%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 : Sun Apr 6 10:08:52 AM UTC 2025 % Result : Theorem 10.19s 2.17s % Output : Proof 12.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n019.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 : Sun Apr 6 03:09:32 EDT 2025 % 0.13/0.35 % CPUTime : % 0.61/0.61 ________ _____ % 0.61/0.61 ___ __ \_________(_)________________________________ % 0.61/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.61 (2023-06-19) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2023 % 0.61/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.61 Amanda Stjerna. % 0.61/0.61 Free software under BSD-3-Clause. % 0.61/0.61 % 0.61/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.62 Running up to 7 provers in parallel. % 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.60/1.29 Prover 2: Preprocessing ... % 3.60/1.29 Prover 5: Preprocessing ... % 3.60/1.29 Prover 6: Preprocessing ... % 3.60/1.29 Prover 3: Preprocessing ... % 3.60/1.29 Prover 4: Preprocessing ... % 3.60/1.30 Prover 1: Preprocessing ... % 3.60/1.30 Prover 0: Preprocessing ... % 8.58/1.96 Prover 0: Proving ... % 8.58/1.97 Prover 4: Constructing countermodel ... % 9.06/1.99 Prover 5: Proving ... % 9.06/2.00 Prover 1: Warning: ignoring some quantifiers % 9.06/2.04 Prover 3: Warning: ignoring some quantifiers % 9.06/2.04 Prover 1: Constructing countermodel ... % 9.06/2.06 Prover 3: Constructing countermodel ... % 9.97/2.11 Prover 6: Proving ... % 10.19/2.16 Prover 0: proved (1529ms) % 10.19/2.16 Prover 3: proved (1530ms) % 10.19/2.17 % 10.19/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.19/2.17 % 10.19/2.17 % 10.19/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.19/2.17 % 10.19/2.17 Prover 5: stopped % 10.19/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.19/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.19/2.18 Prover 6: stopped % 10.19/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.19/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.83/2.28 Prover 7: Preprocessing ... % 10.83/2.28 Prover 10: Preprocessing ... % 10.83/2.29 Prover 8: Preprocessing ... % 11.37/2.30 Prover 11: Preprocessing ... % 11.37/2.33 Prover 2: Proving ... % 11.37/2.33 Prover 2: stopped % 11.37/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.99/2.39 Prover 13: Preprocessing ... % 12.20/2.42 Prover 4: Found proof (size 22) % 12.20/2.42 Prover 1: Found proof (size 22) % 12.20/2.42 Prover 4: proved (1779ms) % 12.20/2.42 Prover 1: proved (1787ms) % 12.30/2.43 Prover 10: Warning: ignoring some quantifiers % 12.30/2.44 Prover 10: Constructing countermodel ... % 12.30/2.45 Prover 7: Warning: ignoring some quantifiers % 12.30/2.45 Prover 10: stopped % 12.30/2.46 Prover 13: stopped % 12.30/2.46 Prover 7: Constructing countermodel ... % 12.30/2.48 Prover 7: stopped % 12.30/2.50 Prover 11: Constructing countermodel ... % 12.30/2.51 Prover 11: stopped % 12.30/2.51 Prover 8: Warning: ignoring some quantifiers % 12.90/2.52 Prover 8: Constructing countermodel ... % 12.90/2.53 Prover 8: stopped % 12.90/2.53 % 12.90/2.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.90/2.53 % 12.90/2.54 % SZS output start Proof for theBenchmark % 12.90/2.54 Assumptions after simplification: % 12.90/2.54 --------------------------------- % 12.90/2.54 % 12.90/2.54 (formula_5_unnamed_formula) % 12.90/2.56 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! [v4: % 12.90/2.56 int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 12.90/2.56 (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : ? % 12.90/2.56 [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & $product(v0, v0) = v5 % 12.90/2.56 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ ($lesseq(v5, v1))))) & ! % 12.90/2.56 [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ (sqrt(v2, % 12.90/2.56 v3) = 0) | ~ (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | % 12.90/2.56 ($lesseq(0, v0) & ? [v4: int] : ? [v5: int] : ($lesseq(1, $difference(v5, % 12.90/2.56 v1)) & $lesseq(v4, v1) & $product($sum(v0, 1), $sum(v0, 1)) = v5 & % 12.90/2.56 $product(v0, v0) = v4))) % 12.90/2.56 % 12.90/2.56 (formula_7_base_case) % 12.90/2.56 ? [v0: general] : (f__integer__(0) = v0 & general(v0) & ! [v1: int] : ! % 12.90/2.56 [v2: general] : ( ~ (f__integer__(v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 12.90/2.56 sqrt(v2, v0) = v3))) % 12.90/2.56 % 12.90/2.56 Further assumptions not needed in the proof: % 12.90/2.56 -------------------------------------------- % 12.90/2.56 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 12.90/2.56 formula_0_unnamed_formula, formula_1_completed_definition_of_composite_1, % 12.90/2.56 formula_2_completed_definition_of_sqrtb_1, % 12.90/2.56 formula_3_completed_definition_of_composite_1, % 12.90/2.56 formula_4_completed_definition_of_prime_1, formula_6_unnamed_formula, % 12.90/2.56 general_universe_ax, maximal_element_ax, minimal_element_ax, % 12.90/2.56 numeral_ordering_ax, numerals_less_than_symbols_ax, p__greater__def_ax, % 12.90/2.56 p__greater_equal__def_ax, p__is_integer__def_ax, p__is_symbolic__def_ax, % 12.90/2.56 p__less__def_ax, strongly_connected_ordering_ax, transitive_ordering_ax % 12.90/2.56 % 12.90/2.56 Those formulas are unsatisfiable: % 12.90/2.56 --------------------------------- % 12.90/2.56 % 12.90/2.56 Begin of proof % 12.90/2.56 | % 12.90/2.56 | ALPHA: (formula_5_unnamed_formula) implies: % 12.90/2.57 | (1) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! % 12.90/2.57 | [v4: int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 12.90/2.57 | (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : % 12.90/2.57 | ? [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & % 12.90/2.57 | $product(v0, v0) = v5 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ % 12.90/2.57 | ($lesseq(v5, v1))))) % 12.90/2.57 | % 12.90/2.57 | DELTA: instantiating (formula_7_base_case) with fresh symbol all_28_0 gives: % 12.90/2.57 | (2) f__integer__(0) = all_28_0 & general(all_28_0) & ! [v0: int] : ! [v1: % 12.90/2.57 | general] : ( ~ (f__integer__(v0) = v1) | ? [v2: int] : ( ~ (v2 = 0) % 12.90/2.57 | & sqrt(v1, all_28_0) = v2)) % 12.90/2.57 | % 12.90/2.57 | ALPHA: (2) implies: % 12.90/2.57 | (3) f__integer__(0) = all_28_0 % 12.90/2.57 | (4) ! [v0: int] : ! [v1: general] : ( ~ (f__integer__(v0) = v1) | ? [v2: % 12.90/2.57 | int] : ( ~ (v2 = 0) & sqrt(v1, all_28_0) = v2)) % 12.90/2.57 | % 12.90/2.57 | GROUND_INST: instantiating (4) with 0, all_28_0, simplifying with (3) gives: % 12.90/2.57 | (5) ? [v0: int] : ( ~ (v0 = 0) & sqrt(all_28_0, all_28_0) = v0) % 12.90/2.57 | % 12.90/2.57 | DELTA: instantiating (5) with fresh symbol all_47_0 gives: % 12.90/2.57 | (6) ~ (all_47_0 = 0) & sqrt(all_28_0, all_28_0) = all_47_0 % 12.90/2.57 | % 12.90/2.57 | ALPHA: (6) implies: % 12.90/2.57 | (7) ~ (all_47_0 = 0) % 12.90/2.57 | (8) sqrt(all_28_0, all_28_0) = all_47_0 % 12.90/2.57 | % 12.90/2.57 | GROUND_INST: instantiating (1) with 0, 0, all_28_0, all_28_0, all_47_0, % 12.90/2.57 | simplifying with (3), (8) gives: % 12.90/2.57 | (9) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ($product(1, 1) = v1 & % 12.90/2.57 | $product(0, 0) = v0 & ( ~ ($lesseq(1, v1)) | ~ ($lesseq(v0, 0))) % 12.90/2.57 | % 12.90/2.57 | BETA: splitting (9) gives: % 12.90/2.57 | % 12.90/2.57 | Case 1: % 12.90/2.57 | | % 12.90/2.58 | | (10) all_47_0 = 0 % 12.90/2.58 | | % 12.90/2.58 | | REDUCE: (7), (10) imply: % 12.90/2.58 | | (11) $false % 12.90/2.58 | | % 12.90/2.58 | | CLOSE: (11) is inconsistent. % 12.90/2.58 | | % 12.90/2.58 | Case 2: % 12.90/2.58 | | % 12.90/2.58 | | (12) ? [v0: int] : ? [v1: int] : ($product(1, 1) = v1 & $product(0, 0) % 12.90/2.58 | | = v0 & ( ~ ($lesseq(1, v1)) | ~ ($lesseq(v0, 0))) % 12.90/2.58 | | % 12.90/2.58 | | DELTA: instantiating (12) with fresh symbols all_62_0, all_62_1 gives: % 12.90/2.58 | | (13) $product(1, 1) = all_62_0 & $product(0, 0) = all_62_1 & ( ~ % 12.90/2.58 | | ($lesseq(1, all_62_0)) | ~ ($lesseq(all_62_1, 0)) % 12.90/2.58 | | % 12.90/2.58 | | ALPHA: (13) implies: % 12.90/2.58 | | (14) $product(0, 0) = all_62_1 % 12.90/2.58 | | (15) $product(1, 1) = all_62_0 % 12.90/2.58 | | (16) ~ ($lesseq(1, all_62_0)) | ~ ($lesseq(all_62_1, 0) % 12.90/2.58 | | % 12.90/2.58 | | THEORY_AXIOM GroebnerMultiplication: % 12.90/2.58 | | (17) ! [v0: int] : (v0 = 1 | ~ ($product(1, 1) = v0)) % 12.90/2.58 | | % 12.90/2.58 | | GROUND_INST: instantiating (17) with all_62_0, simplifying with (15) gives: % 12.90/2.58 | | (18) all_62_0 = 1 % 12.90/2.58 | | % 12.90/2.58 | | THEORY_AXIOM GroebnerMultiplication: % 12.90/2.58 | | (19) ! [v0: int] : (v0 = 0 | ~ ($product(0, 0) = v0)) % 12.90/2.58 | | % 12.90/2.58 | | GROUND_INST: instantiating (19) with all_62_1, simplifying with (14) gives: % 12.90/2.58 | | (20) all_62_1 = 0 % 12.90/2.58 | | % 12.90/2.58 | | BETA: splitting (16) gives: % 12.90/2.58 | | % 12.90/2.58 | | Case 1: % 12.90/2.58 | | | % 12.90/2.58 | | | (21) $lesseq(1, all_62_1) % 12.90/2.58 | | | % 12.90/2.58 | | | REDUCE: (20), (21) imply: % 12.90/2.58 | | | (22) $false % 12.90/2.58 | | | % 12.90/2.58 | | | CLOSE: (22) is inconsistent. % 12.90/2.58 | | | % 12.90/2.58 | | Case 2: % 12.90/2.58 | | | % 12.90/2.58 | | | (23) $lesseq(all_62_0, 0) % 12.90/2.58 | | | % 12.90/2.58 | | | REDUCE: (18), (23) imply: % 12.90/2.58 | | | (24) $false % 12.90/2.58 | | | % 12.90/2.58 | | | CLOSE: (24) is inconsistent. % 12.90/2.58 | | | % 12.90/2.58 | | End of split % 12.90/2.58 | | % 12.90/2.58 | End of split % 12.90/2.58 | % 12.90/2.58 End of proof % 12.90/2.58 % SZS output end Proof for theBenchmark % 12.90/2.58 % 12.90/2.58 1968ms %------------------------------------------------------------------------------