%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW677_1 : TPTP v8.1.2. Released v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.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 : Fri Sep 1 00:51:06 EDT 2023 % Result : Theorem 6.68s 1.83s % Output : Proof 10.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW677_1 : TPTP v8.1.2. Released v6.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.34 % Computer : n001.cluster.edu % 0.11/0.34 % Model : x86_64 x86_64 % 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.34 % Memory : 8042.1875MB % 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.34 % CPULimit : 300 % 0.11/0.34 % WCLimit : 300 % 0.11/0.34 % DateTime : Sun Aug 27 19:00:33 EDT 2023 % 0.11/0.34 % CPUTime : % 0.19/0.63 ________ _____ % 0.19/0.63 ___ __ \_________(_)________________________________ % 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.63 % 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.63 (2023-06-19) % 0.19/0.63 % 0.19/0.63 (c) Philipp Rümmer, 2009-2023 % 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.63 Amanda Stjerna. % 0.19/0.63 Free software under BSD-3-Clause. % 0.19/0.63 % 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.63 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.65 Running up to 7 provers in parallel. % 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.25 Prover 5: Preprocessing ... % 3.10/1.25 Prover 6: Preprocessing ... % 3.10/1.25 Prover 2: Preprocessing ... % 3.10/1.25 Prover 1: Preprocessing ... % 3.10/1.25 Prover 4: Preprocessing ... % 3.10/1.25 Prover 0: Preprocessing ... % 3.10/1.25 Prover 3: Preprocessing ... % 5.36/1.62 Prover 3: Warning: ignoring some quantifiers % 5.36/1.64 Prover 3: Constructing countermodel ... % 5.62/1.65 Prover 6: Proving ... % 5.62/1.66 Prover 1: Warning: ignoring some quantifiers % 5.62/1.66 Prover 4: Warning: ignoring some quantifiers % 5.62/1.69 Prover 0: Proving ... % 5.62/1.69 Prover 1: Constructing countermodel ... % 5.62/1.71 Prover 4: Constructing countermodel ... % 5.62/1.73 Prover 5: Proving ... % 6.30/1.75 Prover 2: Proving ... % 6.68/1.83 Prover 6: proved (1157ms) % 6.68/1.83 % 6.68/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.68/1.83 % 6.68/1.83 Prover 0: stopped % 6.68/1.83 Prover 3: stopped % 6.68/1.83 Prover 5: stopped % 6.68/1.83 Prover 2: stopped % 6.68/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.68/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.68/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.10/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.10/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.13/1.90 Prover 10: Preprocessing ... % 7.13/1.90 Prover 11: Preprocessing ... % 7.50/1.94 Prover 7: Preprocessing ... % 7.78/1.95 Prover 8: Preprocessing ... % 7.78/1.95 Prover 1: gave up % 7.78/1.96 Prover 13: Preprocessing ... % 7.78/1.96 Prover 4: gave up % 7.78/1.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.78/1.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.78/2.01 Prover 10: Warning: ignoring some quantifiers % 7.78/2.01 Prover 11: Warning: ignoring some quantifiers % 7.78/2.03 Prover 10: Constructing countermodel ... % 7.78/2.03 Prover 11: Constructing countermodel ... % 8.54/2.04 Prover 8: Warning: ignoring some quantifiers % 8.54/2.04 Prover 7: Warning: ignoring some quantifiers % 8.54/2.06 Prover 7: Constructing countermodel ... % 8.54/2.06 Prover 19: Preprocessing ... % 8.54/2.06 Prover 8: Constructing countermodel ... % 8.54/2.06 Prover 16: Preprocessing ... % 8.95/2.13 Prover 10: gave up % 8.95/2.14 Prover 11: gave up % 8.95/2.18 Prover 7: gave up % 8.95/2.20 Prover 13: Warning: ignoring some quantifiers % 8.95/2.21 Prover 16: Warning: ignoring some quantifiers % 8.95/2.22 Prover 13: Constructing countermodel ... % 8.95/2.22 Prover 16: Constructing countermodel ... % 8.95/2.23 Prover 19: Warning: ignoring some quantifiers % 8.95/2.24 Prover 19: Constructing countermodel ... % 8.95/2.29 Prover 8: gave up % 8.95/2.32 Prover 13: Found proof (size 19) % 8.95/2.32 Prover 13: proved (463ms) % 8.95/2.32 Prover 19: stopped % 8.95/2.32 Prover 16: stopped % 8.95/2.32 % 8.95/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.95/2.32 % 8.95/2.32 % SZS output start Proof for theBenchmark % 8.95/2.33 Assumptions after simplification: % 8.95/2.33 --------------------------------- % 8.95/2.33 % 8.95/2.33 (formula_004) % 8.95/2.35 ? [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v0 | ~ ($lesseq(-1, % 8.95/2.35 $difference($product(2, v0), v1))) | ~ ($lesseq(0, $difference(v1, % 8.95/2.35 $product(2, v0)))) | ~ (div2(v1) = v2)) & ! [v0: int] : ! [v1: int] % 8.95/2.35 : ( ~ ($lesseq(2, $difference(v0, $product(2, v1)))) | ~ (div2(v0) = v1)) & % 9.82/2.35 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2, v1), % 9.82/2.35 v0))) | ~ (div2(v0) = v1)) & ? [v0: int] : ? [v1: int] : ( ~ % 9.82/2.35 ($lesseq(2, $difference(v0, $product(2, v1)))) | ? [v2: int] : ( ~ (v2 = % 9.82/2.35 v1) & div2(v0) = v2)) & ? [v0: int] : ? [v1: int] : ( ~ ($lesseq(0, % 9.82/2.35 $difference(v0, $product(2, v1)))) | ~ ($lesseq(-1, % 9.82/2.36 $difference($product(2, v1), v0))) | div2(v0) = v1) & ? [v0: int] : ? % 9.82/2.36 [v1: int] : ( ~ ($lesseq(1, $difference($product(2, v1), v0))) | ? [v2: int] % 9.82/2.36 : ( ~ (v2 = v1) & div2(v0) = v2)) % 9.82/2.36 % 9.82/2.36 (formula_007) % 10.72/2.37 ? [v0: int] : ? [v1: int] : ? [v2: Array[Int,Int]] : ? [v3: int] : ? [v4: % 10.72/2.37 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: Array[Int,Int]] % 10.72/2.37 : ? [v9: int] : ? [v10: int] : ? [v11: int] : ($lesseq(1, $difference(v10, % 10.72/2.37 v7)) & $lesseq(v6, v7) & $lesseq(0, v6) & $lesseq(1, $difference(v4, % 10.72/2.37 v1)) & $lesseq(v0, v1) & $lesseq(0, v0) & length(v8) = v10 & length(v2) % 10.72/2.37 = v4 & div2($sum(v7, v6)) = v11 & div2($sum(v1, v0)) = v5 & % 10.72/2.37 Array[Int,Int](v8) & Array[Int,Int](v2) & sorted(v8, 0, $sum(v10, -1)) & % 10.72/2.37 sorted(v2, 0, $sum(v4, -1)) & ~ (select:(Array[Int,Int]*Int)>Int(v8, v11) = % 10.72/2.37 v9) & ! [v12: int] : ( ~ ($lesseq(1, $difference(v9, v12))) | ~ % 10.72/2.37 ($lesseq(-1, v11)) | ~ (select:(Array[Int,Int]*Int)>Int(v8, v11) = v12)) % 10.72/2.37 & ! [v12: int] : ( ~ ($lesseq(v9, v12)) | ~ ($lesseq(v11, v10)) | ~ % 10.72/2.37 (select:(Array[Int,Int]*Int)>Int(v8, v11) = v12)) & ! [v12: int] : ( ~ % 10.72/2.37 ($lesseq(v11, v10)) | ~ ($lesseq(-1, v11)) | ~ % 10.72/2.37 (select:(Array[Int,Int]*Int)>Int(v8, v11) = v12)) & ? [v12: int] : ( ~ % 10.72/2.37 (v12 = v3) & select:(Array[Int,Int]*Int)>Int(v2, v5) = v12 & (($lesseq(1, % 10.72/2.37 $difference(v3, v12)) & $lesseq(v5, -2)) | ($lesseq(1, % 10.72/2.37 $difference(v12, v3)) & $lesseq(1, $difference(v5, v4)))))) % 10.72/2.37 % 10.72/2.37 Further assumptions not needed in the proof: % 10.72/2.37 -------------------------------------------- % 10.72/2.37 formula, formula_001, formula_002, formula_003, formula_005, formula_006 % 10.72/2.37 % 10.72/2.37 Those formulas are unsatisfiable: % 10.72/2.37 --------------------------------- % 10.72/2.37 % 10.72/2.37 Begin of proof % 10.72/2.37 | % 10.72/2.37 | ALPHA: (formula_004) implies: % 10.72/2.37 | (1) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2, % 10.72/2.37 | v1), v0))) | ~ (div2(v0) = v1)) % 10.72/2.38 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference(v0, % 10.72/2.38 | $product(2, v1)))) | ~ (div2(v0) = v1)) % 10.72/2.38 | % 10.72/2.38 | DELTA: instantiating (formula_007) with fresh symbols all_25_0, all_25_1, % 10.72/2.38 | all_25_2, all_25_3, all_25_4, all_25_5, all_25_6, all_25_7, all_25_8, % 10.72/2.38 | all_25_9, all_25_10, all_25_11 gives: % 10.72/2.38 | (3) $lesseq(1, $difference(all_25_1, all_25_4)) & $lesseq(all_25_5, % 10.72/2.38 | all_25_4) & $lesseq(0, all_25_5) & $lesseq(1, $difference(all_25_7, % 10.72/2.38 | all_25_10)) & $lesseq(all_25_11, all_25_10) & $lesseq(0, all_25_11) % 10.72/2.38 | & length(all_25_3) = all_25_1 & length(all_25_9) = all_25_7 & % 10.72/2.38 | div2($sum(all_25_4, all_25_5)) = all_25_0 & div2($sum(all_25_10, % 10.72/2.38 | all_25_11)) = all_25_6 & Array[Int,Int](all_25_3) & % 10.72/2.38 | Array[Int,Int](all_25_9) & sorted(all_25_3, 0, $sum(all_25_1, -1)) & % 10.72/2.38 | sorted(all_25_9, 0, $sum(all_25_7, -1)) & ~ % 10.72/2.38 | (select:(Array[Int,Int]*Int)>Int(all_25_3, all_25_0) = all_25_2) & ! % 10.72/2.39 | [v0: int] : ( ~ ($lesseq(1, $difference(all_25_2, v0))) | ~ % 10.72/2.39 | ($lesseq(-1, all_25_0)) | ~ % 10.72/2.39 | (select:(Array[Int,Int]*Int)>Int(all_25_3, all_25_0) = v0)) & ! [v0: % 10.72/2.39 | int] : ( ~ ($lesseq(all_25_2, v0)) | ~ ($lesseq(all_25_0, all_25_1)) % 10.72/2.39 | | ~ (select:(Array[Int,Int]*Int)>Int(all_25_3, all_25_0) = v0)) & ! % 10.72/2.39 | [v0: int] : ( ~ ($lesseq(all_25_0, all_25_1)) | ~ ($lesseq(-1, % 10.72/2.39 | all_25_0)) | ~ (select:(Array[Int,Int]*Int)>Int(all_25_3, % 10.72/2.39 | all_25_0) = v0)) & ? [v0: int] : ( ~ (v0 = all_25_8) & % 10.72/2.39 | select:(Array[Int,Int]*Int)>Int(all_25_9, all_25_6) = v0 & % 10.72/2.39 | (($lesseq(1, $difference(all_25_8, v0)) & $lesseq(all_25_6, -2)) | % 10.72/2.39 | ($lesseq(1, $difference(v0, all_25_8)) & $lesseq(1, % 10.72/2.39 | $difference(all_25_6, all_25_7))))) % 10.72/2.39 | % 10.72/2.39 | ALPHA: (3) implies: % 10.72/2.39 | (4) $lesseq(0, all_25_11) % 10.72/2.39 | (5) $lesseq(all_25_11, all_25_10) % 10.72/2.39 | (6) $lesseq(1, $difference(all_25_7, all_25_10)) % 10.72/2.39 | (7) div2($sum(all_25_10, all_25_11)) = all_25_6 % 10.72/2.39 | (8) ? [v0: int] : ( ~ (v0 = all_25_8) & % 10.72/2.39 | select:(Array[Int,Int]*Int)>Int(all_25_9, all_25_6) = v0 & % 10.72/2.39 | (($lesseq(1, $difference(all_25_8, v0)) & $lesseq(all_25_6, -2)) | % 10.72/2.39 | ($lesseq(1, $difference(v0, all_25_8)) & $lesseq(1, % 10.72/2.39 | $difference(all_25_6, all_25_7))))) % 10.72/2.39 | % 10.72/2.39 | DELTA: instantiating (8) with fresh symbol all_29_0 gives: % 10.72/2.39 | (9) ~ (all_29_0 = all_25_8) & select:(Array[Int,Int]*Int)>Int(all_25_9, % 10.72/2.39 | all_25_6) = all_29_0 & (($lesseq(1, $difference(all_25_8, all_29_0)) % 10.72/2.39 | & $lesseq(all_25_6, -2)) | ($lesseq(1, $difference(all_29_0, % 10.72/2.39 | all_25_8)) & $lesseq(1, $difference(all_25_6, all_25_7)))) % 10.72/2.39 | % 10.72/2.39 | ALPHA: (9) implies: % 10.72/2.39 | (10) ($lesseq(1, $difference(all_25_8, all_29_0)) & $lesseq(all_25_6, -2)) % 10.72/2.39 | | ($lesseq(1, $difference(all_29_0, all_25_8)) & $lesseq(1, % 10.72/2.39 | $difference(all_25_6, all_25_7))) % 10.72/2.39 | % 10.72/2.39 | GROUND_INST: instantiating (2) with $sum(all_25_10, all_25_11), all_25_6, % 10.72/2.39 | simplifying with (7) gives: % 10.72/2.39 | (11) $lesseq(-1, $difference($difference($product(2, all_25_6), all_25_10), % 10.72/2.39 | all_25_11)) % 10.72/2.40 | % 10.72/2.40 | GROUND_INST: instantiating (1) with $sum(all_25_10, all_25_11), all_25_6, % 10.72/2.40 | simplifying with (7) gives: % 10.72/2.40 | (12) $lesseq(0, $sum($difference(all_25_10, $product(2, all_25_6)), % 10.72/2.40 | all_25_11)) % 10.72/2.40 | % 10.72/2.40 | BETA: splitting (10) gives: % 10.72/2.40 | % 10.72/2.40 | Case 1: % 10.72/2.40 | | % 10.72/2.40 | | (13) $lesseq(1, $difference(all_25_8, all_29_0)) & $lesseq(all_25_6, -2) % 10.72/2.40 | | % 10.72/2.40 | | ALPHA: (13) implies: % 10.72/2.40 | | (14) $lesseq(all_25_6, -2) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (11), (14) imply: % 10.72/2.40 | | (15) $lesseq(3, $difference($product(-1, all_25_10), all_25_11)) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (5), (15) imply: % 10.72/2.40 | | (16) $lesseq(all_25_11, -2) % 10.72/2.40 | | % 10.72/2.40 | | SIMP: (16) implies: % 10.72/2.40 | | (17) $lesseq(all_25_11, -2) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (4), (17) imply: % 10.72/2.40 | | (18) $false % 10.72/2.40 | | % 10.72/2.40 | | CLOSE: (18) is inconsistent. % 10.72/2.40 | | % 10.72/2.40 | Case 2: % 10.72/2.40 | | % 10.72/2.40 | | (19) $lesseq(1, $difference(all_29_0, all_25_8)) & $lesseq(1, % 10.72/2.40 | | $difference(all_25_6, all_25_7)) % 10.72/2.40 | | % 10.72/2.40 | | ALPHA: (19) implies: % 10.72/2.40 | | (20) $lesseq(1, $difference(all_25_6, all_25_7)) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (12), (20) imply: % 10.72/2.40 | | (21) $lesseq(2, $sum($difference(all_25_10, $product(2, all_25_7)), % 10.72/2.40 | | all_25_11)) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (6), (21) imply: % 10.72/2.40 | | (22) $lesseq(4, $difference(all_25_11, all_25_10)) % 10.72/2.40 | | % 10.72/2.40 | | COMBINE_INEQS: (5), (22) imply: % 10.72/2.40 | | (23) $false % 10.72/2.40 | | % 10.72/2.40 | | CLOSE: (23) is inconsistent. % 10.72/2.40 | | % 10.72/2.40 | End of split % 10.72/2.40 | % 10.72/2.40 End of proof % 10.72/2.40 % SZS output end Proof for theBenchmark % 10.72/2.40 % 10.72/2.40 1770ms %------------------------------------------------------------------------------