%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU090+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 : n022.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 17:42:29 EDT 2023 % Result : Theorem 16.21s 2.94s % Output : Proof 16.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU090+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 : Wed Aug 23 15:34:11 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.66 ________ _____ % 0.20/0.66 ___ __ \_________(_)________________________________ % 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.66 % 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.66 (2023-06-19) % 0.20/0.66 % 0.20/0.66 (c) Philipp Rümmer, 2009-2023 % 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.66 Amanda Stjerna. % 0.20/0.66 Free software under BSD-3-Clause. % 0.20/0.66 % 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.66 % 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.37/1.27 Prover 4: Preprocessing ... % 3.37/1.27 Prover 1: Preprocessing ... % 3.37/1.31 Prover 3: Preprocessing ... % 3.37/1.31 Prover 6: Preprocessing ... % 3.37/1.31 Prover 5: Preprocessing ... % 3.37/1.31 Prover 0: Preprocessing ... % 3.37/1.31 Prover 2: Preprocessing ... % 7.11/1.76 Prover 5: Proving ... % 7.11/1.77 Prover 2: Proving ... % 8.17/1.87 Prover 1: Warning: ignoring some quantifiers % 8.17/1.91 Prover 1: Constructing countermodel ... % 8.17/1.91 Prover 3: Warning: ignoring some quantifiers % 8.17/1.93 Prover 6: Proving ... % 8.17/1.96 Prover 3: Constructing countermodel ... % 8.17/1.99 Prover 4: Warning: ignoring some quantifiers % 8.17/2.02 Prover 4: Constructing countermodel ... % 9.53/2.08 Prover 0: Proving ... % 12.57/2.48 Prover 3: gave up % 12.57/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.16/2.55 Prover 7: Preprocessing ... % 13.61/2.65 Prover 7: Warning: ignoring some quantifiers % 13.61/2.67 Prover 7: Constructing countermodel ... % 16.21/2.94 Prover 7: Found proof (size 9) % 16.21/2.94 Prover 7: proved (461ms) % 16.21/2.94 Prover 1: stopped % 16.21/2.94 Prover 5: stopped % 16.21/2.94 Prover 2: stopped % 16.21/2.94 Prover 0: stopped % 16.21/2.94 Prover 6: stopped % 16.21/2.94 Prover 4: stopped % 16.21/2.94 % 16.21/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.21/2.94 % 16.21/2.95 % SZS output start Proof for theBenchmark % 16.21/2.95 Assumptions after simplification: % 16.21/2.95 --------------------------------- % 16.21/2.95 % 16.21/2.95 (d4_zfmisc_1) % 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.21/2.98 $i] : ( ~ (cartesian_product3(v0, v1, v2) = v4) | ~ (cartesian_product2(v4, % 16.21/2.98 v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.21/2.98 (cartesian_product4(v0, v1, v2, v3) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: % 16.21/2.98 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cartesian_product4(v0, % 16.21/2.98 v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.21/2.98 [v5: $i] : (cartesian_product3(v0, v1, v2) = v5 & cartesian_product2(v5, v3) % 16.21/2.98 = v4 & $i(v5) & $i(v4))) % 16.21/2.98 % 16.21/2.98 (fc14_finset_1) % 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 16.21/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 16.21/2.98 % 16.21/2.98 (fc15_finset_1) % 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.21/2.98 (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.21/2.98 ~ finite(v2) | ~ finite(v1) | ~ finite(v0) | finite(v3)) % 16.21/2.98 % 16.21/2.98 (t19_finset_1) % 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 16.21/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 16.21/2.98 % 16.21/2.98 (t20_finset_1) % 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.21/2.98 (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.21/2.98 ~ finite(v2) | ~ finite(v1) | ~ finite(v0) | finite(v3)) % 16.21/2.98 % 16.21/2.98 (t21_finset_1) % 16.21/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.21/2.99 (cartesian_product4(v0, v1, v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 16.21/2.99 $i(v0) & finite(v3) & finite(v2) & finite(v1) & finite(v0) & ~ finite(v4)) % 16.21/2.99 % 16.21/2.99 Further assumptions not needed in the proof: % 16.21/2.99 -------------------------------------------- % 16.21/2.99 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1, % 16.21/2.99 cc1_relat_1, cc1_relset_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, % 16.21/2.99 cc3_ordinal1, cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, % 16.21/2.99 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc4_subset_1, fc5_subset_1, % 16.21/2.99 fc6_subset_1, fc8_arytm_3, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, % 16.21/2.99 rc1_ordinal1, rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 16.21/2.99 rc2_arytm_3, rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1, % 16.21/2.99 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1, % 16.21/2.99 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1, % 16.21/2.99 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 16.21/2.99 t6_boole, t7_boole, t8_boole % 16.21/2.99 % 16.21/2.99 Those formulas are unsatisfiable: % 16.21/2.99 --------------------------------- % 16.21/2.99 % 16.21/2.99 Begin of proof % 16.21/2.99 | % 16.21/2.99 | ALPHA: (d4_zfmisc_1) implies: % 16.21/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 16.21/2.99 | ~ (cartesian_product4(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 16.21/2.99 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (cartesian_product3(v0, v1, v2) % 16.21/2.99 | = v5 & cartesian_product2(v5, v3) = v4 & $i(v5) & $i(v4))) % 16.21/2.99 | % 16.21/2.99 | DELTA: instantiating (t21_finset_1) with fresh symbols all_82_0, all_82_1, % 16.21/2.99 | all_82_2, all_82_3, all_82_4 gives: % 16.21/2.99 | (2) cartesian_product4(all_82_4, all_82_3, all_82_2, all_82_1) = all_82_0 & % 16.21/2.99 | $i(all_82_0) & $i(all_82_1) & $i(all_82_2) & $i(all_82_3) & % 16.21/2.99 | $i(all_82_4) & finite(all_82_1) & finite(all_82_2) & finite(all_82_3) & % 16.21/2.99 | finite(all_82_4) & ~ finite(all_82_0) % 16.21/2.99 | % 16.21/2.99 | ALPHA: (2) implies: % 16.21/2.99 | (3) ~ finite(all_82_0) % 16.21/2.99 | (4) finite(all_82_4) % 16.21/2.99 | (5) finite(all_82_3) % 16.21/2.99 | (6) finite(all_82_2) % 16.21/2.99 | (7) finite(all_82_1) % 16.21/2.99 | (8) $i(all_82_4) % 16.21/2.99 | (9) $i(all_82_3) % 16.21/2.99 | (10) $i(all_82_2) % 16.21/2.99 | (11) $i(all_82_1) % 16.21/2.99 | (12) cartesian_product4(all_82_4, all_82_3, all_82_2, all_82_1) = all_82_0 % 16.21/2.99 | % 16.21/2.99 | GROUND_INST: instantiating (1) with all_82_4, all_82_3, all_82_2, all_82_1, % 16.21/2.99 | all_82_0, simplifying with (8), (9), (10), (11), (12) gives: % 16.21/3.00 | (13) ? [v0: $i] : (cartesian_product3(all_82_4, all_82_3, all_82_2) = v0 & % 16.21/3.00 | cartesian_product2(v0, all_82_1) = all_82_0 & $i(v0) & $i(all_82_0)) % 16.21/3.00 | % 16.21/3.00 | DELTA: instantiating (13) with fresh symbol all_94_0 gives: % 16.21/3.00 | (14) cartesian_product3(all_82_4, all_82_3, all_82_2) = all_94_0 & % 16.21/3.00 | cartesian_product2(all_94_0, all_82_1) = all_82_0 & $i(all_94_0) & % 16.21/3.00 | $i(all_82_0) % 16.21/3.00 | % 16.21/3.00 | ALPHA: (14) implies: % 16.21/3.00 | (15) $i(all_94_0) % 16.21/3.00 | (16) cartesian_product2(all_94_0, all_82_1) = all_82_0 % 16.21/3.00 | (17) cartesian_product3(all_82_4, all_82_3, all_82_2) = all_94_0 % 16.21/3.00 | % 16.21/3.00 | GROUND_INST: instantiating (t20_finset_1) with all_82_4, all_82_3, all_82_2, % 16.21/3.00 | all_94_0, simplifying with (4), (5), (6), (8), (9), (10), (17) % 16.21/3.00 | gives: % 16.21/3.00 | (18) finite(all_94_0) % 16.21/3.00 | % 16.21/3.00 | GROUND_INST: instantiating (t19_finset_1) with all_94_0, all_82_1, all_82_0, % 16.21/3.00 | simplifying with (3), (7), (11), (15), (16), (18) gives: % 16.21/3.00 | (19) $false % 16.21/3.00 | % 16.21/3.00 | CLOSE: (19) is inconsistent. % 16.21/3.00 | % 16.21/3.00 End of proof % 16.21/3.00 % SZS output end Proof for theBenchmark % 16.21/3.00 % 16.21/3.00 2339ms %------------------------------------------------------------------------------