%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC473_1 : TPTP v8.3.0. Released v8.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n024.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 : Tue May 14 09:00:31 EDT 2024 % Result : Theorem 6.78s 1.65s % Output : Proof 8.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC473_1 : TPTP v8.3.0. Released v8.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.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 : Mon May 13 14:57:23 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.65/0.61 Free software under BSD-3-Clause. % 0.65/0.61 % 0.65/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.61 % 0.65/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.62 Running up to 7 provers in parallel. % 0.70/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.27/1.06 Prover 1: Preprocessing ... % 2.27/1.06 Prover 2: Preprocessing ... % 2.27/1.06 Prover 5: Preprocessing ... % 2.27/1.06 Prover 0: Preprocessing ... % 2.27/1.06 Prover 3: Preprocessing ... % 2.27/1.06 Prover 4: Preprocessing ... % 2.27/1.06 Prover 6: Preprocessing ... % 3.68/1.23 Prover 1: Constructing countermodel ... % 3.68/1.23 Prover 6: Constructing countermodel ... % 3.93/1.24 Prover 3: Constructing countermodel ... % 3.93/1.26 Prover 0: Proving ... % 3.93/1.26 Prover 4: Constructing countermodel ... % 3.93/1.29 Prover 2: Proving ... % 3.93/1.29 Prover 5: Proving ... % 4.62/1.34 Prover 1: gave up % 4.62/1.34 Prover 3: gave up % 4.62/1.34 Prover 6: gave up % 4.62/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.62/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.62/1.35 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 4.62/1.37 Prover 8: Preprocessing ... % 4.62/1.37 Prover 7: Preprocessing ... % 4.62/1.38 Prover 9: Preprocessing ... % 5.01/1.42 Prover 8: Warning: ignoring some quantifiers % 5.01/1.43 Prover 8: Constructing countermodel ... % 5.01/1.44 Prover 7: Constructing countermodel ... % 5.01/1.44 Prover 9: Constructing countermodel ... % 6.07/1.56 Prover 8: gave up % 6.07/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.07/1.59 Prover 10: Preprocessing ... % 6.78/1.63 Prover 10: Constructing countermodel ... % 6.78/1.65 Prover 9: proved (298ms) % 6.78/1.65 % 6.78/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.78/1.65 % 6.78/1.65 Prover 0: stopped % 6.78/1.65 Prover 5: stopped % 6.78/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.78/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.78/1.65 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.78/1.66 Prover 2: stopped % 6.78/1.67 Prover 16: Preprocessing ... % 6.78/1.67 Prover 13: Preprocessing ... % 6.78/1.67 Prover 10: gave up % 6.78/1.67 Prover 11: Preprocessing ... % 6.78/1.67 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 6.78/1.68 Prover 19: Preprocessing ... % 7.21/1.71 Prover 13: Warning: ignoring some quantifiers % 7.21/1.71 Prover 16: Warning: ignoring some quantifiers % 7.21/1.71 Prover 16: Constructing countermodel ... % 7.21/1.71 Prover 11: Constructing countermodel ... % 7.21/1.71 Prover 13: Constructing countermodel ... % 7.21/1.74 Prover 19: Warning: ignoring some quantifiers % 7.21/1.75 Prover 19: Constructing countermodel ... % 7.78/1.77 Prover 7: Found proof (size 87) % 7.78/1.77 Prover 7: proved (430ms) % 7.78/1.77 Prover 16: stopped % 7.78/1.77 Prover 13: stopped % 7.78/1.77 Prover 19: stopped % 7.78/1.78 Prover 4: Found proof (size 72) % 7.78/1.78 Prover 4: proved (1142ms) % 7.78/1.78 Prover 11: stopped % 7.78/1.78 % 7.78/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.78/1.78 % 7.78/1.79 % SZS output start Proof for theBenchmark % 7.78/1.79 Assumptions after simplification: % 7.78/1.79 --------------------------------- % 7.78/1.79 % 7.78/1.79 (conjecture_1) % 7.78/1.81 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 7.78/1.81 fast(v0) = v2 & small(v0) = v1) % 7.78/1.81 % 7.78/1.81 (formula_1) % 7.78/1.81 ! [v0: int] : ! [v1: int] : ($difference(v1, v0) = 1 | ~ (small(v0) = v1) | % 7.78/1.81 ? [v2: int] : ($lesseq(v2, 0)mod:(Int*Int)>Int(v0, 2) = v2)) & ! [v0: int] % 7.78/1.81 : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~ (mod:(Int*Int)>Int(v0, 2) = v1) | ? % 7.78/1.81 [v2: int] : (small(v0) = v2 & $product(v0, v0) = $sum($difference(v2, v0), % 7.78/1.81 -1))) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v1)) | ~ % 7.78/1.81 (mod:(Int*Int)>Int(v0, 2) = v1) | small(v0) = $sum(v0, 1)) & ! [v0: int] % 7.97/1.81 : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : ? [v3: int] : % 7.97/1.81 (($sum($difference(v3, v1), v0) = -1 & $product(v0, v0) = % 7.97/1.81 $sum($difference(v1, v0), -1)) | ($lesseq(1, v2) & % 7.97/1.81 mod:(Int*Int)>Int(v0, 2) = v2))) % 7.97/1.81 % 7.97/1.81 (formula_2) % 7.97/1.81 f0 = 0 % 7.97/1.81 % 7.97/1.81 (formula_3) % 7.97/1.82 ! [v0: int] : ! [v1: int] : ( ~ (g0(v0) = v1) | mod:(Int*Int)>Int(v0, 2) = % 7.97/1.82 v1) & ! [v0: int] : ! [v1: int] : ( ~ (mod:(Int*Int)>Int(v0, 2) = v1) | % 7.97/1.82 g0(v0) = v1) % 7.97/1.82 % 7.97/1.82 (formula_4) % 7.97/1.82 ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (h0(v0) = v1)) % 7.97/1.82 % 7.97/1.82 (formula_5) % 7.97/1.82 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 7.97/1.82 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = % 7.97/1.82 f0 | ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2)) % 7.97/1.82 % 7.97/1.82 (formula_6) % 7.97/1.82 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : ? [v3: int] % 7.97/1.82 : (u0(v2, v3) = v1 & h0(v0) = v3 & g0(v0) = v2)) & ! [v0: int] : ! [v1: % 7.97/1.82 int] : ( ~ (h0(v0) = v1) | ? [v2: int] : ? [v3: int] : (v0(v0) = v2 & % 7.97/1.82 u0(v3, v1) = v2 & g0(v0) = v3)) & ! [v0: int] : ! [v1: int] : ( ~ % 7.97/1.82 (g0(v0) = v1) | ? [v2: int] : ? [v3: int] : (v0(v0) = v2 & u0(v1, v3) = v2 % 7.97/1.82 & h0(v0) = v3)) % 7.97/1.82 % 7.97/1.82 (formula_7) % 7.97/1.82 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : (v0(v0) = % 7.97/1.82 v2 & $product(v2, v0) = $sum($difference(v1, v0), -1))) & ! [v0: int] : % 7.97/1.82 ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (fast(v0) = v2 & $product(v1, % 7.97/1.82 v0) = $sum($difference(v2, v0), -1))) % 7.97/1.82 % 7.97/1.82 (function-axioms) % 7.97/1.83 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ % 7.97/1.83 (u0(v3, v2) = v1) | ~ (u0(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 7.97/1.83 [v2: int] : ! [v3: int] : (v1 = v0 | ~ (mod:(Int*Int)>Int(v3, v2) = v1) | ~ % 7.97/1.83 (mod:(Int*Int)>Int(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 7.97/1.83 int] : (v1 = v0 | ~ (fast(v2) = v1) | ~ (fast(v2) = v0)) & ! [v0: int] : % 7.97/1.83 ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (v0(v2) = v1) | ~ (v0(v2) = v0)) & % 7.97/1.83 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (h0(v2) = v1) | ~ % 7.97/1.83 (h0(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 7.97/1.83 (g0(v2) = v1) | ~ (g0(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: % 7.97/1.83 int] : (v1 = v0 | ~ (small(v2) = v1) | ~ (small(v2) = v0)) % 7.97/1.83 % 7.97/1.83 Those formulas are unsatisfiable: % 7.97/1.83 --------------------------------- % 7.97/1.83 % 7.97/1.83 Begin of proof % 7.97/1.83 | % 7.97/1.83 | ALPHA: (formula_1) implies: % 7.97/1.83 | (1) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : ? % 7.97/1.83 | [v3: int] : (($sum($difference(v3, v1), v0) = -1 & $product(v0, v0) = % 7.97/1.83 | $sum($difference(v1, v0), -1)) | ($lesseq(1, v2) & % 7.97/1.83 | mod:(Int*Int)>Int(v0, 2) = v2))) % 7.97/1.83 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v1)) | ~ % 7.97/1.83 | (mod:(Int*Int)>Int(v0, 2) = v1) | small(v0) = $sum(v0, 1)) % 7.97/1.84 | (3) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~ % 7.97/1.84 | (mod:(Int*Int)>Int(v0, 2) = v1) | ? [v2: int] : (small(v0) = v2 & % 7.97/1.84 | $product(v0, v0) = $sum($difference(v2, v0), -1))) % 8.09/1.84 | (4) ! [v0: int] : ! [v1: int] : ($difference(v1, v0) = 1 | ~ (small(v0) % 8.09/1.84 | = v1) | ? [v2: int] : ($lesseq(v2, 0)mod:(Int*Int)>Int(v0, 2) = % 8.09/1.84 | v2)) % 8.09/1.84 | % 8.09/1.84 | ALPHA: (formula_3) implies: % 8.09/1.84 | (5) ! [v0: int] : ! [v1: int] : ( ~ (g0(v0) = v1) | mod:(Int*Int)>Int(v0, % 8.09/1.84 | 2) = v1) % 8.09/1.84 | % 8.09/1.84 | ALPHA: (formula_5) implies: % 8.09/1.84 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = f0 | ~ ($lesseq(1, % 8.09/1.84 | v0)) | ~ (u0(v0, v1) = v2)) % 8.09/1.84 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 8.09/1.84 | 0) | ~ (u0(v0, v1) = v2)) % 8.09/1.84 | % 8.09/1.84 | ALPHA: (formula_6) implies: % 8.09/1.84 | (8) ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : ? % 8.09/1.84 | [v3: int] : (u0(v2, v3) = v1 & h0(v0) = v3 & g0(v0) = v2)) % 8.09/1.84 | % 8.09/1.84 | ALPHA: (formula_7) implies: % 8.09/1.84 | (9) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : % 8.09/1.84 | (v0(v0) = v2 & $product(v2, v0) = $sum($difference(v1, v0), -1))) % 8.09/1.84 | % 8.09/1.84 | ALPHA: (function-axioms) implies: % 8.09/1.84 | (10) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (small(v2) % 8.09/1.84 | = v1) | ~ (small(v2) = v0)) % 8.09/1.84 | (11) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | % 8.09/1.84 | ~ (mod:(Int*Int)>Int(v3, v2) = v1) | ~ (mod:(Int*Int)>Int(v3, v2) % 8.09/1.84 | = v0)) % 8.09/1.84 | % 8.09/1.84 | DELTA: instantiating (conjecture_1) with fresh symbols all_10_0, all_10_1, % 8.09/1.84 | all_10_2 gives: % 8.09/1.84 | (12) ~ (all_10_0 = all_10_1) & $lesseq(0, all_10_2) & fast(all_10_2) = % 8.09/1.84 | all_10_0 & small(all_10_2) = all_10_1 % 8.09/1.84 | % 8.09/1.84 | ALPHA: (12) implies: % 8.09/1.84 | (13) ~ (all_10_0 = all_10_1) % 8.09/1.84 | (14) small(all_10_2) = all_10_1 % 8.09/1.84 | (15) fast(all_10_2) = all_10_0 % 8.09/1.84 | % 8.09/1.84 | GROUND_INST: instantiating (4) with all_10_2, all_10_1, simplifying with (14) % 8.09/1.84 | gives: % 8.09/1.85 | (16) $difference(all_10_1, all_10_2) = 1 | ? [v0: int] : ($lesseq(v0, % 8.09/1.85 | 0)mod:(Int*Int)>Int(all_10_2, 2) = v0) % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (1) with all_10_2, all_10_1, simplifying with (14) % 8.09/1.85 | gives: % 8.09/1.85 | (17) ? [v0: int] : ? [v1: int] : (($sum($difference(v1, all_10_1), % 8.09/1.85 | all_10_2) = -1 & $product(all_10_2, all_10_2) = % 8.09/1.85 | $sum($difference(all_10_1, all_10_2), -1)) | ($lesseq(1, v0) & % 8.09/1.85 | mod:(Int*Int)>Int(all_10_2, 2) = v0)) % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (9) with all_10_2, all_10_0, simplifying with (15) % 8.09/1.85 | gives: % 8.09/1.85 | (18) ? [v0: int] : (v0(all_10_2) = v0 & $product(v0, all_10_2) = % 8.09/1.85 | $sum($difference(all_10_0, all_10_2), -1)) % 8.09/1.85 | % 8.09/1.85 | DELTA: instantiating (18) with fresh symbol all_20_0 gives: % 8.09/1.85 | (19) v0(all_10_2) = all_20_0 & $product(all_20_0, all_10_2) = % 8.09/1.85 | $sum($difference(all_10_0, all_10_2), -1) % 8.09/1.85 | % 8.09/1.85 | ALPHA: (19) implies: % 8.09/1.85 | (20) $product(all_20_0, all_10_2) = $sum($difference(all_10_0, all_10_2), % 8.09/1.85 | -1) % 8.09/1.85 | (21) v0(all_10_2) = all_20_0 % 8.09/1.85 | % 8.09/1.85 | DELTA: instantiating (17) with fresh symbols all_22_0, all_22_1 gives: % 8.09/1.85 | (22) ($sum($difference(all_22_0, all_10_1), all_10_2) = -1 & % 8.09/1.85 | $product(all_10_2, all_10_2) = $sum($difference(all_10_1, all_10_2), % 8.09/1.85 | -1)) | ($lesseq(1, all_22_1) & mod:(Int*Int)>Int(all_10_2, 2) = % 8.09/1.85 | all_22_1) % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (8) with all_10_2, all_20_0, simplifying with (21) % 8.09/1.85 | gives: % 8.09/1.85 | (23) ? [v0: int] : ? [v1: int] : (u0(v0, v1) = all_20_0 & h0(all_10_2) = % 8.09/1.85 | v1 & g0(all_10_2) = v0) % 8.09/1.85 | % 8.09/1.85 | DELTA: instantiating (23) with fresh symbols all_30_0, all_30_1 gives: % 8.09/1.85 | (24) u0(all_30_1, all_30_0) = all_20_0 & h0(all_10_2) = all_30_0 & % 8.09/1.85 | g0(all_10_2) = all_30_1 % 8.09/1.85 | % 8.09/1.85 | ALPHA: (24) implies: % 8.09/1.85 | (25) g0(all_10_2) = all_30_1 % 8.09/1.85 | (26) h0(all_10_2) = all_30_0 % 8.09/1.85 | (27) u0(all_30_1, all_30_0) = all_20_0 % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (formula_4) with all_10_2, all_30_0, simplifying % 8.09/1.85 | with (26) gives: % 8.09/1.85 | (28) all_30_0 = all_10_2 % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (7) with all_30_1, all_30_0, all_20_0, simplifying % 8.09/1.85 | with (27) gives: % 8.09/1.85 | (29) all_30_0 = all_20_0 | ~ ($lesseq(all_30_1, 0) % 8.09/1.85 | % 8.09/1.85 | REDUCE: (27), (28) imply: % 8.09/1.85 | (30) u0(all_30_1, all_10_2) = all_20_0 % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (6) with all_30_1, all_10_2, all_20_0, simplifying % 8.09/1.85 | with (30) gives: % 8.09/1.85 | (31) all_20_0 = f0 | ~ ($lesseq(1, all_30_1)) % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (5) with all_10_2, all_30_1, simplifying with (25) % 8.09/1.85 | gives: % 8.09/1.85 | (32) mod:(Int*Int)>Int(all_10_2, 2) = all_30_1 % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (3) with all_10_2, all_30_1, simplifying with (32) % 8.09/1.85 | gives: % 8.09/1.85 | (33) ~ ($lesseq(all_30_1, 0) | ? [v0: int] : (small(all_10_2) = v0 & % 8.09/1.85 | $product(all_10_2, all_10_2) = $sum($difference(v0, all_10_2), % 8.09/1.85 | -1)) % 8.09/1.85 | % 8.09/1.85 | GROUND_INST: instantiating (2) with all_10_2, all_30_1, simplifying with (32) % 8.09/1.86 | gives: % 8.09/1.86 | (34) ~ ($lesseq(1, all_30_1)) | small(all_10_2) = $sum(all_10_2, 1) % 8.09/1.86 | % 8.09/1.86 | BETA: splitting (16) gives: % 8.09/1.86 | % 8.09/1.86 | Case 1: % 8.09/1.86 | | % 8.09/1.86 | | (35) $difference(all_10_1, all_10_2) = 1 % 8.09/1.86 | | % 8.09/1.86 | | REDUCE: (13), (35) imply: % 8.09/1.86 | | (36) ~ ($difference(all_10_0, all_10_2) = 1) % 8.09/1.86 | | % 8.09/1.86 | | BETA: splitting (22) gives: % 8.09/1.86 | | % 8.09/1.86 | | Case 1: % 8.09/1.86 | | | % 8.09/1.86 | | | (37) $sum($difference(all_22_0, all_10_1), all_10_2) = -1 & % 8.09/1.86 | | | $product(all_10_2, all_10_2) = $sum($difference(all_10_1, % 8.09/1.86 | | | all_10_2), -1) % 8.09/1.86 | | | % 8.09/1.86 | | | ALPHA: (37) implies: % 8.09/1.86 | | | (38) $product(all_10_2, all_10_2) = $sum($difference(all_10_1, % 8.09/1.86 | | | all_10_2), -1) % 8.09/1.86 | | | % 8.09/1.86 | | | REDUCE: (35), (38) imply: % 8.09/1.86 | | | (39) $product(all_10_2, all_10_2) = 0 % 8.09/1.86 | | | % 8.09/1.86 | | | THEORY_AXIOM GroebnerMultiplication: % 8.09/1.86 | | | (40) ! [v0: int] : (v0 = 0 | ~ ($product(v0, v0) = 0)) % 8.09/1.86 | | | % 8.09/1.86 | | | GROUND_INST: instantiating (40) with all_10_2, simplifying with (39) % 8.09/1.86 | | | gives: % 8.09/1.86 | | | (41) all_10_2 = 0 % 8.09/1.86 | | | % 8.09/1.86 | | | REDUCE: (36), (41) imply: % 8.09/1.86 | | | (42) ~ (all_10_0 = 1) % 8.09/1.86 | | | % 8.09/1.86 | | | REDUCE: (20), (41) imply: % 8.09/1.86 | | | (43) $product(all_20_0, 0) = $sum(all_10_0, -1) % 8.09/1.86 | | | % 8.09/1.86 | | | THEORY_AXIOM GroebnerMultiplication: % 8.09/1.86 | | | (44) ! [v0: int] : ! [v1: int] : (v0 = 1 | ~ ($product(v1, 0) = % 8.09/1.86 | | | $sum(v0, -1))) % 8.09/1.86 | | | % 8.09/1.86 | | | GROUND_INST: instantiating (44) with all_10_0, all_20_0, simplifying with % 8.09/1.86 | | | (43) gives: % 8.09/1.86 | | | (45) all_10_0 = 1 % 8.09/1.86 | | | % 8.09/1.86 | | | REDUCE: (42), (45) imply: % 8.09/1.86 | | | (46) $false % 8.09/1.86 | | | % 8.09/1.86 | | | CLOSE: (46) is inconsistent. % 8.09/1.86 | | | % 8.09/1.86 | | Case 2: % 8.09/1.86 | | | % 8.09/1.86 | | | (47) $lesseq(1, all_22_1) & mod:(Int*Int)>Int(all_10_2, 2) = all_22_1 % 8.09/1.86 | | | % 8.09/1.86 | | | ALPHA: (47) implies: % 8.09/1.86 | | | (48) $lesseq(1, all_22_1) % 8.09/1.86 | | | (49) mod:(Int*Int)>Int(all_10_2, 2) = all_22_1 % 8.09/1.86 | | | % 8.09/1.86 | | | REF_CLOSE: (11), (20), (31), (32), (36), (48), (49), (formula_2) are % 8.09/1.86 | | | inconsistent by sub-proof #1. % 8.09/1.86 | | | % 8.09/1.86 | | End of split % 8.09/1.86 | | % 8.09/1.86 | Case 2: % 8.09/1.86 | | % 8.09/1.86 | | (50) ~ ($difference(all_10_1, all_10_2) = 1) % 8.09/1.86 | | % 8.09/1.86 | | BETA: splitting (34) gives: % 8.09/1.86 | | % 8.09/1.86 | | Case 1: % 8.09/1.86 | | | % 8.09/1.86 | | | (51) small(all_10_2) = $sum(all_10_2, 1) % 8.09/1.86 | | | % 8.09/1.86 | | | GROUND_INST: instantiating (10) with all_10_1, $sum(all_10_2, 1), % 8.09/1.86 | | | all_10_2, simplifying with (14), (51) gives: % 8.09/1.86 | | | (52) $difference(all_10_1, all_10_2) = 1 % 8.09/1.86 | | | % 8.09/1.87 | | | REDUCE: (50), (52) imply: % 8.09/1.87 | | | (53) $false % 8.09/1.87 | | | % 8.09/1.87 | | | CLOSE: (53) is inconsistent. % 8.09/1.87 | | | % 8.09/1.87 | | Case 2: % 8.09/1.87 | | | % 8.09/1.87 | | | (54) $lesseq(all_30_1, 0) % 8.09/1.87 | | | (55) ~ (small(all_10_2) = $sum(all_10_2, 1)) % 8.09/1.87 | | | % 8.09/1.87 | | | BETA: splitting (29) gives: % 8.09/1.87 | | | % 8.09/1.87 | | | Case 1: % 8.09/1.87 | | | | % 8.09/1.87 | | | | (56) $lesseq(1, all_30_1) % 8.09/1.87 | | | | % 8.09/1.87 | | | | COMBINE_INEQS: (54), (56) imply: % 8.09/1.87 | | | | (57) $false % 8.09/1.87 | | | | % 8.09/1.87 | | | | CLOSE: (57) is inconsistent. % 8.09/1.87 | | | | % 8.09/1.87 | | | Case 2: % 8.09/1.87 | | | | % 8.09/1.87 | | | | (58) all_30_0 = all_20_0 % 8.09/1.87 | | | | % 8.09/1.87 | | | | COMBINE_EQS: (28), (58) imply: % 8.09/1.87 | | | | (59) all_20_0 = all_10_2 % 8.09/1.87 | | | | % 8.09/1.87 | | | | SIMP: (59) implies: % 8.09/1.87 | | | | (60) all_20_0 = all_10_2 % 8.09/1.87 | | | | % 8.09/1.87 | | | | REDUCE: (20), (60) imply: % 8.09/1.87 | | | | (61) $product(all_10_2, all_10_2) = $sum($difference(all_10_0, % 8.09/1.87 | | | | all_10_2), -1) % 8.09/1.87 | | | | % 8.09/1.87 | | | | BETA: splitting (22) gives: % 8.09/1.87 | | | | % 8.09/1.87 | | | | Case 1: % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | (62) $sum($difference(all_22_0, all_10_1), all_10_2) = -1 & % 8.09/1.87 | | | | | $product(all_10_2, all_10_2) = $sum($difference(all_10_1, % 8.09/1.87 | | | | | all_10_2), -1) % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | ALPHA: (62) implies: % 8.09/1.87 | | | | | (63) $product(all_10_2, all_10_2) = $sum($difference(all_10_1, % 8.09/1.87 | | | | | all_10_2), -1) % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | THEORY_AXIOM GroebnerMultiplication: % 8.09/1.87 | | | | | (64) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 8.09/1.87 | | | | | ($product(v0, v0) = $sum($difference(v2, v0), -1)) | ~ % 8.09/1.87 | | | | | ($product(v0, v0) = $sum($difference(v1, v0), -1))) % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | GROUND_INST: instantiating (64) with all_10_2, all_10_1, all_10_0, % 8.09/1.87 | | | | | simplifying with (61), (63) gives: % 8.09/1.87 | | | | | (65) all_10_0 = all_10_1 % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | REDUCE: (13), (65) imply: % 8.09/1.87 | | | | | (66) $false % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | CLOSE: (66) is inconsistent. % 8.09/1.87 | | | | | % 8.09/1.87 | | | | Case 2: % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | (67) $lesseq(1, all_22_1) & mod:(Int*Int)>Int(all_10_2, 2) = % 8.09/1.87 | | | | | all_22_1 % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | ALPHA: (67) implies: % 8.09/1.87 | | | | | (68) $lesseq(1, all_22_1) % 8.09/1.87 | | | | | (69) mod:(Int*Int)>Int(all_10_2, 2) = all_22_1 % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | BETA: splitting (33) gives: % 8.09/1.87 | | | | | % 8.09/1.87 | | | | | Case 1: % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | (70) $lesseq(1, all_30_1) % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | COMBINE_INEQS: (54), (70) imply: % 8.09/1.87 | | | | | | (71) $false % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | CLOSE: (71) is inconsistent. % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | Case 2: % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | (72) ? [v0: int] : (small(all_10_2) = v0 & $product(all_10_2, % 8.09/1.87 | | | | | | all_10_2) = $sum($difference(v0, all_10_2), -1)) % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | DELTA: instantiating (72) with fresh symbol all_83_0 gives: % 8.09/1.87 | | | | | | (73) small(all_10_2) = all_83_0 & $product(all_10_2, all_10_2) = % 8.09/1.87 | | | | | | $sum($difference(all_83_0, all_10_2), -1) % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | ALPHA: (73) implies: % 8.09/1.87 | | | | | | (74) small(all_10_2) = all_83_0 % 8.09/1.87 | | | | | | (75) $product(all_10_2, all_10_2) = $sum($difference(all_83_0, % 8.09/1.87 | | | | | | all_10_2), -1) % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | THEORY_AXIOM GroebnerMultiplication: % 8.09/1.87 | | | | | | (76) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 8.09/1.87 | | | | | | ($product(v0, v0) = $sum($difference(v2, v0), -1)) | ~ % 8.09/1.87 | | | | | | ($product(v0, v0) = $sum($difference(v1, v0), -1))) % 8.09/1.87 | | | | | | % 8.09/1.87 | | | | | | GROUND_INST: instantiating (76) with all_10_2, all_10_0, all_83_0, % 8.09/1.87 | | | | | | simplifying with (61), (75) gives: % 8.09/1.88 | | | | | | (77) all_83_0 = all_10_0 % 8.09/1.88 | | | | | | % 8.09/1.88 | | | | | | REDUCE: (74), (77) imply: % 8.09/1.88 | | | | | | (78) small(all_10_2) = all_10_0 % 8.09/1.88 | | | | | | % 8.09/1.88 | | | | | | PRED_UNIFY: (55), (78) imply: % 8.09/1.88 | | | | | | (79) ~ ($difference(all_10_0, all_10_2) = 1) % 8.09/1.88 | | | | | | % 8.09/1.88 | | | | | | REF_CLOSE: (11), (20), (31), (32), (68), (69), (79), (formula_2) are % 8.09/1.88 | | | | | | inconsistent by sub-proof #1. % 8.09/1.88 | | | | | | % 8.09/1.88 | | | | | End of split % 8.09/1.88 | | | | | % 8.09/1.88 | | | | End of split % 8.09/1.88 | | | | % 8.09/1.88 | | | End of split % 8.09/1.88 | | | % 8.09/1.88 | | End of split % 8.09/1.88 | | % 8.09/1.88 | End of split % 8.09/1.88 | % 8.09/1.88 End of proof % 8.09/1.88 % 8.09/1.88 Sub-proof #1 shows that the following formulas are inconsistent: % 8.09/1.88 ---------------------------------------------------------------- % 8.09/1.88 (1) all_20_0 = f0 | ~ ($lesseq(1, all_30_1)) % 8.09/1.88 (2) ~ ($difference(all_10_0, all_10_2) = 1) % 8.09/1.88 (3) $product(all_20_0, all_10_2) = $sum($difference(all_10_0, all_10_2), -1) % 8.09/1.88 (4) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ % 8.09/1.88 (mod:(Int*Int)>Int(v3, v2) = v1) | ~ (mod:(Int*Int)>Int(v3, v2) = v0)) % 8.09/1.88 (5) $lesseq(1, all_22_1) % 8.09/1.88 (6) f0 = 0 % 8.09/1.88 (7) mod:(Int*Int)>Int(all_10_2, 2) = all_22_1 % 8.09/1.88 (8) mod:(Int*Int)>Int(all_10_2, 2) = all_30_1 % 8.09/1.88 % 8.09/1.88 Begin of proof % 8.09/1.88 | % 8.09/1.88 | GROUND_INST: instantiating (4) with all_30_1, all_22_1, 2, all_10_2, % 8.09/1.88 | simplifying with (7), (8) gives: % 8.09/1.88 | (9) all_30_1 = all_22_1 % 8.09/1.88 | % 8.09/1.88 | BETA: splitting (1) gives: % 8.09/1.88 | % 8.09/1.88 | Case 1: % 8.09/1.88 | | % 8.09/1.88 | | (10) $lesseq(all_30_1, 0) % 8.09/1.88 | | % 8.09/1.88 | | REDUCE: (9), (10) imply: % 8.09/1.88 | | (11) $lesseq(all_22_1, 0) % 8.09/1.88 | | % 8.09/1.88 | | COMBINE_INEQS: (5), (11) imply: % 8.09/1.88 | | (12) $false % 8.09/1.88 | | % 8.09/1.88 | | CLOSE: (12) is inconsistent. % 8.09/1.88 | | % 8.09/1.88 | Case 2: % 8.09/1.88 | | % 8.09/1.88 | | (13) all_20_0 = f0 % 8.09/1.88 | | % 8.09/1.88 | | COMBINE_EQS: (6), (13) imply: % 8.09/1.88 | | (14) all_20_0 = 0 % 8.09/1.88 | | % 8.09/1.88 | | REDUCE: (3), (14) imply: % 8.09/1.88 | | (15) $product(0, all_10_2) = $sum($difference(all_10_0, all_10_2), -1) % 8.09/1.88 | | % 8.09/1.88 | | THEORY_AXIOM GroebnerMultiplication: % 8.09/1.88 | | (16) ! [v0: int] : ! [v1: int] : ($difference(v1, v0) = 1 | ~ % 8.09/1.88 | | ($product(0, v0) = $sum($difference(v1, v0), -1))) % 8.09/1.88 | | % 8.09/1.88 | | GROUND_INST: instantiating (16) with all_10_2, all_10_0, simplifying with % 8.09/1.88 | | (15) gives: % 8.09/1.88 | | (17) $difference(all_10_0, all_10_2) = 1 % 8.09/1.88 | | % 8.09/1.88 | | REDUCE: (2), (17) imply: % 8.09/1.88 | | (18) $false % 8.09/1.88 | | % 8.09/1.88 | | CLOSE: (18) is inconsistent. % 8.09/1.88 | | % 8.09/1.88 | End of split % 8.09/1.88 | % 8.09/1.88 End of proof % 8.09/1.88 % SZS output end Proof for theBenchmark % 8.09/1.88 % 8.09/1.88 1273ms %------------------------------------------------------------------------------