%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI643_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 17:48:40 EDT 2023 % Result : Theorem 4.57s 1.55s % Output : Proof 5.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : ARI643_1 : TPTP v8.1.2. Released v6.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 18:27:18 EDT 2023 % 0.12/0.33 % CPUTime : % 0.44/0.62 ________ _____ % 0.44/0.62 ___ __ \_________(_)________________________________ % 0.44/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.44/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.44/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.44/0.62 % 0.44/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.44/0.62 (2023-06-19) % 0.44/0.62 % 0.44/0.62 (c) Philipp Rümmer, 2009-2023 % 0.44/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.44/0.62 Amanda Stjerna. % 0.44/0.62 Free software under BSD-3-Clause. % 0.44/0.62 % 0.44/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.44/0.62 % 0.44/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.44/0.64 Running up to 7 provers in parallel. % 0.44/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.44/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.44/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.44/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.44/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.44/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.44/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.15/1.13 Prover 5: Preprocessing ... % 2.15/1.13 Prover 4: Preprocessing ... % 2.15/1.13 Prover 2: Preprocessing ... % 2.15/1.13 Prover 6: Preprocessing ... % 2.15/1.13 Prover 3: Preprocessing ... % 2.15/1.13 Prover 0: Preprocessing ... % 2.15/1.13 Prover 1: Preprocessing ... % 2.26/1.27 Prover 0: Constructing countermodel ... % 2.26/1.27 Prover 1: Constructing countermodel ... % 2.26/1.27 Prover 6: Constructing countermodel ... % 2.26/1.27 Prover 3: Constructing countermodel ... % 2.26/1.27 Prover 4: Constructing countermodel ... % 2.26/1.27 Prover 5: Constructing countermodel ... % 2.26/1.27 Prover 2: Constructing countermodel ... % 4.57/1.54 Prover 2: proved (896ms) % 4.57/1.54 Prover 3: proved (894ms) % 4.57/1.55 % 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.55 % 4.57/1.55 % 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.55 % 4.57/1.55 Prover 0: proved (897ms) % 4.57/1.55 % 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.55 % 4.57/1.55 Prover 6: proved (891ms) % 4.57/1.55 % 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.55 % 4.57/1.55 Prover 5: proved (890ms) % 4.57/1.55 % 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.55 % 4.57/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.57/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.57/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.57/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.57/1.56 Prover 1: Found proof (size 52) % 4.57/1.56 Prover 1: proved (908ms) % 4.57/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.57/1.57 Prover 7: Preprocessing ... % 4.57/1.58 Prover 10: Preprocessing ... % 4.57/1.58 Prover 11: Preprocessing ... % 4.57/1.58 Prover 8: Preprocessing ... % 5.03/1.59 Prover 13: Preprocessing ... % 5.03/1.60 Prover 4: Found proof (size 49) % 5.03/1.60 Prover 4: proved (949ms) % 5.03/1.60 Prover 10: Constructing countermodel ... % 5.03/1.60 Prover 7: Constructing countermodel ... % 5.03/1.60 Prover 8: Constructing countermodel ... % 5.03/1.60 Prover 10: stopped % 5.03/1.60 Prover 7: stopped % 5.03/1.60 Prover 8: stopped % 5.03/1.61 Prover 11: Constructing countermodel ... % 5.03/1.61 Prover 11: stopped % 5.03/1.62 Prover 13: Constructing countermodel ... % 5.03/1.62 Prover 13: stopped % 5.03/1.62 % 5.03/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.03/1.62 % 5.03/1.64 % SZS output start Proof for theBenchmark % 5.03/1.64 Assumptions after simplification: % 5.03/1.64 --------------------------------- % 5.03/1.64 % 5.03/1.64 (conj) % 5.03/1.65 ~ (a = 0) & ? [v0: int] : ( ~ (v0 = 0) & ? [v1: int] : ($lesseq(v1, % 5.03/1.65 0)$product(v0, a) = v1 & (($lesseq(1, $difference(v1, a)) & $lesseq(a, % 5.03/1.65 -1)) | ($lesseq(1, $sum(v1, a)) & $lesseq(1, a))))) % 5.03/1.65 % 5.03/1.65 Those formulas are unsatisfiable: % 5.03/1.65 --------------------------------- % 5.03/1.65 % 5.03/1.65 Begin of proof % 5.03/1.65 | % 5.03/1.65 | ALPHA: (conj) implies: % 5.03/1.66 | (1) ? [v0: int] : ( ~ (v0 = 0) & ? [v1: int] : ($lesseq(v1, % 5.03/1.66 | 0)$product(v0, a) = v1 & (($lesseq(1, $difference(v1, a)) & % 5.03/1.66 | $lesseq(a, -1)) | ($lesseq(1, $sum(v1, a)) & $lesseq(1, a))))) % 5.03/1.66 | % 5.03/1.66 | DELTA: instantiating (1) with fresh symbol all_3_0 gives: % 5.03/1.66 | (2) ~ (all_3_0 = 0) & ? [v0: int] : ($lesseq(v0, 0)$product(all_3_0, a) = % 5.03/1.66 | v0 & (($lesseq(1, $difference(v0, a)) & $lesseq(a, -1)) | ($lesseq(1, % 5.03/1.66 | $sum(v0, a)) & $lesseq(1, a)))) % 5.03/1.66 | % 5.03/1.66 | ALPHA: (2) implies: % 5.03/1.66 | (3) ~ (all_3_0 = 0) % 5.03/1.66 | (4) ? [v0: int] : ($lesseq(v0, 0)$product(all_3_0, a) = v0 & (($lesseq(1, % 5.03/1.66 | $difference(v0, a)) & $lesseq(a, -1)) | ($lesseq(1, $sum(v0, % 5.03/1.66 | a)) & $lesseq(1, a)))) % 5.03/1.66 | % 5.03/1.66 | DELTA: instantiating (4) with fresh symbol all_5_0 gives: % 5.03/1.67 | (5) $lesseq(all_5_0, 0)$product(all_3_0, a) = all_5_0 & (($lesseq(1, % 5.30/1.67 | $difference(all_5_0, a)) & $lesseq(a, -1)) | ($lesseq(1, % 5.30/1.67 | $sum(all_5_0, a)) & $lesseq(1, a))) % 5.30/1.67 | % 5.30/1.67 | ALPHA: (5) implies: % 5.30/1.67 | (6) $lesseq(all_5_0, 0) % 5.30/1.67 | (7) $product(all_3_0, a) = all_5_0 % 5.30/1.67 | (8) ($lesseq(1, $difference(all_5_0, a)) & $lesseq(a, -1)) | ($lesseq(1, % 5.30/1.67 | $sum(all_5_0, a)) & $lesseq(1, a)) % 5.30/1.67 | % 5.30/1.67 | BETA: splitting (8) gives: % 5.30/1.67 | % 5.30/1.67 | Case 1: % 5.30/1.67 | | % 5.30/1.67 | | (9) $lesseq(1, $difference(all_5_0, a)) & $lesseq(a, -1) % 5.30/1.67 | | % 5.30/1.67 | | ALPHA: (9) implies: % 5.30/1.67 | | (10) $lesseq(1, $difference(all_5_0, a)) % 5.30/1.67 | | % 5.30/1.67 | | COMBINE_INEQS: (6), (10) imply: % 5.31/1.67 | | (11) $lesseq(a, -1) % 5.31/1.67 | | % 5.31/1.67 | | THEORY_AXIOM GroebnerMultiplication: % 5.31/1.67 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) | % 5.31/1.67 | | ~ ($lesseq(v1, -1)) | ~ ($lesseq(v0, -1)) | ~ ($product(v1, % 5.31/1.67 | | v0) = v2)) % 5.31/1.68 | | % 5.31/1.68 | | GROUND_INST: instantiating (12) with a, all_3_0, all_5_0, simplifying with % 5.31/1.68 | | (7) gives: % 5.31/1.68 | | (13) ~ ($lesseq(all_5_0, 0) | ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(a, % 5.31/1.68 | | -1)) % 5.31/1.68 | | % 5.31/1.68 | | BETA: splitting (13) gives: % 5.31/1.68 | | % 5.31/1.68 | | Case 1: % 5.31/1.68 | | | % 5.31/1.68 | | | (14) $lesseq(1, all_5_0) % 5.31/1.68 | | | % 5.31/1.68 | | | COMBINE_INEQS: (6), (14) imply: % 5.31/1.68 | | | (15) $false % 5.31/1.68 | | | % 5.31/1.68 | | | CLOSE: (15) is inconsistent. % 5.31/1.68 | | | % 5.31/1.68 | | Case 2: % 5.31/1.68 | | | % 5.31/1.68 | | | (16) ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(a, -1)) % 5.31/1.68 | | | % 5.31/1.68 | | | BETA: splitting (16) gives: % 5.31/1.68 | | | % 5.31/1.68 | | | Case 1: % 5.31/1.68 | | | | % 5.31/1.68 | | | | (17) $lesseq(0, a) % 5.31/1.68 | | | | % 5.31/1.68 | | | | COMBINE_INEQS: (11), (17) imply: % 5.31/1.68 | | | | (18) $false % 5.31/1.68 | | | | % 5.31/1.68 | | | | CLOSE: (18) is inconsistent. % 5.31/1.68 | | | | % 5.31/1.68 | | | Case 2: % 5.31/1.68 | | | | % 5.31/1.68 | | | | (19) $lesseq(0, all_3_0) % 5.31/1.68 | | | | % 5.31/1.68 | | | | STRENGTHEN: (3), (19) imply: % 5.31/1.68 | | | | (20) $lesseq(1, all_3_0) % 5.31/1.68 | | | | % 5.31/1.68 | | | | THEORY_AXIOM GroebnerMultiplication: % 5.31/1.69 | | | | (21) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2, % 5.31/1.69 | | | | $difference($sum(v2, v1), v0))) | ~ ($lesseq(1, v1)) | ~ % 5.31/1.69 | | | | ($lesseq(v0, -1)) | ~ ($product(v1, v0) = v2)) % 5.31/1.69 | | | | % 5.31/1.69 | | | | GROUND_INST: instantiating (21) with a, all_3_0, all_5_0, simplifying % 5.31/1.69 | | | | with (7) gives: % 5.31/1.69 | | | | (22) ~ ($lesseq(2, $difference($sum(all_5_0, all_3_0), a))) | ~ % 5.31/1.69 | | | | ($lesseq(1, all_3_0)) | ~ ($lesseq(a, -1)) % 5.31/1.69 | | | | % 5.31/1.69 | | | | BETA: splitting (22) gives: % 5.31/1.69 | | | | % 5.31/1.69 | | | | Case 1: % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | (23) $lesseq(all_3_0, 0) % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | COMBINE_INEQS: (20), (23) imply: % 5.31/1.69 | | | | | (24) $false % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | CLOSE: (24) is inconsistent. % 5.31/1.69 | | | | | % 5.31/1.69 | | | | Case 2: % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | (25) ~ ($lesseq(2, $difference($sum(all_5_0, all_3_0), a))) | ~ % 5.31/1.69 | | | | | ($lesseq(a, -1)) % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | BETA: splitting (25) gives: % 5.31/1.69 | | | | | % 5.31/1.69 | | | | | Case 1: % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | (26) $lesseq(0, a) % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | COMBINE_INEQS: (11), (26) imply: % 5.31/1.69 | | | | | | (27) $false % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | CLOSE: (27) is inconsistent. % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | Case 2: % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | (28) $lesseq(-1, $sum($difference($product(-1, all_5_0), % 5.31/1.69 | | | | | | all_3_0), a)) % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | COMBINE_INEQS: (10), (28) imply: % 5.31/1.69 | | | | | | (29) $lesseq(all_3_0, 0) % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | COMBINE_INEQS: (20), (29) imply: % 5.31/1.69 | | | | | | (30) $false % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | | CLOSE: (30) is inconsistent. % 5.31/1.69 | | | | | | % 5.31/1.69 | | | | | End of split % 5.31/1.69 | | | | | % 5.31/1.69 | | | | End of split % 5.31/1.69 | | | | % 5.31/1.69 | | | End of split % 5.31/1.69 | | | % 5.31/1.69 | | End of split % 5.31/1.69 | | % 5.31/1.69 | Case 2: % 5.31/1.69 | | % 5.31/1.70 | | (31) $lesseq(1, $sum(all_5_0, a)) & $lesseq(1, a) % 5.31/1.70 | | % 5.31/1.70 | | ALPHA: (31) implies: % 5.31/1.70 | | (32) $lesseq(1, $sum(all_5_0, a)) % 5.31/1.70 | | % 5.31/1.70 | | COMBINE_INEQS: (6), (32) imply: % 5.31/1.70 | | (33) $lesseq(1, a) % 5.31/1.70 | | % 5.31/1.70 | | THEORY_AXIOM GroebnerMultiplication: % 5.31/1.70 | | (34) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) | % 5.31/1.70 | | ~ ($lesseq(1, v1)) | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) % 5.31/1.70 | | = v2)) % 5.31/1.70 | | % 5.31/1.70 | | GROUND_INST: instantiating (34) with a, all_3_0, all_5_0, simplifying with % 5.31/1.70 | | (7) gives: % 5.31/1.70 | | (35) ~ ($lesseq(all_5_0, 0) | ~ ($lesseq(1, all_3_0)) | ~ ($lesseq(1, % 5.31/1.70 | | a)) % 5.31/1.70 | | % 5.31/1.70 | | BETA: splitting (35) gives: % 5.31/1.70 | | % 5.31/1.70 | | Case 1: % 5.31/1.70 | | | % 5.31/1.70 | | | (36) $lesseq(1, all_5_0) % 5.31/1.70 | | | % 5.31/1.70 | | | COMBINE_INEQS: (6), (36) imply: % 5.31/1.70 | | | (37) $false % 5.31/1.70 | | | % 5.31/1.70 | | | CLOSE: (37) is inconsistent. % 5.31/1.70 | | | % 5.31/1.70 | | Case 2: % 5.31/1.70 | | | % 5.31/1.70 | | | (38) ~ ($lesseq(1, all_3_0)) | ~ ($lesseq(1, a)) % 5.31/1.70 | | | % 5.31/1.70 | | | BETA: splitting (38) gives: % 5.31/1.70 | | | % 5.31/1.70 | | | Case 1: % 5.31/1.70 | | | | % 5.31/1.70 | | | | (39) $lesseq(a, 0) % 5.31/1.70 | | | | % 5.31/1.70 | | | | COMBINE_INEQS: (33), (39) imply: % 5.38/1.70 | | | | (40) $false % 5.38/1.70 | | | | % 5.38/1.70 | | | | CLOSE: (40) is inconsistent. % 5.38/1.70 | | | | % 5.38/1.70 | | | Case 2: % 5.38/1.70 | | | | % 5.38/1.70 | | | | (41) $lesseq(all_3_0, 0) % 5.38/1.70 | | | | % 5.38/1.70 | | | | STRENGTHEN: (3), (41) imply: % 5.38/1.70 | | | | (42) $lesseq(all_3_0, -1) % 5.38/1.70 | | | | % 5.38/1.70 | | | | THEORY_AXIOM GroebnerMultiplication: % 5.38/1.70 | | | | (43) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2, % 5.38/1.70 | | | | $sum($difference(v2, v1), v0))) | ~ ($lesseq(v1, -1)) | % 5.38/1.70 | | | | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) = v2)) % 5.38/1.70 | | | | % 5.38/1.71 | | | | GROUND_INST: instantiating (43) with a, all_3_0, all_5_0, simplifying % 5.38/1.71 | | | | with (7) gives: % 5.38/1.71 | | | | (44) ~ ($lesseq(2, $sum($difference(all_5_0, all_3_0), a))) | ~ % 5.38/1.71 | | | | ($lesseq(all_3_0, -1)) | ~ ($lesseq(1, a)) % 5.38/1.71 | | | | % 5.38/1.71 | | | | BETA: splitting (44) gives: % 5.38/1.71 | | | | % 5.38/1.71 | | | | Case 1: % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | (45) $lesseq(0, all_3_0) % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | COMBINE_INEQS: (42), (45) imply: % 5.38/1.71 | | | | | (46) $false % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | CLOSE: (46) is inconsistent. % 5.38/1.71 | | | | | % 5.38/1.71 | | | | Case 2: % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | (47) ~ ($lesseq(2, $sum($difference(all_5_0, all_3_0), a))) | ~ % 5.38/1.71 | | | | | ($lesseq(1, a)) % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | BETA: splitting (47) gives: % 5.38/1.71 | | | | | % 5.38/1.71 | | | | | Case 1: % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | (48) $lesseq(a, 0) % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | COMBINE_INEQS: (33), (48) imply: % 5.38/1.71 | | | | | | (49) $false % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | CLOSE: (49) is inconsistent. % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | Case 2: % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | (50) $lesseq(-1, $difference($difference(all_3_0, all_5_0), a)) % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | COMBINE_INEQS: (32), (50) imply: % 5.38/1.71 | | | | | | (51) $lesseq(0, all_3_0) % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | COMBINE_INEQS: (42), (51) imply: % 5.38/1.71 | | | | | | (52) $false % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | | CLOSE: (52) is inconsistent. % 5.38/1.71 | | | | | | % 5.38/1.71 | | | | | End of split % 5.38/1.71 | | | | | % 5.38/1.71 | | | | End of split % 5.38/1.71 | | | | % 5.38/1.71 | | | End of split % 5.38/1.71 | | | % 5.38/1.71 | | End of split % 5.38/1.71 | | % 5.38/1.71 | End of split % 5.38/1.71 | % 5.38/1.71 End of proof % 5.38/1.71 % SZS output end Proof for theBenchmark % 5.38/1.71 % 5.38/1.71 1085ms %------------------------------------------------------------------------------