%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI649_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 : n021.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 17:48:41 EDT 2023 % Result : Theorem 4.79s 1.45s % Output : Proof 5.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : ARI649_1 : TPTP v8.1.2. Released v6.3.0. % 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 18:00:14 EDT 2023 % 0.14/0.35 % CPUTime : % 0.65/0.66 ________ _____ % 0.65/0.66 ___ __ \_________(_)________________________________ % 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.66 % 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.66 (2023-06-19) % 0.65/0.66 % 0.65/0.66 (c) Philipp Rümmer, 2009-2023 % 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.66 Amanda Stjerna. % 0.65/0.66 Free software under BSD-3-Clause. % 0.65/0.66 % 0.65/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.66 % 0.65/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.68 Running up to 7 provers in parallel. % 0.65/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.26/1.05 Prover 4: Preprocessing ... % 2.26/1.05 Prover 5: Preprocessing ... % 2.26/1.05 Prover 2: Preprocessing ... % 2.26/1.05 Prover 0: Preprocessing ... % 2.26/1.05 Prover 3: Preprocessing ... % 2.26/1.05 Prover 1: Preprocessing ... % 2.26/1.05 Prover 6: Preprocessing ... % 2.26/1.11 Prover 6: Constructing countermodel ... % 2.26/1.11 Prover 3: Constructing countermodel ... % 2.26/1.11 Prover 2: Constructing countermodel ... % 2.26/1.11 Prover 4: Constructing countermodel ... % 2.26/1.11 Prover 1: Constructing countermodel ... % 2.26/1.11 Prover 5: Constructing countermodel ... % 2.26/1.11 Prover 0: Constructing countermodel ... % 4.79/1.44 Prover 2: proved (754ms) % 4.79/1.45 % 4.79/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.79/1.45 % 4.79/1.45 Prover 5: proved (753ms) % 4.79/1.45 % 4.79/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.79/1.45 % 4.79/1.45 Prover 3: stopped % 4.79/1.45 Prover 0: stopped % 4.79/1.45 Prover 6: stopped % 4.79/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.79/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.79/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.79/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.79/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.95/1.47 Prover 13: Preprocessing ... % 4.95/1.47 Prover 11: Preprocessing ... % 4.95/1.47 Prover 8: Preprocessing ... % 4.95/1.47 Prover 10: Preprocessing ... % 4.95/1.48 Prover 7: Preprocessing ... % 4.95/1.48 Prover 8: Constructing countermodel ... % 4.95/1.48 Prover 13: Constructing countermodel ... % 4.95/1.48 Prover 11: Constructing countermodel ... % 4.95/1.49 Prover 7: Constructing countermodel ... % 4.95/1.49 Prover 10: Constructing countermodel ... % 4.95/1.52 Prover 4: Found proof (size 126) % 4.95/1.52 Prover 4: proved (825ms) % 5.38/1.52 Prover 11: stopped % 5.38/1.52 Prover 7: stopped % 5.38/1.52 Prover 1: Found proof (size 126) % 5.38/1.52 Prover 1: proved (835ms) % 5.38/1.52 Prover 8: stopped % 5.38/1.52 Prover 10: stopped % 5.38/1.53 Prover 13: stopped % 5.38/1.53 % 5.38/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.38/1.53 % 5.38/1.54 % SZS output start Proof for theBenchmark % 5.38/1.55 Assumptions after simplification: % 5.38/1.55 --------------------------------- % 5.38/1.55 % 5.38/1.55 (conj) % 5.54/1.55 $lesseq(a, -1) % 5.54/1.55 % 5.54/1.55 (conj_001) % 5.54/1.56 $product(a, a) = 25 % 5.54/1.56 % 5.54/1.56 (conj_002) % 5.54/1.56 ? [v0: int] : ($product(v0, b) = -125 & $product(b, b) = v0) % 5.54/1.56 % 5.54/1.56 (conj_003) % 5.54/1.56 ~ (b = a) % 5.54/1.56 % 5.54/1.56 Those formulas are unsatisfiable: % 5.54/1.56 --------------------------------- % 5.54/1.56 % 5.54/1.56 Begin of proof % 5.54/1.56 | % 5.54/1.56 | DELTA: instantiating (conj_002) with fresh symbol all_4_0 gives: % 5.54/1.56 | (1) $product(all_4_0, b) = -125 & $product(b, b) = all_4_0 % 5.54/1.56 | % 5.54/1.56 | ALPHA: (1) implies: % 5.54/1.56 | (2) $product(b, b) = all_4_0 % 5.54/1.56 | (3) $product(all_4_0, b) = -125 % 5.54/1.56 | % 5.54/1.56 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.56 | (4) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 11)) | ~ ($product(v1, % 5.54/1.56 | v0) = -125) | ~ ($product(v0, v0) = v1)) % 5.54/1.56 | % 5.54/1.57 | GROUND_INST: instantiating (4) with b, all_4_0, simplifying with (2), (3) % 5.54/1.57 | gives: % 5.54/1.57 | (5) $lesseq(12, all_4_0) % 5.54/1.57 | % 5.54/1.57 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.57 | (6) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(122, v1)) | ~ ($product(v1, % 5.54/1.57 | v0) = -125) | ~ ($product(v0, v0) = v1)) % 5.54/1.57 | % 5.54/1.57 | GROUND_INST: instantiating (6) with b, all_4_0, simplifying with (2), (3) % 5.54/1.57 | gives: % 5.54/1.57 | (7) $lesseq(all_4_0, 121) % 5.54/1.57 | % 5.54/1.57 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.57 | (8) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v0, -12)) | ~ ($product(v1, % 5.54/1.57 | v0) = -125) | ~ ($product(v0, v0) = v1)) % 5.54/1.57 | % 5.54/1.57 | GROUND_INST: instantiating (8) with b, all_4_0, simplifying with (2), (3) % 5.54/1.57 | gives: % 5.54/1.57 | (9) $lesseq(-11, b) % 5.54/1.57 | % 5.54/1.57 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.57 | (10) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ ($product(v1, % 5.54/1.57 | v0) = -125) | ~ ($product(v0, v0) = v1)) % 5.54/1.57 | % 5.54/1.57 | GROUND_INST: instantiating (10) with b, all_4_0, simplifying with (2), (3) % 5.54/1.57 | gives: % 5.54/1.57 | (11) $lesseq(b, -1) % 5.54/1.57 | % 5.54/1.57 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.57 | (12) ! [v0: int] : ( ~ ($lesseq(v0, -6)) | ~ ($product(v0, v0) = 25)) % 5.54/1.57 | % 5.54/1.57 | GROUND_INST: instantiating (12) with a, simplifying with (conj_001) gives: % 5.54/1.57 | (13) $lesseq(-5, a) % 5.54/1.57 | % 5.54/1.57 | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.57 | (14) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 121)) | ~ % 5.54/1.57 | ($lesseq(133, $difference(v1, $product(11, v0)))) | ~ ($lesseq(-11, % 5.54/1.57 | v0)) | ~ ($product(v1, v0) = -125)) % 5.54/1.57 | % 5.54/1.57 | GROUND_INST: instantiating (14) with b, all_4_0, simplifying with (3) gives: % 5.54/1.57 | (15) ~ ($lesseq(all_4_0, 121)) | ~ ($lesseq(133, $difference(all_4_0, % 5.54/1.57 | $product(11, b)))) | ~ ($lesseq(-11, b)) % 5.54/1.57 | % 5.54/1.57 | BETA: splitting (15) gives: % 5.54/1.57 | % 5.54/1.57 | Case 1: % 5.54/1.57 | | % 5.54/1.57 | | (16) $lesseq(122, all_4_0) % 5.54/1.57 | | % 5.54/1.57 | | COMBINE_INEQS: (7), (16) imply: % 5.54/1.57 | | (17) $false % 5.54/1.57 | | % 5.54/1.57 | | CLOSE: (17) is inconsistent. % 5.54/1.57 | | % 5.54/1.57 | Case 2: % 5.54/1.57 | | % 5.54/1.57 | | (18) ~ ($lesseq(133, $difference(all_4_0, $product(11, b)))) | ~ % 5.54/1.57 | | ($lesseq(-11, b)) % 5.54/1.57 | | % 5.54/1.58 | | BETA: splitting (18) gives: % 5.54/1.58 | | % 5.54/1.58 | | Case 1: % 5.54/1.58 | | | % 5.54/1.58 | | | (19) $lesseq(b, -12) % 5.54/1.58 | | | % 5.54/1.58 | | | COMBINE_INEQS: (9), (19) imply: % 5.54/1.58 | | | (20) $false % 5.54/1.58 | | | % 5.54/1.58 | | | CLOSE: (20) is inconsistent. % 5.54/1.58 | | | % 5.54/1.58 | | Case 2: % 5.54/1.58 | | | % 5.54/1.58 | | | (21) $lesseq(-132, $difference($product(11, b), all_4_0)) % 5.54/1.58 | | | % 5.54/1.58 | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.58 | | | (22) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-256, % 5.54/1.58 | | | $difference($product(12, v0), $product(11, v1)))) | ~ % 5.54/1.58 | | | ($lesseq(12, v1)) | ~ ($product(v1, v0) = -125)) % 5.54/1.58 | | | % 5.54/1.58 | | | GROUND_INST: instantiating (22) with b, all_4_0, simplifying with (3) % 5.54/1.58 | | | gives: % 5.54/1.58 | | | (23) ~ ($lesseq(-256, $difference($product(12, b), $product(11, % 5.54/1.58 | | | all_4_0)))) | ~ ($lesseq(12, all_4_0)) % 5.54/1.58 | | | % 5.54/1.58 | | | BETA: splitting (23) gives: % 5.54/1.58 | | | % 5.54/1.58 | | | Case 1: % 5.54/1.58 | | | | % 5.54/1.58 | | | | (24) $lesseq(all_4_0, 11) % 5.54/1.58 | | | | % 5.54/1.58 | | | | COMBINE_INEQS: (5), (24) imply: % 5.54/1.58 | | | | (25) $false % 5.54/1.58 | | | | % 5.54/1.58 | | | | CLOSE: (25) is inconsistent. % 5.54/1.58 | | | | % 5.54/1.58 | | | Case 2: % 5.54/1.58 | | | | % 5.54/1.58 | | | | (26) ~ ($lesseq(-256, $difference($product(12, b), $product(11, % 5.54/1.58 | | | | all_4_0)))) | ~ ($lesseq(-11, b)) % 5.54/1.58 | | | | % 5.54/1.58 | | | | BETA: splitting (26) gives: % 5.54/1.58 | | | | % 5.54/1.58 | | | | Case 1: % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | (27) $lesseq(b, -12) % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | COMBINE_INEQS: (9), (27) imply: % 5.54/1.58 | | | | | (28) $false % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | CLOSE: (28) is inconsistent. % 5.54/1.58 | | | | | % 5.54/1.58 | | | | Case 2: % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | (29) $lesseq(257, $difference($product(11, all_4_0), $product(12, % 5.54/1.58 | | | | | b))) % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.58 | | | | | (30) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, % 5.54/1.58 | | | | | $difference($product(-1, v1), $product(2, v0)))) | ~ % 5.54/1.58 | | | | | ($lesseq(v0, -1)) | ~ ($product(v0, v0) = v1)) % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | GROUND_INST: instantiating (30) with b, all_4_0, simplifying with (2) % 5.54/1.58 | | | | | gives: % 5.54/1.58 | | | | | (31) ~ ($lesseq(2, $difference($product(-1, all_4_0), $product(2, % 5.54/1.58 | | | | | b)))) | ~ ($lesseq(b, -1)) % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | BETA: splitting (31) gives: % 5.54/1.58 | | | | | % 5.54/1.58 | | | | | Case 1: % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | (32) $lesseq(0, b) % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | COMBINE_INEQS: (11), (32) imply: % 5.54/1.58 | | | | | | (33) $false % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | CLOSE: (33) is inconsistent. % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | Case 2: % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | (34) $lesseq(-1, $sum(all_4_0, $product(2, b))) % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.58 | | | | | | (35) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-10, $sum(v1, % 5.54/1.58 | | | | | | $product(12, v0)))) | ~ ($lesseq(v0, -1)) | ~ % 5.54/1.58 | | | | | | ($lesseq(-11, v0)) | ~ ($product(v0, v0) = v1)) % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | GROUND_INST: instantiating (35) with b, all_4_0, simplifying with % 5.54/1.58 | | | | | | (2) gives: % 5.54/1.58 | | | | | | (36) ~ ($lesseq(-10, $sum(all_4_0, $product(12, b)))) | ~ % 5.54/1.58 | | | | | | ($lesseq(b, -1)) | ~ ($lesseq(-11, b)) % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | BETA: splitting (36) gives: % 5.54/1.58 | | | | | | % 5.54/1.58 | | | | | | Case 1: % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | (37) $lesseq(0, b) % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | COMBINE_INEQS: (11), (37) imply: % 5.54/1.58 | | | | | | | (38) $false % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | CLOSE: (38) is inconsistent. % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | Case 2: % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | (39) ~ ($lesseq(-10, $sum(all_4_0, $product(12, b)))) | ~ % 5.54/1.58 | | | | | | | ($lesseq(-11, b)) % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | BETA: splitting (39) gives: % 5.54/1.58 | | | | | | | % 5.54/1.58 | | | | | | | Case 1: % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | (40) $lesseq(b, -12) % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | COMBINE_INEQS: (9), (40) imply: % 5.54/1.58 | | | | | | | | (41) $false % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | CLOSE: (41) is inconsistent. % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | Case 2: % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | (42) $lesseq(11, $difference($product(-1, all_4_0), % 5.54/1.58 | | | | | | | | $product(12, b))) % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.58 | | | | | | | | (43) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(122, % 5.54/1.58 | | | | | | | | $difference($product(-1, v1), $product(22, v0)))) % 5.54/1.58 | | | | | | | | | ~ ($lesseq(-11, v0)) | ~ ($product(v0, v0) = v1)) % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | GROUND_INST: instantiating (43) with b, all_4_0, simplifying % 5.54/1.58 | | | | | | | | with (2) gives: % 5.54/1.58 | | | | | | | | (44) ~ ($lesseq(122, $difference($product(-1, all_4_0), % 5.54/1.58 | | | | | | | | $product(22, b)))) | ~ ($lesseq(-11, b)) % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | BETA: splitting (44) gives: % 5.54/1.58 | | | | | | | | % 5.54/1.58 | | | | | | | | Case 1: % 5.54/1.58 | | | | | | | | | % 5.54/1.58 | | | | | | | | | (45) $lesseq(b, -12) % 5.54/1.58 | | | | | | | | | % 5.54/1.59 | | | | | | | | | COMBINE_INEQS: (9), (45) imply: % 5.54/1.59 | | | | | | | | | (46) $false % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | CLOSE: (46) is inconsistent. % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | Case 2: % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | (47) $lesseq(-121, $sum(all_4_0, $product(22, b))) % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.59 | | | | | | | | | (48) ! [v0: int] : ( ~ ($lesseq(v0, -1)) | ~ ($lesseq(-4, % 5.54/1.59 | | | | | | | | | v0)) | ~ ($product(v0, v0) = 25)) % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | GROUND_INST: instantiating (48) with a, simplifying with % 5.54/1.59 | | | | | | | | | (conj_001) gives: % 5.54/1.59 | | | | | | | | | (49) ~ ($lesseq(a, -1)) | ~ ($lesseq(-4, a)) % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | BETA: splitting (49) gives: % 5.54/1.59 | | | | | | | | | % 5.54/1.59 | | | | | | | | | Case 1: % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | (50) $lesseq(0, a) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | COMBINE_INEQS: (50), (conj) imply: % 5.54/1.59 | | | | | | | | | | (51) $false % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | CLOSE: (51) is inconsistent. % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | Case 2: % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | (52) $lesseq(a, -5) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | ANTI_SYMM: (13), (52) imply: % 5.54/1.59 | | | | | | | | | | (53) a = -5 % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | COMBINE_INEQS: (21), (47) imply: % 5.54/1.59 | | | | | | | | | | (54) $lesseq(-7, b) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | SIMP: (54) implies: % 5.54/1.59 | | | | | | | | | | (55) $lesseq(-7, b) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | COMBINE_INEQS: (29), (55) imply: % 5.54/1.59 | | | | | | | | | | (56) $lesseq(16, all_4_0) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | SIMP: (56) implies: % 5.54/1.59 | | | | | | | | | | (57) $lesseq(16, all_4_0) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | COMBINE_INEQS: (42), (57) imply: % 5.54/1.59 | | | | | | | | | | (58) $lesseq(b, -3) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | SIMP: (58) implies: % 5.54/1.59 | | | | | | | | | | (59) $lesseq(b, -3) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | REDUCE: (53), (conj_003) imply: % 5.54/1.59 | | | | | | | | | | (60) ~ (b = -5) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.59 | | | | | | | | | | (61) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 20)) % 5.54/1.59 | | | | | | | | | | | ~ ($lesseq(v0, -3)) | ~ ($lesseq(-7, v0)) | ~ % 5.54/1.59 | | | | | | | | | | ($product(v1, v0) = -125) | ~ ($product(v0, v0) = % 5.54/1.59 | | | | | | | | | | v1)) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | GROUND_INST: instantiating (61) with b, all_4_0, simplifying % 5.54/1.59 | | | | | | | | | | with (2), (3) gives: % 5.54/1.59 | | | | | | | | | | (62) ~ ($lesseq(all_4_0, 20)) | ~ ($lesseq(b, -3)) | ~ % 5.54/1.59 | | | | | | | | | | ($lesseq(-7, b)) % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | BETA: splitting (62) gives: % 5.54/1.59 | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | Case 1: % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | (63) $lesseq(-2, b) % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | COMBINE_INEQS: (59), (63) imply: % 5.54/1.59 | | | | | | | | | | | (64) $false % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | CLOSE: (64) is inconsistent. % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | Case 2: % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | (65) ~ ($lesseq(all_4_0, 20)) | ~ ($lesseq(-7, b)) % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | BETA: splitting (65) gives: % 5.54/1.59 | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | Case 1: % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | (66) $lesseq(b, -8) % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | COMBINE_INEQS: (55), (66) imply: % 5.54/1.59 | | | | | | | | | | | | (67) $false % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | CLOSE: (67) is inconsistent. % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | Case 2: % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | (68) $lesseq(21, all_4_0) % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.59 | | | | | | | | | | | | (69) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(37, % 5.54/1.59 | | | | | | | | | | | | v1)) | ~ ($lesseq(v0, -3)) | ~ % 5.54/1.59 | | | | | | | | | | | | ($lesseq(-7, v0)) | ~ ($product(v1, v0) = -125) % 5.54/1.59 | | | | | | | | | | | | | ~ ($product(v0, v0) = v1)) % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | GROUND_INST: instantiating (69) with b, all_4_0, simplifying % 5.54/1.59 | | | | | | | | | | | | with (2), (3) gives: % 5.54/1.59 | | | | | | | | | | | | (70) ~ ($lesseq(37, all_4_0)) | ~ ($lesseq(b, -3)) | % 5.54/1.59 | | | | | | | | | | | | ~ ($lesseq(-7, b)) % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | BETA: splitting (70) gives: % 5.54/1.59 | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | Case 1: % 5.54/1.59 | | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | | (71) $lesseq(-2, b) % 5.54/1.59 | | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | | COMBINE_INEQS: (59), (71) imply: % 5.54/1.59 | | | | | | | | | | | | | (72) $false % 5.54/1.59 | | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | | CLOSE: (72) is inconsistent. % 5.54/1.59 | | | | | | | | | | | | | % 5.54/1.59 | | | | | | | | | | | | Case 2: % 5.54/1.59 | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | (73) ~ ($lesseq(37, all_4_0)) | ~ ($lesseq(-7, b)) % 5.54/1.60 | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | BETA: splitting (73) gives: % 5.54/1.60 | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | (74) $lesseq(b, -8) % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | COMBINE_INEQS: (55), (74) imply: % 5.54/1.60 | | | | | | | | | | | | | | (75) $false % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | CLOSE: (75) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | (76) $lesseq(all_4_0, 36) % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.60 | | | | | | | | | | | | | | (77) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v0, % 5.54/1.60 | | | | | | | | | | | | | | -7)) | ~ ($lesseq(-7, v0)) | ~ % 5.54/1.60 | | | | | | | | | | | | | | ($product(v1, v0) = -125) | ~ ($product(v0, v0) % 5.54/1.60 | | | | | | | | | | | | | | = v1)) % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (77) with b, all_4_0, simplifying % 5.54/1.60 | | | | | | | | | | | | | | with (2), (3) gives: % 5.54/1.60 | | | | | | | | | | | | | | (78) ~ ($lesseq(b, -7)) | ~ ($lesseq(-7, b)) % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | BETA: splitting (78) gives: % 5.54/1.60 | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | (79) $lesseq(-2, b) % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | COMBINE_INEQS: (59), (79) imply: % 5.54/1.60 | | | | | | | | | | | | | | | (80) $false % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | CLOSE: (80) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 5.54/1.60 | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | (81) $lesseq(b, -8) % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | COMBINE_INEQS: (55), (81) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | (82) $false % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | CLOSE: (82) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | (83) $lesseq(-6, b) % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.60 | | | | | | | | | | | | | | | | (84) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-39, % 5.54/1.60 | | | | | | | | | | | | | | | | $difference($product(-3, v1), $product(5, % 5.54/1.60 | | | | | | | | | | | | | | | | v0)))) | ~ ($lesseq(-1, $sum(v1, % 5.54/1.60 | | | | | | | | | | | | | | | | $product(2, v0)))) | ~ ($lesseq(-7, v0)) % 5.54/1.60 | | | | | | | | | | | | | | | | | ~ ($product(v1, v0) = -125) | ~ % 5.54/1.60 | | | | | | | | | | | | | | | | ($product(v0, v0) = v1)) % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (84) with b, all_4_0, simplifying % 5.54/1.60 | | | | | | | | | | | | | | | | with (2), (3) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | (85) ~ ($lesseq(-39, $difference($product(-3, % 5.54/1.60 | | | | | | | | | | | | | | | | all_4_0), $product(5, b)))) | ~ % 5.54/1.60 | | | | | | | | | | | | | | | | ($lesseq(-1, $sum(all_4_0, $product(2, b)))) | ~ % 5.54/1.60 | | | | | | | | | | | | | | | | ($lesseq(-7, b)) % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | (86) $lesseq(2, $difference($product(-1, all_4_0), % 5.54/1.60 | | | | | | | | | | | | | | | | | $product(2, b))) % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (34), (86) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | | (87) $false % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | CLOSE: (87) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | (88) ~ ($lesseq(-39, $difference($product(-3, % 5.54/1.60 | | | | | | | | | | | | | | | | | all_4_0), $product(5, b)))) | ~ % 5.54/1.60 | | | | | | | | | | | | | | | | | ($lesseq(-7, b)) % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | (89) $lesseq(b, -8) % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (55), (89) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | | | (90) $false % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | CLOSE: (90) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | (91) $lesseq(40, $sum($product(3, all_4_0), $product(5, % 5.54/1.60 | | | | | | | | | | | | | | | | | | b))) % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (42), (68) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | | | (92) $lesseq(b, -3) % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.60 | | | | | | | | | | | | | | | | | | (93) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-614, % 5.54/1.60 | | | | | | | | | | | | | | | | | | $difference($product(10, v0), $product(23, % 5.54/1.60 | | | | | | | | | | | | | | | | | | v1)))) | ~ ($lesseq(40, % 5.54/1.60 | | | | | | | | | | | | | | | | | | $sum($product(3, v1), $product(5, v0)))) | % 5.54/1.60 | | | | | | | | | | | | | | | | | | ~ ($product(v1, v0) = -125) | ~ ($product(v0, % 5.54/1.60 | | | | | | | | | | | | | | | | | | v0) = v1)) % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (93) with b, all_4_0, simplifying % 5.54/1.60 | | | | | | | | | | | | | | | | | | with (2), (3) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | | | (94) ~ ($lesseq(-614, $difference($product(10, b), % 5.54/1.60 | | | | | | | | | | | | | | | | | | $product(23, all_4_0)))) | ~ ($lesseq(40, % 5.54/1.60 | | | | | | | | | | | | | | | | | | $sum($product(3, all_4_0), $product(5, b)))) % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | (95) $lesseq(-39, $difference($product(-3, all_4_0), % 5.54/1.60 | | | | | | | | | | | | | | | | | | | $product(5, b))) % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (91), (95) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | (96) $false % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | CLOSE: (96) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | (97) ~ ($lesseq(-614, $difference($product(10, b), % 5.54/1.60 | | | | | | | | | | | | | | | | | | | $product(23, all_4_0)))) | ~ ($lesseq(-6, % 5.54/1.60 | | | | | | | | | | | | | | | | | | | b)) % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | (98) $lesseq(b, -7) % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (83), (98) imply: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | (99) $false % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | CLOSE: (99) is inconsistent. % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | % 5.54/1.60 | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.60 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | (100) $lesseq(615, $difference($product(23, all_4_0), % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | $product(10, b))) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | (101) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-77, % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | $difference($product(12, v0), v1))) | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | ($lesseq(v1, 36)) | ~ ($lesseq(v0, -3)) | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | ($product(v1, v0) = -125)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with b, all_4_0, simplifying % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | with (3) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | (102) ~ ($lesseq(-77, $difference($product(12, b), % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | all_4_0))) | ~ ($lesseq(all_4_0, 36)) | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | ($lesseq(b, -3)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | (103) $lesseq(37, all_4_0) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (76), (103) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | (104) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | CLOSE: (104) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | (105) ~ ($lesseq(-77, $difference($product(12, b), % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | all_4_0))) | ~ ($lesseq(b, -3)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (106) $lesseq(-2, b) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (59), (106) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (107) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (108) $lesseq(78, $difference(all_4_0, $product(12, b))) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (83), (100) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (109) $lesseq(25, all_4_0) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | SIMP: (109) implies: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (110) $lesseq(25, all_4_0) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (76), (108) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (111) $lesseq(b, -4) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | SIMP: (111) implies: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (112) $lesseq(b, -4) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (113) ! [v0: int] : ! [v1: int] : (v0 = -5 | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v1, 36)) | ~ ($lesseq(25, v1)) | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v0, -4)) | ~ ($product(v1, v0) = -125) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | ~ ($product(v0, v0) = v1)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (113) with b, all_4_0, simplifying % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | with (2), (3) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | (114) b = -5 | ~ ($lesseq(all_4_0, 36)) | ~ % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(25, all_4_0)) | ~ ($lesseq(b, -4)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | (115) ~ ($lesseq(all_4_0, 36)) | ~ ($lesseq(b, -4)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (116) $lesseq(37, all_4_0) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (76), (116) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (117) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (118) $lesseq(-3, b) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (112), (118) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (119) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | (120) b = -5 | ~ ($lesseq(25, all_4_0)) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (121) $lesseq(all_4_0, 24) % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (110), (121) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (122) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (123) b = -5 % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (123) imply: % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | (124) $false % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | | % 5.54/1.61 | | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | | % 5.54/1.61 | | | | | | | | | End of split % 5.54/1.61 | | | | | | | | | % 5.54/1.61 | | | | | | | | End of split % 5.54/1.61 | | | | | | | | % 5.54/1.61 | | | | | | | End of split % 5.54/1.61 | | | | | | | % 5.54/1.61 | | | | | | End of split % 5.54/1.61 | | | | | | % 5.54/1.61 | | | | | End of split % 5.54/1.61 | | | | | % 5.54/1.61 | | | | End of split % 5.54/1.61 | | | | % 5.54/1.61 | | | End of split % 5.54/1.61 | | | % 5.54/1.61 | | End of split % 5.54/1.61 | | % 5.54/1.61 | End of split % 5.54/1.61 | % 5.54/1.61 End of proof % 5.54/1.61 % SZS output end Proof for theBenchmark % 5.54/1.61 % 5.54/1.61 952ms %------------------------------------------------------------------------------