%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI712_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 : n002.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 17:48:54 EDT 2023 % Result : Theorem 5.67s 1.55s % Output : Proof 6.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : ARI712_1 : TPTP v8.1.2. Released v6.3.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 18:55:35 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.47/1.07 Prover 0: Preprocessing ... % 2.47/1.07 Prover 5: Preprocessing ... % 2.47/1.08 Prover 3: Preprocessing ... % 2.47/1.08 Prover 2: Preprocessing ... % 2.47/1.08 Prover 4: Preprocessing ... % 2.47/1.08 Prover 1: Preprocessing ... % 2.47/1.08 Prover 6: Preprocessing ... % 2.84/1.17 Prover 5: Constructing countermodel ... % 2.84/1.17 Prover 0: Constructing countermodel ... % 2.84/1.17 Prover 3: Constructing countermodel ... % 2.84/1.17 Prover 4: Constructing countermodel ... % 2.84/1.17 Prover 2: Constructing countermodel ... % 2.84/1.17 Prover 6: Constructing countermodel ... % 2.84/1.17 Prover 1: Constructing countermodel ... % 5.67/1.55 Prover 2: proved (923ms) % 5.67/1.55 Prover 0: proved (926ms) % 5.67/1.55 Prover 6: proved (921ms) % 5.67/1.55 % 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.67/1.55 % 5.67/1.55 Prover 3: proved (925ms) % 5.67/1.55 % 5.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.67/1.55 % 5.67/1.56 % 5.67/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.67/1.56 % 5.85/1.57 % 5.85/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.85/1.57 % 5.85/1.57 Prover 5: proved (923ms) % 5.85/1.57 % 5.85/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.85/1.57 % 5.85/1.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.85/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.85/1.59 Prover 7: Preprocessing ... % 5.85/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.85/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.85/1.59 Prover 1: Found proof (size 20) % 5.85/1.59 Prover 4: Found proof (size 20) % 5.85/1.59 Prover 4: proved (960ms) % 5.85/1.59 Prover 1: proved (960ms) % 5.85/1.59 Prover 8: Preprocessing ... % 5.85/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.85/1.59 Prover 7: Constructing countermodel ... % 5.85/1.59 Prover 7: stopped % 5.85/1.60 Prover 10: Preprocessing ... % 5.85/1.60 Prover 8: Constructing countermodel ... % 5.85/1.60 Prover 8: stopped % 5.85/1.60 Prover 11: Preprocessing ... % 5.85/1.61 Prover 13: Preprocessing ... % 5.85/1.61 Prover 10: Constructing countermodel ... % 5.85/1.61 Prover 10: stopped % 5.85/1.62 Prover 11: Constructing countermodel ... % 5.85/1.62 Prover 11: stopped % 5.85/1.62 Prover 13: Constructing countermodel ... % 5.85/1.62 Prover 13: stopped % 5.85/1.62 % 5.85/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.85/1.62 % 6.27/1.63 % SZS output start Proof for theBenchmark % 6.27/1.63 Assumptions after simplification: % 6.27/1.63 --------------------------------- % 6.27/1.63 % 6.27/1.63 (conj) % 6.27/1.64 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? % 6.27/1.64 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? % 6.27/1.64 [v10: int] : ? [v11: int] : ? [v12: int] : ? [v13: int] : ? [v14: int] : % 6.27/1.64 ? [v15: int] : ? [v16: int] : ? [v17: int] : ? [v18: int] : ? [v19: int] : % 6.27/1.64 ? [v20: int] : ? [v21: int] : ? [v22: int] : ? [v23: int] : ? [v24: int] % 6.27/1.64 : ( ~ % 6.27/1.64 ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(v24, % 6.27/1.64 v20), v18), v17), v13), v12), v11), v10), v9), % 6.27/1.64 v5), v4), $product(2, d)), $product(2, c)), b) = $product(2, a)) % 6.27/1.64 & $product(v23, a) = v24 & $product(v22, a) = v23 & $product(v21, b) = v22 & % 6.27/1.64 $product(v19, a) = v20 & $product(v18, c) = v21 & $product(v16, a) = v17 & % 6.27/1.64 $product(v15, a) = v16 & $product(v14, b) = v15 & $product(v13, c) = v14 & % 6.27/1.64 $product(v11, a) = v12 & $product(v8, a) = v9 & $product(v7, b) = v8 & % 6.27/1.64 $product(v6, b) = v7 & $product(v3, a) = v4 & $product(v2, b) = v3 & % 6.27/1.64 $product(v1, b) = v2 & $product(v0, d) = v1 & $product(v0, c) = v6 & % 6.27/1.64 $product(d, d) = v0 & $product(d, c) = v18 & $product(d, b) = v19 & % 6.27/1.64 $product(c, c) = v13 & $product(c, b) = v11 & $product(c, a) = v10 & % 6.27/1.64 $product(a, a) = v5) % 6.27/1.64 % 6.27/1.64 (eq) % 6.27/1.64 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? % 6.27/1.64 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : % 6.27/1.64 ($product(v7, b) = v8 & $product(v5, a) = v6 & $product($sum(v4, v2), % 6.27/1.64 $sum($sum(v8, v6), 1)) = v9 & $product(v3, a) = v4 & $product(v1, c) = v2 % 6.27/1.64 & $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(v9, v0), b) % 6.27/1.64 & $product(d, d) = v7 & $product(c, c) = v5 & $product(b, d) = v3 & % 6.27/1.64 $product(a, b) = v1 & $product(a, a) = v0) % 6.27/1.64 % 6.27/1.64 Those formulas are unsatisfiable: % 6.27/1.64 --------------------------------- % 6.27/1.64 % 6.27/1.64 Begin of proof % 6.27/1.65 | % 6.27/1.65 | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1, all_2_2, % 6.27/1.65 | all_2_3, all_2_4, all_2_5, all_2_6, all_2_7, all_2_8, all_2_9 gives: % 6.27/1.65 | (1) $product(all_2_2, b) = all_2_1 & $product(all_2_4, a) = all_2_3 & % 6.27/1.65 | $product($sum(all_2_5, all_2_7), $sum($sum(all_2_1, all_2_3), 1)) = % 6.27/1.65 | all_2_0 & $product(all_2_6, a) = all_2_5 & $product(all_2_8, c) = % 6.27/1.65 | all_2_7 & $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = % 6.27/1.65 | $sum($sum(all_2_0, all_2_9), b) & $product(d, d) = all_2_2 & % 6.27/1.65 | $product(c, c) = all_2_4 & $product(b, d) = all_2_6 & $product(a, b) = % 6.27/1.65 | all_2_8 & $product(a, a) = all_2_9 % 6.27/1.65 | % 6.27/1.65 | ALPHA: (1) implies: % 6.27/1.65 | (2) $product(a, a) = all_2_9 % 6.27/1.65 | (3) $product(a, b) = all_2_8 % 6.27/1.65 | (4) $product(b, d) = all_2_6 % 6.27/1.65 | (5) $product(c, c) = all_2_4 % 6.27/1.65 | (6) $product(d, d) = all_2_2 % 6.27/1.65 | (7) $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(all_2_0, % 6.27/1.65 | all_2_9), b) % 6.27/1.65 | (8) $product(all_2_8, c) = all_2_7 % 6.27/1.65 | (9) $product(all_2_6, a) = all_2_5 % 6.27/1.65 | (10) $product($sum(all_2_5, all_2_7), $sum($sum(all_2_1, all_2_3), 1)) = % 6.27/1.65 | all_2_0 % 6.27/1.65 | (11) $product(all_2_4, a) = all_2_3 % 6.27/1.65 | (12) $product(all_2_2, b) = all_2_1 % 6.27/1.65 | % 6.43/1.65 | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2, % 6.43/1.65 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 6.43/1.65 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 6.43/1.65 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 6.43/1.65 | all_4_24 gives: % 6.43/1.66 | (13) ~ % 6.43/1.66 | ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(all_4_0, % 6.43/1.66 | all_4_4), all_4_6), all_4_7), all_4_11), % 6.43/1.66 | all_4_12), all_4_13), all_4_14), all_4_15), % 6.43/1.66 | all_4_19), all_4_20), $product(2, d)), $product(2, c)), b) % 6.43/1.66 | = $product(2, a)) & $product(all_4_1, a) = all_4_0 & % 6.43/1.66 | $product(all_4_2, a) = all_4_1 & $product(all_4_3, b) = all_4_2 & % 6.43/1.66 | $product(all_4_5, a) = all_4_4 & $product(all_4_6, c) = all_4_3 & % 6.43/1.66 | $product(all_4_8, a) = all_4_7 & $product(all_4_9, a) = all_4_8 & % 6.43/1.66 | $product(all_4_10, b) = all_4_9 & $product(all_4_11, c) = all_4_10 & % 6.43/1.66 | $product(all_4_13, a) = all_4_12 & $product(all_4_16, a) = all_4_15 & % 6.43/1.66 | $product(all_4_17, b) = all_4_16 & $product(all_4_18, b) = all_4_17 & % 6.43/1.66 | $product(all_4_21, a) = all_4_20 & $product(all_4_22, b) = all_4_21 & % 6.43/1.66 | $product(all_4_23, b) = all_4_22 & $product(all_4_24, d) = all_4_23 & % 6.43/1.66 | $product(all_4_24, c) = all_4_18 & $product(d, d) = all_4_24 & % 6.43/1.66 | $product(d, c) = all_4_6 & $product(d, b) = all_4_5 & $product(c, c) = % 6.43/1.66 | all_4_11 & $product(c, b) = all_4_13 & $product(c, a) = all_4_14 & % 6.43/1.66 | $product(a, a) = all_4_19 % 6.43/1.66 | % 6.43/1.66 | ALPHA: (13) implies: % 6.43/1.66 | (14) ~ % 6.43/1.66 | ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(all_4_0, % 6.43/1.66 | all_4_4), all_4_6), all_4_7), all_4_11), % 6.43/1.66 | all_4_12), all_4_13), all_4_14), all_4_15), % 6.43/1.66 | all_4_19), all_4_20), $product(2, d)), $product(2, c)), b) % 6.43/1.66 | = $product(2, a)) % 6.43/1.66 | (15) $product(a, a) = all_4_19 % 6.43/1.66 | (16) $product(c, a) = all_4_14 % 6.43/1.66 | (17) $product(c, b) = all_4_13 % 6.43/1.66 | (18) $product(c, c) = all_4_11 % 6.43/1.66 | (19) $product(d, b) = all_4_5 % 6.43/1.66 | (20) $product(d, c) = all_4_6 % 6.43/1.66 | (21) $product(d, d) = all_4_24 % 6.43/1.66 | (22) $product(all_4_24, c) = all_4_18 % 6.43/1.66 | (23) $product(all_4_24, d) = all_4_23 % 6.43/1.66 | (24) $product(all_4_23, b) = all_4_22 % 6.43/1.66 | (25) $product(all_4_22, b) = all_4_21 % 6.43/1.66 | (26) $product(all_4_21, a) = all_4_20 % 6.43/1.66 | (27) $product(all_4_18, b) = all_4_17 % 6.43/1.66 | (28) $product(all_4_17, b) = all_4_16 % 6.43/1.66 | (29) $product(all_4_16, a) = all_4_15 % 6.43/1.66 | (30) $product(all_4_13, a) = all_4_12 % 6.43/1.66 | (31) $product(all_4_11, c) = all_4_10 % 6.43/1.66 | (32) $product(all_4_10, b) = all_4_9 % 6.43/1.66 | (33) $product(all_4_9, a) = all_4_8 % 6.43/1.66 | (34) $product(all_4_8, a) = all_4_7 % 6.43/1.66 | (35) $product(all_4_6, c) = all_4_3 % 6.43/1.66 | (36) $product(all_4_5, a) = all_4_4 % 6.43/1.67 | (37) $product(all_4_3, b) = all_4_2 % 6.43/1.67 | (38) $product(all_4_2, a) = all_4_1 % 6.43/1.67 | (39) $product(all_4_1, a) = all_4_0 % 6.43/1.67 | % 6.43/1.67 | THEORY_AXIOM GroebnerMultiplication: % 6.43/1.67 | (40) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 6.43/1.67 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 6.43/1.67 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13: % 6.43/1.67 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int] % 6.43/1.67 | : ! [v18: int] : ! [v19: int] : ! [v20: int] : ! [v21: int] : ! % 6.43/1.67 | [v22: int] : ! [v23: int] : ! [v24: int] : ! [v25: int] : ! [v26: % 6.43/1.67 | int] : ! [v27: int] : ! [v28: int] : ! [v29: int] : ! [v30: int] % 6.43/1.67 | : ! [v31: int] : ! [v32: int] : ! [v33: int] : ! [v34: int] : % 6.43/1.67 | ($difference($difference($difference($sum($sum($sum($difference($sum($sum($difference($difference($sum($difference(v34, % 6.43/1.67 | v30), v29), v24), v23), v22), v18), v9), % 6.43/1.67 | v8), v6), v4), $product(2, v3)), $product(2, v2)), v1) = % 6.43/1.67 | $product(2, v0) | ~ ($product(v33, v0) = v34) | ~ ($product(v32, % 6.43/1.67 | v0) = v33) | ~ ($product(v31, v1) = v32) | ~ ($product(v30, % 6.43/1.67 | v2) = v31) | ~ ($product(v28, v0) = v29) | ~ ($product(v27, % 6.43/1.67 | v0) = v28) | ~ ($product(v26, v1) = v27) | ~ ($product(v25, % 6.43/1.67 | v2) = v26) | ~ ($product(v21, v0) = v22) | ~ ($product(v20, % 6.43/1.67 | v1) = v21) | ~ ($product(v19, v1) = v20) | ~ ($product(v17, % 6.43/1.67 | v0) = v18) | ~ ($product(v16, v1) = v17) | ~ ($product(v15, % 6.43/1.67 | v1) = v16) | ~ ($product(v14, v3) = v15) | ~ ($product(v14, % 6.43/1.67 | v2) = v19) | ~ ($product(v11, v1) = v12) | ~ ($product(v9, v0) % 6.43/1.67 | = v10) | ~ ($product($sum(v8, v6), $sum($sum(v12, v10), 1)) = % 6.43/1.67 | v13) | ~ ($product(v7, v0) = v8) | ~ ($product(v5, v2) = v6) | % 6.43/1.67 | ~ ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) = % 6.43/1.67 | $sum($sum(v13, v4), v1)) | ~ ($product(v3, v3) = v14) | ~ % 6.43/1.67 | ($product(v3, v3) = v11) | ~ ($product(v3, v2) = v30) | ~ % 6.43/1.67 | ($product(v2, v2) = v25) | ~ ($product(v2, v2) = v9) | ~ % 6.43/1.67 | ($product(v2, v1) = v24) | ~ ($product(v2, v0) = v23) | ~ % 6.43/1.67 | ($product(v1, v3) = v7) | ~ ($product(v0, v1) = v5) | ~ % 6.43/1.67 | ($product(v0, v0) = v4)) % 6.43/1.67 | % 6.43/1.68 | GROUND_INST: instantiating (40) with a, b, c, d, all_2_9, all_2_8, all_2_7, % 6.43/1.68 | all_2_6, all_2_5, all_2_4, all_2_3, all_2_2, all_2_1, all_2_0, % 6.43/1.68 | all_4_24, all_4_23, all_4_22, all_4_21, all_4_20, all_4_18, % 6.43/1.68 | all_4_17, all_4_16, all_4_15, all_4_14, all_4_13, all_4_11, % 6.43/1.68 | all_4_10, all_4_9, all_4_8, all_4_7, all_4_6, all_4_3, all_4_2, % 6.43/1.68 | all_4_1, all_4_0, simplifying with (2), (3), (4), (5), (6), (7), % 6.43/1.68 | (8), (9), (10), (11), (12), (16), (17), (18), (20), (21), (22), % 6.43/1.68 | (23), (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), % 6.43/1.68 | (35), (37), (38), (39) gives: % 6.43/1.68 | (41) $difference($difference($difference($sum($sum($sum($difference($sum($sum($difference($difference($sum($difference(all_4_0, % 6.43/1.68 | all_4_6), all_4_7), all_4_13), all_4_14), % 6.43/1.68 | all_4_15), all_4_20), all_2_4), all_2_5), all_2_7), % 6.43/1.68 | all_2_9), $product(2, d)), $product(2, c)), b) = $product(2, % 6.43/1.68 | a) % 6.43/1.68 | % 6.43/1.68 | THEORY_AXIOM GroebnerMultiplication: % 6.43/1.68 | (42) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 6.43/1.68 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 6.43/1.68 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13: % 6.43/1.68 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int] % 6.43/1.68 | : ! [v18: int] : ! [v19: int] : ! [v20: int] : ! [v21: int] : ! % 6.43/1.68 | [v22: int] : ! [v23: int] : ! [v24: int] : ! [v25: int] : ! [v26: % 6.43/1.68 | int] : ! [v27: int] : ! [v28: int] : ! [v29: int] : ! [v30: int] % 6.43/1.68 | : ! [v31: int] : ! [v32: int] : % 6.43/1.68 | ($sum($sum($difference($sum($sum($sum(v32, v27), v22), v18), v13), % 6.43/1.68 | v8), v6) = 0 | ~ ($product(v31, v0) = v32) | ~ ($product(v30, % 6.43/1.68 | v0) = v31) | ~ ($product(v29, v1) = v30) | ~ ($product(v28, % 6.43/1.68 | v2) = v29) | ~ ($product(v26, v0) = v27) | ~ ($product(v25, % 6.43/1.68 | v0) = v26) | ~ ($product(v24, v1) = v25) | ~ ($product(v23, % 6.43/1.68 | v2) = v24) | ~ ($product(v21, v0) = v22) | ~ ($product(v20, % 6.43/1.68 | v1) = v21) | ~ ($product(v19, v1) = v20) | ~ ($product(v17, % 6.43/1.68 | v0) = v18) | ~ ($product(v16, v1) = v17) | ~ ($product(v15, % 6.43/1.68 | v1) = v16) | ~ ($product(v14, v3) = v15) | ~ ($product(v14, % 6.43/1.68 | v2) = v19) | ~ ($product(v11, v1) = v12) | ~ ($product(v9, v0) % 6.43/1.68 | = v10) | ~ ($product($sum(v8, v6), $sum($sum(v12, v10), 1)) = % 6.43/1.68 | v13) | ~ ($product(v7, v0) = v8) | ~ ($product(v5, v2) = v6) | % 6.43/1.68 | ~ ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) = % 6.43/1.68 | $sum($sum(v13, v4), v1)) | ~ ($product(v3, v3) = v14) | ~ % 6.43/1.68 | ($product(v3, v3) = v11) | ~ ($product(v3, v2) = v28) | ~ % 6.43/1.68 | ($product(v2, v2) = v23) | ~ ($product(v2, v2) = v9) | ~ % 6.43/1.68 | ($product(v1, v3) = v7) | ~ ($product(v0, v1) = v5) | ~ % 6.43/1.68 | ($product(v0, v0) = v4)) % 6.43/1.68 | % 6.43/1.68 | GROUND_INST: instantiating (42) with a, b, c, d, all_2_9, all_2_8, all_2_7, % 6.43/1.68 | all_2_6, all_2_5, all_2_4, all_2_3, all_2_2, all_2_1, all_2_0, % 6.43/1.68 | all_4_24, all_4_23, all_4_22, all_4_21, all_4_20, all_4_18, % 6.43/1.68 | all_4_17, all_4_16, all_4_15, all_4_11, all_4_10, all_4_9, % 6.43/1.68 | all_4_8, all_4_7, all_4_6, all_4_3, all_4_2, all_4_1, all_4_0, % 6.43/1.68 | simplifying with (2), (3), (4), (5), (6), (7), (8), (9), (10), % 6.43/1.68 | (11), (12), (18), (20), (21), (22), (23), (24), (25), (26), (27), % 6.43/1.68 | (28), (29), (31), (32), (33), (34), (35), (37), (38), (39) gives: % 6.43/1.69 | (43) $sum($sum($difference($sum($sum($sum(all_4_0, all_4_7), all_4_15), % 6.43/1.69 | all_4_20), all_2_0), all_2_5), all_2_7) = 0 % 6.43/1.69 | % 6.43/1.69 | THEORY_AXIOM GroebnerMultiplication: % 6.43/1.69 | (44) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 6.43/1.69 | int] : ! [v5: int] : ! [v6: int] : (v6 = v4 | ~ ($product(v5, v0) % 6.43/1.69 | = v6) | ~ ($product(v3, v0) = v4) | ~ ($product(v2, v1) = v5) | % 6.43/1.69 | ~ ($product(v1, v2) = v3)) % 6.43/1.69 | % 6.43/1.69 | GROUND_INST: instantiating (44) with a, b, d, all_2_6, all_2_5, all_4_5, % 6.43/1.69 | all_4_4, simplifying with (4), (9), (19), (36) gives: % 6.43/1.69 | (45) all_4_4 = all_2_5 % 6.43/1.69 | % 6.43/1.69 | THEORY_AXIOM GroebnerMultiplication: % 6.43/1.69 | (46) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 6.43/1.69 | ($product(v0, v0) = v2) | ~ ($product(v0, v0) = v1)) % 6.43/1.69 | % 6.43/1.69 | GROUND_INST: instantiating (46) with c, all_2_4, all_4_11, simplifying with % 6.43/1.69 | (5), (18) gives: % 6.43/1.69 | (47) all_4_11 = all_2_4 % 6.43/1.69 | % 6.43/1.69 | THEORY_AXIOM GroebnerMultiplication: % 6.43/1.69 | (48) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 6.43/1.69 | int] : ! [v5: int] : ! [v6: int] : (v6 = v4 | ~ ($product(v5, v0) % 6.43/1.69 | = v6) | ~ ($product(v3, v2) = v4) | ~ ($product(v2, v1) = v5) | % 6.43/1.69 | ~ ($product(v0, v1) = v3)) % 6.43/1.69 | % 6.43/1.69 | GROUND_INST: instantiating (48) with a, b, c, all_2_8, all_2_7, all_4_13, % 6.43/1.69 | all_4_12, simplifying with (3), (8), (17), (30) gives: % 6.43/1.69 | (49) all_4_12 = all_2_7 % 6.43/1.69 | % 6.43/1.69 | GROUND_INST: instantiating (46) with a, all_2_9, all_4_19, simplifying with % 6.43/1.69 | (2), (15) gives: % 6.43/1.69 | (50) all_4_19 = all_2_9 % 6.43/1.69 | % 6.43/1.69 | COMBINE_EQS: (41), (43) imply: % 6.43/1.69 | (51) $sum($sum($sum($sum($difference($sum($difference($sum($sum(all_4_6, % 6.43/1.69 | all_4_13), all_4_14), all_2_0), all_2_4), all_2_9), % 6.43/1.69 | $product(2, d)), $product(2, c)), b), $product(2, a)) = 0 % 6.43/1.69 | % 6.43/1.69 | REDUCE: (14), (43), (45), (47), (49), (50), (51) imply: % 6.43/1.69 | (52) $false % 6.43/1.69 | % 6.43/1.69 | CLOSE: (52) is inconsistent. % 6.43/1.69 | % 6.43/1.69 End of proof % 6.43/1.69 % SZS output end Proof for theBenchmark % 6.43/1.69 % 6.43/1.69 1089ms %------------------------------------------------------------------------------