%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI694_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 : n013.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 17:48:50 EDT 2023 % Result : Theorem 3.67s 1.26s % Output : Proof 4.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ARI694_1 : TPTP v8.1.2. Released v6.3.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n013.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 18:38:01 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.27/1.09 Prover 1: Preprocessing ... % 2.27/1.09 Prover 5: Preprocessing ... % 2.27/1.09 Prover 2: Preprocessing ... % 2.27/1.09 Prover 0: Preprocessing ... % 2.27/1.09 Prover 3: Preprocessing ... % 2.27/1.09 Prover 6: Preprocessing ... % 2.64/1.10 Prover 4: Preprocessing ... % 3.04/1.16 Prover 5: Constructing countermodel ... % 3.04/1.16 Prover 6: Constructing countermodel ... % 3.04/1.16 Prover 4: Constructing countermodel ... % 3.04/1.16 Prover 3: Constructing countermodel ... % 3.04/1.16 Prover 0: Constructing countermodel ... % 3.04/1.16 Prover 1: Constructing countermodel ... % 3.04/1.16 Prover 2: Constructing countermodel ... % 3.67/1.26 Prover 2: proved (623ms) % 3.67/1.26 Prover 3: proved (624ms) % 3.67/1.26 % 3.67/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.67/1.26 % 3.67/1.27 Prover 6: proved (621ms) % 3.67/1.27 % 3.67/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.67/1.27 % 3.67/1.27 % 3.67/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.67/1.27 % 3.67/1.28 Prover 0: stopped % 3.67/1.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.67/1.29 Prover 5: stopped % 3.67/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.67/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.67/1.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.67/1.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.67/1.30 Prover 7: Preprocessing ... % 3.67/1.30 Prover 8: Preprocessing ... % 3.67/1.30 Prover 10: Preprocessing ... % 3.67/1.32 Prover 13: Preprocessing ... % 3.67/1.32 Prover 10: Constructing countermodel ... % 3.67/1.32 Prover 11: Preprocessing ... % 3.67/1.32 Prover 7: Constructing countermodel ... % 3.67/1.33 Prover 8: Constructing countermodel ... % 3.67/1.33 Prover 11: Constructing countermodel ... % 3.67/1.34 Prover 13: Constructing countermodel ... % 3.67/1.35 Prover 1: Found proof (size 68) % 3.67/1.35 Prover 1: proved (713ms) % 3.67/1.35 Prover 8: stopped % 3.67/1.35 Prover 7: stopped % 4.18/1.36 Prover 4: Found proof (size 67) % 4.18/1.36 Prover 4: proved (723ms) % 4.18/1.36 Prover 13: stopped % 4.18/1.36 Prover 10: stopped % 4.18/1.37 Prover 11: stopped % 4.18/1.37 % 4.18/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.18/1.37 % 4.18/1.38 % SZS output start Proof for theBenchmark % 4.18/1.39 Assumptions after simplification: % 4.18/1.39 --------------------------------- % 4.18/1.39 % 4.18/1.39 (conj) % 4.18/1.40 ? [v0: int] : ( ~ (v0 = 0) & $lesseq(v0, 1953124) & $lesseq(-1953124, v0) & % 4.18/1.40 ? [v1: int] : $difference($sum($product(1953125, v1), v0), x0) = 4 & ( ~ % 4.18/1.40 ($lesseq(v0, -1)) | ~ ($lesseq(-4, x0))) & ( ~ ($lesseq(1, v0)) | ~ % 4.18/1.40 ($lesseq(x0, -4)))) % 4.18/1.40 % 4.18/1.40 (eq1) % 4.18/1.40 $difference($product(5, x1), x0) = -1 % 4.18/1.40 % 4.18/1.40 (eq2) % 4.18/1.40 $difference($product(5, x2), $product(4, x1)) = -1 % 4.18/1.40 % 4.18/1.40 (eq3) % 4.18/1.40 $difference($product(5, x3), $product(4, x2)) = -1 % 4.18/1.40 % 4.18/1.40 (eq4) % 4.18/1.40 $difference($product(5, x4), $product(4, x3)) = -1 % 4.18/1.40 % 4.18/1.40 (eq5) % 4.18/1.40 $difference($product(5, x5), $product(4, x4)) = -1 % 4.18/1.40 % 4.18/1.40 (eq6) % 4.18/1.40 $difference($product(5, x6), $product(4, x5)) = -1 % 4.18/1.40 % 4.18/1.40 (eq7) % 4.18/1.40 $difference($product(5, x7), $product(4, x6)) = -1 % 4.18/1.40 % 4.18/1.40 (eq8) % 4.18/1.40 $difference($product(5, x8), $product(4, x7)) = -1 % 4.18/1.40 % 4.18/1.40 (eq9) % 4.54/1.40 $difference($product(5, x9), $product(4, x8)) = -1 % 4.54/1.40 % 4.54/1.40 Those formulas are unsatisfiable: % 4.54/1.40 --------------------------------- % 4.54/1.40 % 4.54/1.40 Begin of proof % 4.54/1.40 | % 4.55/1.40 | COMBINE_EQS: (eq1), (eq2) imply: % 4.55/1.40 | (1) $difference($sum($product(5, x2), x1), x0) = -2 % 4.55/1.40 | % 4.55/1.40 | COMBINE_EQS: (1), (eq3) imply: % 4.55/1.40 | (2) $difference($sum($sum($product(5, x3), x2), x1), x0) = -3 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (2), (eq4) imply: % 4.55/1.41 | (3) $difference($sum($sum($sum($product(5, x4), x3), x2), x1), x0) = -4 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (3), (eq5) imply: % 4.55/1.41 | (4) $difference($sum($sum($sum($sum($product(5, x5), x4), x3), x2), x1), % 4.55/1.41 | x0) = -5 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (4), (eq6) imply: % 4.55/1.41 | (5) $difference($sum($sum($sum($sum($sum($product(5, x6), x5), x4), x3), % 4.55/1.41 | x2), x1), x0) = -6 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (5), (eq7) imply: % 4.55/1.41 | (6) $difference($sum($sum($sum($sum($sum($sum($product(5, x7), x6), x5), % 4.55/1.41 | x4), x3), x2), x1), x0) = -7 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (6), (eq8) imply: % 4.55/1.41 | (7) $difference($sum($sum($sum($sum($sum($sum($sum($product(5, x8), x7), % 4.55/1.41 | x6), x5), x4), x3), x2), x1), x0) = -8 % 4.55/1.41 | % 4.55/1.41 | COMBINE_EQS: (7), (eq9) imply: % 4.55/1.41 | (8) $difference($sum($sum($sum($sum($sum($sum($sum($sum($product(5, x9), % 4.55/1.41 | x8), x7), x6), x5), x4), x3), x2), x1), x0) = -9 % 4.55/1.41 | % 4.55/1.41 | DELTA: instantiating (conj) with fresh symbol all_3_0 gives: % 4.55/1.41 | (9) ~ (all_3_0 = 0) & $lesseq(all_3_0, 1953124) & $lesseq(-1953124, % 4.55/1.41 | all_3_0) & ? [v0: int] : $difference($sum($product(1953125, v0), % 4.55/1.41 | all_3_0), x0) = 4 & ( ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(-4, % 4.55/1.41 | x0))) & ( ~ ($lesseq(1, all_3_0)) | ~ ($lesseq(x0, -4))) % 4.55/1.41 | % 4.55/1.41 | ALPHA: (9) implies: % 4.55/1.41 | (10) ~ (all_3_0 = 0) % 4.55/1.41 | (11) $lesseq(-1953124, all_3_0) % 4.55/1.41 | (12) $lesseq(all_3_0, 1953124) % 4.55/1.41 | (13) ? [v0: int] : $difference($sum($product(1953125, v0), all_3_0), x0) = % 4.55/1.41 | 4 % 4.55/1.41 | % 4.55/1.41 | DELTA: instantiating (13) with fresh symbol all_5_0 gives: % 4.55/1.41 | (14) $difference($sum($product(1953125, all_5_0), all_3_0), x0) = 4 % 4.55/1.41 | % 4.55/1.42 | COL_REDUCE: introducing fresh symbol sc_7_0_0 defined by: % 4.55/1.42 | (15) all_5_0 = sc_7_0_0 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (14), (15) imply: % 4.55/1.42 | (16) $sum($difference(all_3_0, x0), $product(1953125, sc_7_0_0)) = 4 % 4.55/1.42 | % 4.55/1.42 | COL_REDUCE: introducing fresh symbol sc_7_0_1 defined by: % 4.55/1.42 | (17) $difference(x9, sc_7_0_1) = -2 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (8), (17) imply: % 4.55/1.42 | (18) $sum($difference($sum($sum($sum($sum($sum($sum($sum(x8, x7), x6), x5), % 4.55/1.42 | x4), x3), x2), x1), x0), $product(5, sc_7_0_1)) = 1 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (7), (18) imply: % 4.55/1.42 | (19) $sum($difference($sum($sum($sum($sum($sum($sum($product(4, x7), % 4.55/1.42 | $product(4, x6)), $product(4, x5)), $product(4, x4)), % 4.55/1.42 | $product(4, x3)), $product(4, x2)), $product(4, x1)), % 4.55/1.42 | $product(4, x0)), $product(25, sc_7_0_1)) = 13 % 4.55/1.42 | % 4.55/1.42 | SIMP: (19) implies: % 4.55/1.42 | (20) $sum($difference($sum($sum($sum($sum($sum($sum($product(4, x7), % 4.55/1.42 | $product(4, x6)), $product(4, x5)), $product(4, x4)), % 4.55/1.42 | $product(4, x3)), $product(4, x2)), $product(4, x1)), % 4.55/1.42 | $product(4, x0)), $product(25, sc_7_0_1)) = 13 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (6), (20) imply: % 4.55/1.42 | (21) $difference($sum($difference($difference($difference($difference($difference($difference(x7, % 4.55/1.42 | $product(3, x6)), $product(3, x5)), $product(3, x4)), % 4.55/1.42 | $product(3, x3)), $product(3, x2)), $product(3, x1)), % 4.55/1.42 | $product(3, x0)), $product(25, sc_7_0_1)) = -20 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (20), (21) imply: % 4.55/1.42 | (22) $sum($difference($sum($sum($sum($sum($sum($product(16, x6), % 4.55/1.42 | $product(16, x5)), $product(16, x4)), $product(16, x3)), % 4.55/1.42 | $product(16, x2)), $product(16, x1)), $product(16, x0)), % 4.55/1.42 | $product(125, sc_7_0_1)) = 93 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (5), (22) imply: % 4.55/1.42 | (23) $sum($difference($sum($sum($sum($sum($sum(x6, $product(13, x5)), % 4.55/1.42 | $product(13, x4)), $product(13, x3)), $product(13, x2)), % 4.55/1.42 | $product(13, x1)), $product(13, x0)), $product(125, sc_7_0_1)) = % 4.55/1.42 | 111 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (22), (23) imply: % 4.55/1.42 | (24) $sum($difference($sum($sum($sum($sum($product(64, x5), $product(64, % 4.55/1.42 | x4)), $product(64, x3)), $product(64, x2)), $product(64, % 4.55/1.42 | x1)), $product(64, x0)), $product(625, sc_7_0_1)) = 561 % 4.55/1.42 | % 4.55/1.42 | SIMP: (24) implies: % 4.55/1.42 | (25) $sum($difference($sum($sum($sum($sum($product(64, x5), $product(64, % 4.55/1.42 | x4)), $product(64, x3)), $product(64, x2)), $product(64, % 4.55/1.42 | x1)), $product(64, x0)), $product(625, sc_7_0_1)) = 561 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (4), (25) imply: % 4.55/1.42 | (26) $difference($sum($difference($difference($difference($difference(x5, % 4.55/1.42 | $product(51, x4)), $product(51, x3)), $product(51, x2)), % 4.55/1.42 | $product(51, x1)), $product(51, x0)), $product(625, sc_7_0_1)) = % 4.55/1.42 | -626 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (25), (26) imply: % 4.55/1.42 | (27) $sum($difference($sum($sum($sum($product(256, x4), $product(256, x3)), % 4.55/1.42 | $product(256, x2)), $product(256, x1)), $product(256, x0)), % 4.55/1.42 | $product(3125, sc_7_0_1)) = 3125 % 4.55/1.42 | % 4.55/1.42 | SIMP: (27) implies: % 4.55/1.42 | (28) $sum($difference($sum($sum($sum($product(256, x4), $product(256, x3)), % 4.55/1.42 | $product(256, x2)), $product(256, x1)), $product(256, x0)), % 4.55/1.42 | $product(3125, sc_7_0_1)) = 3125 % 4.55/1.42 | % 4.55/1.42 | COMBINE_EQS: (3), (28) imply: % 4.55/1.43 | (29) $sum($difference($sum($sum($sum(x4, $product(205, x3)), $product(205, % 4.55/1.43 | x2)), $product(205, x1)), $product(205, x0)), $product(3125, % 4.55/1.43 | sc_7_0_1)) = 3329 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (28), (29) imply: % 4.55/1.43 | (30) $sum($difference($sum($sum($product(1024, x3), $product(1024, x2)), % 4.55/1.43 | $product(1024, x1)), $product(1024, x0)), $product(15625, % 4.55/1.43 | sc_7_0_1)) = 16649 % 4.55/1.43 | % 4.55/1.43 | SIMP: (30) implies: % 4.55/1.43 | (31) $sum($difference($sum($sum($product(1024, x3), $product(1024, x2)), % 4.55/1.43 | $product(1024, x1)), $product(1024, x0)), $product(15625, % 4.55/1.43 | sc_7_0_1)) = 16649 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (2), (31) imply: % 4.55/1.43 | (32) $difference($sum($difference($difference(x3, $product(819, x2)), % 4.55/1.43 | $product(819, x1)), $product(819, x0)), $product(15625, % 4.55/1.43 | sc_7_0_1)) = -17264 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (31), (32) imply: % 4.55/1.43 | (33) $sum($difference($sum($product(4096, x2), $product(4096, x1)), % 4.55/1.43 | $product(4096, x0)), $product(78125, sc_7_0_1)) = 86317 % 4.55/1.43 | % 4.55/1.43 | SIMP: (33) implies: % 4.55/1.43 | (34) $sum($difference($sum($product(4096, x2), $product(4096, x1)), % 4.55/1.43 | $product(4096, x0)), $product(78125, sc_7_0_1)) = 86317 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (1), (34) imply: % 4.55/1.43 | (35) $sum($difference($sum(x2, $product(3277, x1)), $product(3277, x0)), % 4.55/1.43 | $product(78125, sc_7_0_1)) = 87955 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (34), (35) imply: % 4.55/1.43 | (36) $sum($difference($product(16384, x1), $product(16384, x0)), % 4.55/1.43 | $product(390625, sc_7_0_1)) = 439777 % 4.55/1.43 | % 4.55/1.43 | SIMP: (36) implies: % 4.55/1.43 | (37) $sum($difference($product(16384, x1), $product(16384, x0)), % 4.55/1.43 | $product(390625, sc_7_0_1)) = 439777 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (37), (eq1) imply: % 4.55/1.43 | (38) $difference($sum(x1, $product(13107, x0)), $product(390625, sc_7_0_1)) % 4.55/1.43 | = -443054 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (37), (38) imply: % 4.55/1.43 | (39) $difference($product(65536, x0), $product(1953125, sc_7_0_1)) = % 4.55/1.43 | -2215269 % 4.55/1.43 | % 4.55/1.43 | SIMP: (39) implies: % 4.55/1.43 | (40) $difference($product(65536, x0), $product(1953125, sc_7_0_1)) = % 4.55/1.43 | -2215269 % 4.55/1.43 | % 4.55/1.43 | COL_REDUCE: introducing fresh symbol sc_7_0_2 defined by: % 4.55/1.43 | (41) $difference($difference(x0, $product(30, sc_7_0_1)), sc_7_0_2) = -34 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (40), (41) imply: % 4.55/1.43 | (42) $sum($product(12955, sc_7_0_1), $product(65536, sc_7_0_2)) = 12955 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (16), (41) imply: % 4.55/1.43 | (43) $sum($difference($difference(all_3_0, $product(30, sc_7_0_1)), % 4.55/1.43 | sc_7_0_2), $product(1953125, sc_7_0_0)) = -30 % 4.55/1.43 | % 4.55/1.43 | COL_REDUCE: introducing fresh symbol sc_7_0_3 defined by: % 4.55/1.43 | (44) $difference($sum(sc_7_0_1, $product(5, sc_7_0_2)), sc_7_0_3) = 1 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (42), (44) imply: % 4.55/1.43 | (45) $sum($product(761, sc_7_0_2), $product(12955, sc_7_0_3)) = 0 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (43), (44) imply: % 4.55/1.43 | (46) $sum($difference($sum(all_3_0, $product(149, sc_7_0_2)), $product(30, % 4.55/1.43 | sc_7_0_3)), $product(1953125, sc_7_0_0)) = 0 % 4.55/1.43 | % 4.55/1.43 | COL_REDUCE: introducing fresh symbol sc_7_0_4 defined by: % 4.55/1.43 | (47) $sum(sc_7_0_2, $product(17, sc_7_0_3)) = sc_7_0_4 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (45), (47) imply: % 4.55/1.43 | (48) $sum($product(18, sc_7_0_3), $product(761, sc_7_0_4)) = 0 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (47), (48) imply: % 4.55/1.43 | (49) $difference(sc_7_0_2, sc_7_0_3) = $product(762, sc_7_0_4) % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (46), (48), (49) imply: % 4.55/1.43 | (50) $sum($sum($difference(all_3_0, $product(7, sc_7_0_3)), % 4.55/1.43 | $product(108211, sc_7_0_4)), $product(1953125, sc_7_0_0)) = 0 % 4.55/1.43 | % 4.55/1.43 | COL_REDUCE: introducing fresh symbol sc_7_0_5 defined by: % 4.55/1.43 | (51) $sum(sc_7_0_3, $product(42, sc_7_0_4)) = sc_7_0_5 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (48), (51) imply: % 4.55/1.43 | (52) $sum($product(5, sc_7_0_4), $product(18, sc_7_0_5)) = 0 % 4.55/1.43 | % 4.55/1.43 | COMBINE_EQS: (51), (52) imply: % 4.55/1.44 | (53) $sum(sc_7_0_3, $product(2, sc_7_0_4)) = $product(145, sc_7_0_5) % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (50), (52), (53) imply: % 4.55/1.44 | (54) $sum($difference(all_3_0, $product(390625, sc_7_0_5)), % 4.55/1.44 | $product(1953125, sc_7_0_0)) = 0 % 4.55/1.44 | % 4.55/1.44 | COL_REDUCE: introducing fresh symbol sc_7_0_6 defined by: % 4.55/1.44 | (55) $sum(sc_7_0_4, $product(4, sc_7_0_5)) = sc_7_0_6 % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (52), (55) imply: % 4.55/1.44 | (56) $product(2, sc_7_0_5) = $product(5, sc_7_0_6) % 4.55/1.44 | % 4.55/1.44 | SIMP: (56) implies: % 4.55/1.44 | (57) $product(2, sc_7_0_5) = $product(5, sc_7_0_6) % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (54), (57) imply: % 4.55/1.44 | (58) $sum($difference($sum(all_3_0, sc_7_0_5), $product(976565, sc_7_0_6)), % 4.55/1.44 | $product(1953125, sc_7_0_0)) = 0 % 4.55/1.44 | % 4.55/1.44 | COL_REDUCE: introducing fresh symbol sc_7_0_7 defined by: % 4.55/1.44 | (59) $difference(sc_7_0_5, $product(3, sc_7_0_6)) = sc_7_0_7 % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (57), (59) imply: % 4.55/1.44 | (60) $sum(sc_7_0_6, $product(2, sc_7_0_7)) = 0 % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (59), (60) imply: % 4.55/1.44 | (61) $sum(sc_7_0_5, $product(5, sc_7_0_7)) = 0 % 4.55/1.44 | % 4.55/1.44 | COMBINE_EQS: (58), (60), (61) imply: % 4.55/1.44 | (62) $sum($sum(all_3_0, $product(1953125, sc_7_0_7)), $product(1953125, % 4.55/1.44 | sc_7_0_0)) = 0 % 4.55/1.44 | % 4.55/1.44 | REDUCE: (12), (62) imply: % 4.55/1.44 | (63) $lesseq(0, $sum(sc_7_0_7, sc_7_0_0)) % 4.55/1.44 | % 4.55/1.44 | SIMP: (63) implies: % 4.55/1.44 | (64) $lesseq(0, $sum(sc_7_0_7, sc_7_0_0)) % 4.55/1.44 | % 4.55/1.44 | REDUCE: (11), (62) imply: % 4.55/1.44 | (65) $lesseq(sc_7_0_0, $product(-1, sc_7_0_7)) % 4.55/1.44 | % 4.55/1.44 | SIMP: (65) implies: % 4.55/1.44 | (66) $lesseq(sc_7_0_0, $product(-1, sc_7_0_7)) % 4.55/1.44 | % 4.55/1.44 | REDUCE: (10), (62) imply: % 4.55/1.44 | (67) ~ ($sum(sc_7_0_7, sc_7_0_0) = 0) % 4.55/1.44 | % 4.55/1.44 | SIMP: (67) implies: % 4.55/1.44 | (68) ~ ($sum(sc_7_0_7, sc_7_0_0) = 0) % 4.55/1.44 | % 4.55/1.44 | STRENGTHEN: (64), (68) imply: % 4.55/1.44 | (69) $lesseq(1, $sum(sc_7_0_7, sc_7_0_0)) % 4.55/1.44 | % 4.55/1.44 | COMBINE_INEQS: (66), (69) imply: % 4.55/1.44 | (70) $false % 4.55/1.44 | % 4.55/1.44 | CLOSE: (70) is inconsistent. % 4.55/1.44 | % 4.55/1.44 End of proof % 4.55/1.44 % SZS output end Proof for theBenchmark % 4.55/1.44 % 4.55/1.44 827ms %------------------------------------------------------------------------------