%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET911+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 15:27:00 EDT 2023 % Result : Theorem 4.15s 1.48s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET911+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n029.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Sat Aug 26 14:58:25 EDT 2023 % 0.14/0.33 % CPUTime : % 0.17/0.66 ________ _____ % 0.17/0.66 ___ __ \_________(_)________________________________ % 0.17/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.66 % 0.17/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.66 (2023-06-19) % 0.17/0.66 % 0.17/0.66 (c) Philipp Rümmer, 2009-2023 % 0.17/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.66 Amanda Stjerna. % 0.17/0.66 Free software under BSD-3-Clause. % 0.17/0.66 % 0.17/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.66 % 0.17/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.67 Running up to 7 provers in parallel. % 0.17/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.91/1.08 Prover 1: Preprocessing ... % 1.91/1.08 Prover 4: Preprocessing ... % 2.28/1.12 Prover 5: Preprocessing ... % 2.28/1.12 Prover 6: Preprocessing ... % 2.28/1.12 Prover 2: Preprocessing ... % 2.28/1.12 Prover 3: Preprocessing ... % 2.28/1.12 Prover 0: Preprocessing ... % 3.29/1.29 Prover 1: Warning: ignoring some quantifiers % 3.29/1.29 Prover 3: Warning: ignoring some quantifiers % 3.29/1.30 Prover 1: Constructing countermodel ... % 3.29/1.30 Prover 6: Proving ... % 3.29/1.31 Prover 3: Constructing countermodel ... % 3.29/1.31 Prover 5: Proving ... % 3.29/1.32 Prover 4: Constructing countermodel ... % 3.29/1.33 Prover 2: Proving ... % 3.70/1.35 Prover 0: Proving ... % 4.15/1.47 Prover 0: proved (792ms) % 4.15/1.47 Prover 5: proved (782ms) % 4.15/1.47 % 4.15/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.15/1.48 % 4.15/1.48 % 4.15/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.15/1.48 % 4.15/1.48 Prover 2: stopped % 4.15/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.15/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.15/1.51 Prover 3: stopped % 4.15/1.51 Prover 6: stopped % 4.15/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.15/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.15/1.52 Prover 8: Preprocessing ... % 4.15/1.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.15/1.52 Prover 10: Preprocessing ... % 4.15/1.53 Prover 7: Preprocessing ... % 4.15/1.56 Prover 11: Preprocessing ... % 4.15/1.56 Prover 4: Found proof (size 13) % 4.15/1.56 Prover 4: proved (874ms) % 4.15/1.56 Prover 1: Found proof (size 12) % 4.15/1.56 Prover 1: proved (885ms) % 4.15/1.57 Prover 13: Preprocessing ... % 4.15/1.59 Prover 11: stopped % 4.15/1.59 Prover 10: Constructing countermodel ... % 4.15/1.61 Prover 10: stopped % 4.15/1.61 Prover 8: Warning: ignoring some quantifiers % 4.15/1.62 Prover 8: Constructing countermodel ... % 4.15/1.62 Prover 7: Constructing countermodel ... % 4.15/1.63 Prover 8: stopped % 4.15/1.63 Prover 7: stopped % 4.15/1.63 Prover 13: Warning: ignoring some quantifiers % 5.46/1.63 Prover 13: Constructing countermodel ... % 5.46/1.64 Prover 13: stopped % 5.46/1.64 % 5.46/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.46/1.64 % 5.46/1.64 % SZS output start Proof for theBenchmark % 5.46/1.65 Assumptions after simplification: % 5.46/1.65 --------------------------------- % 5.46/1.65 % 5.46/1.65 (l32_zfmisc_1) % 5.46/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 5.46/1.70 (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v1) | ~ % 5.46/1.70 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! % 5.46/1.70 [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 5.46/1.70 (singleton(v0) = v2 & set_intersection2(v1, v2) = v2 & $i(v2))) % 5.46/1.70 % 5.46/1.70 (t52_zfmisc_1) % 5.46/1.71 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & % 5.46/1.71 singleton(v0) = v2 & in(v0, v1) = 0 & set_intersection2(v1, v2) = v3 & % 5.46/1.71 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.46/1.71 % 5.46/1.71 (function-axioms) % 5.83/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.83/1.71 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 5.83/1.71 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.83/1.71 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 5.83/1.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 5.83/1.71 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 5.83/1.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 5.83/1.71 (empty(v2) = v0)) % 5.83/1.71 % 5.83/1.71 Further assumptions not needed in the proof: % 5.83/1.71 -------------------------------------------- % 5.83/1.72 antisymmetry_r2_hidden, commutativity_k3_xboole_0, idempotence_k3_xboole_0, % 5.83/1.72 rc1_xboole_0, rc2_xboole_0 % 5.83/1.72 % 5.83/1.72 Those formulas are unsatisfiable: % 5.83/1.72 --------------------------------- % 5.83/1.72 % 5.83/1.72 Begin of proof % 5.83/1.72 | % 5.83/1.72 | ALPHA: (l32_zfmisc_1) implies: % 5.83/1.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 5.83/1.72 | (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ % 5.83/1.72 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 5.83/1.72 | % 5.83/1.72 | ALPHA: (function-axioms) implies: % 5.83/1.72 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.83/1.72 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.83/1.72 | % 5.83/1.73 | DELTA: instantiating (t52_zfmisc_1) with fresh symbols all_11_0, all_11_1, % 5.83/1.73 | all_11_2, all_11_3 gives: % 5.83/1.73 | (3) ~ (all_11_0 = all_11_1) & singleton(all_11_3) = all_11_1 & % 5.83/1.73 | in(all_11_3, all_11_2) = 0 & set_intersection2(all_11_2, all_11_1) = % 5.83/1.73 | all_11_0 & $i(all_11_0) & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) % 5.83/1.73 | % 5.83/1.73 | ALPHA: (3) implies: % 5.83/1.73 | (4) ~ (all_11_0 = all_11_1) % 5.83/1.73 | (5) $i(all_11_3) % 5.83/1.73 | (6) $i(all_11_2) % 5.83/1.73 | (7) set_intersection2(all_11_2, all_11_1) = all_11_0 % 5.83/1.73 | (8) in(all_11_3, all_11_2) = 0 % 5.83/1.73 | (9) singleton(all_11_3) = all_11_1 % 5.83/1.73 | % 5.83/1.73 | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1, all_11_0, % 5.83/1.73 | simplifying with (5), (6), (7), (9) gives: % 5.83/1.74 | (10) all_11_0 = all_11_1 | ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, % 5.83/1.74 | all_11_2) = v0) % 5.83/1.74 | % 5.83/1.74 | BETA: splitting (10) gives: % 5.83/1.74 | % 5.83/1.74 | Case 1: % 5.83/1.74 | | % 5.83/1.74 | | (11) all_11_0 = all_11_1 % 5.83/1.74 | | % 5.83/1.74 | | REDUCE: (4), (11) imply: % 5.83/1.74 | | (12) $false % 5.83/1.74 | | % 5.83/1.74 | | CLOSE: (12) is inconsistent. % 5.83/1.74 | | % 5.83/1.74 | Case 2: % 5.83/1.74 | | % 5.83/1.74 | | (13) ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, all_11_2) = v0) % 5.83/1.74 | | % 5.83/1.74 | | DELTA: instantiating (13) with fresh symbol all_27_0 gives: % 5.83/1.74 | | (14) ~ (all_27_0 = 0) & in(all_11_3, all_11_2) = all_27_0 % 5.83/1.74 | | % 5.83/1.74 | | ALPHA: (14) implies: % 5.83/1.74 | | (15) ~ (all_27_0 = 0) % 5.83/1.74 | | (16) in(all_11_3, all_11_2) = all_27_0 % 5.83/1.74 | | % 5.83/1.74 | | GROUND_INST: instantiating (2) with 0, all_27_0, all_11_2, all_11_3, % 5.83/1.74 | | simplifying with (8), (16) gives: % 5.83/1.74 | | (17) all_27_0 = 0 % 5.83/1.74 | | % 5.83/1.74 | | REDUCE: (15), (17) imply: % 5.83/1.74 | | (18) $false % 5.83/1.74 | | % 5.83/1.74 | | CLOSE: (18) is inconsistent. % 5.83/1.74 | | % 5.83/1.74 | End of split % 5.83/1.74 | % 5.83/1.74 End of proof % 5.83/1.74 % SZS output end Proof for theBenchmark % 5.83/1.74 % 5.83/1.74 1084ms %------------------------------------------------------------------------------