | REDUCE: (10), (13) imply: % 79.14/11.09 | | (14) $false % 79.14/11.10 | | % 79.14/11.10 | | CLOSE: (14) is inconsistent. % 79.14/11.10 | | % 79.14/11.10 | Case 2: % 79.14/11.10 | | % 79.14/11.10 | | (15) ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ aElementOf0(v0, szNzAzT0) % 79.14/11.10 | | | ~ aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 79.14/11.10 | | ~ sdtlseqdt0(v1, sz00))) & (aElementOf0(v0, slcrc0) | % 79.14/11.10 | | (szszuzczcdt0(v0) = v1 & $i(v1) & sdtlseqdt0(v1, sz00) & % 79.14/11.10 | | aElementOf0(v0, szNzAzT0)))) % 79.14/11.10 | | % 79.14/11.10 | | DELTA: instantiating (15) with fresh symbols all_70_0, all_70_1 gives: % 79.14/11.10 | | (16) $i(all_70_1) & ( ~ aElementOf0(all_70_1, szNzAzT0) | ~ % 79.14/11.10 | | aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0 % 79.14/11.10 | | & $i(all_70_0) & ~ sdtlseqdt0(all_70_0, sz00))) & % 79.14/11.10 | | (aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0 % 79.14/11.10 | | & $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) & % 79.14/11.10 | | aElementOf0(all_70_1, szNzAzT0))) % 79.14/11.10 | | % 79.14/11.10 | | ALPHA: (16) implies: % 79.14/11.10 | | (17) $i(all_70_1) % 79.14/11.10 | | (18) aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0 & % 79.14/11.10 | | $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1, % 79.14/11.10 | | szNzAzT0)) % 79.14/11.10 | | % 79.14/11.10 | | BETA: splitting (18) gives: % 79.14/11.10 | | % 79.14/11.10 | | Case 1: % 79.14/11.10 | | | % 79.14/11.10 | | | (19) aElementOf0(all_70_1, slcrc0) % 79.14/11.10 | | | % 79.14/11.10 | | | GROUND_INST: instantiating (2) with all_70_1, simplifying with (17), (19) % 79.14/11.10 | | | gives: % 79.14/11.10 | | | (20) $false % 79.14/11.10 | | | % 79.14/11.10 | | | CLOSE: (20) is inconsistent. % 79.14/11.10 | | | % 79.14/11.10 | | Case 2: % 79.14/11.10 | | | % 79.14/11.10 | | | (21) szszuzczcdt0(all_70_1) = all_70_0 & $i(all_70_0) & % 79.14/11.10 | | | sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1, szNzAzT0) % 79.14/11.10 | | | % 79.14/11.10 | | | ALPHA: (21) implies: % 79.14/11.10 | | | (22) aElementOf0(all_70_1, szNzAzT0) % 79.14/11.10 | | | (23) sdtlseqdt0(all_70_0, sz00) % 79.14/11.10 | | | (24) szszuzczcdt0(all_70_1) = all_70_0 % 79.14/11.10 | | | % 79.14/11.10 | | | GROUND_INST: instantiating (4) with all_70_1, all_70_0, simplifying with % 79.14/11.10 | | | (17), (22), (23), (24) gives: % 79.14/11.10 | | | (25) $false % 79.14/11.10 | | | % 79.14/11.10 | | | CLOSE: (25) is inconsistent. % 79.14/11.10 | | | % 79.14/11.10 | | End of split % 79.14/11.10 | | % 79.14/11.10 | End of split % 79.14/11.10 | % 79.14/11.10 End of proof % 79.14/11.10 % SZS output end Proof for theBenchmark % 79.14/11.10 % 79.14/11.10 10505ms %------------------------------------------------------------------------------