%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 : Wed Aug 30 22:18:58 EDT 2023 % Result : Theorem 5.94s 1.56s % Output : Proof 8.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : DAT036_1 : TPTP v8.1.2. Released v5.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n011.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Aug 24 14:03:37 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.62/1.08 Prover 1: Preprocessing ... % 2.62/1.08 Prover 4: Preprocessing ... % 2.62/1.12 Prover 2: Preprocessing ... % 2.62/1.12 Prover 6: Preprocessing ... % 3.13/1.13 Prover 0: Preprocessing ... % 3.13/1.13 Prover 5: Preprocessing ... % 3.13/1.13 Prover 3: Preprocessing ... % 5.06/1.40 Prover 5: Proving ... % 5.06/1.40 Prover 1: Constructing countermodel ... % 5.06/1.40 Prover 6: Constructing countermodel ... % 5.06/1.40 Prover 3: Constructing countermodel ... % 5.32/1.43 Prover 2: Proving ... % 5.32/1.43 Prover 4: Constructing countermodel ... % 5.32/1.44 Prover 0: Proving ... % 5.94/1.56 Prover 0: proved (927ms) % 5.94/1.56 % 5.94/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.94/1.56 % 5.94/1.56 Prover 6: stopped % 5.94/1.56 Prover 5: stopped % 5.94/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.94/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.94/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.94/1.57 Prover 2: stopped % 5.94/1.58 Prover 3: stopped % 6.51/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.51/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.51/1.60 Prover 7: Preprocessing ... % 6.51/1.60 Prover 8: Preprocessing ... % 6.51/1.60 Prover 10: Preprocessing ... % 6.51/1.62 Prover 11: Preprocessing ... % 6.51/1.63 Prover 13: Preprocessing ... % 7.20/1.68 Prover 7: Constructing countermodel ... % 7.20/1.68 Prover 10: Constructing countermodel ... % 7.20/1.69 Prover 8: Warning: ignoring some quantifiers % 7.33/1.69 Prover 8: Constructing countermodel ... % 7.33/1.69 Prover 13: Warning: ignoring some quantifiers % 7.33/1.70 Prover 13: Constructing countermodel ... % 7.58/1.75 Prover 11: Constructing countermodel ... % 8.21/1.82 Prover 10: Found proof (size 34) % 8.21/1.82 Prover 10: proved (256ms) % 8.21/1.82 Prover 11: stopped % 8.21/1.82 Prover 8: stopped % 8.21/1.82 Prover 7: stopped % 8.21/1.82 Prover 13: Found proof (size 34) % 8.21/1.82 Prover 13: proved (236ms) % 8.21/1.82 Prover 4: Found proof (size 89) % 8.21/1.82 Prover 4: proved (1191ms) % 8.21/1.83 Prover 1: Found proof (size 104) % 8.21/1.83 Prover 1: proved (1197ms) % 8.21/1.83 % 8.21/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.21/1.83 % 8.21/1.83 % SZS output start Proof for theBenchmark % 8.21/1.83 Assumptions after simplification: % 8.21/1.83 --------------------------------- % 8.21/1.83 % 8.21/1.83 (ax3) % 8.21/1.85 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 8.21/1.85 = v2) | ~ collection(v1) | ~ in(v0, v2)) & ! [v0: int] : ! [v1: % 8.21/1.85 collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ % 8.21/1.85 collection(v1) | ~ in(v0, v1) | ? [v3: int] : ? [v4: int] : ( ~ % 8.21/1.85 ($difference(v4, v3) = -1) & count(v2) = v3 & count(v1) = v4)) & ! [v0: % 8.21/1.85 int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | % 8.21/1.85 ~ collection(v1) | in(v0, v1) | ? [v3: int] : (count(v2) = v3 & count(v1) = % 8.21/1.85 $sum(v3, -1))) % 8.21/1.85 % 8.21/1.85 (ax4) % 8.21/1.86 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 % 8.21/1.86 = v0 | ~ (add(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v3) | in(v0, % 8.21/1.86 v1)) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 8.21/1.86 collection] : ( ~ (add(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v1) | % 8.21/1.86 in(v0, v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 8.21/1.86 (add(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: int] : % 8.21/1.86 (count(v2) = v3 & count(v1) = v3)) & ! [v0: int] : ! [v1: collection] : ! % 8.21/1.86 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | in(v0, v2)) & % 8.21/1.86 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, v1) = % 8.21/1.86 v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] : ? [v4: int] : ( ~ % 8.21/1.86 (v4 = v3) & count(v2) = v3 & count(v1) = v4)) % 8.21/1.86 % 8.21/1.86 (co1) % 8.21/1.86 ? [v0: collection] : ? [v1: int] : ? [v2: int] : ? [v3: collection] : ? % 8.21/1.86 [v4: collection] : ? [v5: int] : ($lesseq(2, $difference(v5, v2)) & add(v1, % 8.21/1.86 v3) = v4 & add(v1, v0) = v3 & count(v4) = v5 & count(v0) = v2 & % 8.21/1.86 collection(v4) & collection(v3) & collection(v0)) % 8.21/1.86 % 8.21/1.86 (function-axioms) % 8.21/1.87 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 8.21/1.87 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 8.21/1.87 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 8.21/1.87 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: int] : ! % 8.21/1.87 [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | ~ % 8.21/1.87 (count(v2) = v0)) % 8.21/1.87 % 8.21/1.87 Further assumptions not needed in the proof: % 8.21/1.87 -------------------------------------------- % 8.21/1.87 ax1, ax2, ax5, ax6, ax7 % 8.21/1.87 % 8.21/1.87 Those formulas are unsatisfiable: % 8.21/1.87 --------------------------------- % 8.21/1.87 % 8.21/1.87 Begin of proof % 8.21/1.87 | % 8.21/1.87 | ALPHA: (ax3) implies: % 8.21/1.87 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 8.21/1.87 | v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] : % 8.21/1.87 | (count(v2) = v3 & count(v1) = $sum(v3, -1))) % 8.21/1.87 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 8.21/1.87 | v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: int] : ? % 8.21/1.87 | [v4: int] : ( ~ ($difference(v4, v3) = -1) & count(v2) = v3 & % 8.21/1.87 | count(v1) = v4)) % 8.21/1.87 | % 8.21/1.87 | ALPHA: (ax4) implies: % 8.21/1.87 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 8.21/1.87 | v1) = v2) | ~ collection(v1) | in(v0, v2)) % 8.21/1.87 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 8.21/1.87 | v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: int] : % 8.21/1.87 | (count(v2) = v3 & count(v1) = v3)) % 8.21/1.87 | % 8.21/1.87 | ALPHA: (function-axioms) implies: % 8.21/1.88 | (5) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 8.21/1.88 | (count(v2) = v1) | ~ (count(v2) = v0)) % 8.21/1.88 | % 8.21/1.88 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2, % 8.21/1.88 | all_13_3, all_13_4, all_13_5 gives: % 8.21/1.88 | (6) $lesseq(2, $difference(all_13_0, all_13_3)) & add(all_13_4, all_13_2) = % 8.21/1.88 | all_13_1 & add(all_13_4, all_13_5) = all_13_2 & count(all_13_1) = % 8.21/1.88 | all_13_0 & count(all_13_5) = all_13_3 & collection(all_13_1) & % 8.21/1.88 | collection(all_13_2) & collection(all_13_5) % 8.21/1.88 | % 8.21/1.88 | ALPHA: (6) implies: % 8.21/1.88 | (7) $lesseq(2, $difference(all_13_0, all_13_3)) % 8.21/1.88 | (8) collection(all_13_5) % 8.21/1.88 | (9) collection(all_13_2) % 8.21/1.88 | (10) count(all_13_5) = all_13_3 % 8.21/1.88 | (11) count(all_13_1) = all_13_0 % 8.21/1.88 | (12) add(all_13_4, all_13_5) = all_13_2 % 8.21/1.88 | (13) add(all_13_4, all_13_2) = all_13_1 % 8.21/1.88 | % 8.21/1.88 | GROUND_INST: instantiating (3) with all_13_4, all_13_5, all_13_2, simplifying % 8.21/1.88 | with (8), (12) gives: % 8.21/1.88 | (14) in(all_13_4, all_13_2) % 8.21/1.88 | % 8.21/1.88 | GROUND_INST: instantiating (1) with all_13_4, all_13_5, all_13_2, simplifying % 8.21/1.88 | with (8), (12) gives: % 8.21/1.88 | (15) in(all_13_4, all_13_5) | ? [v0: int] : (count(all_13_2) = v0 & % 8.21/1.88 | count(all_13_5) = $sum(v0, -1)) % 8.21/1.88 | % 8.21/1.88 | GROUND_INST: instantiating (2) with all_13_4, all_13_2, all_13_1, simplifying % 8.21/1.88 | with (9), (13), (14) gives: % 8.21/1.88 | (16) ? [v0: int] : ? [v1: int] : ( ~ ($difference(v1, v0) = -1) & % 8.21/1.88 | count(all_13_1) = v0 & count(all_13_2) = v1) % 8.21/1.88 | % 8.21/1.88 | GROUND_INST: instantiating (4) with all_13_4, all_13_2, all_13_1, simplifying % 8.21/1.88 | with (9), (13), (14) gives: % 8.21/1.88 | (17) ? [v0: int] : (count(all_13_1) = v0 & count(all_13_2) = v0) % 8.21/1.88 | % 8.21/1.88 | DELTA: instantiating (17) with fresh symbol all_30_0 gives: % 8.21/1.89 | (18) count(all_13_1) = all_30_0 & count(all_13_2) = all_30_0 % 8.21/1.89 | % 8.21/1.89 | ALPHA: (18) implies: % 8.21/1.89 | (19) count(all_13_2) = all_30_0 % 8.21/1.89 | (20) count(all_13_1) = all_30_0 % 8.21/1.89 | % 8.21/1.89 | DELTA: instantiating (16) with fresh symbols all_32_0, all_32_1 gives: % 8.21/1.89 | (21) ~ ($difference(all_32_0, all_32_1) = -1) & count(all_13_1) = all_32_1 % 8.21/1.89 | & count(all_13_2) = all_32_0 % 8.21/1.89 | % 8.21/1.89 | ALPHA: (21) implies: % 8.21/1.89 | (22) count(all_13_1) = all_32_1 % 8.21/1.89 | % 8.21/1.89 | GROUND_INST: instantiating (5) with all_13_0, all_32_1, all_13_1, simplifying % 8.21/1.89 | with (11), (22) gives: % 8.21/1.89 | (23) all_32_1 = all_13_0 % 8.21/1.89 | % 8.21/1.89 | GROUND_INST: instantiating (5) with all_30_0, all_32_1, all_13_1, simplifying % 8.21/1.89 | with (20), (22) gives: % 8.21/1.89 | (24) all_32_1 = all_30_0 % 8.21/1.89 | % 8.21/1.89 | COMBINE_EQS: (23), (24) imply: % 8.21/1.89 | (25) all_30_0 = all_13_0 % 8.21/1.89 | % 8.21/1.89 | SIMP: (25) implies: % 8.21/1.89 | (26) all_30_0 = all_13_0 % 8.21/1.89 | % 8.21/1.89 | REDUCE: (19), (26) imply: % 8.21/1.89 | (27) count(all_13_2) = all_13_0 % 8.21/1.89 | % 8.21/1.89 | BETA: splitting (15) gives: % 8.21/1.89 | % 8.21/1.89 | Case 1: % 8.21/1.89 | | % 8.21/1.89 | | (28) in(all_13_4, all_13_5) % 8.21/1.89 | | % 8.21/1.89 | | GROUND_INST: instantiating (4) with all_13_4, all_13_5, all_13_2, % 8.21/1.89 | | simplifying with (8), (12), (28) gives: % 8.21/1.89 | | (29) ? [v0: int] : (count(all_13_2) = v0 & count(all_13_5) = v0) % 8.21/1.89 | | % 8.21/1.89 | | DELTA: instantiating (29) with fresh symbol all_47_0 gives: % 8.21/1.89 | | (30) count(all_13_2) = all_47_0 & count(all_13_5) = all_47_0 % 8.21/1.89 | | % 8.21/1.89 | | ALPHA: (30) implies: % 8.21/1.89 | | (31) count(all_13_5) = all_47_0 % 8.21/1.89 | | (32) count(all_13_2) = all_47_0 % 8.21/1.89 | | % 8.21/1.89 | | GROUND_INST: instantiating (5) with all_13_3, all_47_0, all_13_5, % 8.21/1.89 | | simplifying with (10), (31) gives: % 8.21/1.89 | | (33) all_47_0 = all_13_3 % 8.21/1.89 | | % 8.21/1.89 | | GROUND_INST: instantiating (5) with all_13_0, all_47_0, all_13_2, % 8.21/1.89 | | simplifying with (27), (32) gives: % 8.21/1.89 | | (34) all_47_0 = all_13_0 % 8.21/1.89 | | % 8.21/1.89 | | COMBINE_EQS: (33), (34) imply: % 8.21/1.89 | | (35) all_13_0 = all_13_3 % 8.21/1.89 | | % 8.21/1.89 | | REDUCE: (7), (35) imply: % 8.21/1.89 | | (36) $false % 8.21/1.89 | | % 8.21/1.89 | | CLOSE: (36) is inconsistent. % 8.21/1.89 | | % 8.21/1.89 | Case 2: % 8.21/1.89 | | % 8.21/1.89 | | (37) ? [v0: int] : (count(all_13_2) = v0 & count(all_13_5) = $sum(v0, % 8.21/1.89 | | -1)) % 8.21/1.90 | | % 8.21/1.90 | | DELTA: instantiating (37) with fresh symbol all_42_0 gives: % 8.21/1.90 | | (38) count(all_13_2) = all_42_0 & count(all_13_5) = $sum(all_42_0, -1) % 8.21/1.90 | | % 8.21/1.90 | | ALPHA: (38) implies: % 8.21/1.90 | | (39) count(all_13_5) = $sum(all_42_0, -1) % 8.21/1.90 | | (40) count(all_13_2) = all_42_0 % 8.21/1.90 | | % 8.21/1.90 | | GROUND_INST: instantiating (5) with all_13_3, $sum(all_42_0, -1), all_13_5, % 8.21/1.90 | | simplifying with (10), (39) gives: % 8.21/1.90 | | (41) $difference(all_42_0, all_13_3) = 1 % 8.21/1.90 | | % 8.21/1.90 | | GROUND_INST: instantiating (5) with all_13_0, all_42_0, all_13_2, % 8.21/1.90 | | simplifying with (27), (40) gives: % 8.21/1.90 | | (42) all_42_0 = all_13_0 % 8.21/1.90 | | % 8.21/1.90 | | COMBINE_EQS: (41), (42) imply: % 8.21/1.90 | | (43) $difference(all_13_0, all_13_3) = 1 % 8.21/1.90 | | % 8.21/1.90 | | REDUCE: (7), (43) imply: % 8.21/1.90 | | (44) $false % 8.21/1.90 | | % 8.21/1.90 | | CLOSE: (44) is inconsistent. % 8.21/1.90 | | % 8.21/1.90 | End of split % 8.21/1.90 | % 8.21/1.90 End of proof % 8.21/1.90 % SZS output end Proof for theBenchmark % 8.21/1.90 % 8.21/1.90 1288ms %------------------------------------------------------------------------------