%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC442_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 : n026.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 09:00:29 EDT 2024 % Result : Theorem 5.68s 1.65s % Output : Proof 6.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : SWC442_1 : TPTP v8.3.0. Released v8.3.0. % 0.09/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n026.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon May 13 14:42:23 EDT 2024 % 0.12/0.33 % CPUTime : % 0.68/0.65 ________ _____ % 0.68/0.65 ___ __ \_________(_)________________________________ % 0.68/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.68/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.68/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.68/0.65 % 0.68/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.68/0.65 (2023-06-19) % 0.68/0.65 % 0.68/0.65 (c) Philipp Rümmer, 2009-2023 % 0.68/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.68/0.65 Amanda Stjerna. % 0.68/0.65 Free software under BSD-3-Clause. % 0.68/0.65 % 0.68/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.68/0.65 % 0.68/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.67 Running up to 7 provers in parallel. % 0.68/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.51/1.21 Prover 1: Preprocessing ... % 2.51/1.21 Prover 4: Preprocessing ... % 2.51/1.21 Prover 2: Preprocessing ... % 2.51/1.21 Prover 3: Preprocessing ... % 2.51/1.21 Prover 0: Preprocessing ... % 2.51/1.22 Prover 6: Preprocessing ... % 2.51/1.22 Prover 5: Preprocessing ... % 3.49/1.36 Prover 1: Constructing countermodel ... % 3.49/1.36 Prover 3: Constructing countermodel ... % 3.49/1.36 Prover 4: Constructing countermodel ... % 3.49/1.36 Prover 6: Constructing countermodel ... % 3.49/1.37 Prover 0: Proving ... % 3.49/1.37 Prover 5: Proving ... % 3.49/1.38 Prover 2: Proving ... % 5.68/1.64 Prover 0: proved (964ms) % 5.68/1.65 % 5.68/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.68/1.65 % 5.68/1.65 Prover 6: stopped % 5.68/1.65 Prover 5: stopped % 5.68/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.68/1.65 Prover 3: stopped % 5.68/1.65 Prover 2: stopped % 5.68/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.68/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.68/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.68/1.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.68/1.68 Prover 11: Preprocessing ... % 5.68/1.68 Prover 8: Preprocessing ... % 5.68/1.69 Prover 7: Preprocessing ... % 5.68/1.69 Prover 4: Found proof (size 29) % 5.68/1.69 Prover 4: proved (1000ms) % 6.14/1.69 Prover 10: Preprocessing ... % 6.14/1.69 Prover 1: stopped % 6.14/1.70 Prover 13: Preprocessing ... % 6.14/1.70 Prover 7: stopped % 6.14/1.71 Prover 10: stopped % 6.14/1.71 Prover 11: stopped % 6.14/1.72 Prover 13: stopped % 6.14/1.72 Prover 8: Warning: ignoring some quantifiers % 6.14/1.72 Prover 8: Constructing countermodel ... % 6.14/1.73 Prover 8: stopped % 6.14/1.73 % 6.14/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.14/1.73 % 6.14/1.73 % SZS output start Proof for theBenchmark % 6.14/1.74 Assumptions after simplification: % 6.14/1.74 --------------------------------- % 6.14/1.74 % 6.14/1.74 (conjecture_1) % 6.14/1.75 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 6.14/1.75 fast(v0) = v2 & small(v0) = v1) % 6.14/1.75 % 6.14/1.75 (formula_1) % 6.14/1.75 ! [v0: int] : ! [v1: int] : ( ~ (f0(v0) = v1) | $product(v0, v0) = v1) % 6.14/1.75 % 6.14/1.75 (formula_2) % 6.14/1.75 g0 = 2 % 6.14/1.75 % 6.14/1.75 (formula_3) % 6.14/1.75 h0 = 2 % 6.14/1.75 % 6.14/1.75 (formula_4) % 6.14/1.76 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 6.14/1.76 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 6.14/1.76 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 6.14/1.76 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 6.14/1.76 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 6.14/1.76 -1), v1) = v3 & f0(v3) = v2)) % 6.14/1.76 % 6.14/1.76 (formula_5) % 6.14/1.76 u0(g0, h0) = v0 % 6.14/1.76 % 6.14/1.76 (formula_6) % 6.14/1.76 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | % 6.14/1.76 div:(Int*Int)>Int($sum($product(2, v0), -2), $sum(v0, 1)) = v1) & ! [v0: % 6.14/1.76 int] : ! [v1: int] : ( ~ (div:(Int*Int)>Int($sum($product(2, v0), -2), % 6.14/1.76 $sum(v0, 1)) = v1) | small(v0) = v1) % 6.14/1.76 % 6.14/1.76 (formula_7) % 6.14/1.76 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | div:(Int*Int)>Int(30, % 6.14/1.76 $sum(v0, 1)) = v1) & ! [v0: int] : ! [v1: int] : ( ~ % 6.14/1.76 (div:(Int*Int)>Int(30, $sum(v0, 1)) = v1) | fast(v0) = v1) % 6.14/1.76 % 6.14/1.76 (function-axioms) % 6.14/1.77 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ % 6.14/1.77 (div:(Int*Int)>Int(v3, v2) = v1) | ~ (div:(Int*Int)>Int(v3, v2) = v0)) & ! % 6.54/1.77 [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (u0(v3, % 6.54/1.77 v2) = v1) | ~ (u0(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 6.54/1.77 [v2: int] : (v1 = v0 | ~ (fast(v2) = v1) | ~ (fast(v2) = v0)) & ! [v0: int] % 6.54/1.77 : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (small(v2) = v1) | ~ (small(v2) % 6.54/1.77 = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 6.54/1.77 (f0(v2) = v1) | ~ (f0(v2) = v0)) % 6.54/1.77 % 6.54/1.77 Those formulas are unsatisfiable: % 6.54/1.77 --------------------------------- % 6.54/1.77 % 6.54/1.77 Begin of proof % 6.54/1.77 | % 6.54/1.77 | ALPHA: (formula_4) implies: % 6.57/1.77 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 6.57/1.77 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 6.57/1.77 | f0(v3) = v2)) % 6.57/1.77 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 6.57/1.77 | 0) | ~ (u0(v0, v1) = v2)) % 6.57/1.77 | % 6.57/1.77 | ALPHA: (formula_6) implies: % 6.57/1.77 | (3) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | % 6.57/1.77 | div:(Int*Int)>Int($sum($product(2, v0), -2), $sum(v0, 1)) = v1) % 6.57/1.77 | % 6.57/1.77 | ALPHA: (formula_7) implies: % 6.57/1.77 | (4) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | % 6.57/1.77 | div:(Int*Int)>Int(30, $sum(v0, 1)) = v1) % 6.57/1.78 | % 6.57/1.78 | ALPHA: (function-axioms) implies: % 6.57/1.78 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | % 6.57/1.78 | ~ (div:(Int*Int)>Int(v3, v2) = v1) | ~ (div:(Int*Int)>Int(v3, v2) = % 6.57/1.78 | v0)) % 6.57/1.78 | % 6.57/1.78 | DELTA: instantiating (conjecture_1) with fresh symbols all_8_0, all_8_1, % 6.57/1.78 | all_8_2 gives: % 6.57/1.78 | (6) ~ (all_8_0 = all_8_1) & $lesseq(0, all_8_2) & fast(all_8_2) = all_8_0 % 6.57/1.78 | & small(all_8_2) = all_8_1 % 6.57/1.78 | % 6.57/1.78 | ALPHA: (6) implies: % 6.57/1.78 | (7) ~ (all_8_0 = all_8_1) % 6.57/1.78 | (8) small(all_8_2) = all_8_1 % 6.57/1.78 | (9) fast(all_8_2) = all_8_0 % 6.57/1.78 | % 6.57/1.78 | REDUCE: (formula_2), (formula_3), (formula_5) imply: % 6.57/1.78 | (10) u0(2, 2) = v0 % 6.57/1.78 | % 6.57/1.78 | GROUND_INST: instantiating (1) with 2, 2, v0, simplifying with (10) gives: % 6.57/1.78 | (11) ? [v0: int] : (u0(1, 2) = v0 & f0(v0) = v0) % 6.57/1.78 | % 6.57/1.78 | GROUND_INST: instantiating (3) with all_8_2, all_8_1, simplifying with (8) % 6.57/1.78 | gives: % 6.57/1.78 | (12) div:(Int*Int)>Int($sum($product(2, v0), -2), $sum(all_8_2, 1)) = % 6.57/1.78 | all_8_1 % 6.57/1.78 | % 6.57/1.78 | GROUND_INST: instantiating (4) with all_8_2, all_8_0, simplifying with (9) % 6.57/1.78 | gives: % 6.57/1.78 | (13) div:(Int*Int)>Int(30, $sum(all_8_2, 1)) = all_8_0 % 6.57/1.78 | % 6.57/1.78 | DELTA: instantiating (11) with fresh symbol all_19_0 gives: % 6.57/1.78 | (14) u0(1, 2) = all_19_0 & f0(all_19_0) = v0 % 6.57/1.78 | % 6.57/1.78 | ALPHA: (14) implies: % 6.57/1.78 | (15) f0(all_19_0) = v0 % 6.57/1.78 | (16) u0(1, 2) = all_19_0 % 6.57/1.78 | % 6.57/1.78 | GROUND_INST: instantiating (formula_1) with all_19_0, v0, simplifying with % 6.57/1.78 | (15) gives: % 6.57/1.79 | (17) $product(all_19_0, all_19_0) = v0 % 6.57/1.79 | % 6.57/1.79 | GROUND_INST: instantiating (1) with 1, 2, all_19_0, simplifying with (16) % 6.57/1.79 | gives: % 6.57/1.79 | (18) ? [v0: int] : (u0(0, 2) = v0 & f0(v0) = all_19_0) % 6.57/1.79 | % 6.57/1.79 | DELTA: instantiating (18) with fresh symbol all_33_0 gives: % 6.57/1.79 | (19) u0(0, 2) = all_33_0 & f0(all_33_0) = all_19_0 % 6.57/1.79 | % 6.57/1.79 | ALPHA: (19) implies: % 6.57/1.79 | (20) f0(all_33_0) = all_19_0 % 6.57/1.79 | (21) u0(0, 2) = all_33_0 % 6.57/1.79 | % 6.57/1.79 | GROUND_INST: instantiating (2) with 0, 2, all_33_0, simplifying with (21) % 6.57/1.79 | gives: % 6.57/1.79 | (22) all_33_0 = 2 % 6.57/1.79 | % 6.57/1.79 | GROUND_INST: instantiating (5) with all_8_0, all_8_1, $sum(all_8_2, 1), 30, % 6.57/1.79 | simplifying with (13) gives: % 6.57/1.79 | (23) all_8_0 = all_8_1 | ~ (div:(Int*Int)>Int(30, $sum(all_8_2, 1)) = % 6.57/1.79 | all_8_1) % 6.57/1.79 | % 6.57/1.79 | REDUCE: (20), (22) imply: % 6.57/1.79 | (24) f0(2) = all_19_0 % 6.57/1.79 | % 6.57/1.79 | GROUND_INST: instantiating (formula_1) with 2, all_19_0, simplifying with (24) % 6.57/1.79 | gives: % 6.57/1.79 | (25) $product(2, 2) = all_19_0 % 6.57/1.79 | % 6.57/1.79 | THEORY_AXIOM GroebnerMultiplication: % 6.57/1.79 | (26) ! [v0: int] : ! [v1: int] : (v0 = 16 | ~ ($product(v1, v1) = v0) | % 6.57/1.79 | ~ ($product(2, 2) = v1)) % 6.57/1.79 | % 6.57/1.79 | GROUND_INST: instantiating (26) with v0, all_19_0, simplifying with (17), (25) % 6.57/1.79 | gives: % 6.57/1.79 | (27) v0 = 16 % 6.57/1.79 | % 6.57/1.79 | REDUCE: (12), (27) imply: % 6.57/1.79 | (28) div:(Int*Int)>Int(30, $sum(all_8_2, 1)) = all_8_1 % 6.57/1.79 | % 6.57/1.79 | BETA: splitting (23) gives: % 6.57/1.79 | % 6.57/1.79 | Case 1: % 6.57/1.79 | | % 6.57/1.79 | | (29) ~ (div:(Int*Int)>Int(30, $sum(all_8_2, 1)) = all_8_1) % 6.57/1.79 | | % 6.57/1.79 | | PRED_UNIFY: (28), (29) imply: % 6.57/1.79 | | (30) $false % 6.57/1.79 | | % 6.57/1.79 | | CLOSE: (30) is inconsistent. % 6.57/1.79 | | % 6.57/1.79 | Case 2: % 6.57/1.79 | | % 6.57/1.79 | | (31) all_8_0 = all_8_1 % 6.57/1.79 | | % 6.57/1.79 | | REDUCE: (7), (31) imply: % 6.57/1.79 | | (32) $false % 6.57/1.79 | | % 6.57/1.79 | | CLOSE: (32) is inconsistent. % 6.57/1.79 | | % 6.57/1.80 | End of split % 6.57/1.80 | % 6.57/1.80 End of proof % 6.57/1.80 % SZS output end Proof for theBenchmark % 6.57/1.80 % 6.57/1.80 1139ms %------------------------------------------------------------------------------