%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT002_1 : TPTP v8.1.2. Released v5.0.0. % 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 22:18:50 EDT 2023 % Result : Theorem 3.67s 1.32s % Output : Proof 4.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : DAT002_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n020.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Aug 24 14:49:30 EDT 2023 % 0.11/0.34 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.24/1.06 Prover 4: Preprocessing ... % 2.24/1.06 Prover 1: Preprocessing ... % 2.63/1.10 Prover 2: Preprocessing ... % 2.63/1.10 Prover 3: Preprocessing ... % 2.63/1.10 Prover 6: Preprocessing ... % 2.63/1.10 Prover 5: Preprocessing ... % 2.63/1.10 Prover 0: Preprocessing ... % 3.41/1.21 Prover 4: Constructing countermodel ... % 3.41/1.21 Prover 1: Constructing countermodel ... % 3.41/1.21 Prover 6: Constructing countermodel ... % 3.41/1.22 Prover 5: Proving ... % 3.41/1.22 Prover 2: Proving ... % 3.41/1.22 Prover 3: Constructing countermodel ... % 3.41/1.23 Prover 0: Proving ... % 3.67/1.32 Prover 3: proved (643ms) % 3.67/1.32 % 3.67/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.67/1.32 % 3.67/1.33 Prover 0: proved (648ms) % 3.67/1.33 % 3.67/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.67/1.33 % 3.67/1.33 Prover 6: stopped % 3.67/1.33 Prover 5: stopped % 3.67/1.33 Prover 2: stopped % 3.67/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.67/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.67/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.67/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.67/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.37/1.35 Prover 8: Preprocessing ... % 4.37/1.36 Prover 11: Preprocessing ... % 4.37/1.36 Prover 10: Preprocessing ... % 4.37/1.37 Prover 7: Preprocessing ... % 4.37/1.37 Prover 13: Preprocessing ... % 4.37/1.40 Prover 1: Found proof (size 34) % 4.37/1.40 Prover 1: proved (724ms) % 4.37/1.40 Prover 4: stopped % 4.37/1.40 Prover 10: Constructing countermodel ... % 4.37/1.40 Prover 8: Warning: ignoring some quantifiers % 4.37/1.41 Prover 11: Constructing countermodel ... % 4.37/1.41 Prover 13: Warning: ignoring some quantifiers % 4.37/1.41 Prover 8: Constructing countermodel ... % 4.37/1.41 Prover 13: Constructing countermodel ... % 4.37/1.41 Prover 8: stopped % 4.37/1.41 Prover 10: stopped % 4.37/1.41 Prover 11: stopped % 4.37/1.42 Prover 13: stopped % 4.37/1.42 Prover 7: Constructing countermodel ... % 4.37/1.42 Prover 7: stopped % 4.37/1.42 % 4.37/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.37/1.42 % 4.37/1.43 % SZS output start Proof for theBenchmark % 4.37/1.43 Assumptions after simplification: % 4.37/1.43 --------------------------------- % 4.37/1.43 % 4.37/1.43 (check_list) % 4.37/1.46 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: list] : ? [v3: list] : ? % 4.37/1.46 [v4: list] : ? [v5: int] : ( ~ (v5 = 0) & mycons(100, nil) = v0 & mycons(7, % 4.37/1.46 v0) = v1 & mycons(4, v1) = v2 & mycons(2, v2) = v3 & mycons(1, v3) = v4 & % 4.37/1.46 fib_sorted(v4) = v5 & list(v4) & list(v3) & list(v2) & list(v1) & list(v0)) % 4.37/1.46 % 4.37/1.46 (double_is_fib_sorted_if_ordered) % 4.37/1.46 list(nil) & ! [v0: int] : ! [v1: int] : ! [v2: list] : ! [v3: list] : ( ~ % 4.37/1.46 ($lesseq(1, $difference(v1, v0))) | ~ (mycons(v1, nil) = v2) | ~ % 4.37/1.46 (mycons(v0, v2) = v3) | fib_sorted(v3) = 0) % 4.37/1.46 % 4.37/1.46 (recursive_fib_sort) % 4.37/1.46 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: list] : ! [v4: list] : % 4.37/1.46 ! [v5: list] : ! [v6: list] : ( ~ ($lesseq(v0, $difference(v2, v1))) | ~ % 4.37/1.46 ($lesseq(1, $difference(v1, v0))) | ~ (mycons(v2, v3) = v4) | ~ % 4.37/1.46 (mycons(v1, v4) = v5) | ~ (mycons(v0, v5) = v6) | ~ list(v3) | ? [v7: % 4.37/1.46 any] : ? [v8: any] : (fib_sorted(v6) = v8 & fib_sorted(v5) = v7 & ( ~ (v7 % 4.37/1.46 = 0) | v8 = 0))) % 4.37/1.46 % 4.37/1.46 (function-axioms) % 4.37/1.46 ! [v0: list] : ! [v1: list] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~ % 4.37/1.46 (mycons(v3, v2) = v1) | ~ (mycons(v3, v2) = v0)) & ! [v0: % 4.37/1.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list] : (v1 = v0 | % 4.37/1.46 ~ (fib_sorted(v2) = v1) | ~ (fib_sorted(v2) = v0)) % 4.37/1.47 % 4.37/1.47 Further assumptions not needed in the proof: % 4.37/1.47 -------------------------------------------- % 4.37/1.47 empty_fib_sorted, single_is_fib_sorted % 4.37/1.47 % 4.37/1.47 Those formulas are unsatisfiable: % 4.37/1.47 --------------------------------- % 4.37/1.47 % 4.37/1.47 Begin of proof % 4.37/1.47 | % 4.37/1.47 | ALPHA: (double_is_fib_sorted_if_ordered) implies: % 4.37/1.47 | (1) ! [v0: int] : ! [v1: int] : ! [v2: list] : ! [v3: list] : ( ~ % 4.37/1.47 | ($lesseq(1, $difference(v1, v0))) | ~ (mycons(v1, nil) = v2) | ~ % 4.37/1.47 | (mycons(v0, v2) = v3) | fib_sorted(v3) = 0) % 4.37/1.47 | % 4.37/1.47 | ALPHA: (check_list) implies: % 4.37/1.47 | (2) list(nil) % 4.37/1.47 | (3) ? [v0: list] : ? [v1: list] : ? [v2: list] : ? [v3: list] : ? [v4: % 4.37/1.47 | list] : ? [v5: int] : ( ~ (v5 = 0) & mycons(100, nil) = v0 & % 4.37/1.47 | mycons(7, v0) = v1 & mycons(4, v1) = v2 & mycons(2, v2) = v3 & % 4.37/1.47 | mycons(1, v3) = v4 & fib_sorted(v4) = v5 & list(v4) & list(v3) & % 4.37/1.47 | list(v2) & list(v1) & list(v0)) % 4.37/1.47 | % 4.37/1.47 | ALPHA: (function-axioms) implies: % 4.37/1.47 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list] % 4.37/1.47 | : (v1 = v0 | ~ (fib_sorted(v2) = v1) | ~ (fib_sorted(v2) = v0)) % 4.37/1.47 | % 4.37/1.48 | DELTA: instantiating (3) with fresh symbols all_9_0, all_9_1, all_9_2, % 4.37/1.48 | all_9_3, all_9_4, all_9_5 gives: % 4.37/1.48 | (5) ~ (all_9_0 = 0) & mycons(100, nil) = all_9_5 & mycons(7, all_9_5) = % 4.37/1.48 | all_9_4 & mycons(4, all_9_4) = all_9_3 & mycons(2, all_9_3) = all_9_2 & % 4.37/1.48 | mycons(1, all_9_2) = all_9_1 & fib_sorted(all_9_1) = all_9_0 & % 4.37/1.48 | list(all_9_1) & list(all_9_2) & list(all_9_3) & list(all_9_4) & % 4.37/1.48 | list(all_9_5) % 4.37/1.48 | % 4.37/1.48 | ALPHA: (5) implies: % 4.37/1.48 | (6) ~ (all_9_0 = 0) % 4.37/1.48 | (7) list(all_9_5) % 4.37/1.48 | (8) list(all_9_4) % 4.37/1.48 | (9) fib_sorted(all_9_1) = all_9_0 % 4.37/1.48 | (10) mycons(1, all_9_2) = all_9_1 % 4.37/1.48 | (11) mycons(2, all_9_3) = all_9_2 % 4.37/1.48 | (12) mycons(4, all_9_4) = all_9_3 % 4.37/1.48 | (13) mycons(7, all_9_5) = all_9_4 % 4.37/1.48 | (14) mycons(100, nil) = all_9_5 % 4.37/1.48 | % 4.37/1.48 | GROUND_INST: instantiating (recursive_fib_sort) with 1, 2, 4, all_9_4, % 4.37/1.48 | all_9_3, all_9_2, all_9_1, simplifying with (8), (10), (11), (12) % 4.37/1.48 | gives: % 4.37/1.48 | (15) ? [v0: any] : ? [v1: any] : (fib_sorted(all_9_1) = v1 & % 4.37/1.48 | fib_sorted(all_9_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.37/1.48 | % 4.37/1.48 | GROUND_INST: instantiating (recursive_fib_sort) with 2, 4, 7, all_9_5, % 4.37/1.48 | all_9_4, all_9_3, all_9_2, simplifying with (7), (11), (12), (13) % 4.37/1.48 | gives: % 4.37/1.49 | (16) ? [v0: any] : ? [v1: any] : (fib_sorted(all_9_2) = v1 & % 4.37/1.49 | fib_sorted(all_9_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.37/1.49 | % 4.37/1.49 | GROUND_INST: instantiating (recursive_fib_sort) with 4, 7, 100, nil, all_9_5, % 4.37/1.49 | all_9_4, all_9_3, simplifying with (2), (12), (13), (14) gives: % 4.37/1.49 | (17) ? [v0: any] : ? [v1: any] : (fib_sorted(all_9_3) = v1 & % 4.37/1.49 | fib_sorted(all_9_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.37/1.49 | % 4.37/1.49 | GROUND_INST: instantiating (1) with 7, 100, all_9_5, all_9_4, simplifying with % 4.37/1.49 | (13), (14) gives: % 4.37/1.49 | (18) fib_sorted(all_9_4) = 0 % 4.37/1.49 | % 4.37/1.49 | DELTA: instantiating (16) with fresh symbols all_17_0, all_17_1 gives: % 4.37/1.49 | (19) fib_sorted(all_9_2) = all_17_0 & fib_sorted(all_9_3) = all_17_1 & ( ~ % 4.37/1.49 | (all_17_1 = 0) | all_17_0 = 0) % 4.37/1.49 | % 4.37/1.49 | ALPHA: (19) implies: % 4.37/1.49 | (20) fib_sorted(all_9_3) = all_17_1 % 4.37/1.49 | (21) fib_sorted(all_9_2) = all_17_0 % 4.37/1.49 | (22) ~ (all_17_1 = 0) | all_17_0 = 0 % 4.37/1.49 | % 4.37/1.49 | DELTA: instantiating (15) with fresh symbols all_19_0, all_19_1 gives: % 4.37/1.49 | (23) fib_sorted(all_9_1) = all_19_0 & fib_sorted(all_9_2) = all_19_1 & ( ~ % 4.37/1.49 | (all_19_1 = 0) | all_19_0 = 0) % 4.37/1.49 | % 4.37/1.49 | ALPHA: (23) implies: % 4.37/1.49 | (24) fib_sorted(all_9_2) = all_19_1 % 4.37/1.49 | (25) fib_sorted(all_9_1) = all_19_0 % 4.37/1.49 | (26) ~ (all_19_1 = 0) | all_19_0 = 0 % 4.37/1.49 | % 4.37/1.49 | DELTA: instantiating (17) with fresh symbols all_21_0, all_21_1 gives: % 4.37/1.49 | (27) fib_sorted(all_9_3) = all_21_0 & fib_sorted(all_9_4) = all_21_1 & ( ~ % 4.37/1.49 | (all_21_1 = 0) | all_21_0 = 0) % 4.37/1.49 | % 4.37/1.49 | ALPHA: (27) implies: % 4.37/1.49 | (28) fib_sorted(all_9_4) = all_21_1 % 4.37/1.49 | (29) fib_sorted(all_9_3) = all_21_0 % 4.37/1.49 | (30) ~ (all_21_1 = 0) | all_21_0 = 0 % 4.37/1.49 | % 4.37/1.49 | GROUND_INST: instantiating (4) with 0, all_21_1, all_9_4, simplifying with % 4.37/1.49 | (18), (28) gives: % 4.37/1.49 | (31) all_21_1 = 0 % 4.37/1.49 | % 4.37/1.49 | GROUND_INST: instantiating (4) with all_17_1, all_21_0, all_9_3, simplifying % 4.37/1.49 | with (20), (29) gives: % 4.37/1.50 | (32) all_21_0 = all_17_1 % 4.90/1.50 | % 4.90/1.50 | GROUND_INST: instantiating (4) with all_17_0, all_19_1, all_9_2, simplifying % 4.90/1.50 | with (21), (24) gives: % 4.90/1.50 | (33) all_19_1 = all_17_0 % 4.90/1.50 | % 4.90/1.50 | GROUND_INST: instantiating (4) with all_9_0, all_19_0, all_9_1, simplifying % 4.90/1.50 | with (9), (25) gives: % 4.90/1.50 | (34) all_19_0 = all_9_0 % 4.90/1.50 | % 4.90/1.50 | BETA: splitting (30) gives: % 4.90/1.50 | % 4.90/1.50 | Case 1: % 4.90/1.50 | | % 4.90/1.50 | | (35) ~ (all_21_1 = 0) % 4.90/1.50 | | % 4.90/1.50 | | REDUCE: (31), (35) imply: % 4.90/1.50 | | (36) $false % 4.90/1.50 | | % 4.90/1.50 | | CLOSE: (36) is inconsistent. % 4.90/1.50 | | % 4.90/1.50 | Case 2: % 4.90/1.50 | | % 4.90/1.50 | | (37) all_21_0 = 0 % 4.90/1.50 | | % 4.90/1.50 | | COMBINE_EQS: (32), (37) imply: % 4.90/1.50 | | (38) all_17_1 = 0 % 4.90/1.50 | | % 4.90/1.50 | | BETA: splitting (26) gives: % 4.90/1.50 | | % 4.90/1.50 | | Case 1: % 4.90/1.50 | | | % 4.90/1.50 | | | (39) ~ (all_19_1 = 0) % 4.90/1.50 | | | % 4.90/1.50 | | | REDUCE: (33), (39) imply: % 4.90/1.50 | | | (40) ~ (all_17_0 = 0) % 4.90/1.50 | | | % 4.90/1.50 | | | BETA: splitting (22) gives: % 4.90/1.50 | | | % 4.90/1.50 | | | Case 1: % 4.90/1.50 | | | | % 4.90/1.50 | | | | (41) ~ (all_17_1 = 0) % 4.90/1.50 | | | | % 4.90/1.50 | | | | REDUCE: (38), (41) imply: % 4.90/1.50 | | | | (42) $false % 4.90/1.50 | | | | % 4.90/1.50 | | | | CLOSE: (42) is inconsistent. % 4.90/1.50 | | | | % 4.90/1.50 | | | Case 2: % 4.90/1.50 | | | | % 4.90/1.50 | | | | (43) all_17_0 = 0 % 4.90/1.50 | | | | % 4.90/1.50 | | | | REDUCE: (40), (43) imply: % 4.90/1.50 | | | | (44) $false % 4.90/1.50 | | | | % 4.90/1.50 | | | | CLOSE: (44) is inconsistent. % 4.90/1.50 | | | | % 4.90/1.50 | | | End of split % 4.90/1.50 | | | % 4.90/1.50 | | Case 2: % 4.90/1.50 | | | % 4.90/1.50 | | | (45) all_19_0 = 0 % 4.90/1.50 | | | % 4.90/1.50 | | | COMBINE_EQS: (34), (45) imply: % 4.90/1.50 | | | (46) all_9_0 = 0 % 4.90/1.50 | | | % 4.90/1.50 | | | SIMP: (46) implies: % 4.90/1.50 | | | (47) all_9_0 = 0 % 4.90/1.50 | | | % 4.90/1.50 | | | REDUCE: (6), (47) imply: % 4.90/1.50 | | | (48) $false % 4.90/1.50 | | | % 4.90/1.50 | | | CLOSE: (48) is inconsistent. % 4.90/1.50 | | | % 4.90/1.50 | | End of split % 4.90/1.50 | | % 4.90/1.50 | End of split % 4.90/1.50 | % 4.90/1.50 End of proof % 4.90/1.50 % SZS output end Proof for theBenchmark % 4.90/1.50 % 4.90/1.50 848ms %------------------------------------------------------------------------------