%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT032_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 : n004.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 22:18:57 EDT 2023 % Result : Theorem 6.63s 1.67s % Output : Proof 10.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT032_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n004.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Thu Aug 24 14:29:23 EDT 2023 % 0.17/0.35 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.40/1.08 Prover 4: Preprocessing ... % 2.40/1.08 Prover 1: Preprocessing ... % 2.91/1.12 Prover 5: Preprocessing ... % 2.91/1.12 Prover 6: Preprocessing ... % 2.91/1.12 Prover 3: Preprocessing ... % 2.91/1.12 Prover 0: Preprocessing ... % 2.91/1.12 Prover 2: Preprocessing ... % 5.09/1.45 Prover 1: Constructing countermodel ... % 5.09/1.45 Prover 6: Constructing countermodel ... % 5.09/1.45 Prover 3: Constructing countermodel ... % 5.09/1.46 Prover 5: Proving ... % 5.09/1.46 Prover 2: Proving ... % 5.09/1.48 Prover 4: Constructing countermodel ... % 5.60/1.49 Prover 0: Proving ... % 6.63/1.67 Prover 6: proved (1048ms) % 6.63/1.67 % 6.63/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.63/1.67 % 6.63/1.67 Prover 2: stopped % 6.63/1.67 Prover 5: stopped % 6.63/1.68 Prover 0: stopped % 6.63/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.63/1.68 Prover 3: stopped % 6.63/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.63/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.63/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.63/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.63/1.71 Prover 7: Preprocessing ... % 6.63/1.71 Prover 8: Preprocessing ... % 6.63/1.72 Prover 11: Preprocessing ... % 7.31/1.72 Prover 10: Preprocessing ... % 7.31/1.73 Prover 13: Preprocessing ... % 7.83/1.80 Prover 8: Warning: ignoring some quantifiers % 7.83/1.81 Prover 7: Constructing countermodel ... % 7.83/1.82 Prover 8: Constructing countermodel ... % 7.83/1.83 Prover 10: Constructing countermodel ... % 7.83/1.83 Prover 13: Warning: ignoring some quantifiers % 7.83/1.85 Prover 13: Constructing countermodel ... % 7.83/1.85 Prover 11: Constructing countermodel ... % 9.47/2.07 Prover 10: Found proof (size 102) % 9.47/2.07 Prover 10: proved (379ms) % 9.47/2.07 Prover 7: stopped % 9.47/2.07 Prover 11: stopped % 9.47/2.07 Prover 8: stopped % 9.47/2.07 Prover 4: stopped % 9.47/2.07 Prover 13: Found proof (size 97) % 9.47/2.07 Prover 13: proved (383ms) % 9.47/2.08 Prover 1: Found proof (size 135) % 9.47/2.08 Prover 1: proved (1467ms) % 9.47/2.08 % 9.47/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.47/2.08 % 9.47/2.09 % SZS output start Proof for theBenchmark % 9.47/2.09 Assumptions after simplification: % 9.47/2.09 --------------------------------- % 9.47/2.09 % 9.47/2.09 (ax5) % 10.07/2.11 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 % 10.07/2.11 = v0 | ~ (remove(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v1) | in(v0, % 10.07/2.11 v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 10.07/2.11 collection] : ( ~ (remove(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v3) % 10.07/2.11 | in(v0, v1)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( % 10.07/2.11 ~ (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v2)) & ! [v0: int] % 10.07/2.11 : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ % 10.07/2.11 collection(v1) | ~ in(v0, v1) | ? [v3: int] : (count(v2) = v3 & count(v1) % 10.07/2.11 = $sum(v3, 1))) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] % 10.07/2.11 : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] : % 10.07/2.12 ? [v4: int] : ( ~ ($difference(v4, v3) = 1) & count(v2) = v3 & count(v1) = % 10.07/2.12 v4)) % 10.07/2.12 % 10.07/2.12 (ax6) % 10.07/2.12 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 10.07/2.12 = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: int] : ? [v4: int] : % 10.07/2.12 ( ~ (v4 = v3) & count(v2) = v3 & count(v1) = v4)) & ! [v0: int] : ! [v1: % 10.07/2.12 collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ % 10.07/2.12 collection(v1) | in(v0, v1) | ? [v3: int] : (count(v2) = v3 & count(v1) = % 10.07/2.12 v3)) % 10.07/2.12 % 10.07/2.12 (co1) % 10.07/2.12 ? [v0: collection] : ? [v1: collection] : ? [v2: int] : ? [v3: collection] % 10.07/2.12 : ? [v4: int] : ($lesseq(v4, 5) & $lesseq(7, v2) & remove(5, v0) = v1 & % 10.07/2.12 remove(4, v0) = v3 & count(v3) = v4 & count(v1) = v2 & collection(v3) & % 10.07/2.12 collection(v1) & collection(v0)) % 10.07/2.12 % 10.07/2.12 (function-axioms) % 10.07/2.12 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 10.07/2.12 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 10.07/2.12 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 10.07/2.12 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: int] : ! % 10.07/2.12 [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | ~ % 10.07/2.12 (count(v2) = v0)) % 10.07/2.12 % 10.07/2.12 Further assumptions not needed in the proof: % 10.07/2.12 -------------------------------------------- % 10.07/2.12 ax1, ax2, ax3, ax4, ax7 % 10.07/2.12 % 10.07/2.12 Those formulas are unsatisfiable: % 10.07/2.12 --------------------------------- % 10.07/2.12 % 10.07/2.12 Begin of proof % 10.07/2.12 | % 10.07/2.12 | ALPHA: (ax5) implies: % 10.07/2.13 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] % 10.07/2.13 | : ? [v4: int] : ( ~ ($difference(v4, v3) = 1) & count(v2) = v3 & % 10.07/2.13 | count(v1) = v4)) % 10.07/2.13 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: % 10.07/2.13 | int] : (count(v2) = v3 & count(v1) = $sum(v3, 1))) % 10.07/2.13 | % 10.07/2.13 | ALPHA: (ax6) implies: % 10.07/2.13 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] % 10.07/2.13 | : (count(v2) = v3 & count(v1) = v3)) % 10.07/2.13 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: % 10.07/2.13 | int] : ? [v4: int] : ( ~ (v4 = v3) & count(v2) = v3 & count(v1) = % 10.07/2.13 | v4)) % 10.07/2.13 | % 10.07/2.13 | ALPHA: (function-axioms) implies: % 10.07/2.13 | (5) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 10.07/2.13 | (count(v2) = v1) | ~ (count(v2) = v0)) % 10.07/2.13 | % 10.07/2.13 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2, % 10.07/2.13 | all_13_3, all_13_4 gives: % 10.07/2.13 | (6) $lesseq(all_13_0, 5) & $lesseq(7, all_13_2) & remove(5, all_13_4) = % 10.07/2.13 | all_13_3 & remove(4, all_13_4) = all_13_1 & count(all_13_1) = all_13_0 % 10.07/2.13 | & count(all_13_3) = all_13_2 & collection(all_13_1) & % 10.07/2.13 | collection(all_13_3) & collection(all_13_4) % 10.07/2.13 | % 10.07/2.13 | ALPHA: (6) implies: % 10.07/2.13 | (7) $lesseq(7, all_13_2) % 10.07/2.13 | (8) $lesseq(all_13_0, 5) % 10.07/2.13 | (9) collection(all_13_4) % 10.07/2.13 | (10) count(all_13_3) = all_13_2 % 10.07/2.13 | (11) count(all_13_1) = all_13_0 % 10.07/2.13 | (12) remove(4, all_13_4) = all_13_1 % 10.07/2.13 | (13) remove(5, all_13_4) = all_13_3 % 10.07/2.13 | % 10.07/2.14 | GROUND_INST: instantiating (1) with 4, all_13_4, all_13_1, simplifying with % 10.07/2.14 | (9), (12) gives: % 10.07/2.14 | (14) in(4, all_13_4) | ? [v0: int] : ? [v1: int] : ( ~ ($difference(v1, % 10.07/2.14 | v0) = 1) & count(all_13_1) = v0 & count(all_13_4) = v1) % 10.07/2.14 | % 10.07/2.14 | GROUND_INST: instantiating (3) with 4, all_13_4, all_13_1, simplifying with % 10.07/2.14 | (9), (12) gives: % 10.07/2.14 | (15) in(4, all_13_4) | ? [v0: int] : (count(all_13_1) = v0 & % 10.07/2.14 | count(all_13_4) = v0) % 10.07/2.14 | % 10.07/2.14 | GROUND_INST: instantiating (3) with 5, all_13_4, all_13_3, simplifying with % 10.07/2.14 | (9), (13) gives: % 10.07/2.14 | (16) in(5, all_13_4) | ? [v0: int] : (count(all_13_3) = v0 & % 10.07/2.14 | count(all_13_4) = v0) % 10.07/2.14 | % 10.07/2.14 | BETA: splitting (15) gives: % 10.07/2.14 | % 10.07/2.14 | Case 1: % 10.07/2.14 | | % 10.07/2.14 | | (17) in(4, all_13_4) % 10.07/2.14 | | % 10.07/2.14 | | GROUND_INST: instantiating (4) with 4, all_13_4, all_13_1, simplifying with % 10.07/2.14 | | (9), (12), (17) gives: % 10.07/2.14 | | (18) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0 & % 10.07/2.14 | | count(all_13_4) = v1) % 10.07/2.14 | | % 10.07/2.14 | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (12), (13), (16), (17), (18) % 10.07/2.14 | | are inconsistent by sub-proof #1. % 10.07/2.14 | | % 10.07/2.14 | Case 2: % 10.07/2.14 | | % 10.07/2.14 | | (19) ? [v0: int] : (count(all_13_1) = v0 & count(all_13_4) = v0) % 10.07/2.14 | | % 10.07/2.14 | | DELTA: instantiating (19) with fresh symbol all_32_0 gives: % 10.07/2.14 | | (20) count(all_13_1) = all_32_0 & count(all_13_4) = all_32_0 % 10.07/2.14 | | % 10.07/2.14 | | ALPHA: (20) implies: % 10.07/2.14 | | (21) count(all_13_4) = all_32_0 % 10.07/2.14 | | (22) count(all_13_1) = all_32_0 % 10.07/2.14 | | % 10.07/2.14 | | BETA: splitting (14) gives: % 10.07/2.14 | | % 10.07/2.14 | | Case 1: % 10.07/2.14 | | | % 10.07/2.14 | | | (23) in(4, all_13_4) % 10.07/2.14 | | | % 10.07/2.14 | | | GROUND_INST: instantiating (4) with 4, all_13_4, all_13_1, simplifying % 10.07/2.14 | | | with (9), (12), (23) gives: % 10.07/2.14 | | | (24) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0 % 10.07/2.14 | | | & count(all_13_4) = v1) % 10.07/2.14 | | | % 10.07/2.15 | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (12), (13), (16), (23), % 10.07/2.15 | | | (24) are inconsistent by sub-proof #1. % 10.07/2.15 | | | % 10.07/2.15 | | Case 2: % 10.07/2.15 | | | % 10.07/2.15 | | | (25) ? [v0: int] : ? [v1: int] : ( ~ ($difference(v1, v0) = 1) & % 10.07/2.15 | | | count(all_13_1) = v0 & count(all_13_4) = v1) % 10.07/2.15 | | | % 10.07/2.15 | | | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1 gives: % 10.07/2.15 | | | (26) ~ ($difference(all_38_0, all_38_1) = 1) & count(all_13_1) = % 10.07/2.15 | | | all_38_1 & count(all_13_4) = all_38_0 % 10.07/2.15 | | | % 10.07/2.15 | | | ALPHA: (26) implies: % 10.07/2.15 | | | (27) count(all_13_1) = all_38_1 % 10.07/2.15 | | | % 10.07/2.15 | | | GROUND_INST: instantiating (5) with all_13_0, all_38_1, all_13_1, % 10.07/2.15 | | | simplifying with (11), (27) gives: % 10.07/2.15 | | | (28) all_38_1 = all_13_0 % 10.07/2.15 | | | % 10.07/2.15 | | | GROUND_INST: instantiating (5) with all_32_0, all_38_1, all_13_1, % 10.07/2.15 | | | simplifying with (22), (27) gives: % 10.07/2.15 | | | (29) all_38_1 = all_32_0 % 10.07/2.15 | | | % 10.07/2.15 | | | COMBINE_EQS: (28), (29) imply: % 10.07/2.15 | | | (30) all_32_0 = all_13_0 % 10.07/2.15 | | | % 10.07/2.15 | | | SIMP: (30) implies: % 10.07/2.15 | | | (31) all_32_0 = all_13_0 % 10.07/2.15 | | | % 10.07/2.15 | | | REDUCE: (21), (31) imply: % 10.07/2.15 | | | (32) count(all_13_4) = all_13_0 % 10.07/2.15 | | | % 10.07/2.15 | | | BETA: splitting (16) gives: % 10.07/2.15 | | | % 10.07/2.15 | | | Case 1: % 10.07/2.15 | | | | % 10.07/2.15 | | | | (33) in(5, all_13_4) % 10.07/2.15 | | | | % 10.07/2.15 | | | | GROUND_INST: instantiating (2) with 5, all_13_4, all_13_3, simplifying % 10.07/2.15 | | | | with (9), (13), (33) gives: % 10.07/2.15 | | | | (34) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = % 10.07/2.15 | | | | $sum(v0, 1)) % 10.07/2.15 | | | | % 10.07/2.15 | | | | DELTA: instantiating (34) with fresh symbol all_54_0 gives: % 10.07/2.15 | | | | (35) count(all_13_3) = all_54_0 & count(all_13_4) = $sum(all_54_0, 1) % 10.07/2.15 | | | | % 10.07/2.15 | | | | ALPHA: (35) implies: % 10.07/2.15 | | | | (36) count(all_13_4) = $sum(all_54_0, 1) % 10.07/2.15 | | | | (37) count(all_13_3) = all_54_0 % 10.07/2.15 | | | | % 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_0, $sum(all_54_0, 1), % 10.07/2.15 | | | | all_13_4, simplifying with (32), (36) gives: % 10.07/2.15 | | | | (38) $difference(all_54_0, all_13_0) = -1 % 10.07/2.15 | | | | % 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_2, all_54_0, all_13_3, % 10.07/2.15 | | | | simplifying with (10), (37) gives: % 10.07/2.15 | | | | (39) all_54_0 = all_13_2 % 10.07/2.15 | | | | % 10.07/2.15 | | | | COMBINE_EQS: (38), (39) imply: % 10.07/2.15 | | | | (40) $difference(all_13_0, all_13_2) = 1 % 10.07/2.15 | | | | % 10.07/2.15 | | | | SIMP: (40) implies: % 10.07/2.15 | | | | (41) $difference(all_13_0, all_13_2) = 1 % 10.07/2.15 | | | | % 10.07/2.15 | | | | REDUCE: (8), (41) imply: % 10.07/2.15 | | | | (42) $lesseq(all_13_2, 4) % 10.07/2.15 | | | | % 10.07/2.15 | | | | COMBINE_INEQS: (7), (42) imply: % 10.07/2.15 | | | | (43) $false % 10.07/2.15 | | | | % 10.07/2.15 | | | | CLOSE: (43) is inconsistent. % 10.07/2.15 | | | | % 10.07/2.15 | | | Case 2: % 10.07/2.15 | | | | % 10.07/2.15 | | | | (44) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = v0) % 10.07/2.15 | | | | % 10.07/2.15 | | | | DELTA: instantiating (44) with fresh symbol all_48_0 gives: % 10.07/2.15 | | | | (45) count(all_13_3) = all_48_0 & count(all_13_4) = all_48_0 % 10.07/2.15 | | | | % 10.07/2.15 | | | | ALPHA: (45) implies: % 10.07/2.15 | | | | (46) count(all_13_4) = all_48_0 % 10.07/2.15 | | | | (47) count(all_13_3) = all_48_0 % 10.07/2.15 | | | | % 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_0, all_48_0, all_13_4, % 10.07/2.15 | | | | simplifying with (32), (46) gives: % 10.07/2.15 | | | | (48) all_48_0 = all_13_0 % 10.07/2.15 | | | | % 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_2, all_48_0, all_13_3, % 10.07/2.15 | | | | simplifying with (10), (47) gives: % 10.07/2.16 | | | | (49) all_48_0 = all_13_2 % 10.07/2.16 | | | | % 10.07/2.16 | | | | COMBINE_EQS: (48), (49) imply: % 10.07/2.16 | | | | (50) all_13_0 = all_13_2 % 10.07/2.16 | | | | % 10.07/2.16 | | | | SIMP: (50) implies: % 10.07/2.16 | | | | (51) all_13_0 = all_13_2 % 10.07/2.16 | | | | % 10.07/2.16 | | | | REDUCE: (8), (51) imply: % 10.07/2.16 | | | | (52) $lesseq(all_13_2, 5) % 10.07/2.16 | | | | % 10.07/2.16 | | | | COMBINE_INEQS: (7), (52) imply: % 10.07/2.16 | | | | (53) $false % 10.07/2.16 | | | | % 10.07/2.16 | | | | CLOSE: (53) is inconsistent. % 10.07/2.16 | | | | % 10.07/2.16 | | | End of split % 10.07/2.16 | | | % 10.07/2.16 | | End of split % 10.07/2.16 | | % 10.07/2.16 | End of split % 10.07/2.16 | % 10.07/2.16 End of proof % 10.07/2.16 % 10.07/2.16 Sub-proof #1 shows that the following formulas are inconsistent: % 10.07/2.16 ---------------------------------------------------------------- % 10.07/2.16 (1) count(all_13_3) = all_13_2 % 10.07/2.16 (2) remove(5, all_13_4) = all_13_3 % 10.07/2.16 (3) $lesseq(7, all_13_2) % 10.07/2.16 (4) collection(all_13_4) % 10.07/2.16 (5) in(4, all_13_4) % 10.07/2.16 (6) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 10.07/2.16 (count(v2) = v1) | ~ (count(v2) = v0)) % 10.07/2.16 (7) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.07/2.16 (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: % 10.07/2.16 int] : (count(v2) = v3 & count(v1) = $sum(v3, 1))) % 10.07/2.16 (8) in(5, all_13_4) | ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) % 10.07/2.16 = v0) % 10.07/2.16 (9) remove(4, all_13_4) = all_13_1 % 10.07/2.16 (10) count(all_13_1) = all_13_0 % 10.07/2.16 (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0 & % 10.07/2.16 count(all_13_4) = v1) % 10.07/2.16 (12) $lesseq(all_13_0, 5) % 10.07/2.16 % 10.07/2.16 Begin of proof % 10.07/2.16 | % 10.07/2.16 | GROUND_INST: instantiating (7) with 4, all_13_4, all_13_1, simplifying with % 10.07/2.16 | (4), (5), (9) gives: % 10.07/2.16 | (13) ? [v0: int] : (count(all_13_1) = v0 & count(all_13_4) = $sum(v0, 1)) % 10.07/2.16 | % 10.07/2.16 | DELTA: instantiating (13) with fresh symbol all_38_0 gives: % 10.07/2.16 | (14) count(all_13_1) = all_38_0 & count(all_13_4) = $sum(all_38_0, 1) % 10.07/2.16 | % 10.07/2.16 | ALPHA: (14) implies: % 10.07/2.16 | (15) count(all_13_4) = $sum(all_38_0, 1) % 10.07/2.16 | (16) count(all_13_1) = all_38_0 % 10.07/2.16 | % 10.07/2.16 | DELTA: instantiating (11) with fresh symbols all_40_0, all_40_1 gives: % 10.07/2.16 | (17) ~ (all_40_0 = all_40_1) & count(all_13_1) = all_40_1 & % 10.07/2.16 | count(all_13_4) = all_40_0 % 10.07/2.16 | % 10.07/2.16 | ALPHA: (17) implies: % 10.07/2.16 | (18) count(all_13_1) = all_40_1 % 10.07/2.16 | % 10.07/2.16 | GROUND_INST: instantiating (6) with all_13_0, all_40_1, all_13_1, simplifying % 10.07/2.16 | with (10), (18) gives: % 10.07/2.16 | (19) all_40_1 = all_13_0 % 10.07/2.16 | % 10.07/2.16 | GROUND_INST: instantiating (6) with all_38_0, all_40_1, all_13_1, simplifying % 10.07/2.16 | with (16), (18) gives: % 10.07/2.16 | (20) all_40_1 = all_38_0 % 10.07/2.16 | % 10.07/2.16 | COMBINE_EQS: (19), (20) imply: % 10.07/2.16 | (21) all_38_0 = all_13_0 % 10.07/2.16 | % 10.07/2.16 | SIMP: (21) implies: % 10.07/2.16 | (22) all_38_0 = all_13_0 % 10.07/2.16 | % 10.07/2.16 | REDUCE: (15), (22) imply: % 10.07/2.16 | (23) count(all_13_4) = $sum(all_13_0, 1) % 10.07/2.16 | % 10.07/2.16 | BETA: splitting (8) gives: % 10.07/2.16 | % 10.07/2.16 | Case 1: % 10.07/2.16 | | % 10.07/2.16 | | (24) in(5, all_13_4) % 10.07/2.16 | | % 10.07/2.16 | | GROUND_INST: instantiating (7) with 5, all_13_4, all_13_3, simplifying with % 10.07/2.16 | | (2), (4), (24) gives: % 10.07/2.16 | | (25) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = $sum(v0, % 10.07/2.16 | | 1)) % 10.07/2.16 | | % 10.07/2.16 | | DELTA: instantiating (25) with fresh symbol all_56_0 gives: % 10.07/2.16 | | (26) count(all_13_3) = all_56_0 & count(all_13_4) = $sum(all_56_0, 1) % 10.07/2.16 | | % 10.07/2.16 | | ALPHA: (26) implies: % 10.07/2.16 | | (27) count(all_13_4) = $sum(all_56_0, 1) % 10.07/2.17 | | (28) count(all_13_3) = all_56_0 % 10.07/2.17 | | % 10.07/2.17 | | GROUND_INST: instantiating (6) with $sum(all_13_0, 1), $sum(all_56_0, 1), % 10.07/2.17 | | all_13_4, simplifying with (23), (27) gives: % 10.07/2.17 | | (29) all_56_0 = all_13_0 % 10.07/2.17 | | % 10.07/2.17 | | GROUND_INST: instantiating (6) with all_13_2, all_56_0, all_13_3, % 10.07/2.17 | | simplifying with (1), (28) gives: % 10.07/2.17 | | (30) all_56_0 = all_13_2 % 10.07/2.17 | | % 10.07/2.17 | | COMBINE_EQS: (29), (30) imply: % 10.07/2.17 | | (31) all_13_0 = all_13_2 % 10.07/2.17 | | % 10.07/2.17 | | SIMP: (31) implies: % 10.07/2.17 | | (32) all_13_0 = all_13_2 % 10.07/2.17 | | % 10.07/2.17 | | REDUCE: (12), (32) imply: % 10.07/2.17 | | (33) $lesseq(all_13_2, 5) % 10.07/2.17 | | % 10.07/2.17 | | COMBINE_INEQS: (3), (33) imply: % 10.07/2.17 | | (34) $false % 10.07/2.17 | | % 10.07/2.17 | | CLOSE: (34) is inconsistent. % 10.07/2.17 | | % 10.07/2.17 | Case 2: % 10.07/2.17 | | % 10.07/2.17 | | (35) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = v0) % 10.07/2.17 | | % 10.07/2.17 | | DELTA: instantiating (35) with fresh symbol all_50_0 gives: % 10.07/2.17 | | (36) count(all_13_3) = all_50_0 & count(all_13_4) = all_50_0 % 10.07/2.17 | | % 10.07/2.17 | | ALPHA: (36) implies: % 10.07/2.17 | | (37) count(all_13_4) = all_50_0 % 10.07/2.17 | | (38) count(all_13_3) = all_50_0 % 10.07/2.17 | | % 10.07/2.17 | | GROUND_INST: instantiating (6) with $sum(all_13_0, 1), all_50_0, all_13_4, % 10.07/2.17 | | simplifying with (23), (37) gives: % 10.07/2.17 | | (39) $difference(all_50_0, all_13_0) = 1 % 10.07/2.17 | | % 10.07/2.17 | | GROUND_INST: instantiating (6) with all_13_2, all_50_0, all_13_3, % 10.07/2.17 | | simplifying with (1), (38) gives: % 10.07/2.17 | | (40) all_50_0 = all_13_2 % 10.07/2.17 | | % 10.07/2.17 | | COMBINE_EQS: (39), (40) imply: % 10.07/2.17 | | (41) $difference(all_13_0, all_13_2) = -1 % 10.07/2.17 | | % 10.07/2.17 | | SIMP: (41) implies: % 10.07/2.17 | | (42) $difference(all_13_0, all_13_2) = -1 % 10.07/2.17 | | % 10.07/2.17 | | REDUCE: (12), (42) imply: % 10.07/2.17 | | (43) $lesseq(all_13_2, 6) % 10.07/2.17 | | % 10.07/2.17 | | COMBINE_INEQS: (3), (43) imply: % 10.07/2.17 | | (44) $false % 10.07/2.17 | | % 10.07/2.17 | | CLOSE: (44) is inconsistent. % 10.07/2.17 | | % 10.07/2.17 | End of split % 10.07/2.17 | % 10.07/2.17 End of proof % 10.07/2.17 % SZS output end Proof for theBenchmark % 10.07/2.17 % 10.07/2.17 1578ms %------------------------------------------------------------------------------