0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : princess-casc +printProof -timeout=%d %s 0.03/0.24 % Computer : n136.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 04:34:25 CDT 2018 0.03/0.24 % CPUTime : 0.07/0.44 ________ _____ 0.07/0.44 ___ __ \_________(_)________________________________ 0.07/0.44 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.07/0.44 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.07/0.44 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.07/0.44 0.07/0.44 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.07/0.44 (CASC 2017-07-17) 0.07/0.44 0.07/0.44 (c) Philipp Rümmer, 2009-2017 0.07/0.44 (contributions by Peter Backeman, Peter Baumgartner, 0.07/0.44 Angelo Brillout, Aleksandar Zeljic) 0.07/0.44 Free software under GNU Lesser General Public License (LGPL). 0.07/0.44 Bug reports to ph_r@gmx.net 0.07/0.44 0.07/0.44 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.07/0.44 0.07/0.45 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... 0.07/0.47 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 1.07/0.79 Prover 0: Warning: using theory to encode multiplication: GroebnerMultiplication 1.07/0.80 Prover 0: Preprocessing ... 1.17/0.88 Prover 0: Constructing countermodel ... 2.00/1.18 Prover 0: proved (708ms) 2.00/1.18 2.00/1.18 VALID 2.00/1.18 % SZS status Theorem for theBenchmark 2.00/1.18 2.00/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 2.16/1.21 Prover 1: Warning: using theory to encode multiplication: GroebnerMultiplication 2.16/1.21 Prover 1: Preprocessing ... 2.16/1.24 Prover 1: Constructing countermodel ... 2.64/1.39 Prover 1: Found proof (size 14) 2.75/1.39 Prover 1: proved (201ms) 2.75/1.39 2.75/1.39 2.75/1.39 % SZS output start Proof for theBenchmark 2.75/1.40 Assumptions after simplification: 2.75/1.40 --------------------------------- 2.75/1.40 2.75/1.40 (conj) 2.75/1.40 ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? [v4: $int] 2.75/1.40 : ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 2.75/1.40 $int] : ? [v10: $int] : ? [v11: $int] : ( ~ 2.75/1.40 ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(v11, 2.75/1.40 v10), v9), $product(2, v8)), v7), v6), v5), 2.75/1.40 v4), v3), $product(2, v2)), v1), $product(2, v0)), 2.75/1.40 $product(2, d)), $product(2, c)), b) = 0) & $product(v8, a) = v11 & 2.75/1.40 $product(v5, a) = v9 & $product(v3, a) = v7 & $product(v0, a) = v1 & 2.75/1.40 $product(d, c) = v10 & $product(d, b) = v0 & $product(d, a) = v8 & 2.75/1.40 $product(c, c) = v6 & $product(c, b) = v5 & $product(c, a) = v3 & 2.75/1.40 $product(b, a) = v4 & $product(a, a) = v2) 2.75/1.40 2.75/1.40 (eq) 2.75/1.41 ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($product(v1, $sum(a, 2)) = v2 2.75/1.41 & $sum($product($sum($sum($sum(d, c), b), a), $sum(c, 2)), $product(-1, 2.75/1.41 $sum($sum(v2, v0), b))) = 0 & $product($sum(b, a), $sum($sum(d, c), 1)) 2.75/1.41 = v1 & $product(a, a) = v0) 2.75/1.41 2.75/1.41 Those formulas are unsatisfiable: 2.75/1.41 --------------------------------- 2.75/1.41 2.75/1.41 Begin of proof 2.75/1.41 | 2.75/1.41 | DELTA: instantiating (conj) with fresh symbols all_0_0, all_0_1, all_0_2, 2.75/1.41 | all_0_3, all_0_4, all_0_5, all_0_6, all_0_7, all_0_8, all_0_9, 2.75/1.41 | all_0_10, all_0_11 gives: 2.75/1.42 | (1) ~ 2.75/1.42 | ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_0_0, 2.75/1.42 | all_0_1), all_0_2), $product(2, 2.75/1.42 | all_0_3)), all_0_4), all_0_5), all_0_6), 2.75/1.42 | all_0_7), all_0_8), $product(2, all_0_9)), all_0_10), 2.75/1.42 | $product(2, all_0_11)), $product(2, d)), $product(2, c)), b) 2.75/1.42 | = 0) & $product(all_0_3, a) = all_0_0 & $product(all_0_6, a) = 2.75/1.42 | all_0_2 & $product(all_0_8, a) = all_0_4 & $product(all_0_11, a) = 2.75/1.42 | all_0_10 & $product(d, c) = all_0_1 & $product(d, b) = all_0_11 & 2.75/1.42 | $product(d, a) = all_0_3 & $product(c, c) = all_0_5 & $product(c, b) = 2.75/1.42 | all_0_6 & $product(c, a) = all_0_8 & $product(b, a) = all_0_7 & 2.75/1.42 | $product(a, a) = all_0_9 2.75/1.42 | 2.75/1.42 | ALPHA: (1) implies: 2.75/1.42 | (2) ~ 2.75/1.42 | ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_0_0, 2.75/1.42 | all_0_1), all_0_2), $product(2, 2.75/1.42 | all_0_3)), all_0_4), all_0_5), all_0_6), 2.75/1.42 | all_0_7), all_0_8), $product(2, all_0_9)), all_0_10), 2.75/1.42 | $product(2, all_0_11)), $product(2, d)), $product(2, c)), b) 2.75/1.42 | = 0) 2.75/1.42 | (3) $product(a, a) = all_0_9 2.75/1.42 | (4) $product(b, a) = all_0_7 2.75/1.42 | (5) $product(c, a) = all_0_8 2.75/1.42 | (6) $product(c, b) = all_0_6 2.75/1.42 | (7) $product(c, c) = all_0_5 2.75/1.42 | (8) $product(d, a) = all_0_3 2.75/1.42 | (9) $product(d, b) = all_0_11 2.75/1.42 | (10) $product(d, c) = all_0_1 2.75/1.42 | (11) $product(all_0_11, a) = all_0_10 2.75/1.42 | (12) $product(all_0_8, a) = all_0_4 2.75/1.42 | (13) $product(all_0_6, a) = all_0_2 2.75/1.42 | (14) $product(all_0_3, a) = all_0_0 2.75/1.42 | 2.75/1.42 | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1, all_2_2 gives: 2.75/1.42 | (15) $product(all_2_1, $sum(a, 2)) = all_2_0 & 2.75/1.42 | $sum($product($sum($sum($sum(d, c), b), a), $sum(c, 2)), $product(-1, 2.75/1.42 | $sum($sum(all_2_0, all_2_2), b))) = 0 & $product($sum(b, a), 2.75/1.42 | $sum($sum(d, c), 1)) = all_2_1 & $product(a, a) = all_2_2 2.75/1.42 | 2.75/1.42 | ALPHA: (15) implies: 2.75/1.42 | (16) $product(a, a) = all_2_2 2.87/1.43 | (17) $product($sum(b, a), $sum($sum(d, c), 1)) = all_2_1 2.87/1.43 | (18) $sum($product($sum($sum($sum(d, c), b), a), $sum(c, 2)), $product(-1, 2.87/1.43 | $sum($sum(all_2_0, all_2_2), b))) = 0 2.87/1.43 | (19) $product(all_2_1, $sum(a, 2)) = all_2_0 2.87/1.43 | 2.87/1.43 | THEORY_AXIOM GroebnerMultiplication: 2.87/1.43 | (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 2.87/1.43 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ! [v8: 2.87/1.43 | $int] : ! [v9: $int] : ! [v10: $int] : ! [v11: $int] : ! [v12: 2.87/1.43 | $int] : ! [v13: $int] : ! [v14: $int] : ! [v15: $int] : ! [v16: 2.87/1.43 | $int] : ! [v17: $int] : 2.87/1.43 | ($difference($difference($sum($difference($difference($difference($difference($sum($difference($difference($difference($difference($product(2, 2.87/1.43 | v17), $product(3, v16)), v14), v13), v12), 2.87/1.43 | v11), v10), v9), v7), v5), v4), $product(2, v3)), 2.87/1.43 | $product(2, v2)) = v0 | ~ ($product(v16, $sum(v0, 2)) = v17) | ~ 2.87/1.43 | ($product(v11, v0) = v14) | ~ ($product(v8, v0) = v12) | ~ 2.87/1.43 | ($product(v6, v0) = v10) | ~ ($product(v4, v0) = v5) | ~ 2.87/1.43 | ($sum($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)), 2.87/1.43 | $product(-1, $sum($sum(v17, v15), v1))) = 0) | ~ ($product(v3, 2.87/1.43 | v2) = v13) | ~ ($product(v3, v1) = v4) | ~ ($product(v3, v0) = 2.87/1.43 | v11) | ~ ($product(v2, v2) = v9) | ~ ($product(v2, v1) = v8) | 2.87/1.43 | ~ ($product(v2, v0) = v6) | ~ ($product($sum(v1, v0), $sum($sum(v3, 2.87/1.43 | v2), 1)) = v16) | ~ ($product(v1, v0) = v7) | ~ 2.87/1.43 | ($product(v0, v0) = v15)) 2.87/1.43 | 2.87/1.44 | GROUND_INST: instantiating (20) with a, b, c, d, all_0_11, all_0_10, all_0_8, 2.87/1.44 | all_0_7, all_0_6, all_0_5, all_0_4, all_0_3, all_0_2, all_0_1, 2.87/1.44 | all_0_0, all_2_2, all_2_1, all_2_0, simplifying with (4), (5), 2.87/1.44 | (6), (7), (8), (9), (10), (11), (12), (13), (14), (16), (17), 2.87/1.44 | (18), (19) gives: 2.87/1.44 | (21) $difference($difference($sum($difference($difference($difference($difference($sum($difference($difference($difference($difference($product(2, 2.87/1.44 | all_2_0), $product(3, all_2_1)), all_0_0), 2.87/1.44 | all_0_1), all_0_2), all_0_3), all_0_4), all_0_5), 2.87/1.44 | all_0_7), all_0_10), all_0_11), $product(2, d)), $product(2, 2.87/1.44 | c)) = a 2.87/1.44 | 2.87/1.44 | THEORY_AXIOM GroebnerMultiplication: 2.91/1.44 | (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 2.91/1.44 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ! [v8: 2.91/1.44 | $int] : 2.91/1.44 | ($difference($difference($difference($difference($difference(v8, v7), 2.91/1.44 | v6), v5), v4), v1) = v0 | ~ ($product(v3, v1) = v4) | ~ 2.91/1.44 | ($product(v3, v0) = v7) | ~ ($product(v2, v1) = v6) | ~ 2.91/1.44 | ($product(v2, v0) = v5) | ~ ($product($sum(v1, v0), $sum($sum(v3, 2.91/1.44 | v2), 1)) = v8)) 2.91/1.44 | 2.91/1.44 | GROUND_INST: instantiating (22) with a, b, c, d, all_0_11, all_0_8, all_0_6, 2.91/1.44 | all_0_3, all_2_1, simplifying with (5), (6), (8), (9), (17) 2.91/1.44 | gives: 2.91/1.44 | (23) $difference($difference($difference($difference($difference(all_2_1, 2.91/1.44 | all_0_3), all_0_6), all_0_8), all_0_11), b) = a 2.91/1.44 | 2.91/1.44 | THEORY_AXIOM GroebnerMultiplication: 2.91/1.44 | (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 2.91/1.44 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ! [v8: 2.91/1.44 | $int] : ! [v9: $int] : ! [v10: $int] : ! [v11: $int] : ! [v12: 2.91/1.44 | $int] : ! [v13: $int] : ! [v14: $int] : ! [v15: $int] : ! [v16: 2.91/1.44 | $int] : 2.91/1.44 | ($difference($difference($difference($difference($difference($difference(v16, 2.91/1.44 | $product(2, v15)), v13), v12), v10), v8), v6) = v5 | ~ 2.91/1.44 | ($product(v15, $sum(v0, 2)) = v16) | ~ ($product(v11, v0) = v13) | 2.91/1.44 | ~ ($product(v9, v0) = v12) | ~ ($product(v7, v0) = v10) | ~ 2.91/1.44 | ($product(v4, v0) = v5) | ~ ($sum($product($sum($sum($sum(v3, v2), 2.91/1.44 | v1), v0), $sum(v2, 2)), $product(-1, $sum($sum(v16, v14), 2.91/1.44 | v1))) = 0) | ~ ($product(v3, v1) = v4) | ~ ($product(v3, 2.91/1.44 | v0) = v11) | ~ ($product(v2, v1) = v9) | ~ ($product(v2, v0) = 2.91/1.44 | v7) | ~ ($product($sum(v1, v0), $sum($sum(v3, v2), 1)) = v15) | 2.91/1.44 | ~ ($product(v1, v0) = v8) | ~ ($product(v0, v0) = v14) | ~ 2.91/1.44 | ($product(v0, v0) = v6)) 2.91/1.44 | 2.91/1.44 | GROUND_INST: instantiating (24) with a, b, c, d, all_0_11, all_0_10, all_0_9, 2.91/1.44 | all_0_8, all_0_7, all_0_6, all_0_4, all_0_3, all_0_2, all_0_0, 2.91/1.44 | all_2_2, all_2_1, all_2_0, simplifying with (3), (4), (5), (6), 2.91/1.44 | (8), (9), (11), (12), (13), (14), (16), (17), (18), (19) gives: 2.91/1.44 | (25) $difference($difference($difference($difference($difference($difference(all_2_0, 2.91/1.44 | $product(2, all_2_1)), all_0_0), all_0_2), all_0_4), 2.91/1.44 | all_0_7), all_0_9) = all_0_10 2.91/1.44 | 2.91/1.44 | COMBINE_EQS: (21), (25) imply: 2.91/1.45 | (26) $difference($difference($sum($sum($sum($sum($difference($sum($sum($sum($difference($sum(all_2_1, 2.91/1.45 | all_0_0), all_0_1), all_0_2), all_0_3), 2.91/1.45 | all_0_4), all_0_5), all_0_7), $product(2, all_0_9)), 2.91/1.45 | all_0_10), all_0_11), $product(2, d)), $product(2, c)) = a 2.91/1.45 | 2.91/1.45 | COMBINE_EQS: (23), (26) imply: 2.91/1.45 | (27) $sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_0_0, 2.91/1.45 | all_0_1), all_0_2), $product(2, all_0_3)), 2.91/1.45 | all_0_4), all_0_5), all_0_6), all_0_7), 2.91/1.45 | all_0_8), $product(2, all_0_9)), all_0_10), $product(2, 2.91/1.45 | all_0_11)), $product(2, d)), $product(2, c)), b) = 0 2.91/1.45 | 2.91/1.45 | REDUCE: (2), (27) imply: 2.91/1.45 | (28) ~ (0 = 0) 2.91/1.45 | 2.91/1.45 | CLOSE: (28) is inconsistent. 2.91/1.45 | 2.91/1.45 End of proof 2.91/1.45 % SZS output end Proof for theBenchmark 2.91/1.45 2.91/1.45 994ms 2.91/1.47 EOF