%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT106+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 : n031.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 06:17:31 AM UTC 2026 % Result : Unsatisfiable 16.59s 3.24s % Output : Proof 20.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.34 % Computer : n031.cluster.edu % 0.10/0.34 % Model : x86_64 x86_64 % 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.34 % Memory : 8046.5625MB % 0.10/0.34 % OS : Linux 6.8.0-71-generic % 0.10/0.34 % CPULimit : 300 % 0.10/0.34 % WCLimit : 300 % 0.10/0.34 % DateTime : Mon Sep 7 14:44:56 UTC 2026 % 0.10/0.34 % CPUTime : % 0.10/0.36 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. % 0.85/0.84 ________ _____ % 0.85/0.84 ___ __ \_________(_)________________________________ % 0.85/0.84 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.85/0.84 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.85/0.84 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.85/0.84 % 0.85/0.84 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.85/0.84 (2023-06-19) % 0.85/0.84 % 0.85/0.84 (c) Philipp Rümmer, 2009-2023 % 0.85/0.84 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.85/0.84 Amanda Stjerna. % 0.85/0.84 Free software under BSD-3-Clause. % 0.85/0.84 % 0.85/0.84 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.85/0.84 % 0.85/0.84 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.85/0.87 Running up to 7 provers in parallel. % 0.85/0.88 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.85/0.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.85/0.89 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.85/0.89 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.85/0.89 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.85/0.89 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.85/0.89 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.85/1.77 Prover 4: Preprocessing ... % 4.85/1.78 Prover 1: Preprocessing ... % 5.62/1.88 Prover 3: Preprocessing ... % 5.62/1.88 Prover 0: Preprocessing ... % 5.62/1.88 Prover 2: Preprocessing ... % 5.62/1.88 Prover 5: Preprocessing ... % 5.62/1.88 Prover 6: Preprocessing ... % 12.63/2.78 Prover 2: Proving ... % 12.63/2.78 Prover 5: Proving ... % 13.42/2.80 Prover 6: Proving ... % 13.42/2.84 Prover 1: Constructing countermodel ... % 13.42/2.86 Prover 3: Constructing countermodel ... % 14.24/2.98 Prover 4: Constructing countermodel ... % 16.59/3.20 Prover 0: Proving ... % 16.59/3.23 Prover 3: proved (2346ms) % 16.59/3.23 % 16.59/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.59/3.24 % 16.59/3.24 Prover 2: stopped % 16.59/3.24 Prover 5: stopped % 16.59/3.24 Prover 1: Found proof (size 10) % 16.59/3.25 Prover 6: stopped % 16.59/3.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.59/3.25 Prover 1: proved (2363ms) % 16.59/3.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.59/3.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.59/3.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.59/3.25 Prover 4: stopped % 16.59/3.25 Prover 0: stopped % 17.36/3.35 Prover 10: Preprocessing ... % 17.36/3.39 Prover 7: Preprocessing ... % 17.36/3.39 Prover 11: Preprocessing ... % 17.36/3.39 Prover 8: Preprocessing ... % 18.14/3.42 Prover 10: stopped % 18.14/3.44 Prover 7: stopped % 18.14/3.48 Prover 11: stopped % 19.79/3.75 Prover 8: Warning: ignoring some quantifiers % 19.79/3.76 Prover 8: Constructing countermodel ... % 19.79/3.80 Prover 8: stopped % 19.79/3.80 % 19.79/3.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.79/3.80 % 20.29/3.80 % SZS output start Proof for theBenchmark % 20.29/3.81 Assumptions after simplification: % 20.29/3.81 --------------------------------- % 20.29/3.82 % 20.29/3.82 (in_lopen) % 20.29/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.29/3.88 (in_lopen(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 20.29/3.88 any] : ? [v5: any] : (leq(v0, v2) = v5 & less(v1, v0) = v4 & ( ~ (v5 = 0) % 20.29/3.88 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 20.29/3.88 (in_lopen(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, % 20.29/3.88 v2) = 0 & less(v1, v0) = 0)) % 20.29/3.88 % 20.29/3.88 (irreflexive) % 20.29/3.88 ! [v0: $i] : ( ~ (less(v0, v0) = 0) | ~ $i(v0)) % 20.29/3.88 % 20.29/3.88 (less_leq_trans) % 20.29/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v1, v2) = 0) | ~ (less(v0, % 20.29/3.89 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) = 0) % 20.29/3.89 % 20.29/3.89 (ord_v600_v800) % 20.29/3.89 less(v600, v800) = 0 & $i(v800) & $i(v600) % 20.29/3.89 % 20.29/3.89 (wit_in_lopen) % 20.29/3.89 in_lopen(w, v0, v600) = 0 & $i(w) & $i(v600) & $i(v0) % 20.29/3.89 % 20.29/3.89 (wit_leq) % 20.29/3.89 leq(v800, w) = 0 & $i(w) & $i(v800) % 20.29/3.89 % 20.29/3.89 Further assumptions not needed in the proof: % 20.29/3.89 -------------------------------------------- % 20.29/3.89 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 20.29/3.89 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 20.29/3.89 conflict_is_verdict, distinct, in_closed, in_open, in_ropen, leq_antisym, % 20.29/3.89 leq_def, leq_less_trans, leq_trans, less_implies_leq, ord_v0_v600, transitive, % 20.29/3.89 trichotomy, unknown_is_verdict, val_v0, val_v600, val_v800, verdict_enum, % 20.29/3.89 verdicts_distinct_cf_cp, verdicts_distinct_cf_un, verdicts_distinct_cp_un, % 20.29/3.89 wit_val % 20.29/3.89 % 20.29/3.89 Those formulas are unsatisfiable: % 20.29/3.89 --------------------------------- % 20.29/3.89 % 20.29/3.89 Begin of proof % 20.77/3.90 | % 20.77/3.90 | ALPHA: (in_lopen) implies: % 20.77/3.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in_lopen(v0, v1, v2) = % 20.77/3.90 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, v2) = 0 & % 20.77/3.90 | less(v1, v0) = 0)) % 20.77/3.90 | % 20.77/3.90 | ALPHA: (ord_v600_v800) implies: % 20.77/3.90 | (2) less(v600, v800) = 0 % 20.77/3.90 | % 20.77/3.90 | ALPHA: (wit_in_lopen) implies: % 20.77/3.91 | (3) $i(v0) % 20.77/3.91 | (4) $i(v600) % 20.77/3.91 | (5) in_lopen(w, v0, v600) = 0 % 20.77/3.91 | % 20.77/3.91 | ALPHA: (wit_leq) implies: % 20.77/3.91 | (6) $i(v800) % 20.77/3.91 | (7) $i(w) % 20.77/3.91 | (8) leq(v800, w) = 0 % 20.77/3.91 | % 20.77/3.92 | GROUND_INST: instantiating (less_leq_trans) with v600, v800, w, simplifying % 20.77/3.92 | with (2), (4), (6), (7), (8) gives: % 20.77/3.92 | (9) less(v600, w) = 0 % 20.77/3.92 | % 20.77/3.92 | GROUND_INST: instantiating (1) with w, v0, v600, simplifying with (3), (4), % 20.77/3.92 | (5), (7) gives: % 20.77/3.92 | (10) leq(w, v600) = 0 & less(v0, w) = 0 % 20.77/3.92 | % 20.77/3.92 | ALPHA: (10) implies: % 20.77/3.92 | (11) leq(w, v600) = 0 % 20.77/3.92 | % 20.77/3.92 | GROUND_INST: instantiating (less_leq_trans) with v600, w, v600, simplifying % 20.77/3.92 | with (4), (7), (9), (11) gives: % 20.77/3.92 | (12) less(v600, v600) = 0 % 20.77/3.92 | % 20.77/3.92 | GROUND_INST: instantiating (irreflexive) with v600, simplifying with (4), (12) % 20.77/3.92 | gives: % 20.77/3.92 | (13) $false % 20.77/3.93 | % 20.77/3.93 | CLOSE: (13) is inconsistent. % 20.77/3.93 | % 20.77/3.93 End of proof % 20.77/3.93 % SZS output end Proof for theBenchmark % 20.77/3.93 % 20.77/3.93 3085ms %------------------------------------------------------------------------------