%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT089+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 : n014.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 14.94s 2.72s % Output : Proof 19.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT089+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.36 % Computer : n014.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Mon Sep 7 14:00:26 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.38 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. % 0.70/0.72 ________ _____ % 0.70/0.72 ___ __ \_________(_)________________________________ % 0.70/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.72 % 0.70/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.72 (2023-06-19) % 0.70/0.72 % 0.70/0.72 (c) Philipp Rümmer, 2009-2023 % 0.70/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.72 Amanda Stjerna. % 0.70/0.72 Free software under BSD-3-Clause. % 0.70/0.72 % 0.70/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.72 % 0.70/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.74 Running up to 7 provers in parallel. % 0.70/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.01/1.38 Prover 1: Preprocessing ... % 4.01/1.39 Prover 4: Preprocessing ... % 4.77/1.46 Prover 6: Preprocessing ... % 4.77/1.46 Prover 3: Preprocessing ... % 4.77/1.46 Prover 0: Preprocessing ... % 4.77/1.46 Prover 2: Preprocessing ... % 4.77/1.46 Prover 5: Preprocessing ... % 10.45/2.16 Prover 2: Proving ... % 10.45/2.19 Prover 5: Proving ... % 12.54/2.43 Prover 6: Proving ... % 12.54/2.45 Prover 3: Constructing countermodel ... % 12.54/2.47 Prover 1: Constructing countermodel ... % 13.33/2.58 Prover 3: gave up % 13.33/2.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.12/2.60 Prover 4: Constructing countermodel ... % 14.12/2.62 Prover 0: Proving ... % 14.94/2.71 Prover 7: Preprocessing ... % 14.94/2.71 Prover 0: proved (1964ms) % 14.94/2.72 % 14.94/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.94/2.72 % 14.94/2.72 Prover 2: stopped % 14.94/2.72 Prover 5: stopped % 14.94/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.94/2.73 Prover 6: stopped % 14.94/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.94/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.94/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.94/2.75 Prover 1: gave up % 14.94/2.76 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.70/2.85 Prover 8: Preprocessing ... % 15.70/2.85 Prover 10: Preprocessing ... % 15.70/2.87 Prover 16: Preprocessing ... % 15.70/2.89 Prover 13: Preprocessing ... % 16.50/2.93 Prover 7: Warning: ignoring some quantifiers % 16.50/2.94 Prover 11: Preprocessing ... % 16.50/2.96 Prover 7: Constructing countermodel ... % 16.50/3.02 Prover 4: Found proof (size 14) % 16.50/3.02 Prover 4: proved (2266ms) % 16.50/3.02 Prover 13: stopped % 16.50/3.06 Prover 16: Warning: ignoring some quantifiers % 16.50/3.06 Prover 7: stopped % 17.80/3.08 Prover 16: Constructing countermodel ... % 17.80/3.10 Prover 10: Warning: ignoring some quantifiers % 17.80/3.11 Prover 16: stopped % 17.80/3.12 Prover 10: Constructing countermodel ... % 17.80/3.12 Prover 11: stopped % 17.80/3.15 Prover 10: stopped % 18.64/3.23 Prover 8: Warning: ignoring some quantifiers % 18.64/3.25 Prover 8: Constructing countermodel ... % 18.64/3.28 Prover 8: stopped % 18.64/3.28 % 18.64/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.64/3.29 % 18.64/3.29 % SZS output start Proof for theBenchmark % 19.13/3.30 Assumptions after simplification: % 19.13/3.30 --------------------------------- % 19.13/3.30 % 19.13/3.30 (leq_def) % 19.13/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (less(v0, % 19.13/3.37 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 19.13/3.37 leq(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 19.13/3.37 ~ (leq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 19.13/3.37 less(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (leq(v0, % 19.13/3.37 v1) = 0) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0) & ! [v0: $i] : ! % 19.13/3.37 [v1: int] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! % 19.13/3.37 [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) & % 19.13/3.37 ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (less(v0, v0) = v1) | ~ $i(v0) % 19.13/3.37 | leq(v0, v0) = 0) % 19.13/3.37 % 19.13/3.37 (odrl604) % 19.13/3.38 $i(v5) & $i(o) & ? [v0: int] : ( ~ (v0 = 0) & prec(v5, v5, o, o) = v0) % 19.13/3.38 % 19.13/3.38 (prec_oo) % 19.13/3.39 $i(o) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (prec(v0, v1, % 19.13/3.39 o, o) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 19.13/3.39 leq(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 19.13/3.39 ~ (leq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 19.13/3.39 prec(v0, v1, o, o) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (prec(v0, v1, % 19.13/3.39 o, o) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) & ! [v0: $i] : ! % 19.13/3.39 [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | prec(v0, v1, o, o) % 19.13/3.39 = 0) % 19.13/3.39 % 19.13/3.39 Further assumptions not needed in the proof: % 19.13/3.39 -------------------------------------------- % 19.13/3.39 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 19.13/3.39 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 19.13/3.39 conflict_is_verdict, disjoint_def, ep_c_is_ep, ep_o_is_ep, ep_type_enum, % 19.13/3.39 ep_types_distinct, in_closed, in_lopen, in_open, in_ropen, irreflexive, % 19.13/3.39 leq_antisym, leq_less_trans, leq_trans, less_implies_leq, less_leq_trans, % 19.13/3.39 lower_tag_eq, lower_tag_gt, lower_tag_gteq, lower_tag_lt, lower_tag_lteq, % 19.13/3.39 prec_cc, prec_co, prec_oc, transitive, trichotomy, unknown_is_verdict, % 19.13/3.39 upper_tag_eq, upper_tag_gt, upper_tag_gteq, upper_tag_lt, upper_tag_lteq, % 19.13/3.39 val_v5, verdict_enum, verdicts_distinct_cf_cp, verdicts_distinct_cf_un, % 19.13/3.39 verdicts_distinct_cp_un % 19.13/3.39 % 19.13/3.39 Those formulas are unsatisfiable: % 19.13/3.39 --------------------------------- % 19.13/3.39 % 19.13/3.39 Begin of proof % 19.13/3.39 | % 19.13/3.39 | ALPHA: (leq_def) implies: % 19.13/3.39 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ~ % 19.13/3.39 | $i(v0)) % 19.13/3.39 | % 19.13/3.39 | ALPHA: (prec_oo) implies: % 19.13/3.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (prec(v0, v1, % 19.13/3.40 | o, o) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 19.13/3.40 | & leq(v0, v1) = v3)) % 19.13/3.40 | % 19.13/3.40 | ALPHA: (odrl604) implies: % 19.13/3.40 | (3) $i(v5) % 19.13/3.40 | (4) ? [v0: int] : ( ~ (v0 = 0) & prec(v5, v5, o, o) = v0) % 19.13/3.40 | % 19.62/3.40 | DELTA: instantiating (4) with fresh symbol all_31_0 gives: % 19.62/3.40 | (5) ~ (all_31_0 = 0) & prec(v5, v5, o, o) = all_31_0 % 19.62/3.40 | % 19.62/3.40 | ALPHA: (5) implies: % 19.62/3.40 | (6) ~ (all_31_0 = 0) % 19.62/3.40 | (7) prec(v5, v5, o, o) = all_31_0 % 19.62/3.40 | % 19.62/3.40 | GROUND_INST: instantiating (2) with v5, v5, all_31_0, simplifying with (3), % 19.62/3.40 | (7) gives: % 19.62/3.40 | (8) all_31_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(v5, v5) = v0) % 19.62/3.40 | % 19.62/3.40 | BETA: splitting (8) gives: % 19.62/3.40 | % 19.62/3.41 | Case 1: % 19.62/3.41 | | % 19.62/3.41 | | (9) all_31_0 = 0 % 19.62/3.41 | | % 19.62/3.41 | | REDUCE: (6), (9) imply: % 19.62/3.41 | | (10) $false % 19.62/3.41 | | % 19.62/3.41 | | CLOSE: (10) is inconsistent. % 19.62/3.41 | | % 19.62/3.41 | Case 2: % 19.62/3.41 | | % 19.62/3.41 | | (11) ? [v0: int] : ( ~ (v0 = 0) & leq(v5, v5) = v0) % 19.62/3.41 | | % 19.62/3.41 | | DELTA: instantiating (11) with fresh symbol all_40_0 gives: % 19.62/3.41 | | (12) ~ (all_40_0 = 0) & leq(v5, v5) = all_40_0 % 19.62/3.41 | | % 19.62/3.41 | | ALPHA: (12) implies: % 19.62/3.41 | | (13) ~ (all_40_0 = 0) % 19.62/3.41 | | (14) leq(v5, v5) = all_40_0 % 19.62/3.41 | | % 19.62/3.41 | | GROUND_INST: instantiating (1) with v5, all_40_0, simplifying with (3), (14) % 19.62/3.41 | | gives: % 19.62/3.41 | | (15) all_40_0 = 0 % 19.62/3.41 | | % 19.62/3.41 | | REDUCE: (13), (15) imply: % 19.62/3.41 | | (16) $false % 19.62/3.41 | | % 19.62/3.41 | | CLOSE: (16) is inconsistent. % 19.62/3.41 | | % 19.62/3.41 | End of split % 19.62/3.41 | % 19.62/3.41 End of proof % 19.62/3.41 % SZS output end Proof for theBenchmark % 19.62/3.41 % 19.62/3.41 2689ms %------------------------------------------------------------------------------