%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT099_1 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 22:19:10 EDT 2023 % Result : Theorem 5.19s 1.41s % Output : Proof 6.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT099_1 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.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 : Thu Aug 24 14:30:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.83/0.97 Prover 4: Preprocessing ... % 1.83/0.98 Prover 1: Preprocessing ... % 2.41/1.01 Prover 6: Preprocessing ... % 2.41/1.01 Prover 3: Preprocessing ... % 2.41/1.01 Prover 5: Preprocessing ... % 2.41/1.01 Prover 2: Preprocessing ... % 2.41/1.01 Prover 0: Preprocessing ... % 3.23/1.18 Prover 4: Constructing countermodel ... % 3.23/1.18 Prover 1: Constructing countermodel ... % 3.23/1.18 Prover 2: Proving ... % 3.23/1.18 Prover 3: Constructing countermodel ... % 3.23/1.18 Prover 6: Proving ... % 3.23/1.18 Prover 5: Proving ... % 3.23/1.18 Prover 0: Proving ... % 5.19/1.41 Prover 0: proved (792ms) % 5.19/1.41 % 5.19/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.19/1.41 % 5.19/1.41 Prover 3: proved (775ms) % 5.19/1.41 % 5.19/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.19/1.41 % 5.19/1.43 Prover 5: stopped % 5.19/1.45 Prover 2: stopped % 5.19/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.19/1.45 Prover 6: stopped % 5.19/1.45 Prover 1: Found proof (size 42) % 5.19/1.45 Prover 7: Preprocessing ... % 5.19/1.45 Prover 1: proved (808ms) % 5.19/1.45 Prover 4: Found proof (size 34) % 5.19/1.45 Prover 4: proved (799ms) % 5.19/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.19/1.45 Prover 8: Preprocessing ... % 5.19/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.19/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.19/1.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.19/1.47 Prover 11: Preprocessing ... % 5.19/1.47 Prover 13: Preprocessing ... % 5.19/1.48 Prover 10: Preprocessing ... % 5.19/1.48 Prover 11: stopped % 5.19/1.49 Prover 13: stopped % 5.19/1.49 Prover 7: Warning: ignoring some quantifiers % 5.19/1.49 Prover 10: stopped % 5.19/1.49 Prover 7: Constructing countermodel ... % 5.19/1.49 Prover 7: stopped % 5.19/1.50 Prover 8: Warning: ignoring some quantifiers % 5.19/1.50 Prover 8: Constructing countermodel ... % 5.19/1.51 Prover 8: stopped % 5.19/1.51 % 5.19/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.19/1.51 % 5.19/1.51 % SZS output start Proof for theBenchmark % 5.19/1.51 Assumptions after simplification: % 5.19/1.51 --------------------------------- % 5.19/1.51 % 5.19/1.51 (c) % 5.86/1.53 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: list] : (cons(3, v0) = v1 % 5.86/1.53 & cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & list(v1) & list(v0) & ? % 5.86/1.53 [v3: int] : ? [v4: int] : ( ~ (v4 = 0) & $lesseq(4, v3) & inRange(v3, v2) = % 5.86/1.53 v4)) % 5.86/1.53 % 5.86/1.53 (inRange) % 6.08/1.54 list(nil) & ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~ % 6.08/1.54 (inRange(v0, v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : ! % 6.08/1.54 [v4: list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, v3)) | % 6.08/1.54 ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 6.08/1.54 inRange(v0, v4) = v5)))) & ! [v0: int] : ! [v1: list] : (v1 = nil | % 6.08/1.54 ~ (inRange(v0, v1) = 0) | ~ list(v1) | ? [v2: int] : ? [v3: list] : % 6.08/1.54 ($lesseq(1, $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 & % 6.08/1.54 cons(v2, v3) = v1 & list(v3))) % 6.08/1.54 % 6.08/1.54 Further assumptions not needed in the proof: % 6.08/1.54 -------------------------------------------- % 6.08/1.54 l1, l2, l3, l4 % 6.08/1.54 % 6.08/1.54 Those formulas are unsatisfiable: % 6.08/1.54 --------------------------------- % 6.08/1.54 % 6.08/1.54 Begin of proof % 6.08/1.54 | % 6.08/1.54 | ALPHA: (inRange) implies: % 6.08/1.54 | (1) ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~ (inRange(v0, % 6.08/1.54 | v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : ! [v4: % 6.08/1.54 | list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, % 6.08/1.54 | v3)) | ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] : % 6.08/1.55 | ( ~ (v5 = 0) & inRange(v0, v4) = v5)))) % 6.08/1.55 | % 6.08/1.55 | ALPHA: (c) implies: % 6.08/1.55 | (2) list(nil) % 6.12/1.55 | (3) ? [v0: list] : ? [v1: list] : ? [v2: list] : (cons(3, v0) = v1 & % 6.12/1.55 | cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & list(v1) & list(v0) % 6.12/1.55 | & ? [v3: int] : ? [v4: int] : ( ~ (v4 = 0) & $lesseq(4, v3) & % 6.12/1.55 | inRange(v3, v2) = v4)) % 6.12/1.55 | % 6.12/1.55 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2 % 6.12/1.55 | gives: % 6.12/1.55 | (4) cons(3, all_11_2) = all_11_1 & cons(2, nil) = all_11_2 & cons(1, % 6.12/1.55 | all_11_1) = all_11_0 & list(all_11_0) & list(all_11_1) & % 6.12/1.55 | list(all_11_2) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 6.12/1.55 | $lesseq(4, v0) & inRange(v0, all_11_0) = v1) % 6.12/1.55 | % 6.12/1.55 | ALPHA: (4) implies: % 6.12/1.55 | (5) list(all_11_2) % 6.12/1.55 | (6) list(all_11_1) % 6.12/1.55 | (7) list(all_11_0) % 6.12/1.55 | (8) cons(1, all_11_1) = all_11_0 % 6.12/1.55 | (9) cons(2, nil) = all_11_2 % 6.12/1.55 | (10) cons(3, all_11_2) = all_11_1 % 6.12/1.55 | (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & $lesseq(4, v0) & % 6.12/1.55 | inRange(v0, all_11_0) = v1) % 6.12/1.55 | % 6.12/1.55 | DELTA: instantiating (11) with fresh symbols all_13_0, all_13_1 gives: % 6.12/1.55 | (12) ~ (all_13_0 = 0) & $lesseq(4, all_13_1) & inRange(all_13_1, all_11_0) % 6.12/1.55 | = all_13_0 % 6.12/1.55 | % 6.12/1.55 | ALPHA: (12) implies: % 6.12/1.55 | (13) ~ (all_13_0 = 0) % 6.12/1.56 | (14) $lesseq(4, all_13_1) % 6.12/1.56 | (15) inRange(all_13_1, all_11_0) = all_13_0 % 6.12/1.56 | % 6.12/1.56 | GROUND_INST: instantiating (1) with all_13_1, all_11_0, all_13_0, simplifying % 6.12/1.56 | with (7), (15) gives: % 6.12/1.56 | (16) all_13_0 = 0 | ( ~ (all_11_0 = nil) & ! [v0: int] : ! [v1: list] : ( % 6.12/1.56 | ~ ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | % 6.12/1.56 | ~ (cons(v0, v1) = all_11_0) | ~ list(v1) | ? [v2: int] : ( ~ (v2 % 6.12/1.56 | = 0) & inRange(all_13_1, v1) = v2))) % 6.12/1.56 | % 6.12/1.56 | BETA: splitting (16) gives: % 6.12/1.56 | % 6.12/1.56 | Case 1: % 6.12/1.56 | | % 6.12/1.56 | | (17) all_13_0 = 0 % 6.12/1.56 | | % 6.12/1.56 | | REDUCE: (13), (17) imply: % 6.12/1.56 | | (18) $false % 6.12/1.56 | | % 6.12/1.56 | | CLOSE: (18) is inconsistent. % 6.12/1.56 | | % 6.12/1.56 | Case 2: % 6.12/1.56 | | % 6.12/1.56 | | (19) ~ (all_11_0 = nil) & ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1, % 6.12/1.56 | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~ % 6.12/1.56 | | (cons(v0, v1) = all_11_0) | ~ list(v1) | ? [v2: int] : ( ~ (v2 = % 6.12/1.56 | | 0) & inRange(all_13_1, v1) = v2)) % 6.12/1.56 | | % 6.12/1.56 | | ALPHA: (19) implies: % 6.12/1.56 | | (20) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1, $difference(all_13_1, % 6.12/1.56 | | v0))) | ~ ($lesseq(0, v0)) | ~ (cons(v0, v1) = all_11_0) | % 6.12/1.56 | | ~ list(v1) | ? [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1) % 6.12/1.56 | | = v2)) % 6.12/1.56 | | % 6.12/1.56 | | GROUND_INST: instantiating (20) with 1, all_11_1, simplifying with (6), (8) % 6.12/1.56 | | gives: % 6.12/1.56 | | (21) ~ ($lesseq(2, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) & % 6.12/1.56 | | inRange(all_13_1, all_11_1) = v0) % 6.12/1.56 | | % 6.12/1.56 | | BETA: splitting (21) gives: % 6.12/1.56 | | % 6.12/1.56 | | Case 1: % 6.12/1.56 | | | % 6.12/1.56 | | | (22) $lesseq(all_13_1, 1) % 6.12/1.56 | | | % 6.12/1.57 | | | COMBINE_INEQS: (14), (22) imply: % 6.12/1.57 | | | (23) $false % 6.12/1.57 | | | % 6.12/1.57 | | | CLOSE: (23) is inconsistent. % 6.12/1.57 | | | % 6.12/1.57 | | Case 2: % 6.12/1.57 | | | % 6.12/1.57 | | | (24) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, all_11_1) = v0) % 6.12/1.57 | | | % 6.12/1.57 | | | DELTA: instantiating (24) with fresh symbol all_34_0 gives: % 6.12/1.57 | | | (25) ~ (all_34_0 = 0) & inRange(all_13_1, all_11_1) = all_34_0 % 6.12/1.57 | | | % 6.12/1.57 | | | ALPHA: (25) implies: % 6.12/1.57 | | | (26) ~ (all_34_0 = 0) % 6.12/1.57 | | | (27) inRange(all_13_1, all_11_1) = all_34_0 % 6.12/1.57 | | | % 6.12/1.57 | | | GROUND_INST: instantiating (1) with all_13_1, all_11_1, all_34_0, % 6.12/1.57 | | | simplifying with (6), (27) gives: % 6.12/1.57 | | | (28) all_34_0 = 0 | ( ~ (all_11_1 = nil) & ! [v0: int] : ! [v1: list] % 6.12/1.57 | | | : ( ~ ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, % 6.12/1.57 | | | v0)) | ~ (cons(v0, v1) = all_11_1) | ~ list(v1) | ? % 6.12/1.57 | | | [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2))) % 6.12/1.57 | | | % 6.12/1.57 | | | BETA: splitting (28) gives: % 6.12/1.57 | | | % 6.12/1.57 | | | Case 1: % 6.12/1.57 | | | | % 6.12/1.57 | | | | (29) all_34_0 = 0 % 6.12/1.57 | | | | % 6.12/1.57 | | | | REDUCE: (26), (29) imply: % 6.12/1.57 | | | | (30) $false % 6.12/1.57 | | | | % 6.12/1.57 | | | | CLOSE: (30) is inconsistent. % 6.12/1.57 | | | | % 6.12/1.57 | | | Case 2: % 6.12/1.57 | | | | % 6.12/1.57 | | | | (31) ~ (all_11_1 = nil) & ! [v0: int] : ! [v1: list] : ( ~ % 6.12/1.57 | | | | ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) % 6.12/1.57 | | | | | ~ (cons(v0, v1) = all_11_1) | ~ list(v1) | ? [v2: int] : % 6.12/1.57 | | | | ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2)) % 6.12/1.57 | | | | % 6.12/1.57 | | | | ALPHA: (31) implies: % 6.12/1.57 | | | | (32) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1, % 6.12/1.57 | | | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~ % 6.12/1.57 | | | | (cons(v0, v1) = all_11_1) | ~ list(v1) | ? [v2: int] : ( ~ % 6.12/1.57 | | | | (v2 = 0) & inRange(all_13_1, v1) = v2)) % 6.12/1.57 | | | | % 6.12/1.57 | | | | GROUND_INST: instantiating (32) with 3, all_11_2, simplifying with (5), % 6.12/1.57 | | | | (10) gives: % 6.12/1.57 | | | | (33) ~ ($lesseq(4, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) & % 6.12/1.57 | | | | inRange(all_13_1, all_11_2) = v0) % 6.12/1.57 | | | | % 6.12/1.57 | | | | BETA: splitting (33) gives: % 6.12/1.57 | | | | % 6.12/1.57 | | | | Case 1: % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | (34) $lesseq(all_13_1, 3) % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | COMBINE_INEQS: (14), (34) imply: % 6.12/1.57 | | | | | (35) $false % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | CLOSE: (35) is inconsistent. % 6.12/1.57 | | | | | % 6.12/1.57 | | | | Case 2: % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | (36) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, all_11_2) = % 6.12/1.57 | | | | | v0) % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | DELTA: instantiating (36) with fresh symbol all_48_0 gives: % 6.12/1.57 | | | | | (37) ~ (all_48_0 = 0) & inRange(all_13_1, all_11_2) = all_48_0 % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | ALPHA: (37) implies: % 6.12/1.57 | | | | | (38) ~ (all_48_0 = 0) % 6.12/1.57 | | | | | (39) inRange(all_13_1, all_11_2) = all_48_0 % 6.12/1.57 | | | | | % 6.12/1.57 | | | | | GROUND_INST: instantiating (1) with all_13_1, all_11_2, all_48_0, % 6.12/1.57 | | | | | simplifying with (5), (39) gives: % 6.12/1.58 | | | | | (40) all_48_0 = 0 | ( ~ (all_11_2 = nil) & ! [v0: int] : ! [v1: % 6.12/1.58 | | | | | list] : ( ~ ($lesseq(1, $difference(all_13_1, v0))) | ~ % 6.12/1.58 | | | | | ($lesseq(0, v0)) | ~ (cons(v0, v1) = all_11_2) | ~ % 6.12/1.58 | | | | | list(v1) | ? [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, % 6.12/1.58 | | | | | v1) = v2))) % 6.12/1.58 | | | | | % 6.12/1.58 | | | | | BETA: splitting (40) gives: % 6.12/1.58 | | | | | % 6.12/1.58 | | | | | Case 1: % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | (41) all_48_0 = 0 % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | REDUCE: (38), (41) imply: % 6.12/1.58 | | | | | | (42) $false % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | CLOSE: (42) is inconsistent. % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | Case 2: % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | (43) ~ (all_11_2 = nil) & ! [v0: int] : ! [v1: list] : ( ~ % 6.12/1.58 | | | | | | ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, % 6.12/1.58 | | | | | | v0)) | ~ (cons(v0, v1) = all_11_2) | ~ list(v1) | ? % 6.12/1.58 | | | | | | [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2)) % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | ALPHA: (43) implies: % 6.12/1.58 | | | | | | (44) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1, % 6.12/1.58 | | | | | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~ % 6.12/1.58 | | | | | | (cons(v0, v1) = all_11_2) | ~ list(v1) | ? [v2: int] : ( % 6.12/1.58 | | | | | | ~ (v2 = 0) & inRange(all_13_1, v1) = v2)) % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | GROUND_INST: instantiating (44) with 2, nil, simplifying with (2), % 6.12/1.58 | | | | | | (9) gives: % 6.12/1.58 | | | | | | (45) ~ ($lesseq(3, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) & % 6.12/1.58 | | | | | | inRange(all_13_1, nil) = v0) % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | BETA: splitting (45) gives: % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | | Case 1: % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | (46) $lesseq(all_13_1, 2) % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | COMBINE_INEQS: (14), (46) imply: % 6.12/1.58 | | | | | | | (47) $false % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | CLOSE: (47) is inconsistent. % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | Case 2: % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, nil) = v0) % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | DELTA: instantiating (48) with fresh symbol all_62_0 gives: % 6.12/1.58 | | | | | | | (49) ~ (all_62_0 = 0) & inRange(all_13_1, nil) = all_62_0 % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | ALPHA: (49) implies: % 6.12/1.58 | | | | | | | (50) ~ (all_62_0 = 0) % 6.12/1.58 | | | | | | | (51) inRange(all_13_1, nil) = all_62_0 % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | GROUND_INST: instantiating (1) with all_13_1, nil, all_62_0, % 6.12/1.58 | | | | | | | simplifying with (2), (51) gives: % 6.12/1.58 | | | | | | | (52) all_62_0 = 0 % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | REDUCE: (50), (52) imply: % 6.12/1.58 | | | | | | | (53) $false % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | | CLOSE: (53) is inconsistent. % 6.12/1.58 | | | | | | | % 6.12/1.58 | | | | | | End of split % 6.12/1.58 | | | | | | % 6.12/1.58 | | | | | End of split % 6.12/1.58 | | | | | % 6.12/1.58 | | | | End of split % 6.12/1.58 | | | | % 6.12/1.58 | | | End of split % 6.12/1.58 | | | % 6.12/1.58 | | End of split % 6.12/1.58 | | % 6.12/1.58 | End of split % 6.12/1.58 | % 6.12/1.58 End of proof % 6.12/1.58 % SZS output end Proof for theBenchmark % 6.12/1.58 % 6.12/1.58 982ms %------------------------------------------------------------------------------