%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:30 AM UTC 2026 % Result : Theorem 13.64s 2.53s % Output : Proof 17.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.34 % Computer : n029.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Mon Sep 7 14:19:57 UTC 2026 % 0.07/0.34 % CPUTime : % 0.12/0.36 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.72/0.70 ________ _____ % 0.72/0.70 ___ __ \_________(_)________________________________ % 0.72/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.72/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.72/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.72/0.70 % 0.72/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.72/0.70 (2023-06-19) % 0.72/0.70 % 0.72/0.70 (c) Philipp Rümmer, 2009-2023 % 0.72/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.72/0.70 Amanda Stjerna. % 0.72/0.70 Free software under BSD-3-Clause. % 0.72/0.70 % 0.72/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.72/0.70 % 0.72/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.72 Running up to 7 provers in parallel. % 0.72/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.45/1.29 Prover 4: Preprocessing ... % 4.23/1.33 Prover 1: Preprocessing ... % 4.23/1.36 Prover 5: Preprocessing ... % 4.23/1.36 Prover 0: Preprocessing ... % 4.23/1.36 Prover 3: Preprocessing ... % 4.23/1.36 Prover 6: Preprocessing ... % 4.23/1.37 Prover 2: Preprocessing ... % 8.94/2.01 Prover 2: Proving ... % 8.94/2.01 Prover 5: Proving ... % 10.00/2.12 Prover 6: Proving ... % 10.00/2.13 Prover 1: Constructing countermodel ... % 10.00/2.13 Prover 3: Constructing countermodel ... % 11.27/2.23 Prover 4: Constructing countermodel ... % 11.27/2.26 Prover 0: Proving ... % 11.27/2.29 Prover 6: gave up % 11.27/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.05/2.31 Prover 3: gave up % 12.05/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.05/2.33 Prover 1: gave up % 12.05/2.33 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.05/2.39 Prover 7: Preprocessing ... % 12.86/2.40 Prover 8: Preprocessing ... % 12.86/2.47 Prover 9: Preprocessing ... % 13.64/2.53 Prover 0: proved (1788ms) % 13.64/2.53 % 13.64/2.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.64/2.53 % 13.64/2.54 Prover 5: stopped % 13.64/2.55 Prover 2: stopped % 13.64/2.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.64/2.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.64/2.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.44/2.60 Prover 7: Warning: ignoring some quantifiers % 14.44/2.65 Prover 7: Constructing countermodel ... % 14.44/2.65 Prover 11: Preprocessing ... % 14.44/2.67 Prover 13: Preprocessing ... % 14.44/2.69 Prover 10: Preprocessing ... % 15.24/2.74 Prover 4: Found proof (size 13) % 15.24/2.74 Prover 4: proved (2004ms) % 15.24/2.74 Prover 7: stopped % 15.24/2.74 Prover 11: stopped % 15.24/2.75 Prover 10: stopped % 15.24/2.79 Prover 8: Warning: ignoring some quantifiers % 15.99/2.80 Prover 8: Constructing countermodel ... % 15.99/2.82 Prover 13: Warning: ignoring some quantifiers % 15.99/2.83 Prover 8: stopped % 15.99/2.84 Prover 13: Constructing countermodel ... % 15.99/2.86 Prover 13: stopped % 16.60/2.97 Prover 9: Constructing countermodel ... % 16.60/2.98 Prover 9: stopped % 16.60/2.98 % 16.60/2.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.60/2.98 % 16.60/2.99 % SZS output start Proof for theBenchmark % 16.60/3.00 Assumptions after simplification: % 16.60/3.00 --------------------------------- % 16.60/3.00 % 16.60/3.00 (in_open) % 17.22/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.22/3.05 (in_open(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.22/3.05 any] : ? [v5: any] : (less(v1, v0) = v4 & less(v0, v2) = v5 & ( ~ (v5 = % 17.22/3.05 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 17.22/3.05 (in_open(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (less(v1, % 17.22/3.05 v0) = 0 & less(v0, v2) = 0)) % 17.22/3.05 % 17.22/3.05 (irreflexive) % 17.22/3.05 ! [v0: $i] : ( ~ (less(v0, v0) = 0) | ~ $i(v0)) % 17.22/3.05 % 17.22/3.05 (leq_less_trans) % 17.22/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0, % 17.22/3.06 v1) = 0) | ~ (less(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.22/3.06 ? [v4: int] : ( ~ (v4 = 0) & less(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] % 17.22/3.06 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (less(v1, v2) = 0) | ~ (less(v0, % 17.22/3.06 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 17.22/3.06 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 17.22/3.06 (leq(v0, v1) = 0) | ~ (less(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 17.22/3.06 $i(v0) | less(v0, v2) = 0) % 17.22/3.06 % 17.22/3.06 (less_implies_leq) % 17.22/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = v2) | % 17.22/3.07 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & less(v0, v1) = v3)) & % 17.22/3.07 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.22/3.07 leq(v0, v1) = 0) % 17.22/3.07 % 17.22/3.07 (odrl423) % 17.22/3.07 $i(v600) & $i(v0) & ? [v0: $i] : (in_open(v0, v0, v600) = 0 & less(v600, v0) % 17.22/3.07 = 0 & $i(v0)) % 17.22/3.07 % 17.22/3.07 Further assumptions not needed in the proof: % 17.22/3.07 -------------------------------------------- % 17.22/3.07 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 17.22/3.07 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 17.22/3.07 conflict_is_verdict, distinct, in_closed, in_lopen, in_ropen, leq_antisym, % 17.22/3.07 leq_def, leq_trans, less_leq_trans, ord_v0_v600, transitive, trichotomy, % 17.22/3.07 unknown_is_verdict, val_v0, val_v600, verdict_enum, verdicts_distinct_cf_cp, % 17.22/3.07 verdicts_distinct_cf_un, verdicts_distinct_cp_un % 17.22/3.07 % 17.22/3.07 Those formulas are unsatisfiable: % 17.22/3.07 --------------------------------- % 17.22/3.07 % 17.22/3.07 Begin of proof % 17.22/3.07 | % 17.22/3.07 | ALPHA: (less_implies_leq) implies: % 17.22/3.08 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ % 17.22/3.08 | $i(v0) | leq(v0, v1) = 0) % 17.22/3.08 | % 17.22/3.08 | ALPHA: (leq_less_trans) implies: % 17.22/3.08 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v0, v1) = 0) | ~ % 17.22/3.08 | (less(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) % 17.22/3.08 | = 0) % 17.22/3.08 | % 17.22/3.08 | ALPHA: (in_open) implies: % 17.22/3.08 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in_open(v0, v1, v2) = 0) % 17.22/3.08 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (less(v1, v0) = 0 & less(v0, % 17.22/3.08 | v2) = 0)) % 17.22/3.08 | % 17.22/3.08 | ALPHA: (odrl423) implies: % 17.22/3.08 | (4) $i(v0) % 17.22/3.08 | (5) $i(v600) % 17.22/3.08 | (6) ? [v0: $i] : (in_open(v0, v0, v600) = 0 & less(v600, v0) = 0 & $i(v0)) % 17.22/3.08 | % 17.22/3.09 | DELTA: instantiating (6) with fresh symbol all_25_0 gives: % 17.22/3.09 | (7) in_open(all_25_0, v0, v600) = 0 & less(v600, all_25_0) = 0 & % 17.22/3.09 | $i(all_25_0) % 17.22/3.09 | % 17.22/3.09 | ALPHA: (7) implies: % 17.22/3.09 | (8) $i(all_25_0) % 17.22/3.09 | (9) less(v600, all_25_0) = 0 % 17.22/3.09 | (10) in_open(all_25_0, v0, v600) = 0 % 17.22/3.09 | % 17.22/3.09 | GROUND_INST: instantiating (1) with v600, all_25_0, simplifying with (5), (8), % 17.22/3.09 | (9) gives: % 17.22/3.09 | (11) leq(v600, all_25_0) = 0 % 17.22/3.09 | % 17.22/3.09 | GROUND_INST: instantiating (3) with all_25_0, v0, v600, simplifying with (4), % 17.22/3.09 | (5), (8), (10) gives: % 17.22/3.09 | (12) less(all_25_0, v600) = 0 & less(v0, all_25_0) = 0 % 17.22/3.09 | % 17.22/3.09 | ALPHA: (12) implies: % 17.22/3.09 | (13) less(all_25_0, v600) = 0 % 17.22/3.09 | % 17.22/3.09 | GROUND_INST: instantiating (2) with v600, all_25_0, v600, simplifying with % 17.22/3.09 | (5), (8), (11), (13) gives: % 17.22/3.09 | (14) less(v600, v600) = 0 % 17.22/3.09 | % 17.22/3.09 | GROUND_INST: instantiating (irreflexive) with v600, simplifying with (5), (14) % 17.22/3.09 | gives: % 17.22/3.10 | (15) $false % 17.22/3.10 | % 17.22/3.10 | CLOSE: (15) is inconsistent. % 17.22/3.10 | % 17.22/3.10 End of proof % 17.22/3.10 % SZS output end Proof for theBenchmark % 17.22/3.10 % 17.22/3.10 2395ms %------------------------------------------------------------------------------