%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 : Thu Aug 31 15:25:33 EDT 2023 % Result : Theorem 4.62s 1.33s % Output : Proof 5.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n010.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 12:23:04 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 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 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 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 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 1.81/0.95 Prover 4: Preprocessing ... % 1.81/0.95 Prover 1: Preprocessing ... % 1.81/0.99 Prover 0: Preprocessing ... % 1.81/0.99 Prover 6: Preprocessing ... % 1.81/0.99 Prover 5: Preprocessing ... % 1.81/0.99 Prover 2: Preprocessing ... % 1.81/0.99 Prover 3: Preprocessing ... % 3.82/1.20 Prover 5: Proving ... % 3.90/1.20 Prover 2: Proving ... % 3.90/1.21 Prover 6: Proving ... % 3.90/1.21 Prover 3: Constructing countermodel ... % 3.90/1.21 Prover 1: Constructing countermodel ... % 3.90/1.23 Prover 0: Proving ... % 3.90/1.25 Prover 4: Constructing countermodel ... % 4.62/1.33 Prover 3: proved (705ms) % 4.62/1.33 % 4.62/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.62/1.33 % 4.62/1.34 Prover 5: stopped % 4.62/1.34 Prover 2: stopped % 4.62/1.34 Prover 6: stopped % 4.62/1.34 Prover 0: stopped % 4.62/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.62/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.62/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.62/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.62/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.62/1.36 Prover 7: Preprocessing ... % 4.62/1.36 Prover 8: Preprocessing ... % 4.62/1.36 Prover 10: Preprocessing ... % 4.62/1.38 Prover 13: Preprocessing ... % 4.62/1.38 Prover 11: Preprocessing ... % 4.62/1.39 Prover 1: Found proof (size 14) % 4.62/1.39 Prover 4: Found proof (size 14) % 4.62/1.39 Prover 1: proved (765ms) % 4.62/1.39 Prover 4: proved (752ms) % 4.62/1.40 Prover 7: Warning: ignoring some quantifiers % 4.62/1.40 Prover 13: stopped % 4.62/1.41 Prover 11: stopped % 4.62/1.41 Prover 10: Warning: ignoring some quantifiers % 4.62/1.41 Prover 7: Constructing countermodel ... % 4.62/1.41 Prover 10: Constructing countermodel ... % 4.62/1.42 Prover 7: stopped % 4.62/1.42 Prover 10: stopped % 5.29/1.43 Prover 8: Warning: ignoring some quantifiers % 5.29/1.43 Prover 8: Constructing countermodel ... % 5.29/1.44 Prover 8: stopped % 5.29/1.44 % 5.29/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.29/1.44 % 5.29/1.44 % SZS output start Proof for theBenchmark % 5.29/1.45 Assumptions after simplification: % 5.29/1.45 --------------------------------- % 5.29/1.45 % 5.29/1.45 (difference_empty_set) % 5.29/1.48 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 5.29/1.48 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 5.29/1.48 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.29/1.48 (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = % 5.29/1.48 0) % 5.29/1.48 % 5.29/1.48 (empty_set_subset) % 5.29/1.48 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, % 5.29/1.48 v0) = v1) | ~ $i(v0)) % 5.29/1.48 % 5.29/1.48 (prove_no_difference_with_empty_set) % 5.29/1.48 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 5.29/1.48 difference(empty_set, v0) = v1 & $i(v1) & $i(v0)) % 5.29/1.48 % 5.29/1.48 Further assumptions not needed in the proof: % 5.29/1.48 -------------------------------------------- % 5.29/1.48 difference_defn, empty_defn, empty_set_defn, equal_defn, reflexivity_of_subset, % 5.29/1.48 subset_defn % 5.29/1.48 % 5.29/1.48 Those formulas are unsatisfiable: % 5.29/1.48 --------------------------------- % 5.29/1.48 % 5.29/1.48 Begin of proof % 5.29/1.48 | % 5.29/1.48 | ALPHA: (empty_set_subset) implies: % 5.29/1.48 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1) % 5.29/1.48 | | ~ $i(v0)) % 5.29/1.48 | % 5.29/1.48 | ALPHA: (difference_empty_set) implies: % 5.29/1.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 5.29/1.49 | (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( % 5.29/1.49 | ~ (v3 = 0) & subset(v0, v1) = v3)) % 5.29/1.49 | % 5.29/1.49 | ALPHA: (prove_no_difference_with_empty_set) implies: % 5.29/1.49 | (3) $i(empty_set) % 5.29/1.49 | (4) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 5.29/1.49 | difference(empty_set, v0) = v1 & $i(v1) & $i(v0)) % 5.29/1.49 | % 5.29/1.49 | DELTA: instantiating (4) with fresh symbols all_12_0, all_12_1 gives: % 5.29/1.49 | (5) ~ (all_12_0 = empty_set) & difference(empty_set, all_12_1) = all_12_0 % 5.29/1.49 | & $i(all_12_0) & $i(all_12_1) % 5.29/1.49 | % 5.29/1.49 | ALPHA: (5) implies: % 5.29/1.49 | (6) ~ (all_12_0 = empty_set) % 5.29/1.49 | (7) $i(all_12_1) % 5.29/1.49 | (8) difference(empty_set, all_12_1) = all_12_0 % 5.29/1.49 | % 5.29/1.49 | GROUND_INST: instantiating (2) with empty_set, all_12_1, all_12_0, simplifying % 5.29/1.49 | with (3), (7), (8) gives: % 5.29/1.49 | (9) all_12_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, % 5.29/1.49 | all_12_1) = v0) % 5.29/1.49 | % 5.29/1.49 | BETA: splitting (9) gives: % 5.29/1.49 | % 5.29/1.49 | Case 1: % 5.29/1.49 | | % 5.29/1.49 | | (10) all_12_0 = empty_set % 5.29/1.49 | | % 5.29/1.49 | | REDUCE: (6), (10) imply: % 5.29/1.49 | | (11) $false % 5.29/1.49 | | % 5.29/1.49 | | CLOSE: (11) is inconsistent. % 5.29/1.49 | | % 5.29/1.49 | Case 2: % 5.29/1.49 | | % 5.29/1.50 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_12_1) = v0) % 5.29/1.50 | | % 5.29/1.50 | | DELTA: instantiating (12) with fresh symbol all_21_0 gives: % 5.29/1.50 | | (13) ~ (all_21_0 = 0) & subset(empty_set, all_12_1) = all_21_0 % 5.29/1.50 | | % 5.29/1.50 | | ALPHA: (13) implies: % 5.29/1.50 | | (14) ~ (all_21_0 = 0) % 5.29/1.50 | | (15) subset(empty_set, all_12_1) = all_21_0 % 5.29/1.50 | | % 5.29/1.50 | | GROUND_INST: instantiating (1) with all_12_1, all_21_0, simplifying with % 5.29/1.50 | | (7), (15) gives: % 5.29/1.50 | | (16) all_21_0 = 0 % 5.29/1.50 | | % 5.29/1.50 | | REDUCE: (14), (16) imply: % 5.29/1.50 | | (17) $false % 5.29/1.50 | | % 5.29/1.50 | | CLOSE: (17) is inconsistent. % 5.29/1.50 | | % 5.29/1.50 | End of split % 5.29/1.50 | % 5.29/1.50 End of proof % 5.29/1.50 % SZS output end Proof for theBenchmark % 5.29/1.50 % 5.29/1.50 892ms %------------------------------------------------------------------------------