%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN415+1 : TPTP v8.1.2. Released v2.0.0. % 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 : Fri Sep 1 03:27:36 EDT 2023 % Result : Theorem 3.50s 1.19s % Output : Proof 4.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN415+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n026.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 : Sat Aug 26 21:07:03 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.56/0.94 Prover 4: Preprocessing ... % 1.56/0.95 Prover 1: Preprocessing ... % 2.18/0.99 Prover 3: Preprocessing ... % 2.18/0.99 Prover 5: Preprocessing ... % 2.18/0.99 Prover 0: Preprocessing ... % 2.18/0.99 Prover 2: Preprocessing ... % 2.18/0.99 Prover 6: Preprocessing ... % 2.49/1.09 Prover 3: Constructing countermodel ... % 2.49/1.09 Prover 1: Constructing countermodel ... % 2.49/1.09 Prover 5: Constructing countermodel ... % 2.49/1.09 Prover 0: Proving ... % 2.49/1.09 Prover 4: Constructing countermodel ... % 2.49/1.09 Prover 2: Constructing countermodel ... % 2.49/1.09 Prover 6: Proving ... % 3.50/1.19 Prover 5: proved (561ms) % 3.50/1.19 % 3.50/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.50/1.19 % 3.50/1.19 Prover 2: stopped % 3.50/1.19 Prover 3: stopped % 3.50/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.50/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.50/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.50/1.19 Prover 6: stopped % 3.50/1.19 Prover 0: stopped % 3.50/1.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.50/1.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.50/1.20 Prover 7: Preprocessing ... % 3.50/1.21 Prover 10: Preprocessing ... % 3.50/1.21 Prover 8: Preprocessing ... % 3.50/1.21 Prover 11: Preprocessing ... % 3.50/1.22 Prover 13: Preprocessing ... % 3.50/1.23 Prover 10: Constructing countermodel ... % 3.50/1.24 Prover 8: Warning: ignoring some quantifiers % 3.50/1.24 Prover 7: Constructing countermodel ... % 3.50/1.24 Prover 13: Constructing countermodel ... % 3.50/1.24 Prover 8: Constructing countermodel ... % 3.50/1.24 Prover 1: Found proof (size 22) % 3.50/1.24 Prover 1: proved (617ms) % 3.50/1.25 Prover 8: stopped % 3.50/1.25 Prover 4: stopped % 3.50/1.25 Prover 10: stopped % 3.50/1.25 Prover 13: stopped % 3.50/1.25 Prover 7: stopped % 3.50/1.26 Prover 11: Constructing countermodel ... % 3.50/1.27 Prover 11: stopped % 3.50/1.27 % 3.50/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.50/1.27 % 4.12/1.27 % SZS output start Proof for theBenchmark % 4.12/1.27 Assumptions after simplification: % 4.12/1.27 --------------------------------- % 4.12/1.27 % 4.12/1.27 (kalish317) % 4.18/1.31 ( ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) = 0) | ~ % 4.18/1.31 $i(v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0) | ? [v1: % 4.18/1.31 $i] : ( ~ (v1 = v0) & f(v1) = 0 & $i(v1))) & ? [v0: $i] : (f(v0) = 0 & % 4.18/1.31 $i(v0))) | ( ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | % 4.18/1.31 ~ (f(v1) = 0) | ~ $i(v1))) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) % 4.18/1.31 & f(v1) = 0 & f(v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i] : ( ~ (f(v0) = % 4.18/1.31 0) | ~ $i(v0)))) % 4.18/1.31 % 4.18/1.31 Those formulas are unsatisfiable: % 4.18/1.31 --------------------------------- % 4.18/1.31 % 4.18/1.31 Begin of proof % 4.18/1.31 | % 4.18/1.31 | BETA: splitting (kalish317) gives: % 4.18/1.31 | % 4.18/1.31 | Case 1: % 4.18/1.31 | | % 4.18/1.32 | | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) = % 4.18/1.32 | | 0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (f(v0) = 0) | ~ % 4.18/1.32 | | $i(v0) | ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & $i(v1))) & ? % 4.18/1.32 | | [v0: $i] : (f(v0) = 0 & $i(v0)) % 4.30/1.32 | | % 4.30/1.32 | | ALPHA: (1) implies: % 4.30/1.32 | | (2) ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = % 4.30/1.32 | | v0) & f(v1) = 0 & $i(v1))) % 4.30/1.32 | | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (f(v1) = 0) | ~ (f(v0) = % 4.30/1.32 | | 0) | ~ $i(v1) | ~ $i(v0)) % 4.30/1.32 | | (4) ? [v0: $i] : (f(v0) = 0 & $i(v0)) % 4.30/1.32 | | % 4.30/1.32 | | DELTA: instantiating (4) with fresh symbol all_10_0 gives: % 4.30/1.32 | | (5) f(all_10_0) = 0 & $i(all_10_0) % 4.30/1.32 | | % 4.30/1.32 | | ALPHA: (5) implies: % 4.30/1.32 | | (6) $i(all_10_0) % 4.30/1.33 | | (7) f(all_10_0) = 0 % 4.30/1.33 | | % 4.30/1.33 | | GROUND_INST: instantiating (2) with all_10_0, simplifying with (6), (7) % 4.30/1.33 | | gives: % 4.30/1.33 | | (8) ? [v0: any] : ( ~ (v0 = all_10_0) & f(v0) = 0 & $i(v0)) % 4.30/1.33 | | % 4.30/1.33 | | DELTA: instantiating (8) with fresh symbol all_17_0 gives: % 4.30/1.33 | | (9) ~ (all_17_0 = all_10_0) & f(all_17_0) = 0 & $i(all_17_0) % 4.30/1.33 | | % 4.30/1.33 | | ALPHA: (9) implies: % 4.30/1.33 | | (10) ~ (all_17_0 = all_10_0) % 4.30/1.33 | | (11) $i(all_17_0) % 4.30/1.33 | | (12) f(all_17_0) = 0 % 4.30/1.33 | | % 4.30/1.33 | | GROUND_INST: instantiating (3) with all_10_0, all_17_0, simplifying with % 4.30/1.33 | | (6), (7), (11), (12) gives: % 4.30/1.33 | | (13) all_17_0 = all_10_0 % 4.30/1.33 | | % 4.30/1.33 | | REDUCE: (10), (13) imply: % 4.30/1.33 | | (14) $false % 4.30/1.33 | | % 4.30/1.33 | | CLOSE: (14) is inconsistent. % 4.30/1.33 | | % 4.30/1.33 | Case 2: % 4.30/1.33 | | % 4.30/1.33 | | (15) ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 4.30/1.33 | | (f(v1) = 0) | ~ $i(v1))) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 4.30/1.33 | | = v0) & f(v1) = 0 & f(v0) = 0 & $i(v1) & $i(v0)) | ! [v0: $i] % 4.30/1.33 | | : ( ~ (f(v0) = 0) | ~ $i(v0))) % 4.30/1.33 | | % 4.30/1.33 | | ALPHA: (15) implies: % 4.30/1.34 | | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & f(v0) = 0 & % 4.30/1.34 | | $i(v1) & $i(v0)) | ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0)) % 4.30/1.34 | | (17) ? [v0: $i] : (f(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 4.30/1.34 | | (f(v1) = 0) | ~ $i(v1))) % 4.30/1.34 | | % 4.30/1.34 | | DELTA: instantiating (17) with fresh symbol all_9_0 gives: % 4.30/1.34 | | (18) f(all_9_0) = 0 & $i(all_9_0) & ! [v0: any] : (v0 = all_9_0 | ~ % 4.30/1.34 | | (f(v0) = 0) | ~ $i(v0)) % 4.30/1.34 | | % 4.30/1.34 | | ALPHA: (18) implies: % 4.30/1.34 | | (19) $i(all_9_0) % 4.30/1.34 | | (20) f(all_9_0) = 0 % 4.30/1.34 | | (21) ! [v0: any] : (v0 = all_9_0 | ~ (f(v0) = 0) | ~ $i(v0)) % 4.30/1.34 | | % 4.30/1.34 | | BETA: splitting (16) gives: % 4.30/1.34 | | % 4.30/1.34 | | Case 1: % 4.30/1.34 | | | % 4.30/1.34 | | | (22) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & f(v1) = 0 & f(v0) = 0 % 4.30/1.34 | | | & $i(v1) & $i(v0)) % 4.30/1.34 | | | % 4.30/1.34 | | | DELTA: instantiating (22) with fresh symbols all_18_0, all_18_1 gives: % 4.30/1.34 | | | (23) ~ (all_18_0 = all_18_1) & f(all_18_0) = 0 & f(all_18_1) = 0 & % 4.30/1.34 | | | $i(all_18_0) & $i(all_18_1) % 4.30/1.34 | | | % 4.30/1.34 | | | ALPHA: (23) implies: % 4.30/1.34 | | | (24) ~ (all_18_0 = all_18_1) % 4.30/1.34 | | | (25) $i(all_18_1) % 4.30/1.34 | | | (26) $i(all_18_0) % 4.30/1.34 | | | (27) f(all_18_1) = 0 % 4.30/1.34 | | | (28) f(all_18_0) = 0 % 4.30/1.34 | | | % 4.30/1.34 | | | GROUND_INST: instantiating (21) with all_18_1, simplifying with (25), (27) % 4.30/1.34 | | | gives: % 4.30/1.34 | | | (29) all_18_1 = all_9_0 % 4.30/1.34 | | | % 4.30/1.34 | | | GROUND_INST: instantiating (21) with all_18_0, simplifying with (26), (28) % 4.30/1.34 | | | gives: % 4.30/1.34 | | | (30) all_18_0 = all_9_0 % 4.30/1.34 | | | % 4.30/1.35 | | | REDUCE: (24), (29), (30) imply: % 4.30/1.35 | | | (31) $false % 4.30/1.35 | | | % 4.30/1.35 | | | CLOSE: (31) is inconsistent. % 4.30/1.35 | | | % 4.30/1.35 | | Case 2: % 4.30/1.35 | | | % 4.30/1.35 | | | (32) ! [v0: $i] : ( ~ (f(v0) = 0) | ~ $i(v0)) % 4.30/1.35 | | | % 4.30/1.35 | | | GROUND_INST: instantiating (32) with all_9_0, simplifying with (19), (20) % 4.30/1.35 | | | gives: % 4.30/1.35 | | | (33) $false % 4.30/1.35 | | | % 4.30/1.35 | | | CLOSE: (33) is inconsistent. % 4.30/1.35 | | | % 4.30/1.35 | | End of split % 4.30/1.35 | | % 4.30/1.35 | End of split % 4.30/1.35 | % 4.30/1.35 End of proof % 4.30/1.35 % SZS output end Proof for theBenchmark % 4.30/1.35 % 4.30/1.35 741ms %------------------------------------------------------------------------------