%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI697_1 : TPTP v8.1.2. Released v6.3.0. % 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:48:51 EDT 2023 % Result : Theorem 2.93s 1.14s % Output : Proof 3.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : ARI697_1 : TPTP v8.1.2. Released v6.3.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 18:46:18 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.01 Prover 3: Preprocessing ... % 2.15/1.01 Prover 1: Preprocessing ... % 2.15/1.01 Prover 6: Preprocessing ... % 2.15/1.01 Prover 5: Preprocessing ... % 2.15/1.01 Prover 2: Preprocessing ... % 2.15/1.02 Prover 0: Preprocessing ... % 2.15/1.02 Prover 4: Preprocessing ... % 2.71/1.08 Prover 0: Constructing countermodel ... % 2.71/1.08 Prover 5: Constructing countermodel ... % 2.71/1.08 Prover 4: Constructing countermodel ... % 2.71/1.08 Prover 1: Constructing countermodel ... % 2.71/1.08 Prover 6: Constructing countermodel ... % 2.71/1.08 Prover 2: Constructing countermodel ... % 2.71/1.08 Prover 3: Constructing countermodel ... % 2.93/1.14 Prover 2: proved (499ms) % 2.93/1.14 Prover 0: proved (500ms) % 2.93/1.14 % 2.93/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 2.93/1.14 % 2.93/1.14 % 2.93/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 2.93/1.14 % 3.16/1.14 Prover 3: stopped % 3.16/1.14 Prover 5: stopped % 3.16/1.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.16/1.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.16/1.15 Prover 6: stopped % 3.16/1.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.16/1.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.16/1.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.16/1.16 Prover 8: Preprocessing ... % 3.16/1.17 Prover 11: Preprocessing ... % 3.16/1.17 Prover 10: Preprocessing ... % 3.16/1.17 Prover 13: Preprocessing ... % 3.16/1.18 Prover 7: Preprocessing ... % 3.16/1.18 Prover 11: Constructing countermodel ... % 3.16/1.19 Prover 13: Constructing countermodel ... % 3.16/1.19 Prover 10: Constructing countermodel ... % 3.16/1.19 Prover 7: Constructing countermodel ... % 3.16/1.20 Prover 8: Constructing countermodel ... % 3.16/1.22 Prover 13: Found proof (size 39) % 3.16/1.22 Prover 4: Found proof (size 39) % 3.16/1.22 Prover 7: Found proof (size 39) % 3.16/1.22 Prover 13: proved (73ms) % 3.16/1.22 Prover 4: proved (585ms) % 3.16/1.22 Prover 7: proved (85ms) % 3.16/1.22 Prover 10: Found proof (size 39) % 3.16/1.22 Prover 10: proved (79ms) % 3.16/1.22 Prover 1: Found proof (size 40) % 3.16/1.22 Prover 1: proved (589ms) % 3.16/1.22 Prover 11: Found proof (size 39) % 3.16/1.22 Prover 11: proved (74ms) % 3.16/1.22 Prover 8: stopped % 3.16/1.23 % 3.16/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.16/1.23 % 3.16/1.23 % SZS output start Proof for theBenchmark % 3.16/1.24 Assumptions after simplification: % 3.16/1.24 --------------------------------- % 3.16/1.24 % 3.16/1.24 (conj) % 3.16/1.24 ? [v0: int] : ? [v1: int] : ($sum($product(2, v1), v0) = x5 & ~ (v0 = 0) & % 3.16/1.24 $lesseq(v0, 1) & $lesseq(-1, v0) & ( ~ (v0 = 1) | ~ ($lesseq(x5, 0)) & ( ~ % 3.16/1.24 (v0 = -1) | ~ ($lesseq(0, x5)))) % 3.16/1.24 % 3.16/1.25 (eq1) % 3.16/1.25 $difference($sum($difference(x5, x4), x3), $product(2, x2)) = $product(5, x1) % 3.16/1.25 % 3.16/1.25 (eq2) % 3.16/1.25 $sum($sum($difference($difference($product(101, x5), $product(3, x4)), % 3.16/1.25 $product(5, x3)), $product(62, x2)), $product(9, x1)) = 0 % 3.16/1.25 % 3.16/1.25 (eq3) % 3.16/1.25 $sum($sum($difference($product(98, x5), $product(67, x4)), $product(11, x3)), % 3.16/1.25 $product(34, x2)) = $product(56, x1) % 3.16/1.25 % 3.16/1.25 Those formulas are unsatisfiable: % 3.16/1.25 --------------------------------- % 3.16/1.25 % 3.16/1.25 Begin of proof % 3.16/1.25 | % 3.16/1.25 | COMBINE_EQS: (eq1), (eq3) imply: % 3.16/1.25 | (1) $sum($sum($difference($product(31, x4), $product(87, x3)), % 3.16/1.25 | $product(230, x2)), $product(434, x1)) = 0 % 3.16/1.25 | % 3.16/1.25 | COMBINE_EQS: (eq1), (eq2) imply: % 3.16/1.25 | (2) $sum($sum($difference($product(49, x4), $product(53, x3)), % 3.16/1.25 | $product(132, x2)), $product(257, x1)) = 0 % 3.16/1.25 | % 3.16/1.25 | SIMP: (2) implies: % 3.16/1.25 | (3) $sum($sum($difference($product(49, x4), $product(53, x3)), % 3.16/1.25 | $product(132, x2)), $product(257, x1)) = 0 % 3.16/1.25 | % 3.16/1.25 | COMBINE_EQS: (1), (3) imply: % 3.16/1.25 | (4) $sum($sum($difference(x4, $product(1017, x3)), $product(2786, x2)), % 3.16/1.25 | $product(5162, x1)) = 0 % 3.16/1.25 | % 3.16/1.25 | COMBINE_EQS: (3), (4) imply: % 3.16/1.26 | (5) $difference($product(2620, x3), $product(7178, x2)) = $product(13299, % 3.16/1.26 | x1) % 3.16/1.26 | % 3.16/1.26 | SIMP: (5) implies: % 3.16/1.26 | (6) $difference($product(2620, x3), $product(7178, x2)) = $product(13299, % 3.16/1.26 | x1) % 3.16/1.26 | % 3.16/1.26 | COMBINE_EQS: (4), (eq1) imply: % 3.16/1.26 | (7) $sum($sum($difference(x5, $product(1016, x3)), $product(2784, x2)), % 3.16/1.26 | $product(5157, x1)) = 0 % 3.16/1.26 | % 3.16/1.26 | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1 gives: % 3.16/1.26 | (8) $sum($product(2, all_3_0), all_3_1) = x5 & ~ (all_3_1 = 0) & % 3.16/1.26 | $lesseq(all_3_1, 1) & $lesseq(-1, all_3_1) & ( ~ (all_3_1 = 1) | ~ % 3.16/1.26 | ($lesseq(x5, 0)) & ( ~ (all_3_1 = -1) | ~ ($lesseq(0, x5))) % 3.16/1.26 | % 3.16/1.26 | ALPHA: (8) implies: % 3.16/1.26 | (9) $sum($product(2, all_3_0), all_3_1) = x5 % 3.16/1.26 | (10) ~ (all_3_1 = 0) % 3.16/1.26 | (11) $lesseq(-1, all_3_1) % 3.16/1.26 | (12) $lesseq(all_3_1, 1) % 3.16/1.26 | % 3.16/1.26 | COMBINE_EQS: (7), (9) imply: % 3.16/1.26 | (13) $sum($sum($difference($sum($product(2, all_3_0), all_3_1), % 3.16/1.26 | $product(1016, x3)), $product(2784, x2)), $product(5157, x1)) = % 3.16/1.26 | 0 % 3.16/1.26 | % 3.16/1.26 | COL_REDUCE: introducing fresh symbol sc_5_0_0 defined by: % 3.16/1.26 | (14) $sum($sum($difference(all_3_0, $product(508, x3)), $product(1392, % 3.16/1.26 | x2)), $product(2578, x1)) = sc_5_0_0 % 3.16/1.26 | % 3.16/1.26 | COMBINE_EQS: (13), (14) imply: % 3.16/1.26 | (15) $sum($sum(all_3_1, x1), $product(2, sc_5_0_0)) = 0 % 3.16/1.26 | % 3.16/1.26 | COL_REDUCE: introducing fresh symbol sc_5_0_1 defined by: % 3.16/1.26 | (16) $difference($difference(x3, $product(3, x2)), $product(5, x1)) = % 3.16/1.26 | sc_5_0_1 % 3.16/1.26 | % 3.16/1.27 | COMBINE_EQS: (6), (16) imply: % 3.16/1.27 | (17) $sum($difference($product(682, x2), $product(199, x1)), $product(2620, % 3.16/1.27 | sc_5_0_1)) = 0 % 3.16/1.27 | % 3.16/1.27 | COL_REDUCE: introducing fresh symbol sc_5_0_2 defined by: % 3.16/1.27 | (18) $sum(x2, $product(4, sc_5_0_1)) = sc_5_0_2 % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (17), (18) imply: % 3.16/1.27 | (19) $sum($product(199, x1), $product(108, sc_5_0_1)) = $product(682, % 3.16/1.27 | sc_5_0_2) % 3.16/1.27 | % 3.16/1.27 | SIMP: (19) implies: % 3.16/1.27 | (20) $sum($product(199, x1), $product(108, sc_5_0_1)) = $product(682, % 3.16/1.27 | sc_5_0_2) % 3.16/1.27 | % 3.16/1.27 | COL_REDUCE: introducing fresh symbol sc_5_0_3 defined by: % 3.16/1.27 | (21) $difference($sum(x1, sc_5_0_1), $product(3, sc_5_0_2)) = sc_5_0_3 % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (20), (21) imply: % 3.16/1.27 | (22) $sum($product(91, sc_5_0_1), $product(85, sc_5_0_2)) = $product(199, % 3.16/1.27 | sc_5_0_3) % 3.16/1.27 | % 3.16/1.27 | SIMP: (22) implies: % 3.16/1.27 | (23) $sum($product(91, sc_5_0_1), $product(85, sc_5_0_2)) = $product(199, % 3.16/1.27 | sc_5_0_3) % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (15), (21) imply: % 3.16/1.27 | (24) $sum($sum($sum($difference(all_3_1, sc_5_0_1), $product(3, sc_5_0_2)), % 3.16/1.27 | sc_5_0_3), $product(2, sc_5_0_0)) = 0 % 3.16/1.27 | % 3.16/1.27 | COL_REDUCE: introducing fresh symbol sc_5_0_4 defined by: % 3.16/1.27 | (25) $difference($sum(sc_5_0_1, sc_5_0_2), $product(2, sc_5_0_3)) = % 3.16/1.27 | sc_5_0_4 % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (23), (25) imply: % 3.16/1.27 | (26) $sum($product(6, sc_5_0_2), $product(17, sc_5_0_3)) = $product(91, % 3.16/1.27 | sc_5_0_4) % 3.16/1.27 | % 3.16/1.27 | SIMP: (26) implies: % 3.16/1.27 | (27) $sum($product(6, sc_5_0_2), $product(17, sc_5_0_3)) = $product(91, % 3.16/1.27 | sc_5_0_4) % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (24), (25), (27) imply: % 3.16/1.27 | (28) $sum($sum($difference($difference(all_3_1, $product(2, sc_5_0_2)), % 3.16/1.27 | $product(18, sc_5_0_3)), $product(90, sc_5_0_4)), $product(2, % 3.16/1.27 | sc_5_0_0)) = 0 % 3.16/1.27 | % 3.16/1.27 | COL_REDUCE: introducing fresh symbol sc_5_0_5 defined by: % 3.16/1.27 | (29) $difference($sum(sc_5_0_2, $product(3, sc_5_0_3)), $product(15, % 3.16/1.27 | sc_5_0_4)) = sc_5_0_5 % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (27), (29) imply: % 3.16/1.27 | (30) $sum(sc_5_0_3, sc_5_0_4) = $product(6, sc_5_0_5) % 3.16/1.27 | % 3.16/1.27 | SIMP: (30) implies: % 3.16/1.27 | (31) $sum(sc_5_0_3, sc_5_0_4) = $product(6, sc_5_0_5) % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (29), (31) imply: % 3.16/1.27 | (32) $sum($difference(sc_5_0_2, $product(18, sc_5_0_4)), $product(17, % 3.16/1.27 | sc_5_0_5)) = 0 % 3.16/1.27 | % 3.16/1.27 | COMBINE_EQS: (28), (31), (32) imply: % 3.16/1.27 | (33) $sum($difference($sum(all_3_1, $product(72, sc_5_0_4)), $product(74, % 3.16/1.27 | sc_5_0_5)), $product(2, sc_5_0_0)) = 0 % 3.16/1.27 | % 3.16/1.27 | REDUCE: (12), (33) imply: % 3.16/1.27 | (34) $lesseq(0, $sum($difference($product(36, sc_5_0_4), $product(37, % 3.16/1.27 | sc_5_0_5)), sc_5_0_0)) % 3.16/1.27 | % 3.16/1.27 | SIMP: (34) implies: % 3.16/1.27 | (35) $lesseq(0, $sum($difference($product(36, sc_5_0_4), $product(37, % 3.16/1.27 | sc_5_0_5)), sc_5_0_0)) % 3.16/1.27 | % 3.16/1.28 | REDUCE: (11), (33) imply: % 3.16/1.28 | (36) $lesseq(sc_5_0_0, $difference($product(37, sc_5_0_5), $product(36, % 3.16/1.28 | sc_5_0_4))) % 3.16/1.28 | % 3.16/1.28 | SIMP: (36) implies: % 3.16/1.28 | (37) $lesseq(sc_5_0_0, $difference($product(37, sc_5_0_5), $product(36, % 3.16/1.28 | sc_5_0_4))) % 3.16/1.28 | % 3.16/1.28 | REDUCE: (10), (33) imply: % 3.16/1.28 | (38) ~ ($sum($difference($product(36, sc_5_0_4), $product(37, sc_5_0_5)), % 3.16/1.28 | sc_5_0_0) = 0) % 3.16/1.28 | % 3.16/1.28 | SIMP: (38) implies: % 3.16/1.28 | (39) ~ ($sum($difference($product(36, sc_5_0_4), $product(37, sc_5_0_5)), % 3.16/1.28 | sc_5_0_0) = 0) % 3.16/1.28 | % 3.16/1.28 | STRENGTHEN: (35), (39) imply: % 3.16/1.28 | (40) $lesseq(1, $sum($difference($product(36, sc_5_0_4), $product(37, % 3.16/1.28 | sc_5_0_5)), sc_5_0_0)) % 3.16/1.28 | % 3.16/1.28 | COMBINE_INEQS: (37), (40) imply: % 3.16/1.28 | (41) $false % 3.16/1.28 | % 3.16/1.28 | CLOSE: (41) is inconsistent. % 3.16/1.28 | % 3.16/1.28 End of proof % 3.16/1.28 % SZS output end Proof for theBenchmark % 3.16/1.28 % 3.16/1.28 662ms %------------------------------------------------------------------------------