%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC484_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 : 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 : Tue May 14 09:00:32 EDT 2024 % Result : Theorem 6.11s 1.55s % Output : Proof 7.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWC484_1 : TPTP v8.3.0. Released v8.3.0. % 0.04/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n020.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Mon May 13 15:02:08 EDT 2024 % 0.14/0.35 % CPUTime : % 0.54/0.61 ________ _____ % 0.54/0.61 ___ __ \_________(_)________________________________ % 0.54/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.61 % 0.54/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.61 (2023-06-19) % 0.54/0.61 % 0.54/0.61 (c) Philipp Rümmer, 2009-2023 % 0.54/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.61 Amanda Stjerna. % 0.54/0.61 Free software under BSD-3-Clause. % 0.54/0.61 % 0.54/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.61 % 0.54/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.63 Running up to 7 provers in parallel. % 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 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 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 % 2.49/1.03 Prover 1: Preprocessing ... % 2.49/1.03 Prover 0: Preprocessing ... % 2.49/1.03 Prover 6: Preprocessing ... % 2.49/1.03 Prover 3: Preprocessing ... % 2.49/1.04 Prover 4: Preprocessing ... % 2.49/1.04 Prover 5: Preprocessing ... % 2.49/1.04 Prover 2: Preprocessing ... % 3.59/1.21 Prover 3: Constructing countermodel ... % 3.59/1.21 Prover 6: Constructing countermodel ... % 3.59/1.22 Prover 1: Constructing countermodel ... % 3.59/1.22 Prover 0: Proving ... % 3.59/1.23 Prover 4: Constructing countermodel ... % 3.59/1.23 Prover 2: Proving ... % 3.98/1.24 Prover 5: Proving ... % 6.11/1.54 Prover 2: proved (906ms) % 6.11/1.55 % 6.11/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.11/1.55 % 6.24/1.56 Prover 5: proved (909ms) % 6.24/1.56 % 6.24/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.24/1.56 % 6.24/1.56 Prover 3: stopped % 6.24/1.56 Prover 6: stopped % 6.24/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.24/1.56 Prover 0: stopped % 6.24/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.24/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.24/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.24/1.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.24/1.59 Prover 11: Preprocessing ... % 6.24/1.59 Prover 8: Preprocessing ... % 6.24/1.59 Prover 7: Preprocessing ... % 6.24/1.60 Prover 10: Preprocessing ... % 6.24/1.61 Prover 13: Preprocessing ... % 6.24/1.62 Prover 4: Found proof (size 29) % 6.24/1.62 Prover 4: proved (981ms) % 6.24/1.62 Prover 8: Warning: ignoring some quantifiers % 6.24/1.62 Prover 1: stopped % 6.24/1.62 Prover 8: Constructing countermodel ... % 6.24/1.63 Prover 8: stopped % 6.24/1.63 Prover 10: Constructing countermodel ... % 6.77/1.63 Prover 10: stopped % 6.77/1.63 Prover 7: Constructing countermodel ... % 6.77/1.63 Prover 7: stopped % 6.77/1.64 Prover 11: Constructing countermodel ... % 6.77/1.64 Prover 13: stopped % 6.77/1.64 Prover 11: stopped % 6.77/1.64 % 6.77/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.77/1.64 % 6.77/1.65 % SZS output start Proof for theBenchmark % 6.77/1.65 Assumptions after simplification: % 6.77/1.65 --------------------------------- % 6.77/1.65 % 6.77/1.65 (conjecture_1) % 6.77/1.67 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 6.77/1.67 fast(v0) = v2 & small(v0) = v1) % 6.77/1.67 % 6.77/1.67 (formula_1) % 6.77/1.67 ! [v0: int] : ! [v1: int] : ( ~ (f0(v0) = v1) | $product(v0, v0) = v1) % 6.77/1.67 % 6.77/1.67 (formula_2) % 6.77/1.67 g0 = 2 % 6.77/1.67 % 6.77/1.67 (formula_3) % 6.77/1.67 h0 = 2 % 6.77/1.67 % 6.77/1.67 (formula_4) % 7.00/1.67 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 7.00/1.67 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 7.00/1.67 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 7.00/1.67 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 7.00/1.67 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 7.00/1.67 -1), v1) = v3 & f0(v3) = v2)) % 7.00/1.67 % 7.00/1.67 (formula_5) % 7.00/1.67 u0(g0, h0) = v0 % 7.00/1.67 % 7.00/1.67 (formula_6) % 7.00/1.67 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | % 7.00/1.67 mod:(Int*Int)>Int($sum(v0, 1), v0) = $sum($difference($product(2, v0), v1), % 7.00/1.67 2)) & ! [v0: int] : ! [v1: int] : ( ~ (mod:(Int*Int)>Int($sum(v0, 1), % 7.00/1.67 v0) = v1) | small(v0) = $sum($difference($product(2, v0), v1), 2)) % 7.00/1.67 % 7.00/1.68 (formula_7) % 7.00/1.68 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | mod:(Int*Int)>Int($sum(v0, % 7.00/1.68 1), 16) = $sum($difference($product(2, v0), v1), 2)) & ! [v0: int] : ! % 7.00/1.68 [v1: int] : ( ~ (mod:(Int*Int)>Int($sum(v0, 1), 16) = v1) | fast(v0) = % 7.00/1.68 $sum($difference($product(2, v0), v1), 2)) % 7.00/1.68 % 7.00/1.68 (function-axioms) % 7.00/1.68 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ % 7.00/1.68 (mod:(Int*Int)>Int(v3, v2) = v1) | ~ (mod:(Int*Int)>Int(v3, v2) = v0)) & ! % 7.00/1.68 [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (u0(v3, % 7.00/1.68 v2) = v1) | ~ (u0(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 7.00/1.68 [v2: int] : (v1 = v0 | ~ (fast(v2) = v1) | ~ (fast(v2) = v0)) & ! [v0: int] % 7.00/1.68 : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (small(v2) = v1) | ~ (small(v2) % 7.00/1.68 = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 7.00/1.68 (f0(v2) = v1) | ~ (f0(v2) = v0)) % 7.00/1.68 % 7.00/1.68 Those formulas are unsatisfiable: % 7.00/1.68 --------------------------------- % 7.00/1.68 % 7.00/1.68 Begin of proof % 7.00/1.68 | % 7.00/1.68 | ALPHA: (formula_4) implies: % 7.00/1.69 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 7.00/1.69 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 7.00/1.69 | f0(v3) = v2)) % 7.00/1.69 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 7.00/1.69 | 0) | ~ (u0(v0, v1) = v2)) % 7.00/1.69 | % 7.00/1.69 | ALPHA: (formula_6) implies: % 7.00/1.69 | (3) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | % 7.00/1.69 | mod:(Int*Int)>Int($sum(v0, 1), v0) = $sum($difference($product(2, % 7.00/1.69 | v0), v1), 2)) % 7.00/1.69 | % 7.00/1.69 | ALPHA: (formula_7) implies: % 7.00/1.69 | (4) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | % 7.00/1.69 | mod:(Int*Int)>Int($sum(v0, 1), 16) = $sum($difference($product(2, % 7.00/1.69 | v0), v1), 2)) % 7.00/1.69 | % 7.00/1.69 | ALPHA: (function-axioms) implies: % 7.00/1.69 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | % 7.00/1.69 | ~ (mod:(Int*Int)>Int(v3, v2) = v1) | ~ (mod:(Int*Int)>Int(v3, v2) = % 7.00/1.69 | v0)) % 7.00/1.69 | % 7.00/1.69 | DELTA: instantiating (conjecture_1) with fresh symbols all_8_0, all_8_1, % 7.00/1.69 | all_8_2 gives: % 7.00/1.69 | (6) ~ (all_8_0 = all_8_1) & $lesseq(0, all_8_2) & fast(all_8_2) = all_8_0 % 7.00/1.69 | & small(all_8_2) = all_8_1 % 7.00/1.69 | % 7.00/1.69 | ALPHA: (6) implies: % 7.00/1.69 | (7) ~ (all_8_0 = all_8_1) % 7.00/1.69 | (8) small(all_8_2) = all_8_1 % 7.00/1.69 | (9) fast(all_8_2) = all_8_0 % 7.00/1.69 | % 7.00/1.69 | REDUCE: (formula_2), (formula_3), (formula_5) imply: % 7.00/1.69 | (10) u0(2, 2) = v0 % 7.00/1.69 | % 7.00/1.69 | GROUND_INST: instantiating (1) with 2, 2, v0, simplifying with (10) gives: % 7.00/1.70 | (11) ? [v0: int] : (u0(1, 2) = v0 & f0(v0) = v0) % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (3) with all_8_2, all_8_1, simplifying with (8) % 7.00/1.70 | gives: % 7.00/1.70 | (12) mod:(Int*Int)>Int($sum(all_8_2, 1), v0) = $sum($difference($product(2, % 7.00/1.70 | all_8_2), all_8_1), 2) % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (4) with all_8_2, all_8_0, simplifying with (9) % 7.00/1.70 | gives: % 7.00/1.70 | (13) mod:(Int*Int)>Int($sum(all_8_2, 1), 16) = $sum($difference($product(2, % 7.00/1.70 | all_8_2), all_8_0), 2) % 7.00/1.70 | % 7.00/1.70 | DELTA: instantiating (11) with fresh symbol all_19_0 gives: % 7.00/1.70 | (14) u0(1, 2) = all_19_0 & f0(all_19_0) = v0 % 7.00/1.70 | % 7.00/1.70 | ALPHA: (14) implies: % 7.00/1.70 | (15) f0(all_19_0) = v0 % 7.00/1.70 | (16) u0(1, 2) = all_19_0 % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (formula_1) with all_19_0, v0, simplifying with % 7.00/1.70 | (15) gives: % 7.00/1.70 | (17) $product(all_19_0, all_19_0) = v0 % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (1) with 1, 2, all_19_0, simplifying with (16) % 7.00/1.70 | gives: % 7.00/1.70 | (18) ? [v0: int] : (u0(0, 2) = v0 & f0(v0) = all_19_0) % 7.00/1.70 | % 7.00/1.70 | DELTA: instantiating (18) with fresh symbol all_33_0 gives: % 7.00/1.70 | (19) u0(0, 2) = all_33_0 & f0(all_33_0) = all_19_0 % 7.00/1.70 | % 7.00/1.70 | ALPHA: (19) implies: % 7.00/1.70 | (20) f0(all_33_0) = all_19_0 % 7.00/1.70 | (21) u0(0, 2) = all_33_0 % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (2) with 0, 2, all_33_0, simplifying with (21) % 7.00/1.70 | gives: % 7.00/1.70 | (22) all_33_0 = 2 % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (5) with $sum($difference($product(2, all_8_2), % 7.00/1.70 | all_8_0), 2), $sum($difference($product(2, all_8_2), % 7.00/1.70 | all_8_1), 2), 16, $sum(all_8_2, 1), simplifying with (13) % 7.00/1.70 | gives: % 7.00/1.70 | (23) all_8_0 = all_8_1 | ~ (mod:(Int*Int)>Int($sum(all_8_2, 1), 16) = % 7.00/1.70 | $sum($difference($product(2, all_8_2), all_8_1), 2)) % 7.00/1.70 | % 7.00/1.70 | REDUCE: (20), (22) imply: % 7.00/1.70 | (24) f0(2) = all_19_0 % 7.00/1.70 | % 7.00/1.70 | GROUND_INST: instantiating (formula_1) with 2, all_19_0, simplifying with (24) % 7.00/1.70 | gives: % 7.00/1.70 | (25) $product(2, 2) = all_19_0 % 7.00/1.70 | % 7.00/1.70 | THEORY_AXIOM GroebnerMultiplication: % 7.00/1.71 | (26) ! [v0: int] : ! [v1: int] : (v0 = 16 | ~ ($product(v1, v1) = v0) | % 7.00/1.71 | ~ ($product(2, 2) = v1)) % 7.00/1.71 | % 7.00/1.71 | GROUND_INST: instantiating (26) with v0, all_19_0, simplifying with (17), (25) % 7.00/1.71 | gives: % 7.00/1.71 | (27) v0 = 16 % 7.00/1.71 | % 7.00/1.71 | REDUCE: (12), (27) imply: % 7.00/1.71 | (28) mod:(Int*Int)>Int($sum(all_8_2, 1), 16) = $sum($difference($product(2, % 7.00/1.71 | all_8_2), all_8_1), 2) % 7.00/1.71 | % 7.00/1.71 | BETA: splitting (23) gives: % 7.00/1.71 | % 7.00/1.71 | Case 1: % 7.00/1.71 | | % 7.00/1.71 | | (29) ~ (mod:(Int*Int)>Int($sum(all_8_2, 1), 16) = % 7.00/1.71 | | $sum($difference($product(2, all_8_2), all_8_1), 2)) % 7.00/1.71 | | % 7.00/1.71 | | PRED_UNIFY: (28), (29) imply: % 7.00/1.71 | | (30) $false % 7.00/1.71 | | % 7.00/1.71 | | CLOSE: (30) is inconsistent. % 7.00/1.71 | | % 7.00/1.71 | Case 2: % 7.00/1.71 | | % 7.00/1.71 | | (31) all_8_0 = all_8_1 % 7.00/1.71 | | % 7.00/1.71 | | REDUCE: (7), (31) imply: % 7.00/1.71 | | (32) $false % 7.00/1.71 | | % 7.00/1.71 | | CLOSE: (32) is inconsistent. % 7.00/1.71 | | % 7.00/1.71 | End of split % 7.00/1.71 | % 7.00/1.71 End of proof % 7.00/1.71 % SZS output end Proof for theBenchmark % 7.00/1.71 % 7.00/1.71 1096ms %------------------------------------------------------------------------------