%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET903+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 : n014.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 15:26:57 EDT 2023 % Result : Theorem 3.47s 1.43s % Output : Proof 5.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n014.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 08:30:02 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.59/1.00 Prover 1: Preprocessing ... % 2.16/1.01 Prover 4: Preprocessing ... % 2.16/1.05 Prover 5: Preprocessing ... % 2.16/1.05 Prover 3: Preprocessing ... % 2.16/1.05 Prover 2: Preprocessing ... % 2.16/1.05 Prover 6: Preprocessing ... % 2.16/1.06 Prover 0: Preprocessing ... % 3.47/1.23 Prover 1: Warning: ignoring some quantifiers % 3.47/1.25 Prover 3: Warning: ignoring some quantifiers % 3.47/1.26 Prover 5: Proving ... % 3.47/1.26 Prover 6: Proving ... % 3.47/1.26 Prover 1: Constructing countermodel ... % 3.47/1.27 Prover 3: Constructing countermodel ... % 3.47/1.27 Prover 4: Constructing countermodel ... % 3.47/1.28 Prover 2: Proving ... % 3.47/1.30 Prover 0: Proving ... % 3.47/1.43 Prover 3: proved (800ms) % 3.47/1.43 % 3.47/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.47/1.43 % 3.47/1.44 Prover 2: stopped % 4.55/1.44 Prover 0: stopped % 4.55/1.44 Prover 5: stopped % 4.55/1.44 Prover 6: stopped % 4.55/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.55/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.55/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.55/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.55/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.55/1.47 Prover 8: Preprocessing ... % 4.55/1.47 Prover 10: Preprocessing ... % 4.55/1.48 Prover 7: Preprocessing ... % 4.55/1.48 Prover 13: Preprocessing ... % 4.55/1.49 Prover 11: Preprocessing ... % 4.55/1.49 Prover 1: Found proof (size 16) % 4.55/1.49 Prover 1: proved (867ms) % 4.55/1.49 Prover 4: Found proof (size 15) % 4.55/1.49 Prover 4: proved (863ms) % 4.55/1.50 Prover 13: stopped % 4.55/1.51 Prover 11: stopped % 5.46/1.53 Prover 8: Warning: ignoring some quantifiers % 5.46/1.53 Prover 8: Constructing countermodel ... % 5.46/1.54 Prover 8: stopped % 5.46/1.55 Prover 10: Constructing countermodel ... % 5.46/1.55 Prover 7: Constructing countermodel ... % 5.46/1.56 Prover 10: stopped % 5.46/1.56 Prover 7: stopped % 5.46/1.56 % 5.46/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.46/1.56 % 5.46/1.56 % SZS output start Proof for theBenchmark % 5.46/1.57 Assumptions after simplification: % 5.46/1.57 --------------------------------- % 5.46/1.57 % 5.46/1.57 (t43_zfmisc_1) % 5.46/1.60 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 5.46/1.60 (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 5.46/1.60 | ~ $i(v0) | (v3 = v2 & v1 = empty_set) | (v3 = v1 & v2 = v1) | (v3 = v1 & % 5.46/1.60 v2 = empty_set)) % 5.46/1.60 % 5.46/1.60 (t44_zfmisc_1) % 5.46/1.60 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 5.46/1.60 (v2 = v1) & ~ (v2 = empty_set) & ~ (v1 = empty_set) & singleton(v0) = v3 & % 5.46/1.60 set_union2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.46/1.60 % 5.46/1.60 Further assumptions not needed in the proof: % 5.46/1.60 -------------------------------------------- % 5.46/1.60 commutativity_k2_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 5.46/1.60 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0 % 5.46/1.60 % 5.46/1.60 Those formulas are unsatisfiable: % 5.46/1.60 --------------------------------- % 5.46/1.60 % 5.46/1.60 Begin of proof % 5.46/1.60 | % 5.46/1.60 | ALPHA: (t43_zfmisc_1) implies: % 5.46/1.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 5.46/1.61 | (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ % 5.46/1.61 | $i(v1) | ~ $i(v0) | (v3 = v2 & v1 = empty_set) | (v3 = v1 & v2 = v1) % 5.46/1.61 | | (v3 = v1 & v2 = empty_set)) % 5.46/1.61 | % 5.46/1.61 | ALPHA: (t44_zfmisc_1) implies: % 5.46/1.61 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = v1) & % 5.46/1.61 | ~ (v2 = empty_set) & ~ (v1 = empty_set) & singleton(v0) = v3 & % 5.46/1.61 | set_union2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.46/1.61 | % 5.46/1.61 | DELTA: instantiating (2) with fresh symbols all_14_0, all_14_1, all_14_2, % 5.46/1.61 | all_14_3 gives: % 5.46/1.61 | (3) ~ (all_14_1 = all_14_2) & ~ (all_14_1 = empty_set) & ~ (all_14_2 = % 5.46/1.61 | empty_set) & singleton(all_14_3) = all_14_0 & set_union2(all_14_2, % 5.46/1.61 | all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & % 5.46/1.61 | $i(all_14_3) % 5.46/1.61 | % 5.46/1.61 | ALPHA: (3) implies: % 5.91/1.61 | (4) ~ (all_14_2 = empty_set) % 5.91/1.61 | (5) ~ (all_14_1 = empty_set) % 5.91/1.61 | (6) ~ (all_14_1 = all_14_2) % 5.91/1.61 | (7) $i(all_14_3) % 5.91/1.62 | (8) $i(all_14_2) % 5.91/1.62 | (9) $i(all_14_1) % 5.91/1.62 | (10) set_union2(all_14_2, all_14_1) = all_14_0 % 5.91/1.62 | (11) singleton(all_14_3) = all_14_0 % 5.91/1.62 | % 5.91/1.62 | GROUND_INST: instantiating (1) with all_14_3, all_14_2, all_14_1, all_14_0, % 5.91/1.62 | simplifying with (7), (8), (9), (10), (11) gives: % 5.91/1.62 | (12) (all_14_0 = all_14_1 & all_14_2 = empty_set) | (all_14_0 = all_14_2 & % 5.91/1.62 | all_14_1 = all_14_2) | (all_14_0 = all_14_2 & all_14_1 = empty_set) % 5.91/1.62 | % 5.91/1.62 | BETA: splitting (12) gives: % 5.91/1.62 | % 5.91/1.62 | Case 1: % 5.91/1.62 | | % 5.91/1.62 | | (13) all_14_0 = all_14_1 & all_14_2 = empty_set % 5.91/1.62 | | % 5.91/1.62 | | ALPHA: (13) implies: % 5.91/1.62 | | (14) all_14_2 = empty_set % 5.91/1.62 | | % 5.91/1.62 | | REDUCE: (4), (14) imply: % 5.91/1.62 | | (15) $false % 5.91/1.62 | | % 5.91/1.62 | | CLOSE: (15) is inconsistent. % 5.91/1.62 | | % 5.91/1.62 | Case 2: % 5.91/1.62 | | % 5.91/1.62 | | (16) (all_14_0 = all_14_2 & all_14_1 = all_14_2) | (all_14_0 = all_14_2 & % 5.91/1.62 | | all_14_1 = empty_set) % 5.91/1.62 | | % 5.91/1.62 | | BETA: splitting (16) gives: % 5.91/1.62 | | % 5.91/1.62 | | Case 1: % 5.91/1.62 | | | % 5.91/1.62 | | | (17) all_14_0 = all_14_2 & all_14_1 = all_14_2 % 5.91/1.62 | | | % 5.91/1.62 | | | ALPHA: (17) implies: % 5.91/1.62 | | | (18) all_14_1 = all_14_2 % 5.91/1.62 | | | % 5.91/1.62 | | | REDUCE: (6), (18) imply: % 5.91/1.62 | | | (19) $false % 5.91/1.62 | | | % 5.91/1.62 | | | CLOSE: (19) is inconsistent. % 5.91/1.62 | | | % 5.91/1.62 | | Case 2: % 5.91/1.62 | | | % 5.91/1.62 | | | (20) all_14_0 = all_14_2 & all_14_1 = empty_set % 5.91/1.62 | | | % 5.91/1.62 | | | ALPHA: (20) implies: % 5.91/1.62 | | | (21) all_14_1 = empty_set % 5.91/1.62 | | | % 5.91/1.62 | | | REDUCE: (5), (21) imply: % 5.91/1.62 | | | (22) $false % 5.91/1.62 | | | % 5.91/1.62 | | | CLOSE: (22) is inconsistent. % 5.91/1.62 | | | % 5.91/1.62 | | End of split % 5.91/1.62 | | % 5.91/1.62 | End of split % 5.91/1.62 | % 5.91/1.62 End of proof % 5.91/1.62 % SZS output end Proof for theBenchmark % 5.91/1.62 % 5.91/1.63 1022ms %------------------------------------------------------------------------------