%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT071+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 : n018.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 06:17:29 AM UTC 2026 % Result : Theorem 14.03s 2.73s % Output : Proof 18.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT071+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.35 % Computer : n018.cluster.edu % 0.10/0.35 % Model : x86_64 x86_64 % 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.35 % Memory : 8046.5625MB % 0.10/0.35 % OS : Linux 6.8.0-71-generic % 0.10/0.35 % CPULimit : 300 % 0.10/0.35 % WCLimit : 300 % 0.10/0.35 % DateTime : Mon Sep 7 13:56:37 UTC 2026 % 0.10/0.36 % CPUTime : % 0.14/0.37 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. % 0.71/0.72 ________ _____ % 0.71/0.72 ___ __ \_________(_)________________________________ % 0.71/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.72 % 0.71/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.72 (2023-06-19) % 0.71/0.72 % 0.71/0.72 (c) Philipp Rümmer, 2009-2023 % 0.71/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.72 Amanda Stjerna. % 0.71/0.72 Free software under BSD-3-Clause. % 0.71/0.72 % 0.71/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.72 % 0.71/0.72 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.74 Running up to 7 provers in parallel. % 0.71/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.56/1.54 Prover 4: Preprocessing ... % 4.56/1.57 Prover 1: Preprocessing ... % 5.32/1.61 Prover 5: Preprocessing ... % 5.32/1.61 Prover 0: Preprocessing ... % 5.32/1.61 Prover 3: Preprocessing ... % 5.32/1.61 Prover 2: Preprocessing ... % 5.32/1.62 Prover 6: Preprocessing ... % 11.66/2.45 Prover 5: Proving ... % 11.66/2.46 Prover 2: Proving ... % 12.47/2.54 Prover 3: Constructing countermodel ... % 12.47/2.55 Prover 1: Constructing countermodel ... % 12.47/2.58 Prover 6: Proving ... % 13.23/2.64 Prover 4: Constructing countermodel ... % 14.03/2.72 Prover 3: proved (1970ms) % 14.03/2.72 % 14.03/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.03/2.73 % 14.03/2.73 Prover 2: stopped % 14.03/2.73 Prover 5: stopped % 14.03/2.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.03/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.03/2.73 Prover 0: Proving ... % 14.03/2.73 Prover 0: stopped % 14.03/2.74 Prover 6: stopped % 14.03/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.03/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.03/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.03/2.77 Prover 1: Found proof (size 13) % 14.03/2.77 Prover 1: proved (2022ms) % 14.03/2.77 Prover 4: stopped % 14.84/2.86 Prover 13: Preprocessing ... % 14.84/2.87 Prover 7: Preprocessing ... % 14.84/2.88 Prover 11: Preprocessing ... % 14.84/2.89 Prover 10: Preprocessing ... % 14.84/2.89 Prover 8: Preprocessing ... % 15.62/2.95 Prover 7: stopped % 15.62/2.95 Prover 10: stopped % 15.62/2.98 Prover 13: stopped % 16.56/3.05 Prover 11: stopped % 17.40/3.25 Prover 8: Warning: ignoring some quantifiers % 17.40/3.28 Prover 8: Constructing countermodel ... % 17.90/3.31 Prover 8: stopped % 17.90/3.31 % 17.90/3.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.90/3.31 % 17.90/3.32 % SZS output start Proof for theBenchmark % 17.90/3.33 Assumptions after simplification: % 17.90/3.33 --------------------------------- % 17.90/3.33 % 17.90/3.33 (axis_conflict_def) % 17.90/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.90/3.39 | ~ (axis_conflict(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.90/3.39 $i(v1) | ~ $i(v0) | ? [v5: $i] : (in_closed(v5, v2, v3) = 0 & % 17.90/3.39 in_closed(v5, v0, v1) = 0 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.90/3.39 $i] : ! [v3: $i] : ( ~ (axis_conflict(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ % 17.90/3.39 $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ( ~ (in_closed(v4, v0, v1) = % 17.90/3.39 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & in_closed(v4, v2, v3) = % 17.90/3.39 v5))) % 17.90/3.39 % 17.90/3.39 (conflict_hyp) % 17.90/3.40 axis_conflict(n0, n5, n10, n15) = 0 & $i(n15) & $i(n10) & $i(n5) & $i(n0) % 17.90/3.40 % 17.90/3.40 (no_false_conflict) % 18.36/3.40 $i(n15) & $i(n10) & $i(n5) & $i(n0) & ? [v0: $i] : (in_closed(v0, n10, n15) = % 18.36/3.40 0 & in_closed(v0, n0, n5) = 0 & $i(v0)) % 18.36/3.40 % 18.36/3.40 (function-axioms) % 18.36/3.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 18.36/3.43 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 18.36/3.43 : ! [v9: $i] : ! [v10: $i] : (v1 = v0 | ~ (in_box3(v10, v9, v8, v7, v6, v5, % 18.36/3.43 v4, v3, v2) = v1) | ~ (in_box3(v10, v9, v8, v7, v6, v5, v4, v3, v2) = % 18.36/3.43 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.36/3.43 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 18.36/3.43 ! [v8: $i] : ! [v9: $i] : (v1 = v0 | ~ (box2_conflict(v9, v8, v7, v6, v5, % 18.36/3.43 v4, v3, v2) = v1) | ~ (box2_conflict(v9, v8, v7, v6, v5, v4, v3, v2) = % 18.36/3.43 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.36/3.43 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 18.36/3.43 ! [v8: $i] : ! [v9: $i] : (v1 = v0 | ~ (box2_compatible(v9, v8, v7, v6, v5, % 18.36/3.43 v4, v3, v2) = v1) | ~ (box2_compatible(v9, v8, v7, v6, v5, v4, v3, v2) % 18.36/3.43 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.36/3.43 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 18.36/3.43 (v1 = v0 | ~ (in_box2(v7, v6, v5, v4, v3, v2) = v1) | ~ (in_box2(v7, v6, v5, % 18.36/3.43 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.36/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 18.36/3.43 (v1 = v0 | ~ (axis_subsumes(v5, v4, v3, v2) = v1) | ~ (axis_subsumes(v5, v4, % 18.36/3.43 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 18.36/3.43 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 18.36/3.43 (axis_compatible(v5, v4, v3, v2) = v1) | ~ (axis_compatible(v5, v4, v3, v2) % 18.36/3.43 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.36/3.43 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 18.36/3.43 (axis_conflict(v5, v4, v3, v2) = v1) | ~ (axis_conflict(v5, v4, v3, v2) = % 18.36/3.43 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.36/3.43 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | % 18.36/3.43 ~ (in_open(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.36/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 18.36/3.43 (in_ropen(v4, v3, v2) = v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: % 18.36/3.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.36/3.43 : ! [v4: $i] : (v1 = v0 | ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, % 18.36/3.43 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 18.36/3.43 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, % 18.36/3.43 v2) = v1) | ~ (in_closed(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 18.36/3.43 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (box_verdict(v3, v2) = v1) | ~ % 18.36/3.43 (box_verdict(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.36/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) % 18.36/3.43 = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.36/3.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) % 18.36/3.43 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.36/3.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ % 18.36/3.43 (is_verdict(v2) = v0)) % 18.36/3.43 % 18.36/3.43 Further assumptions not needed in the proof: % 18.36/3.43 -------------------------------------------- % 18.36/3.43 axis_compatible_def, axis_subsumes_def, box2_conflict, box2_overlap, % 18.36/3.43 box_compatible, box_conflict, box_unknown, box_verdict_total, % 18.36/3.43 compatible_is_verdict, conflict_is_verdict, in_box2, in_box3, in_closed, % 18.36/3.43 in_lopen, in_open, in_ropen, irreflexive, leq_antisym, leq_def, leq_less_trans, % 18.36/3.43 leq_trans, less_implies_leq, less_leq_trans, order_0_5, order_10_15, order_5_10, % 18.36/3.43 shape_closed, shape_lopen, shape_open, shape_point, shape_ropen, transitive, % 18.36/3.43 trichotomy, unknown_is_verdict, verdict_enum, verdicts_distinct_cf_cp, % 18.36/3.43 verdicts_distinct_cf_un, verdicts_distinct_cp_un % 18.36/3.43 % 18.36/3.43 Those formulas are unsatisfiable: % 18.36/3.43 --------------------------------- % 18.36/3.43 % 18.36/3.43 Begin of proof % 18.36/3.43 | % 18.36/3.43 | ALPHA: (axis_conflict_def) implies: % 18.36/3.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.36/3.44 | (axis_conflict(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 18.36/3.44 | $i(v1) | ~ $i(v0) | ! [v4: $i] : ( ~ (in_closed(v4, v0, v1) = 0) | % 18.36/3.44 | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & in_closed(v4, v2, v3) = % 18.36/3.44 | v5))) % 18.36/3.44 | % 18.36/3.44 | ALPHA: (conflict_hyp) implies: % 18.36/3.44 | (2) axis_conflict(n0, n5, n10, n15) = 0 % 18.36/3.44 | % 18.36/3.44 | ALPHA: (no_false_conflict) implies: % 18.36/3.44 | (3) $i(n0) % 18.36/3.44 | (4) $i(n5) % 18.36/3.44 | (5) $i(n10) % 18.36/3.44 | (6) $i(n15) % 18.36/3.44 | (7) ? [v0: $i] : (in_closed(v0, n10, n15) = 0 & in_closed(v0, n0, n5) = 0 % 18.36/3.44 | & $i(v0)) % 18.36/3.44 | % 18.36/3.44 | ALPHA: (function-axioms) implies: % 18.36/3.45 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.36/3.45 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) % 18.36/3.45 | | ~ (in_closed(v4, v3, v2) = v0)) % 18.36/3.45 | % 18.36/3.45 | DELTA: instantiating (7) with fresh symbol all_34_0 gives: % 18.36/3.45 | (9) in_closed(all_34_0, n10, n15) = 0 & in_closed(all_34_0, n0, n5) = 0 & % 18.36/3.45 | $i(all_34_0) % 18.36/3.45 | % 18.36/3.45 | ALPHA: (9) implies: % 18.36/3.45 | (10) $i(all_34_0) % 18.36/3.45 | (11) in_closed(all_34_0, n0, n5) = 0 % 18.36/3.45 | (12) in_closed(all_34_0, n10, n15) = 0 % 18.36/3.45 | % 18.36/3.45 | GROUND_INST: instantiating (1) with n0, n5, n10, n15, simplifying with (2), % 18.36/3.45 | (3), (4), (5), (6) gives: % 18.36/3.46 | (13) ! [v0: $i] : ( ~ (in_closed(v0, n0, n5) = 0) | ~ $i(v0) | ? [v1: % 18.36/3.46 | int] : ( ~ (v1 = 0) & in_closed(v0, n10, n15) = v1)) % 18.36/3.46 | % 18.36/3.46 | GROUND_INST: instantiating (13) with all_34_0, simplifying with (10), (11) % 18.36/3.46 | gives: % 18.36/3.46 | (14) ? [v0: int] : ( ~ (v0 = 0) & in_closed(all_34_0, n10, n15) = v0) % 18.36/3.46 | % 18.36/3.46 | DELTA: instantiating (14) with fresh symbol all_42_0 gives: % 18.36/3.46 | (15) ~ (all_42_0 = 0) & in_closed(all_34_0, n10, n15) = all_42_0 % 18.36/3.46 | % 18.36/3.46 | ALPHA: (15) implies: % 18.36/3.46 | (16) ~ (all_42_0 = 0) % 18.36/3.46 | (17) in_closed(all_34_0, n10, n15) = all_42_0 % 18.36/3.46 | % 18.36/3.46 | GROUND_INST: instantiating (8) with 0, all_42_0, n15, n10, all_34_0, % 18.36/3.46 | simplifying with (12), (17) gives: % 18.36/3.46 | (18) all_42_0 = 0 % 18.36/3.46 | % 18.36/3.46 | REDUCE: (16), (18) imply: % 18.36/3.46 | (19) $false % 18.36/3.46 | % 18.36/3.46 | CLOSE: (19) is inconsistent. % 18.36/3.46 | % 18.36/3.46 End of proof % 18.36/3.46 % SZS output end Proof for theBenchmark % 18.36/3.46 % 18.36/3.46 2743ms %------------------------------------------------------------------------------