%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI661_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 : n020.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 17:48:43 EDT 2023 % Result : Theorem 4.68s 1.41s % Output : Proof 5.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI661_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 : n020.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 18:27:58 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.61/0.63 Running up to 7 provers in parallel. % 0.61/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.61/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.97/1.01 Prover 1: Preprocessing ... % 1.97/1.01 Prover 4: Preprocessing ... % 1.97/1.01 Prover 0: Preprocessing ... % 1.97/1.01 Prover 6: Preprocessing ... % 1.97/1.01 Prover 3: Preprocessing ... % 1.97/1.01 Prover 2: Preprocessing ... % 1.97/1.01 Prover 5: Preprocessing ... % 2.23/1.07 Prover 1: Constructing countermodel ... % 2.23/1.07 Prover 6: Constructing countermodel ... % 2.23/1.07 Prover 0: Constructing countermodel ... % 2.23/1.07 Prover 5: Constructing countermodel ... % 2.23/1.07 Prover 2: Constructing countermodel ... % 2.23/1.07 Prover 4: Constructing countermodel ... % 2.23/1.07 Prover 3: Constructing countermodel ... % 4.68/1.41 Prover 6: proved (763ms) % 4.68/1.41 % 4.68/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.68/1.41 % 4.68/1.41 Prover 0: stopped % 4.68/1.41 Prover 5: stopped % 4.68/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.68/1.41 Prover 3: stopped % 4.68/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.68/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.68/1.42 Prover 2: stopped % 4.87/1.42 Prover 8: Preprocessing ... % 4.87/1.42 Prover 10: Preprocessing ... % 4.87/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.87/1.43 Prover 8: Constructing countermodel ... % 4.87/1.43 Prover 10: Constructing countermodel ... % 4.87/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.87/1.44 Prover 11: Preprocessing ... % 4.87/1.44 Prover 13: Preprocessing ... % 4.87/1.44 Prover 7: Preprocessing ... % 4.87/1.44 Prover 11: Constructing countermodel ... % 4.87/1.45 Prover 7: Constructing countermodel ... % 4.87/1.45 Prover 13: Constructing countermodel ... % 4.87/1.46 Prover 4: Found proof (size 94) % 4.87/1.46 Prover 4: proved (814ms) % 4.87/1.46 Prover 13: stopped % 4.87/1.46 Prover 10: stopped % 4.87/1.46 Prover 7: stopped % 4.87/1.46 Prover 8: stopped % 4.87/1.46 Prover 11: stopped % 4.87/1.47 Prover 1: Found proof (size 94) % 4.87/1.47 Prover 1: proved (827ms) % 4.87/1.47 % 4.87/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.87/1.47 % 4.87/1.48 % SZS output start Proof for theBenchmark % 4.87/1.48 Assumptions after simplification: % 4.87/1.48 --------------------------------- % 4.87/1.48 % 4.87/1.48 (conj) % 4.87/1.49 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ($product(v2, a) = % 4.87/1.49 v3 & $product(v1, a) = v2 & $product(v0, a) = v1 & $product(a, a) = v0 & % 4.87/1.49 (($lesseq(v3, 39) & $lesseq(3, a)) | ($lesseq(40, v3) & $lesseq(a, 2)))) % 4.87/1.49 % 4.87/1.49 Those formulas are unsatisfiable: % 4.87/1.49 --------------------------------- % 4.87/1.49 % 4.87/1.49 Begin of proof % 4.87/1.49 | % 4.87/1.49 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2, % 4.87/1.49 | all_2_3 gives: % 4.87/1.49 | (1) $product(all_2_1, a) = all_2_0 & $product(all_2_2, a) = all_2_1 & % 4.87/1.49 | $product(all_2_3, a) = all_2_2 & $product(a, a) = all_2_3 & % 4.87/1.49 | (($lesseq(all_2_0, 39) & $lesseq(3, a)) | ($lesseq(40, all_2_0) & % 4.87/1.49 | $lesseq(a, 2))) % 4.87/1.49 | % 4.87/1.49 | ALPHA: (1) implies: % 4.87/1.49 | (2) $product(a, a) = all_2_3 % 4.87/1.49 | (3) $product(all_2_3, a) = all_2_2 % 4.87/1.49 | (4) $product(all_2_2, a) = all_2_1 % 4.87/1.49 | (5) $product(all_2_1, a) = all_2_0 % 4.87/1.49 | (6) ($lesseq(all_2_0, 39) & $lesseq(3, a)) | ($lesseq(40, all_2_0) & % 4.87/1.49 | $lesseq(a, 2)) % 4.87/1.49 | % 4.87/1.49 | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.50 | (7) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ ($product(v0, % 4.87/1.50 | v0) = v1)) % 4.87/1.50 | % 4.87/1.50 | GROUND_INST: instantiating (7) with a, all_2_3, simplifying with (2) gives: % 4.87/1.50 | (8) $lesseq(0, all_2_3) % 4.87/1.50 | % 4.87/1.50 | BETA: splitting (6) gives: % 4.87/1.50 | % 4.87/1.50 | Case 1: % 4.87/1.50 | | % 4.87/1.50 | | (9) $lesseq(all_2_0, 39) & $lesseq(3, a) % 4.87/1.50 | | % 4.87/1.50 | | ALPHA: (9) implies: % 4.87/1.50 | | (10) $lesseq(3, a) % 4.87/1.50 | | (11) $lesseq(all_2_0, 39) % 4.87/1.50 | | % 4.87/1.50 | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.50 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( ~ % 4.87/1.50 | | ($lesseq(v3, 39)) | ~ ($lesseq(6, v1)) | ~ ($lesseq(3, v0)) | ~ % 4.87/1.50 | | ($product(v2, v0) = v3) | ~ ($product(v1, v0) = v2)) % 4.87/1.50 | | % 4.87/1.50 | | GROUND_INST: instantiating (12) with a, all_2_2, all_2_1, all_2_0, % 4.87/1.50 | | simplifying with (4), (5) gives: % 4.87/1.50 | | (13) ~ ($lesseq(all_2_0, 39)) | ~ ($lesseq(6, all_2_2)) | ~ % 4.87/1.50 | | ($lesseq(3, a)) % 4.87/1.50 | | % 4.87/1.50 | | BETA: splitting (13) gives: % 4.87/1.50 | | % 4.87/1.50 | | Case 1: % 4.87/1.50 | | | % 4.87/1.50 | | | (14) $lesseq(40, all_2_0) % 4.87/1.50 | | | % 4.87/1.50 | | | COMBINE_INEQS: (11), (14) imply: % 4.87/1.50 | | | (15) $false % 4.87/1.50 | | | % 4.87/1.50 | | | CLOSE: (15) is inconsistent. % 4.87/1.50 | | | % 4.87/1.50 | | Case 2: % 4.87/1.50 | | | % 4.87/1.50 | | | (16) ~ ($lesseq(6, all_2_2)) | ~ ($lesseq(3, a)) % 4.87/1.50 | | | % 4.87/1.50 | | | BETA: splitting (16) gives: % 4.87/1.50 | | | % 4.87/1.50 | | | Case 1: % 4.87/1.50 | | | | % 4.87/1.50 | | | | (17) $lesseq(a, 2) % 4.87/1.50 | | | | % 4.87/1.50 | | | | COMBINE_INEQS: (10), (17) imply: % 4.87/1.50 | | | | (18) $false % 4.87/1.50 | | | | % 4.87/1.50 | | | | CLOSE: (18) is inconsistent. % 4.87/1.50 | | | | % 4.87/1.50 | | | Case 2: % 4.87/1.50 | | | | % 4.87/1.50 | | | | (19) $lesseq(all_2_2, 5) % 4.87/1.50 | | | | % 4.87/1.50 | | | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.51 | | | | (20) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 8)) | ~ % 4.87/1.51 | | | | ($lesseq(3, v0)) | ~ ($product(v0, v0) = v1)) % 4.87/1.51 | | | | % 4.87/1.51 | | | | GROUND_INST: instantiating (20) with a, all_2_3, simplifying with (2) % 4.87/1.51 | | | | gives: % 4.87/1.51 | | | | (21) ~ ($lesseq(all_2_3, 8)) | ~ ($lesseq(3, a)) % 4.87/1.51 | | | | % 4.87/1.51 | | | | BETA: splitting (21) gives: % 4.87/1.51 | | | | % 4.87/1.51 | | | | Case 1: % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | (22) $lesseq(a, 2) % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | COMBINE_INEQS: (10), (22) imply: % 4.87/1.51 | | | | | (23) $false % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | CLOSE: (23) is inconsistent. % 4.87/1.51 | | | | | % 4.87/1.51 | | | | Case 2: % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | (24) $lesseq(9, all_2_3) % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.51 | | | | | (25) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 4.87/1.51 | | | | | $difference($product(3, v1), v2))) | ~ ($lesseq(0, v1)) % 4.87/1.51 | | | | | | ~ ($lesseq(3, v0)) | ~ ($product(v1, v0) = v2)) % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | GROUND_INST: instantiating (25) with a, all_2_3, all_2_2, simplifying % 4.87/1.51 | | | | | with (3) gives: % 4.87/1.51 | | | | | (26) ~ ($lesseq(1, $difference($product(3, all_2_3), all_2_2))) | % 4.87/1.51 | | | | | ~ ($lesseq(0, all_2_3)) | ~ ($lesseq(3, a)) % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | BETA: splitting (26) gives: % 4.87/1.51 | | | | | % 4.87/1.51 | | | | | Case 1: % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | (27) $lesseq(all_2_3, -1) % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | COMBINE_INEQS: (8), (27) imply: % 4.87/1.51 | | | | | | (28) $false % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | CLOSE: (28) is inconsistent. % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | Case 2: % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | (29) ~ ($lesseq(1, $difference($product(3, all_2_3), all_2_2))) % 4.87/1.51 | | | | | | | ~ ($lesseq(3, a)) % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | BETA: splitting (29) gives: % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | | Case 1: % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | (30) $lesseq(a, 2) % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | COMBINE_INEQS: (10), (30) imply: % 4.87/1.51 | | | | | | | (31) $false % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | CLOSE: (31) is inconsistent. % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | Case 2: % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | (32) $lesseq(0, $difference(all_2_2, $product(3, all_2_3))) % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | COMBINE_INEQS: (19), (32) imply: % 4.87/1.51 | | | | | | | (33) $lesseq(all_2_3, 1) % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | SIMP: (33) implies: % 4.87/1.51 | | | | | | | (34) $lesseq(all_2_3, 1) % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | COMBINE_INEQS: (24), (34) imply: % 4.87/1.51 | | | | | | | (35) $false % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | | CLOSE: (35) is inconsistent. % 4.87/1.51 | | | | | | | % 4.87/1.51 | | | | | | End of split % 4.87/1.51 | | | | | | % 4.87/1.51 | | | | | End of split % 4.87/1.51 | | | | | % 4.87/1.51 | | | | End of split % 4.87/1.51 | | | | % 4.87/1.51 | | | End of split % 4.87/1.51 | | | % 4.87/1.51 | | End of split % 4.87/1.51 | | % 4.87/1.51 | Case 2: % 4.87/1.51 | | % 4.87/1.51 | | (36) $lesseq(40, all_2_0) & $lesseq(a, 2) % 4.87/1.51 | | % 4.87/1.51 | | ALPHA: (36) implies: % 4.87/1.51 | | (37) $lesseq(a, 2) % 4.87/1.51 | | (38) $lesseq(40, all_2_0) % 4.87/1.51 | | % 4.87/1.51 | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.51 | | (39) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(9, v2)) | % 4.87/1.51 | | ~ ($lesseq(v0, 2)) | ~ ($product(v1, v0) = v2) | ~ ($product(v0, % 4.87/1.51 | | v0) = v1)) % 4.87/1.51 | | % 4.87/1.52 | | GROUND_INST: instantiating (39) with a, all_2_3, all_2_2, simplifying with % 4.87/1.52 | | (2), (3) gives: % 4.87/1.52 | | (40) ~ ($lesseq(9, all_2_2)) | ~ ($lesseq(a, 2)) % 4.87/1.52 | | % 4.87/1.52 | | BETA: splitting (40) gives: % 4.87/1.52 | | % 4.87/1.52 | | Case 1: % 4.87/1.52 | | | % 4.87/1.52 | | | (41) $lesseq(3, a) % 4.87/1.52 | | | % 4.87/1.52 | | | COMBINE_INEQS: (37), (41) imply: % 4.87/1.52 | | | (42) $false % 4.87/1.52 | | | % 4.87/1.52 | | | CLOSE: (42) is inconsistent. % 4.87/1.52 | | | % 4.87/1.52 | | Case 2: % 4.87/1.52 | | | % 4.87/1.52 | | | (43) $lesseq(all_2_2, 8) % 4.87/1.52 | | | % 4.87/1.52 | | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.52 | | | (44) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 4.87/1.52 | | | $difference(v2, $product(2, v1)))) | ~ ($lesseq(0, v1)) | % 4.87/1.52 | | | ~ ($lesseq(v0, 2)) | ~ ($product(v1, v0) = v2)) % 4.87/1.52 | | | % 4.87/1.52 | | | GROUND_INST: instantiating (44) with a, all_2_3, all_2_2, simplifying with % 4.87/1.52 | | | (3) gives: % 4.87/1.52 | | | (45) ~ ($lesseq(1, $difference(all_2_2, $product(2, all_2_3)))) | ~ % 4.87/1.52 | | | ($lesseq(0, all_2_3)) | ~ ($lesseq(a, 2)) % 4.87/1.52 | | | % 4.87/1.52 | | | BETA: splitting (45) gives: % 4.87/1.52 | | | % 4.87/1.52 | | | Case 1: % 4.87/1.52 | | | | % 4.87/1.52 | | | | (46) $lesseq(all_2_3, -1) % 4.87/1.52 | | | | % 4.87/1.52 | | | | COMBINE_INEQS: (8), (46) imply: % 4.87/1.52 | | | | (47) $false % 4.87/1.52 | | | | % 4.87/1.52 | | | | CLOSE: (47) is inconsistent. % 4.87/1.52 | | | | % 4.87/1.52 | | | Case 2: % 4.87/1.52 | | | | % 4.87/1.52 | | | | (48) ~ ($lesseq(1, $difference(all_2_2, $product(2, all_2_3)))) | ~ % 4.87/1.52 | | | | ($lesseq(a, 2)) % 4.87/1.52 | | | | % 4.87/1.52 | | | | BETA: splitting (48) gives: % 4.87/1.52 | | | | % 4.87/1.52 | | | | Case 1: % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | (49) $lesseq(3, a) % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | COMBINE_INEQS: (37), (49) imply: % 4.87/1.52 | | | | | (50) $false % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | CLOSE: (50) is inconsistent. % 4.87/1.52 | | | | | % 4.87/1.52 | | | | Case 2: % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | (51) $lesseq(all_2_2, $product(2, all_2_3)) % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | THEORY_AXIOM GroebnerMultiplication: % 4.87/1.52 | | | | | (52) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ( % 4.87/1.52 | | | | | ~ ($lesseq(1, $difference($difference($product(4, v2), v3), % 4.87/1.52 | | | | | $product(4, v1)))) | ~ ($lesseq(v2, $product(2, v1))) % 4.87/1.52 | | | | | | ~ ($lesseq(v0, 2)) | ~ ($product(v2, v0) = v3) | ~ % 4.87/1.52 | | | | | ($product(v1, v0) = v2)) % 4.87/1.52 | | | | | % 4.87/1.52 | | | | | GROUND_INST: instantiating (52) with a, all_2_3, all_2_2, all_2_1, % 4.87/1.52 | | | | | simplifying with (3), (4) gives: % 5.35/1.52 | | | | | (53) ~ ($lesseq(1, $difference($difference($product(4, all_2_2), % 5.35/1.52 | | | | | all_2_1), $product(4, all_2_3)))) | ~ % 5.35/1.52 | | | | | ($lesseq(all_2_2, $product(2, all_2_3))) | ~ ($lesseq(a, 2)) % 5.35/1.52 | | | | | % 5.35/1.52 | | | | | BETA: splitting (53) gives: % 5.35/1.52 | | | | | % 5.35/1.52 | | | | | Case 1: % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | (54) $lesseq(1, $difference(all_2_2, $product(2, all_2_3))) % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | COMBINE_INEQS: (51), (54) imply: % 5.35/1.52 | | | | | | (55) $false % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | CLOSE: (55) is inconsistent. % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | Case 2: % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | (56) ~ ($lesseq(1, $difference($difference($product(4, all_2_2), % 5.35/1.52 | | | | | | all_2_1), $product(4, all_2_3)))) | ~ ($lesseq(a, % 5.35/1.52 | | | | | | 2)) % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | BETA: splitting (56) gives: % 5.35/1.52 | | | | | | % 5.35/1.52 | | | | | | Case 1: % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | | (57) $lesseq(3, a) % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | | COMBINE_INEQS: (37), (57) imply: % 5.35/1.52 | | | | | | | (58) $false % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | | CLOSE: (58) is inconsistent. % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | Case 2: % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | | (59) $lesseq(0, $sum($difference(all_2_1, $product(4, % 5.35/1.52 | | | | | | | all_2_2)), $product(4, all_2_3))) % 5.35/1.52 | | | | | | | % 5.35/1.52 | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.35/1.53 | | | | | | | (60) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] % 5.35/1.53 | | | | | | | : ! [v4: int] : ( ~ ($lesseq(1, % 5.35/1.53 | | | | | | | $difference($sum($difference(v4, $product(6, v3)), % 5.35/1.53 | | | | | | | $product(12, v2)), $product(8, v1)))) | ~ % 5.35/1.53 | | | | | | | ($lesseq(0, $sum($difference(v3, $product(4, v2)), % 5.35/1.53 | | | | | | | $product(4, v1)))) | ~ ($lesseq(v0, 2)) | ~ % 5.35/1.53 | | | | | | | ($product(v3, v0) = v4) | ~ ($product(v2, v0) = v3) | % 5.35/1.53 | | | | | | | ~ ($product(v1, v0) = v2)) % 5.35/1.53 | | | | | | | % 5.35/1.53 | | | | | | | GROUND_INST: instantiating (60) with a, all_2_3, all_2_2, all_2_1, % 5.35/1.53 | | | | | | | all_2_0, simplifying with (3), (4), (5) gives: % 5.35/1.53 | | | | | | | (61) ~ ($lesseq(1, $difference($sum($difference(all_2_0, % 5.35/1.53 | | | | | | | $product(6, all_2_1)), $product(12, all_2_2)), % 5.35/1.53 | | | | | | | $product(8, all_2_3)))) | ~ ($lesseq(0, % 5.35/1.53 | | | | | | | $sum($difference(all_2_1, $product(4, all_2_2)), % 5.35/1.53 | | | | | | | $product(4, all_2_3)))) | ~ ($lesseq(a, 2)) % 5.35/1.53 | | | | | | | % 5.35/1.53 | | | | | | | BETA: splitting (61) gives: % 5.35/1.53 | | | | | | | % 5.35/1.53 | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | (62) $lesseq(1, $difference($difference($product(4, all_2_2), % 5.35/1.53 | | | | | | | | all_2_1), $product(4, all_2_3))) % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | COMBINE_INEQS: (59), (62) imply: % 5.35/1.53 | | | | | | | | (63) $false % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | CLOSE: (63) is inconsistent. % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | Case 2: % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | (64) ~ ($lesseq(1, $difference($sum($difference(all_2_0, % 5.35/1.53 | | | | | | | | $product(6, all_2_1)), $product(12, all_2_2)), % 5.35/1.53 | | | | | | | | $product(8, all_2_3)))) | ~ ($lesseq(a, 2)) % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | BETA: splitting (64) gives: % 5.35/1.53 | | | | | | | | % 5.35/1.53 | | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | (65) $lesseq(3, a) % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | COMBINE_INEQS: (37), (65) imply: % 5.35/1.53 | | | | | | | | | (66) $false % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | CLOSE: (66) is inconsistent. % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | Case 2: % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | (67) $lesseq(0, $sum($difference($difference($product(6, % 5.35/1.53 | | | | | | | | | all_2_1), all_2_0), $product(12, all_2_2)), % 5.35/1.53 | | | | | | | | | $product(8, all_2_3))) % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | CUT: with $lesseq(all_2_1, 0): % 5.35/1.53 | | | | | | | | | % 5.35/1.53 | | | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | (68) $lesseq(all_2_1, 0) % 5.35/1.53 | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.35/1.53 | | | | | | | | | | (69) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: % 5.35/1.53 | | | | | | | | | | int] : ! [v4: int] : ( ~ ($lesseq(40, v4)) | ~ % 5.35/1.53 | | | | | | | | | | ($lesseq(v3, 0) | ~ ($lesseq(0, v1)) | ~ % 5.35/1.53 | | | | | | | | | | ($product(v3, v0) = v4) | ~ ($product(v2, v0) = % 5.35/1.53 | | | | | | | | | | v3) | ~ ($product(v1, v0) = v2)) % 5.35/1.53 | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | GROUND_INST: instantiating (69) with a, all_2_3, all_2_2, % 5.35/1.53 | | | | | | | | | | all_2_1, all_2_0, simplifying with (3), (4), (5) % 5.35/1.53 | | | | | | | | | | gives: % 5.35/1.53 | | | | | | | | | | (70) ~ ($lesseq(40, all_2_0)) | ~ ($lesseq(all_2_1, 0) % 5.35/1.53 | | | | | | | | | | | ~ ($lesseq(0, all_2_3)) % 5.35/1.53 | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | BETA: splitting (70) gives: % 5.35/1.53 | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | (71) ~ ($lesseq(40, all_2_0)) | ~ ($lesseq(all_2_1, % 5.35/1.53 | | | | | | | | | | | 0) % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | BETA: splitting (71) gives: % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | (72) $lesseq(all_2_0, 39) % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | COMBINE_INEQS: (38), (72) imply: % 5.35/1.53 | | | | | | | | | | | | (73) $false % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | CLOSE: (73) is inconsistent. % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | Case 2: % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | (74) $lesseq(1, all_2_1) % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | COMBINE_INEQS: (68), (74) imply: % 5.35/1.53 | | | | | | | | | | | | (75) $false % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | CLOSE: (75) is inconsistent. % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | End of split % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | Case 2: % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | (76) ~ ($lesseq(1, all_2_0)) | ~ ($lesseq(0, % 5.35/1.53 | | | | | | | | | | | all_2_3)) % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | BETA: splitting (76) gives: % 5.35/1.53 | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | Case 1: % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | (77) $lesseq(all_2_3, -1) % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | COMBINE_INEQS: (8), (77) imply: % 5.35/1.53 | | | | | | | | | | | | (78) $false % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | | CLOSE: (78) is inconsistent. % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.53 | | | | | | | | | | | Case 2: % 5.35/1.53 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | (79) $lesseq(all_2_0, 0) % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | COMBINE_INEQS: (38), (79) imply: % 5.35/1.54 | | | | | | | | | | | | (80) $false % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | CLOSE: (80) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | (81) $lesseq(1, all_2_1) % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.35/1.54 | | | | | | | | | | (82) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: % 5.35/1.54 | | | | | | | | | | int] : ! [v4: int] : ( ~ ($lesseq(0, % 5.35/1.54 | | | | | | | | | | $sum($difference($difference($product(6, v3), % 5.35/1.54 | | | | | | | | | | v4), $product(12, v2)), $product(8, % 5.35/1.54 | | | | | | | | | | v1)))) | ~ ($lesseq(40, v4)) | ~ % 5.35/1.54 | | | | | | | | | | ($lesseq(1, v3)) | ~ ($lesseq(v2, 8)) | ~ % 5.35/1.54 | | | | | | | | | | ($lesseq(v0, 2)) | ~ ($product(v3, v0) = v4) | ~ % 5.35/1.54 | | | | | | | | | | ($product(v2, v0) = v3) | ~ ($product(v0, v0) = % 5.35/1.54 | | | | | | | | | | v1)) % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | GROUND_INST: instantiating (82) with a, all_2_3, all_2_2, % 5.35/1.54 | | | | | | | | | | all_2_1, all_2_0, simplifying with (2), (4), (5) % 5.35/1.54 | | | | | | | | | | gives: % 5.35/1.54 | | | | | | | | | | (83) ~ ($lesseq(0, % 5.35/1.54 | | | | | | | | | | $sum($difference($difference($product(6, % 5.35/1.54 | | | | | | | | | | all_2_1), all_2_0), $product(12, % 5.35/1.54 | | | | | | | | | | all_2_2)), $product(8, all_2_3)))) | ~ % 5.35/1.54 | | | | | | | | | | ($lesseq(40, all_2_0)) | ~ ($lesseq(1, all_2_1)) | % 5.35/1.54 | | | | | | | | | | ~ ($lesseq(all_2_2, 8)) | ~ ($lesseq(a, 2)) % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | BETA: splitting (83) gives: % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | Case 1: % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | (84) ~ ($lesseq(0, % 5.35/1.54 | | | | | | | | | | | $sum($difference($difference($product(6, % 5.35/1.54 | | | | | | | | | | | all_2_1), all_2_0), $product(12, % 5.35/1.54 | | | | | | | | | | | all_2_2)), $product(8, all_2_3)))) | ~ % 5.35/1.54 | | | | | | | | | | | ($lesseq(40, all_2_0)) | ~ ($lesseq(1, all_2_1)) % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | BETA: splitting (84) gives: % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | Case 1: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | (85) $lesseq(1, $difference($sum($difference(all_2_0, % 5.35/1.54 | | | | | | | | | | | | $product(6, all_2_1)), $product(12, % 5.35/1.54 | | | | | | | | | | | | all_2_2)), $product(8, all_2_3))) % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | COMBINE_INEQS: (67), (85) imply: % 5.35/1.54 | | | | | | | | | | | | (86) $false % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | CLOSE: (86) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | (87) ~ ($lesseq(40, all_2_0)) | ~ ($lesseq(1, % 5.35/1.54 | | | | | | | | | | | | all_2_1)) % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | BETA: splitting (87) gives: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | Case 1: % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | (88) $lesseq(all_2_0, 39) % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | COMBINE_INEQS: (38), (88) imply: % 5.35/1.54 | | | | | | | | | | | | | (89) $false % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | CLOSE: (89) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | (90) $lesseq(all_2_1, 0) % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | COMBINE_INEQS: (81), (90) imply: % 5.35/1.54 | | | | | | | | | | | | | (91) $false % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | CLOSE: (91) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | (92) ~ ($lesseq(33, all_2_0)) | ~ ($lesseq(all_2_2, % 5.35/1.54 | | | | | | | | | | | 8)) | ~ ($lesseq(a, 2)) % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | BETA: splitting (92) gives: % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | Case 1: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | (93) $lesseq(9, all_2_2) % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | COMBINE_INEQS: (43), (93) imply: % 5.35/1.54 | | | | | | | | | | | | (94) $false % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | CLOSE: (94) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | (95) ~ ($lesseq(33, all_2_0)) | ~ ($lesseq(a, 2)) % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | BETA: splitting (95) gives: % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | Case 1: % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | (96) $lesseq(3, a) % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | COMBINE_INEQS: (37), (96) imply: % 5.35/1.54 | | | | | | | | | | | | | (97) $false % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | CLOSE: (97) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | Case 2: % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | (98) $lesseq(all_2_0, 32) % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | COMBINE_INEQS: (38), (98) imply: % 5.35/1.54 | | | | | | | | | | | | | (99) $false % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | | CLOSE: (99) is inconsistent. % 5.35/1.54 | | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | | % 5.35/1.54 | | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | | % 5.35/1.54 | | | | | | | | | End of split % 5.35/1.54 | | | | | | | | | % 5.35/1.54 | | | | | | | | End of split % 5.35/1.54 | | | | | | | | % 5.35/1.54 | | | | | | | End of split % 5.35/1.54 | | | | | | | % 5.35/1.54 | | | | | | End of split % 5.35/1.54 | | | | | | % 5.35/1.54 | | | | | End of split % 5.35/1.54 | | | | | % 5.35/1.54 | | | | End of split % 5.35/1.54 | | | | % 5.35/1.54 | | | End of split % 5.35/1.54 | | | % 5.35/1.54 | | End of split % 5.35/1.54 | | % 5.35/1.54 | End of split % 5.35/1.54 | % 5.35/1.54 End of proof % 5.35/1.54 % SZS output end Proof for theBenchmark % 5.35/1.54 % 5.35/1.54 922ms %------------------------------------------------------------------------------