%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET971+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 : n028.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 15:27:14 EDT 2023 % Result : Theorem 4.10s 1.35s % Output : Proof 5.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n028.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 11:43:37 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 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 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 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 % 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.09/0.98 Prover 1: Preprocessing ... % 2.09/0.98 Prover 4: Preprocessing ... % 2.09/1.02 Prover 2: Preprocessing ... % 2.09/1.02 Prover 5: Preprocessing ... % 2.09/1.02 Prover 6: Preprocessing ... % 2.09/1.02 Prover 3: Preprocessing ... % 2.09/1.02 Prover 0: Preprocessing ... % 3.49/1.17 Prover 1: Warning: ignoring some quantifiers % 3.49/1.17 Prover 3: Warning: ignoring some quantifiers % 3.49/1.17 Prover 6: Proving ... % 3.49/1.17 Prover 5: Proving ... % 3.49/1.18 Prover 0: Proving ... % 3.49/1.18 Prover 3: Constructing countermodel ... % 3.49/1.18 Prover 1: Constructing countermodel ... % 3.49/1.19 Prover 4: Constructing countermodel ... % 3.49/1.19 Prover 2: Proving ... % 4.10/1.35 Prover 3: proved (711ms) % 4.10/1.35 % 4.10/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.10/1.35 % 4.10/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.10/1.35 Prover 2: stopped % 4.10/1.35 Prover 6: stopped % 4.10/1.36 Prover 5: stopped % 4.10/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.10/1.37 Prover 7: Preprocessing ... % 4.10/1.37 Prover 0: stopped % 4.10/1.38 Prover 8: Preprocessing ... % 4.10/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.10/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.10/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.10/1.40 Prover 10: Preprocessing ... % 4.10/1.40 Prover 11: Preprocessing ... % 4.10/1.41 Prover 13: Preprocessing ... % 4.10/1.42 Prover 8: Warning: ignoring some quantifiers % 4.10/1.42 Prover 7: Warning: ignoring some quantifiers % 4.10/1.42 Prover 7: Constructing countermodel ... % 4.10/1.42 Prover 8: Constructing countermodel ... % 4.10/1.43 Prover 10: Warning: ignoring some quantifiers % 4.10/1.43 Prover 10: Constructing countermodel ... % 4.10/1.45 Prover 13: Warning: ignoring some quantifiers % 4.10/1.45 Prover 13: Constructing countermodel ... % 4.10/1.47 Prover 1: Found proof (size 25) % 4.10/1.47 Prover 1: proved (834ms) % 5.46/1.47 Prover 4: Found proof (size 34) % 5.46/1.47 Prover 4: proved (838ms) % 5.46/1.47 Prover 13: stopped % 5.46/1.47 Prover 8: stopped % 5.46/1.47 Prover 10: stopped % 5.46/1.47 Prover 7: stopped % 5.46/1.48 Prover 11: Constructing countermodel ... % 5.46/1.49 Prover 11: stopped % 5.46/1.49 % 5.46/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.46/1.49 % 5.46/1.50 % SZS output start Proof for theBenchmark % 5.46/1.50 Assumptions after simplification: % 5.46/1.50 --------------------------------- % 5.46/1.50 % 5.46/1.50 (commutativity_k3_xboole_0) % 5.89/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 5.89/1.53 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 5.89/1.53 % 5.89/1.53 (t123_zfmisc_1) % 5.89/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 5.89/1.53 $i] : ! [v6: $i] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ % 5.89/1.53 (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ~ % 5.89/1.53 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : % 5.89/1.53 (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 & % 5.89/1.53 set_intersection2(v0, v1) = v7 & $i(v8) & $i(v7) & $i(v6))) % 5.89/1.53 % 5.89/1.53 (t124_zfmisc_1) % 5.89/1.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.89/1.54 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & cartesian_product2(v1, v2) % 5.89/1.54 = v5 & cartesian_product2(v0, v3) = v4 & cartesian_product2(v0, v2) = v7 & % 5.89/1.54 subset(v2, v3) = 0 & subset(v0, v1) = 0 & set_intersection2(v4, v5) = v6 & % 5.89/1.54 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.89/1.54 % 5.89/1.54 (t28_xboole_1) % 5.89/1.54 ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 5.89/1.54 set_intersection2(v0, v1) = v0) % 5.89/1.54 % 5.89/1.54 (function-axioms) % 5.89/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.89/1.54 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 5.89/1.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 5.89/1.54 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! % 5.89/1.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.89/1.54 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 5.89/1.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 5.89/1.54 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.89/1.55 % 5.89/1.55 Further assumptions not needed in the proof: % 5.89/1.55 -------------------------------------------- % 5.89/1.55 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 5.89/1.55 % 5.89/1.55 Those formulas are unsatisfiable: % 5.89/1.55 --------------------------------- % 5.89/1.55 % 5.89/1.55 Begin of proof % 5.89/1.55 | % 5.89/1.55 | ALPHA: (function-axioms) implies: % 5.89/1.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.89/1.55 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = % 5.89/1.55 | v0)) % 5.89/1.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.89/1.55 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = % 5.89/1.55 | v0)) % 5.89/1.55 | % 5.89/1.55 | DELTA: instantiating (t124_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 5.89/1.55 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7 gives: % 5.89/1.56 | (3) ~ (all_14_0 = all_14_1) & cartesian_product2(all_14_6, all_14_5) = % 5.89/1.56 | all_14_2 & cartesian_product2(all_14_7, all_14_4) = all_14_3 & % 5.89/1.56 | cartesian_product2(all_14_7, all_14_5) = all_14_0 & subset(all_14_5, % 5.89/1.56 | all_14_4) = 0 & subset(all_14_7, all_14_6) = 0 & % 5.89/1.56 | set_intersection2(all_14_3, all_14_2) = all_14_1 & $i(all_14_0) & % 5.89/1.56 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) & % 5.89/1.56 | $i(all_14_5) & $i(all_14_6) & $i(all_14_7) % 5.89/1.56 | % 5.89/1.56 | ALPHA: (3) implies: % 5.89/1.56 | (4) ~ (all_14_0 = all_14_1) % 5.89/1.56 | (5) $i(all_14_7) % 5.89/1.56 | (6) $i(all_14_6) % 5.89/1.56 | (7) $i(all_14_5) % 5.89/1.56 | (8) $i(all_14_4) % 5.89/1.56 | (9) $i(all_14_3) % 5.89/1.56 | (10) $i(all_14_2) % 5.89/1.56 | (11) set_intersection2(all_14_3, all_14_2) = all_14_1 % 5.89/1.56 | (12) subset(all_14_7, all_14_6) = 0 % 5.89/1.56 | (13) subset(all_14_5, all_14_4) = 0 % 5.89/1.56 | (14) cartesian_product2(all_14_7, all_14_5) = all_14_0 % 5.89/1.56 | (15) cartesian_product2(all_14_7, all_14_4) = all_14_3 % 5.89/1.56 | (16) cartesian_product2(all_14_6, all_14_5) = all_14_2 % 5.89/1.56 | % 5.89/1.56 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_3, % 5.89/1.56 | all_14_2, all_14_1, simplifying with (9), (10), (11) gives: % 5.89/1.56 | (17) set_intersection2(all_14_2, all_14_3) = all_14_1 & $i(all_14_1) % 5.89/1.56 | % 5.89/1.56 | ALPHA: (17) implies: % 5.89/1.56 | (18) set_intersection2(all_14_2, all_14_3) = all_14_1 % 5.89/1.56 | % 5.89/1.56 | GROUND_INST: instantiating (t28_xboole_1) with all_14_7, all_14_6, simplifying % 5.89/1.56 | with (5), (6), (12) gives: % 5.89/1.56 | (19) set_intersection2(all_14_7, all_14_6) = all_14_7 % 5.89/1.56 | % 5.89/1.56 | GROUND_INST: instantiating (t28_xboole_1) with all_14_5, all_14_4, simplifying % 5.89/1.56 | with (7), (8), (13) gives: % 5.89/1.56 | (20) set_intersection2(all_14_5, all_14_4) = all_14_5 % 5.89/1.56 | % 5.89/1.57 | GROUND_INST: instantiating (t123_zfmisc_1) with all_14_7, all_14_6, all_14_4, % 5.89/1.57 | all_14_5, all_14_3, all_14_2, all_14_1, simplifying with (5), % 5.89/1.57 | (6), (7), (8), (11), (15), (16) gives: % 5.89/1.57 | (21) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(v0, v1) = all_14_1 & % 5.89/1.57 | set_intersection2(all_14_4, all_14_5) = v1 & % 5.89/1.57 | set_intersection2(all_14_7, all_14_6) = v0 & $i(v1) & $i(v0) & % 5.89/1.57 | $i(all_14_1)) % 5.89/1.57 | % 5.89/1.57 | DELTA: instantiating (21) with fresh symbols all_22_0, all_22_1 gives: % 5.89/1.57 | (22) cartesian_product2(all_22_1, all_22_0) = all_14_1 & % 5.89/1.57 | set_intersection2(all_14_4, all_14_5) = all_22_0 & % 5.89/1.57 | set_intersection2(all_14_7, all_14_6) = all_22_1 & $i(all_22_0) & % 5.89/1.57 | $i(all_22_1) & $i(all_14_1) % 5.89/1.57 | % 5.89/1.57 | ALPHA: (22) implies: % 5.89/1.57 | (23) $i(all_22_1) % 5.89/1.57 | (24) set_intersection2(all_14_7, all_14_6) = all_22_1 % 5.89/1.57 | (25) set_intersection2(all_14_4, all_14_5) = all_22_0 % 5.89/1.57 | (26) cartesian_product2(all_22_1, all_22_0) = all_14_1 % 5.89/1.57 | % 5.89/1.57 | GROUND_INST: instantiating (1) with all_14_7, all_22_1, all_14_6, all_14_7, % 5.89/1.57 | simplifying with (19), (24) gives: % 5.89/1.57 | (27) all_22_1 = all_14_7 % 5.89/1.57 | % 5.89/1.57 | REDUCE: (26), (27) imply: % 5.89/1.57 | (28) cartesian_product2(all_14_7, all_22_0) = all_14_1 % 5.89/1.57 | % 5.89/1.57 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_4, % 5.89/1.57 | all_14_5, all_22_0, simplifying with (7), (8), (25) gives: % 5.89/1.57 | (29) set_intersection2(all_14_5, all_14_4) = all_22_0 & $i(all_22_0) % 5.89/1.57 | % 5.89/1.57 | ALPHA: (29) implies: % 5.89/1.57 | (30) set_intersection2(all_14_5, all_14_4) = all_22_0 % 5.89/1.57 | % 5.89/1.57 | GROUND_INST: instantiating (t123_zfmisc_1) with all_14_6, all_14_7, all_14_5, % 5.89/1.57 | all_14_4, all_14_2, all_14_3, all_14_1, simplifying with (5), % 5.89/1.57 | (6), (7), (8), (15), (16), (18) gives: % 5.89/1.57 | (31) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(v0, v1) = all_14_1 & % 5.89/1.57 | set_intersection2(all_14_5, all_14_4) = v1 & % 5.89/1.57 | set_intersection2(all_14_6, all_14_7) = v0 & $i(v1) & $i(v0) & % 5.89/1.57 | $i(all_14_1)) % 5.89/1.57 | % 5.89/1.57 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives: % 5.89/1.58 | (32) cartesian_product2(all_34_1, all_34_0) = all_14_1 & % 5.89/1.58 | set_intersection2(all_14_5, all_14_4) = all_34_0 & % 5.89/1.58 | set_intersection2(all_14_6, all_14_7) = all_34_1 & $i(all_34_0) & % 5.89/1.58 | $i(all_34_1) & $i(all_14_1) % 5.89/1.58 | % 5.89/1.58 | ALPHA: (32) implies: % 5.89/1.58 | (33) set_intersection2(all_14_5, all_14_4) = all_34_0 % 5.89/1.58 | % 5.89/1.58 | GROUND_INST: instantiating (1) with all_14_5, all_34_0, all_14_4, all_14_5, % 5.89/1.58 | simplifying with (20), (33) gives: % 5.89/1.58 | (34) all_34_0 = all_14_5 % 5.89/1.58 | % 5.89/1.58 | GROUND_INST: instantiating (1) with all_22_0, all_34_0, all_14_4, all_14_5, % 5.89/1.58 | simplifying with (30), (33) gives: % 5.89/1.58 | (35) all_34_0 = all_22_0 % 5.89/1.58 | % 5.89/1.58 | COMBINE_EQS: (34), (35) imply: % 5.89/1.58 | (36) all_22_0 = all_14_5 % 5.89/1.58 | % 5.89/1.58 | REDUCE: (28), (36) imply: % 5.89/1.58 | (37) cartesian_product2(all_14_7, all_14_5) = all_14_1 % 5.89/1.58 | % 5.89/1.58 | GROUND_INST: instantiating (2) with all_14_0, all_14_1, all_14_5, all_14_7, % 5.89/1.58 | simplifying with (14), (37) gives: % 5.89/1.58 | (38) all_14_0 = all_14_1 % 5.89/1.58 | % 5.89/1.58 | REDUCE: (4), (38) imply: % 5.89/1.58 | (39) $false % 5.89/1.58 | % 5.89/1.58 | CLOSE: (39) is inconsistent. % 5.89/1.58 | % 5.89/1.58 End of proof % 5.89/1.58 % SZS output end Proof for theBenchmark % 5.89/1.58 % 5.89/1.58 967ms %------------------------------------------------------------------------------