%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI662_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 : n012.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 17:48:44 EDT 2023 % Result : Theorem 5.92s 1.65s % Output : Proof 7.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI662_1 : TPTP v8.1.2. Released v6.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 18:29:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.65 ________ _____ % 0.21/0.65 ___ __ \_________(_)________________________________ % 0.21/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.65 % 0.21/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.65 (2023-06-19) % 0.21/0.65 % 0.21/0.65 (c) Philipp Rümmer, 2009-2023 % 0.21/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.65 Amanda Stjerna. % 0.21/0.65 Free software under BSD-3-Clause. % 0.21/0.65 % 0.21/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.65 % 0.21/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.67 Running up to 7 provers in parallel. % 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.97/1.09 Prover 3: Preprocessing ... % 1.97/1.09 Prover 5: Preprocessing ... % 1.97/1.09 Prover 1: Preprocessing ... % 1.97/1.09 Prover 4: Preprocessing ... % 1.97/1.09 Prover 6: Preprocessing ... % 1.97/1.09 Prover 0: Preprocessing ... % 1.97/1.09 Prover 2: Preprocessing ... % 2.46/1.16 Prover 2: Constructing countermodel ... % 2.46/1.16 Prover 6: Constructing countermodel ... % 2.46/1.16 Prover 4: Constructing countermodel ... % 2.46/1.16 Prover 1: Constructing countermodel ... % 2.46/1.16 Prover 0: Constructing countermodel ... % 2.46/1.16 Prover 3: Constructing countermodel ... % 2.46/1.16 Prover 5: Constructing countermodel ... % 5.92/1.65 Prover 0: proved (973ms) % 5.92/1.65 % 5.92/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.92/1.65 % 5.92/1.65 Prover 3: stopped % 5.92/1.65 Prover 2: stopped % 6.35/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.35/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.35/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.35/1.66 Prover 6: stopped % 6.35/1.67 Prover 5: stopped % 6.35/1.67 Prover 10: Preprocessing ... % 6.35/1.67 Prover 8: Preprocessing ... % 6.35/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.35/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.35/1.68 Prover 7: Preprocessing ... % 6.35/1.68 Prover 10: Constructing countermodel ... % 6.35/1.68 Prover 11: Preprocessing ... % 6.35/1.68 Prover 8: Constructing countermodel ... % 6.35/1.68 Prover 13: Preprocessing ... % 6.35/1.68 Prover 7: Constructing countermodel ... % 6.35/1.69 Prover 11: Constructing countermodel ... % 6.35/1.71 Prover 13: Constructing countermodel ... % 6.35/1.75 Prover 1: Found proof (size 108) % 6.35/1.75 Prover 1: proved (1078ms) % 6.35/1.75 Prover 13: stopped % 6.35/1.75 Prover 10: stopped % 6.35/1.75 Prover 4: Found proof (size 108) % 6.35/1.75 Prover 4: proved (1076ms) % 7.10/1.75 Prover 7: stopped % 7.10/1.75 Prover 8: stopped % 7.10/1.76 Prover 11: stopped % 7.10/1.76 % 7.10/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.10/1.76 % 7.10/1.76 % SZS output start Proof for theBenchmark % 7.10/1.77 Assumptions after simplification: % 7.10/1.77 --------------------------------- % 7.10/1.77 % 7.10/1.77 (conj) % 7.10/1.78 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? % 7.10/1.78 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : % 7.10/1.78 ($product(v8, a) = v9 & $product(v7, a) = v8 & $product(v6, a) = v7 & % 7.10/1.78 $product(v5, a) = v6 & $product(v4, a) = v5 & $product(v3, a) = v4 & % 7.10/1.78 $product(v2, a) = v3 & $product(v1, a) = v2 & $product(v0, a) = v1 & % 7.10/1.78 $product(a, a) = v0 & (($lesseq(v9, 999) & $lesseq(2, a)) | ($lesseq(1000, % 7.10/1.78 v9) & $lesseq(a, 1)))) % 7.10/1.78 % 7.10/1.78 Those formulas are unsatisfiable: % 7.10/1.78 --------------------------------- % 7.10/1.78 % 7.10/1.78 Begin of proof % 7.10/1.78 | % 7.10/1.78 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2, % 7.10/1.78 | all_2_3, all_2_4, all_2_5, all_2_6, all_2_7, all_2_8, all_2_9 gives: % 7.10/1.78 | (1) $product(all_2_1, a) = all_2_0 & $product(all_2_2, a) = all_2_1 & % 7.10/1.78 | $product(all_2_3, a) = all_2_2 & $product(all_2_4, a) = all_2_3 & % 7.10/1.78 | $product(all_2_5, a) = all_2_4 & $product(all_2_6, a) = all_2_5 & % 7.10/1.78 | $product(all_2_7, a) = all_2_6 & $product(all_2_8, a) = all_2_7 & % 7.10/1.78 | $product(all_2_9, a) = all_2_8 & $product(a, a) = all_2_9 & % 7.10/1.78 | (($lesseq(all_2_0, 999) & $lesseq(2, a)) | ($lesseq(1000, all_2_0) & % 7.10/1.78 | $lesseq(a, 1))) % 7.10/1.78 | % 7.10/1.78 | ALPHA: (1) implies: % 7.10/1.78 | (2) $product(a, a) = all_2_9 % 7.10/1.78 | (3) $product(all_2_9, a) = all_2_8 % 7.10/1.78 | (4) $product(all_2_8, a) = all_2_7 % 7.10/1.79 | (5) $product(all_2_7, a) = all_2_6 % 7.10/1.79 | (6) $product(all_2_6, a) = all_2_5 % 7.10/1.79 | (7) $product(all_2_5, a) = all_2_4 % 7.10/1.79 | (8) $product(all_2_4, a) = all_2_3 % 7.10/1.79 | (9) $product(all_2_3, a) = all_2_2 % 7.10/1.79 | (10) $product(all_2_2, a) = all_2_1 % 7.10/1.79 | (11) $product(all_2_1, a) = all_2_0 % 7.10/1.79 | (12) ($lesseq(all_2_0, 999) & $lesseq(2, a)) | ($lesseq(1000, all_2_0) & % 7.10/1.79 | $lesseq(a, 1)) % 7.10/1.79 | % 7.10/1.79 | THEORY_AXIOM GroebnerMultiplication: % 7.10/1.79 | (13) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ ($product(v0, % 7.10/1.79 | v0) = v1)) % 7.10/1.79 | % 7.10/1.79 | GROUND_INST: instantiating (13) with a, all_2_9, simplifying with (2) gives: % 7.10/1.79 | (14) $lesseq(0, all_2_9) % 7.10/1.79 | % 7.10/1.79 | BETA: splitting (12) gives: % 7.10/1.79 | % 7.10/1.79 | Case 1: % 7.10/1.79 | | % 7.10/1.79 | | (15) $lesseq(all_2_0, 999) & $lesseq(2, a) % 7.10/1.79 | | % 7.10/1.79 | | ALPHA: (15) implies: % 7.10/1.79 | | (16) $lesseq(2, a) % 7.10/1.79 | | (17) $lesseq(all_2_0, 999) % 7.10/1.79 | | % 7.10/1.79 | | THEORY_AXIOM GroebnerMultiplication: % 7.10/1.79 | | (18) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 7.10/1.79 | | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : % 7.10/1.79 | | ! [v9: int] : ( ~ ($lesseq(v9, 999)) | ~ ($lesseq(5, v1)) | ~ % 7.10/1.79 | | ($lesseq(2, v0)) | ~ ($product(v8, v0) = v9) | ~ ($product(v7, % 7.10/1.79 | | v0) = v8) | ~ ($product(v6, v0) = v7) | ~ ($product(v5, v0) % 7.10/1.79 | | = v6) | ~ ($product(v4, v0) = v5) | ~ ($product(v3, v0) = v4) % 7.10/1.79 | | | ~ ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 7.10/1.79 | | % 7.10/1.79 | | GROUND_INST: instantiating (18) with a, all_2_8, all_2_7, all_2_6, all_2_5, % 7.10/1.79 | | all_2_4, all_2_3, all_2_2, all_2_1, all_2_0, simplifying with % 7.10/1.79 | | (4), (5), (6), (7), (8), (9), (10), (11) gives: % 7.10/1.79 | | (19) ~ ($lesseq(all_2_0, 999)) | ~ ($lesseq(5, all_2_8)) | ~ % 7.10/1.79 | | ($lesseq(2, a)) % 7.30/1.79 | | % 7.30/1.79 | | BETA: splitting (19) gives: % 7.30/1.79 | | % 7.30/1.79 | | Case 1: % 7.30/1.79 | | | % 7.30/1.79 | | | (20) $lesseq(1000, all_2_0) % 7.30/1.79 | | | % 7.30/1.79 | | | COMBINE_INEQS: (17), (20) imply: % 7.30/1.79 | | | (21) $false % 7.30/1.79 | | | % 7.30/1.79 | | | CLOSE: (21) is inconsistent. % 7.30/1.80 | | | % 7.30/1.80 | | Case 2: % 7.30/1.80 | | | % 7.30/1.80 | | | (22) ~ ($lesseq(5, all_2_8)) | ~ ($lesseq(2, a)) % 7.30/1.80 | | | % 7.30/1.80 | | | BETA: splitting (22) gives: % 7.30/1.80 | | | % 7.30/1.80 | | | Case 1: % 7.30/1.80 | | | | % 7.30/1.80 | | | | (23) $lesseq(a, 1) % 7.30/1.80 | | | | % 7.30/1.80 | | | | COMBINE_INEQS: (16), (23) imply: % 7.30/1.80 | | | | (24) $false % 7.30/1.80 | | | | % 7.30/1.80 | | | | CLOSE: (24) is inconsistent. % 7.30/1.80 | | | | % 7.30/1.80 | | | Case 2: % 7.30/1.80 | | | | % 7.30/1.80 | | | | (25) $lesseq(all_2_8, 4) % 7.30/1.80 | | | | % 7.30/1.80 | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.80 | | | | (26) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 3)) | ~ % 7.30/1.80 | | | | ($lesseq(2, v0)) | ~ ($product(v0, v0) = v1)) % 7.30/1.80 | | | | % 7.30/1.80 | | | | GROUND_INST: instantiating (26) with a, all_2_9, simplifying with (2) % 7.30/1.80 | | | | gives: % 7.30/1.80 | | | | (27) ~ ($lesseq(all_2_9, 3)) | ~ ($lesseq(2, a)) % 7.30/1.80 | | | | % 7.30/1.80 | | | | BETA: splitting (27) gives: % 7.30/1.80 | | | | % 7.30/1.80 | | | | Case 1: % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | (28) $lesseq(a, 1) % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | COMBINE_INEQS: (16), (28) imply: % 7.30/1.80 | | | | | (29) $false % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | CLOSE: (29) is inconsistent. % 7.30/1.80 | | | | | % 7.30/1.80 | | | | Case 2: % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | (30) $lesseq(4, all_2_9) % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.80 | | | | | (31) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 7.30/1.80 | | | | | $difference($product(2, v1), v2))) | ~ ($lesseq(0, v1)) % 7.30/1.80 | | | | | | ~ ($lesseq(2, v0)) | ~ ($product(v1, v0) = v2)) % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | GROUND_INST: instantiating (31) with a, all_2_9, all_2_8, simplifying % 7.30/1.80 | | | | | with (3) gives: % 7.30/1.80 | | | | | (32) ~ ($lesseq(1, $difference($product(2, all_2_9), all_2_8))) | % 7.30/1.80 | | | | | ~ ($lesseq(0, all_2_9)) | ~ ($lesseq(2, a)) % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | BETA: splitting (32) gives: % 7.30/1.80 | | | | | % 7.30/1.80 | | | | | Case 1: % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | (33) $lesseq(all_2_9, -1) % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | COMBINE_INEQS: (14), (33) imply: % 7.30/1.80 | | | | | | (34) $false % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | CLOSE: (34) is inconsistent. % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | Case 2: % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | (35) ~ ($lesseq(1, $difference($product(2, all_2_9), all_2_8))) % 7.30/1.80 | | | | | | | ~ ($lesseq(2, a)) % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | BETA: splitting (35) gives: % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | | Case 1: % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | (36) $lesseq(a, 1) % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | COMBINE_INEQS: (16), (36) imply: % 7.30/1.80 | | | | | | | (37) $false % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | CLOSE: (37) is inconsistent. % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | Case 2: % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | (38) $lesseq(0, $difference(all_2_8, $product(2, all_2_9))) % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | COMBINE_INEQS: (25), (38) imply: % 7.30/1.80 | | | | | | | (39) $lesseq(all_2_9, 2) % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | SIMP: (39) implies: % 7.30/1.80 | | | | | | | (40) $lesseq(all_2_9, 2) % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | COMBINE_INEQS: (30), (40) imply: % 7.30/1.80 | | | | | | | (41) $false % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | | CLOSE: (41) is inconsistent. % 7.30/1.80 | | | | | | | % 7.30/1.80 | | | | | | End of split % 7.30/1.80 | | | | | | % 7.30/1.80 | | | | | End of split % 7.30/1.80 | | | | | % 7.30/1.80 | | | | End of split % 7.30/1.80 | | | | % 7.30/1.80 | | | End of split % 7.30/1.80 | | | % 7.30/1.80 | | End of split % 7.30/1.80 | | % 7.30/1.80 | Case 2: % 7.30/1.80 | | % 7.30/1.80 | | (42) $lesseq(1000, all_2_0) & $lesseq(a, 1) % 7.30/1.80 | | % 7.30/1.80 | | ALPHA: (42) implies: % 7.30/1.80 | | (43) $lesseq(a, 1) % 7.30/1.80 | | (44) $lesseq(1000, all_2_0) % 7.30/1.80 | | % 7.30/1.80 | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.81 | | (45) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2, v2)) | % 7.30/1.81 | | ~ ($lesseq(v0, 1)) | ~ ($product(v1, v0) = v2) | ~ ($product(v0, % 7.30/1.81 | | v0) = v1)) % 7.30/1.81 | | % 7.30/1.81 | | GROUND_INST: instantiating (45) with a, all_2_9, all_2_8, simplifying with % 7.30/1.81 | | (2), (3) gives: % 7.30/1.81 | | (46) ~ ($lesseq(2, all_2_8)) | ~ ($lesseq(a, 1)) % 7.30/1.81 | | % 7.30/1.81 | | BETA: splitting (46) gives: % 7.30/1.81 | | % 7.30/1.81 | | Case 1: % 7.30/1.81 | | | % 7.30/1.81 | | | (47) $lesseq(2, a) % 7.30/1.81 | | | % 7.30/1.81 | | | COMBINE_INEQS: (43), (47) imply: % 7.30/1.81 | | | (48) $false % 7.30/1.81 | | | % 7.30/1.81 | | | CLOSE: (48) is inconsistent. % 7.30/1.81 | | | % 7.30/1.81 | | Case 2: % 7.30/1.81 | | | % 7.30/1.81 | | | (49) $lesseq(all_2_8, 1) % 7.30/1.81 | | | % 7.30/1.81 | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.81 | | | (50) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 7.30/1.81 | | | $difference(v2, v1))) | ~ ($lesseq(0, v1)) | ~ % 7.30/1.81 | | | ($lesseq(v0, 1)) | ~ ($product(v1, v0) = v2)) % 7.30/1.81 | | | % 7.30/1.81 | | | GROUND_INST: instantiating (50) with a, all_2_9, all_2_8, simplifying with % 7.30/1.81 | | | (3) gives: % 7.30/1.81 | | | (51) ~ ($lesseq(1, $difference(all_2_8, all_2_9))) | ~ ($lesseq(0, % 7.30/1.81 | | | all_2_9)) | ~ ($lesseq(a, 1)) % 7.30/1.81 | | | % 7.30/1.81 | | | BETA: splitting (51) gives: % 7.30/1.81 | | | % 7.30/1.81 | | | Case 1: % 7.30/1.81 | | | | % 7.30/1.81 | | | | (52) $lesseq(all_2_9, -1) % 7.30/1.81 | | | | % 7.30/1.81 | | | | COMBINE_INEQS: (14), (52) imply: % 7.30/1.81 | | | | (53) $false % 7.30/1.81 | | | | % 7.30/1.81 | | | | CLOSE: (53) is inconsistent. % 7.30/1.81 | | | | % 7.30/1.81 | | | Case 2: % 7.30/1.81 | | | | % 7.30/1.81 | | | | (54) ~ ($lesseq(1, $difference(all_2_8, all_2_9))) | ~ ($lesseq(a, % 7.30/1.81 | | | | 1)) % 7.30/1.81 | | | | % 7.30/1.81 | | | | BETA: splitting (54) gives: % 7.30/1.81 | | | | % 7.30/1.81 | | | | Case 1: % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | (55) $lesseq(2, a) % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | COMBINE_INEQS: (43), (55) imply: % 7.30/1.81 | | | | | (56) $false % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | CLOSE: (56) is inconsistent. % 7.30/1.81 | | | | | % 7.30/1.81 | | | | Case 2: % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | (57) $lesseq(all_2_8, all_2_9) % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.81 | | | | | (58) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( % 7.30/1.81 | | | | | ~ ($lesseq(1, $difference($difference($product(2, v2), v3), % 7.30/1.81 | | | | | v1))) | ~ ($lesseq(v2, v1)) | ~ ($lesseq(v0, 1)) | % 7.30/1.81 | | | | | ~ ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | GROUND_INST: instantiating (58) with a, all_2_9, all_2_8, all_2_7, % 7.30/1.81 | | | | | simplifying with (3), (4) gives: % 7.30/1.81 | | | | | (59) ~ ($lesseq(1, $difference($difference($product(2, all_2_8), % 7.30/1.81 | | | | | all_2_7), all_2_9))) | ~ ($lesseq(all_2_8, all_2_9)) % 7.30/1.81 | | | | | | ~ ($lesseq(a, 1)) % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | BETA: splitting (59) gives: % 7.30/1.81 | | | | | % 7.30/1.81 | | | | | Case 1: % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | (60) $lesseq(1, $difference(all_2_8, all_2_9)) % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | COMBINE_INEQS: (57), (60) imply: % 7.30/1.81 | | | | | | (61) $false % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | CLOSE: (61) is inconsistent. % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | Case 2: % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | (62) ~ ($lesseq(1, $difference($difference($product(2, all_2_8), % 7.30/1.81 | | | | | | all_2_7), all_2_9))) | ~ ($lesseq(a, 1)) % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | BETA: splitting (62) gives: % 7.30/1.81 | | | | | | % 7.30/1.81 | | | | | | Case 1: % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | | (63) $lesseq(2, a) % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | | COMBINE_INEQS: (43), (63) imply: % 7.30/1.81 | | | | | | | (64) $false % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | | CLOSE: (64) is inconsistent. % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | Case 2: % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | | (65) $lesseq(0, $sum($difference(all_2_7, $product(2, % 7.30/1.81 | | | | | | | all_2_8)), all_2_9)) % 7.30/1.81 | | | | | | | % 7.30/1.81 | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.82 | | | | | | | (66) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] % 7.30/1.82 | | | | | | | : ! [v4: int] : ( ~ ($lesseq(1, % 7.30/1.82 | | | | | | | $difference($sum($difference(v4, $product(3, v3)), % 7.30/1.82 | | | | | | | $product(3, v2)), v1))) | ~ ($lesseq(0, % 7.30/1.82 | | | | | | | $sum($difference(v3, $product(2, v2)), v1))) | ~ % 7.30/1.82 | | | | | | | ($lesseq(v0, 1)) | ~ ($product(v3, v0) = v4) | ~ % 7.30/1.82 | | | | | | | ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 7.30/1.82 | | | | | | | % 7.30/1.82 | | | | | | | GROUND_INST: instantiating (66) with a, all_2_9, all_2_8, all_2_7, % 7.30/1.82 | | | | | | | all_2_6, simplifying with (3), (4), (5) gives: % 7.30/1.82 | | | | | | | (67) ~ ($lesseq(1, $difference($sum($difference(all_2_6, % 7.30/1.82 | | | | | | | $product(3, all_2_7)), $product(3, all_2_8)), % 7.30/1.82 | | | | | | | all_2_9))) | ~ ($lesseq(0, % 7.30/1.82 | | | | | | | $sum($difference(all_2_7, $product(2, all_2_8)), % 7.30/1.82 | | | | | | | all_2_9))) | ~ ($lesseq(a, 1)) % 7.30/1.82 | | | | | | | % 7.30/1.82 | | | | | | | BETA: splitting (67) gives: % 7.30/1.82 | | | | | | | % 7.30/1.82 | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | (68) $lesseq(1, $difference($difference($product(2, all_2_8), % 7.30/1.82 | | | | | | | | all_2_7), all_2_9)) % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | COMBINE_INEQS: (65), (68) imply: % 7.30/1.82 | | | | | | | | (69) $false % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | CLOSE: (69) is inconsistent. % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | Case 2: % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | (70) ~ ($lesseq(1, $difference($sum($difference(all_2_6, % 7.30/1.82 | | | | | | | | $product(3, all_2_7)), $product(3, all_2_8)), % 7.30/1.82 | | | | | | | | all_2_9))) | ~ ($lesseq(a, 1)) % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | BETA: splitting (70) gives: % 7.30/1.82 | | | | | | | | % 7.30/1.82 | | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | (71) $lesseq(2, a) % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | COMBINE_INEQS: (43), (71) imply: % 7.30/1.82 | | | | | | | | | (72) $false % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | CLOSE: (72) is inconsistent. % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | Case 2: % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | (73) $lesseq(0, $sum($difference($difference($product(3, % 7.30/1.82 | | | | | | | | | all_2_7), all_2_6), $product(3, all_2_8)), % 7.30/1.82 | | | | | | | | | all_2_9)) % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | CUT: with $lesseq(all_2_1, 0): % 7.30/1.82 | | | | | | | | | % 7.30/1.82 | | | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | (74) $lesseq(all_2_1, 0) % 7.30/1.82 | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.82 | | | | | | | | | | (75) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: % 7.30/1.82 | | | | | | | | | | int] : ! [v4: int] : ! [v5: int] : ! [v6: int] % 7.30/1.82 | | | | | | | | | | : ! [v7: int] : ! [v8: int] : ! [v9: int] : ! % 7.30/1.82 | | | | | | | | | | [v10: int] : ( ~ ($lesseq(1000, v10)) | ~ % 7.30/1.82 | | | | | | | | | | ($lesseq(v9, 0) | ~ ($lesseq(0, v1)) | ~ % 7.30/1.82 | | | | | | | | | | ($product(v9, v0) = v10) | ~ ($product(v8, v0) % 7.30/1.82 | | | | | | | | | | = v9) | ~ ($product(v7, v0) = v8) | ~ % 7.30/1.82 | | | | | | | | | | ($product(v6, v0) = v7) | ~ ($product(v5, v0) = % 7.30/1.82 | | | | | | | | | | v6) | ~ ($product(v4, v0) = v5) | ~ % 7.30/1.82 | | | | | | | | | | ($product(v3, v0) = v4) | ~ ($product(v2, v0) = % 7.30/1.82 | | | | | | | | | | v3) | ~ ($product(v1, v0) = v2)) % 7.30/1.82 | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | GROUND_INST: instantiating (75) with a, all_2_9, all_2_8, % 7.30/1.82 | | | | | | | | | | all_2_7, all_2_6, all_2_5, all_2_4, all_2_3, % 7.30/1.82 | | | | | | | | | | all_2_2, all_2_1, all_2_0, simplifying with (3), % 7.30/1.82 | | | | | | | | | | (4), (5), (6), (7), (8), (9), (10), (11) gives: % 7.30/1.82 | | | | | | | | | | (76) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(all_2_1, % 7.30/1.82 | | | | | | | | | | 0) | ~ ($lesseq(0, all_2_9)) % 7.30/1.82 | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | BETA: splitting (76) gives: % 7.30/1.82 | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | (77) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(all_2_1, % 7.30/1.82 | | | | | | | | | | | 0) % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | BETA: splitting (77) gives: % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | (78) $lesseq(all_2_0, 999) % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | COMBINE_INEQS: (44), (78) imply: % 7.30/1.82 | | | | | | | | | | | | (79) $false % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | CLOSE: (79) is inconsistent. % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | Case 2: % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | (80) $lesseq(1, all_2_1) % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | COMBINE_INEQS: (74), (80) imply: % 7.30/1.82 | | | | | | | | | | | | (81) $false % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | CLOSE: (81) is inconsistent. % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | End of split % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | Case 2: % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | (82) ~ ($lesseq(1, all_2_0)) | ~ ($lesseq(0, % 7.30/1.82 | | | | | | | | | | | all_2_9)) % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | BETA: splitting (82) gives: % 7.30/1.82 | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | Case 1: % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | (83) $lesseq(all_2_9, -1) % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | COMBINE_INEQS: (14), (83) imply: % 7.30/1.82 | | | | | | | | | | | | (84) $false % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | CLOSE: (84) is inconsistent. % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | Case 2: % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | (85) $lesseq(all_2_0, 0) % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.82 | | | | | | | | | | | | COMBINE_INEQS: (44), (85) imply: % 7.30/1.82 | | | | | | | | | | | | (86) $false % 7.30/1.82 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | CLOSE: (86) is inconsistent. % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | End of split % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | End of split % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | Case 2: % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | (87) $lesseq(1, all_2_1) % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.83 | | | | | | | | | | (88) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: % 7.30/1.83 | | | | | | | | | | int] : ! [v4: int] : ! [v5: int] : ! [v6: int] % 7.30/1.83 | | | | | | | | | | : ! [v7: int] : ! [v8: int] : ! [v9: int] : ( ~ % 7.30/1.83 | | | | | | | | | | ($lesseq(1000, v9)) | ~ ($lesseq(1, v8)) | ~ % 7.30/1.83 | | | | | | | | | | ($lesseq(v4, 999)) | ~ ($lesseq(v1, 1)) | ~ % 7.30/1.83 | | | | | | | | | | ($lesseq(v0, 1)) | ~ ($product(v8, v0) = v9) | ~ % 7.30/1.83 | | | | | | | | | | ($product(v7, v0) = v8) | ~ ($product(v6, v0) = % 7.30/1.83 | | | | | | | | | | v7) | ~ ($product(v5, v0) = v6) | ~ % 7.30/1.83 | | | | | | | | | | ($product(v4, v0) = v5) | ~ ($product(v3, v0) = % 7.30/1.83 | | | | | | | | | | v4) | ~ ($product(v2, v0) = v3) | ~ % 7.30/1.83 | | | | | | | | | | ($product(v1, v0) = v2)) % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | GROUND_INST: instantiating (88) with a, all_2_8, all_2_7, % 7.30/1.83 | | | | | | | | | | all_2_6, all_2_5, all_2_4, all_2_3, all_2_2, % 7.30/1.83 | | | | | | | | | | all_2_1, all_2_0, simplifying with (4), (5), (6), % 7.30/1.83 | | | | | | | | | | (7), (8), (9), (10), (11) gives: % 7.30/1.83 | | | | | | | | | | (89) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(1, % 7.30/1.83 | | | | | | | | | | all_2_1)) | ~ ($lesseq(all_2_5, 999)) | ~ % 7.30/1.83 | | | | | | | | | | ($lesseq(all_2_8, 1)) | ~ ($lesseq(a, 1)) % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | BETA: splitting (89) gives: % 7.30/1.83 | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | Case 1: % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | (90) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(1, % 7.30/1.83 | | | | | | | | | | | all_2_1)) % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | BETA: splitting (90) gives: % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | Case 1: % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | (91) $lesseq(all_2_0, 999) % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | COMBINE_INEQS: (44), (91) imply: % 7.30/1.83 | | | | | | | | | | | | (92) $false % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | CLOSE: (92) is inconsistent. % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | Case 2: % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | (93) $lesseq(all_2_1, 0) % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | COMBINE_INEQS: (87), (93) imply: % 7.30/1.83 | | | | | | | | | | | | (94) $false % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | CLOSE: (94) is inconsistent. % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | End of split % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | Case 2: % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | (95) ~ ($lesseq(all_2_5, 999)) | ~ ($lesseq(all_2_8, % 7.30/1.83 | | | | | | | | | | | 1)) | ~ ($lesseq(a, 1)) % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | BETA: splitting (95) gives: % 7.30/1.83 | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | Case 1: % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | (96) $lesseq(2, all_2_8) % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | COMBINE_INEQS: (49), (96) imply: % 7.30/1.83 | | | | | | | | | | | | (97) $false % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | CLOSE: (97) is inconsistent. % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | Case 2: % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | (98) ~ ($lesseq(all_2_5, 999)) | ~ ($lesseq(a, 1)) % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | BETA: splitting (98) gives: % 7.30/1.83 | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | Case 1: % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | (99) $lesseq(2, a) % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | COMBINE_INEQS: (43), (99) imply: % 7.30/1.83 | | | | | | | | | | | | | (100) $false % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | CLOSE: (100) is inconsistent. % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | Case 2: % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | (101) $lesseq(1000, all_2_5) % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 7.30/1.83 | | | | | | | | | | | | | (102) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 7.30/1.83 | | | | | | | | | | | | | [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: % 7.30/1.83 | | | | | | | | | | | | | int] : ! [v7: int] : ! [v8: int] : ! [v9: % 7.30/1.83 | | | | | | | | | | | | | int] : ! [v10: int] : ( ~ ($lesseq(1000, v10)) % 7.30/1.83 | | | | | | | | | | | | | | ~ ($lesseq(1, v9)) | ~ ($lesseq(2, v5)) | ~ % 7.30/1.83 | | | | | | | | | | | | | ($lesseq(0, % 7.30/1.83 | | | | | | | | | | | | | $sum($difference($difference($product(3, % 7.30/1.83 | | | | | | | | | | | | | v3), v4), $product(3, v2)), v1))) | % 7.30/1.83 | | | | | | | | | | | | | ~ ($lesseq(v2, 1)) | ~ ($lesseq(v0, 1)) | ~ % 7.30/1.83 | | | | | | | | | | | | | ($product(v9, v0) = v10) | ~ ($product(v8, v0) % 7.30/1.83 | | | | | | | | | | | | | = v9) | ~ ($product(v7, v0) = v8) | ~ % 7.30/1.83 | | | | | | | | | | | | | ($product(v6, v0) = v7) | ~ ($product(v5, v0) = % 7.30/1.83 | | | | | | | | | | | | | v6) | ~ ($product(v4, v0) = v5) | ~ % 7.30/1.83 | | | | | | | | | | | | | ($product(v3, v0) = v4) | ~ ($product(v2, v0) = % 7.30/1.83 | | | | | | | | | | | | | v3) | ~ ($product(v1, v0) = v2)) % 7.30/1.83 | | | | | | | | | | | | | % 7.30/1.83 | | | | | | | | | | | | | GROUND_INST: instantiating (102) with a, all_2_9, all_2_8, % 7.30/1.83 | | | | | | | | | | | | | all_2_7, all_2_6, all_2_5, all_2_4, all_2_3, % 7.30/1.83 | | | | | | | | | | | | | all_2_2, all_2_1, all_2_0, simplifying with (3), % 7.30/1.83 | | | | | | | | | | | | | (4), (5), (6), (7), (8), (9), (10), (11) gives: % 7.30/1.84 | | | | | | | | | | | | | (103) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(1, % 7.30/1.84 | | | | | | | | | | | | | all_2_1)) | ~ ($lesseq(2, all_2_5)) | ~ % 7.30/1.84 | | | | | | | | | | | | | ($lesseq(0, % 7.30/1.84 | | | | | | | | | | | | | $sum($difference($difference($product(3, % 7.30/1.84 | | | | | | | | | | | | | all_2_7), all_2_6), $product(3, % 7.30/1.84 | | | | | | | | | | | | | all_2_8)), all_2_9))) | ~ % 7.30/1.84 | | | | | | | | | | | | | ($lesseq(all_2_8, 1)) | ~ ($lesseq(a, 1)) % 7.30/1.84 | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | BETA: splitting (103) gives: % 7.30/1.84 | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | Case 1: % 7.30/1.84 | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | (104) ~ ($lesseq(1000, all_2_0)) | ~ ($lesseq(1, % 7.30/1.84 | | | | | | | | | | | | | | all_2_1)) | ~ ($lesseq(0, % 7.30/1.84 | | | | | | | | | | | | | | $sum($difference($difference($product(3, % 7.30/1.84 | | | | | | | | | | | | | | all_2_7), all_2_6), $product(3, % 7.30/1.84 | | | | | | | | | | | | | | all_2_8)), all_2_9))) % 7.30/1.84 | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | BETA: splitting (104) gives: % 7.30/1.84 | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | Case 1: % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | (105) $lesseq(all_2_0, 999) % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | COMBINE_INEQS: (44), (105) imply: % 7.30/1.84 | | | | | | | | | | | | | | | (106) $false % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | Case 2: % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | (107) ~ ($lesseq(1, all_2_1)) | ~ ($lesseq(0, % 7.30/1.84 | | | | | | | | | | | | | | | $sum($difference($difference($product(3, % 7.30/1.84 | | | | | | | | | | | | | | | all_2_7), all_2_6), $product(3, % 7.30/1.84 | | | | | | | | | | | | | | | all_2_8)), all_2_9))) % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 7.30/1.84 | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | Case 1: % 7.30/1.84 | | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | | (108) $lesseq(all_2_1, 0) % 7.30/1.84 | | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | | COMBINE_INEQS: (87), (108) imply: % 7.30/1.84 | | | | | | | | | | | | | | | | (109) $false % 7.30/1.84 | | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | | CLOSE: (109) is inconsistent. % 7.30/1.84 | | | | | | | | | | | | | | | | % 7.30/1.84 | | | | | | | | | | | | | | | Case 2: % 7.30/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | (110) $lesseq(1, $difference($sum($difference(all_2_6, % 7.45/1.84 | | | | | | | | | | | | | | | | $product(3, all_2_7)), $product(3, % 7.45/1.84 | | | | | | | | | | | | | | | | all_2_8)), all_2_9)) % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | COMBINE_INEQS: (73), (110) imply: % 7.45/1.84 | | | | | | | | | | | | | | | | (111) $false % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | Case 2: % 7.45/1.84 | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | (112) ~ ($lesseq(2, all_2_5)) | ~ ($lesseq(all_2_8, % 7.45/1.84 | | | | | | | | | | | | | | 1)) | ~ ($lesseq(a, 1)) % 7.45/1.84 | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | BETA: splitting (112) gives: % 7.45/1.84 | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | Case 1: % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | (113) $lesseq(2, all_2_8) % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | COMBINE_INEQS: (49), (113) imply: % 7.45/1.84 | | | | | | | | | | | | | | | (114) $false % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | CLOSE: (114) is inconsistent. % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | Case 2: % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | (115) ~ ($lesseq(2, all_2_5)) | ~ ($lesseq(a, 1)) % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | Case 1: % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | (116) $lesseq(2, a) % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | COMBINE_INEQS: (43), (116) imply: % 7.45/1.84 | | | | | | | | | | | | | | | | (117) $false % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | Case 2: % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | (118) $lesseq(all_2_5, 1) % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | COMBINE_INEQS: (101), (118) imply: % 7.45/1.84 | | | | | | | | | | | | | | | | (119) $false % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 7.45/1.84 | | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | | % 7.45/1.84 | | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | | % 7.45/1.84 | | | | | | | | | End of split % 7.45/1.84 | | | | | | | | | % 7.45/1.84 | | | | | | | | End of split % 7.45/1.84 | | | | | | | | % 7.45/1.84 | | | | | | | End of split % 7.45/1.84 | | | | | | | % 7.45/1.84 | | | | | | End of split % 7.45/1.84 | | | | | | % 7.45/1.84 | | | | | End of split % 7.45/1.84 | | | | | % 7.45/1.84 | | | | End of split % 7.45/1.84 | | | | % 7.45/1.84 | | | End of split % 7.45/1.84 | | | % 7.45/1.84 | | End of split % 7.45/1.84 | | % 7.45/1.84 | End of split % 7.45/1.84 | % 7.45/1.84 End of proof % 7.45/1.84 % SZS output end Proof for theBenchmark % 7.45/1.84 % 7.45/1.84 1186ms %------------------------------------------------------------------------------