%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYP116_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 : Tue May 5 07:14:22 PM UTC 2026 % Result : Unsatisfiable 4.45s 1.36s % Output : Proof 4.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYP116_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n007.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon May 4 17:50:08 EDT 2026 % 0.16/0.34 % CPUTime : % 0.49/0.62 ________ _____ % 0.49/0.62 ___ __ \_________(_)________________________________ % 0.49/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.62 % 0.49/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.62 (2023-06-19) % 0.49/0.62 % 0.49/0.62 (c) Philipp Rümmer, 2009-2023 % 0.49/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.62 Amanda Stjerna. % 0.49/0.62 Free software under BSD-3-Clause. % 0.49/0.62 % 0.49/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.62 % 0.49/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.63 Running up to 7 provers in parallel. % 0.66/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.62/0.99 Prover 4: Preprocessing ... % 1.62/0.99 Prover 1: Preprocessing ... % 2.39/1.04 Prover 3: Preprocessing ... % 2.39/1.04 Prover 2: Preprocessing ... % 2.39/1.04 Prover 0: Preprocessing ... % 2.39/1.04 Prover 5: Preprocessing ... % 2.39/1.04 Prover 6: Preprocessing ... % 2.39/1.10 Prover 5: Proving ... % 2.39/1.10 Prover 2: Proving ... % 2.39/1.11 Prover 1: Constructing countermodel ... % 2.39/1.11 Prover 3: Constructing countermodel ... % 2.39/1.11 Prover 4: Constructing countermodel ... % 3.09/1.12 Prover 6: Constructing countermodel ... % 3.09/1.12 Prover 0: Proving ... % 3.70/1.21 Prover 6: gave up % 3.70/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.70/1.21 Prover 3: gave up % 3.70/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.70/1.22 Prover 4: gave up % 3.70/1.22 Prover 1: gave up % 3.70/1.23 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 3.70/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.70/1.24 Prover 9: Preprocessing ... % 3.70/1.24 Prover 10: Preprocessing ... % 3.70/1.25 Prover 7: Preprocessing ... % 3.70/1.25 Prover 8: Preprocessing ... % 3.70/1.26 Prover 10: Warning: ignoring some quantifiers % 3.70/1.26 Prover 10: Constructing countermodel ... % 3.70/1.26 Prover 7: Warning: ignoring some quantifiers % 3.70/1.28 Prover 8: Warning: ignoring some quantifiers % 3.70/1.28 Prover 7: Constructing countermodel ... % 3.70/1.28 Prover 9: Constructing countermodel ... % 3.70/1.28 Prover 8: Constructing countermodel ... % 4.45/1.30 Prover 9: gave up % 4.45/1.32 Prover 10: Found proof (size 29) % 4.45/1.32 Prover 10: proved (80ms) % 4.45/1.32 Prover 7: Found proof (size 29) % 4.45/1.32 Prover 7: proved (110ms) % 4.45/1.32 Prover 8: stopped % 4.45/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.45/1.32 Prover 0: stopped % 4.45/1.32 Prover 5: stopped % 4.45/1.32 Prover 2: proved (684ms) % 4.45/1.33 Prover 11: Preprocessing ... % 4.45/1.35 Prover 11: Constructing countermodel ... % 4.45/1.36 Prover 11: stopped % 4.45/1.36 % 4.45/1.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.45/1.36 % 4.45/1.36 % SZS output start Proof for theBenchmark % 4.45/1.37 Assumptions after simplification: % 4.45/1.37 --------------------------------- % 4.45/1.37 % 4.45/1.37 (ax1) % 4.45/1.37 ~ ($lesseq(0, npa)) | ~ p(npa) % 4.45/1.37 % 4.45/1.37 (ax2) % 4.45/1.37 ~ ($lesseq(0, npb)) | p(npb) % 4.45/1.37 % 4.45/1.37 (ax3) % 4.45/1.37 ~ ($lesseq(npa, -1)) | ~ q(npa) % 4.45/1.37 % 4.45/1.37 (ax4) % 4.45/1.37 ~ ($lesseq(npb, -1)) | q(npb) % 4.45/1.37 % 4.45/1.37 (ax5) % 4.45/1.37 ! [v0: int] : (npb = npa | ~ r(v0)) % 4.45/1.37 % 4.45/1.37 (ax6) % 4.45/1.37 ? [v0: int] : r(v0) % 4.45/1.37 % 4.45/1.37 Those formulas are unsatisfiable: % 4.45/1.37 --------------------------------- % 4.45/1.37 % 4.45/1.37 Begin of proof % 4.45/1.37 | % 4.45/1.37 | DELTA: instantiating (ax6) with fresh symbol all_3_0 gives: % 4.45/1.37 | (1) r(all_3_0) % 4.45/1.37 | % 4.45/1.38 | GROUND_INST: instantiating (ax5) with all_3_0, simplifying with (1) gives: % 4.45/1.38 | (2) npb = npa % 4.45/1.38 | % 4.45/1.38 | BETA: splitting (ax4) gives: % 4.45/1.38 | % 4.45/1.38 | Case 1: % 4.45/1.38 | | % 4.45/1.38 | | (3) q(npb) % 4.45/1.38 | | % 4.45/1.38 | | REDUCE: (2), (3) imply: % 4.45/1.38 | | (4) q(npa) % 4.45/1.38 | | % 4.45/1.38 | | BETA: splitting (ax3) gives: % 4.45/1.38 | | % 4.45/1.38 | | Case 1: % 4.45/1.38 | | | % 4.45/1.38 | | | (5) ~ q(npa) % 4.45/1.38 | | | % 4.45/1.38 | | | PRED_UNIFY: (4), (5) imply: % 4.45/1.38 | | | (6) $false % 4.45/1.38 | | | % 4.45/1.38 | | | CLOSE: (6) is inconsistent. % 4.45/1.38 | | | % 4.45/1.38 | | Case 2: % 4.45/1.38 | | | % 4.45/1.38 | | | (7) $lesseq(0, npa) % 4.45/1.38 | | | % 4.45/1.38 | | | REF_CLOSE: (2), (7), (ax1), (ax2) are inconsistent by sub-proof #1. % 4.45/1.38 | | | % 4.45/1.38 | | End of split % 4.45/1.38 | | % 4.45/1.38 | Case 2: % 4.45/1.38 | | % 4.45/1.38 | | (8) $lesseq(0, npb) % 4.45/1.38 | | % 4.45/1.38 | | REDUCE: (2), (8) imply: % 4.45/1.38 | | (9) $lesseq(0, npa) % 4.45/1.38 | | % 4.45/1.38 | | REF_CLOSE: (2), (9), (ax1), (ax2) are inconsistent by sub-proof #1. % 4.45/1.38 | | % 4.45/1.38 | End of split % 4.45/1.38 | % 4.45/1.38 End of proof % 4.45/1.38 % 4.45/1.38 Sub-proof #1 shows that the following formulas are inconsistent: % 4.45/1.38 ---------------------------------------------------------------- % 4.45/1.38 (1) ~ ($lesseq(0, npa)) | ~ p(npa) % 4.45/1.38 (2) ~ ($lesseq(0, npb)) | p(npb) % 4.45/1.38 (3) npb = npa % 4.45/1.38 (4) $lesseq(0, npa) % 4.45/1.38 % 4.45/1.38 Begin of proof % 4.45/1.38 | % 4.45/1.38 | BETA: splitting (1) gives: % 4.45/1.38 | % 4.45/1.38 | Case 1: % 4.45/1.38 | | % 4.45/1.38 | | (5) ~ p(npa) % 4.45/1.38 | | % 4.45/1.38 | | BETA: splitting (2) gives: % 4.45/1.38 | | % 4.45/1.38 | | Case 1: % 4.45/1.38 | | | % 4.45/1.38 | | | (6) p(npb) % 4.45/1.38 | | | % 4.45/1.38 | | | REDUCE: (3), (6) imply: % 4.45/1.38 | | | (7) p(npa) % 4.45/1.38 | | | % 4.45/1.38 | | | PRED_UNIFY: (5), (7) imply: % 4.45/1.38 | | | (8) $false % 4.45/1.38 | | | % 4.45/1.38 | | | CLOSE: (8) is inconsistent. % 4.45/1.38 | | | % 4.45/1.38 | | Case 2: % 4.45/1.38 | | | % 4.45/1.39 | | | (9) $lesseq(npb, -1) % 4.45/1.39 | | | % 4.45/1.39 | | | REDUCE: (3), (9) imply: % 4.45/1.39 | | | (10) $lesseq(npa, -1) % 4.45/1.39 | | | % 4.45/1.39 | | | COMBINE_INEQS: (4), (10) imply: % 4.45/1.39 | | | (11) $false % 4.45/1.39 | | | % 4.45/1.39 | | | CLOSE: (11) is inconsistent. % 4.45/1.39 | | | % 4.45/1.39 | | End of split % 4.45/1.39 | | % 4.45/1.39 | Case 2: % 4.45/1.39 | | % 4.45/1.39 | | (12) $lesseq(npa, -1) % 4.45/1.39 | | % 4.45/1.39 | | COMBINE_INEQS: (4), (12) imply: % 4.45/1.39 | | (13) $false % 4.45/1.39 | | % 4.45/1.39 | | CLOSE: (13) is inconsistent. % 4.45/1.39 | | % 4.45/1.39 | End of split % 4.45/1.39 | % 4.45/1.39 End of proof % 4.45/1.39 % SZS output end Proof for theBenchmark % 4.45/1.39 % 4.45/1.39 767ms %------------------------------------------------------------------------------