%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT332_1 : TPTP v8.1.2. Released v7.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 22:19:43 EDT 2023 % Result : Unsatisfiable 9.11s 1.92s % Output : Proof 9.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : DAT332_1 : TPTP v8.1.2. Released v7.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n023.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 15:00:12 EDT 2023 % 0.13/0.34 % CPUTime : % 0.49/0.60 ________ _____ % 0.49/0.60 ___ __ \_________(_)________________________________ % 0.49/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.60 % 0.49/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.60 (2023-06-19) % 0.49/0.60 % 0.49/0.60 (c) Philipp Rümmer, 2009-2023 % 0.49/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.60 Amanda Stjerna. % 0.49/0.60 Free software under BSD-3-Clause. % 0.49/0.60 % 0.49/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.60 % 0.49/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.62 Running up to 7 provers in parallel. % 0.49/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.49/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.49/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.49/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.49/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.49/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.49/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.73/1.04 Prover 4: Preprocessing ... % 2.73/1.05 Prover 1: Preprocessing ... % 2.73/1.08 Prover 2: Preprocessing ... % 2.73/1.08 Prover 5: Preprocessing ... % 2.73/1.08 Prover 6: Preprocessing ... % 2.73/1.08 Prover 3: Preprocessing ... % 2.73/1.08 Prover 0: Preprocessing ... % 4.31/1.31 Prover 1: Warning: ignoring some quantifiers % 4.31/1.32 Prover 4: Warning: ignoring some quantifiers % 4.90/1.36 Prover 3: Warning: ignoring some quantifiers % 4.90/1.36 Prover 1: Constructing countermodel ... % 4.90/1.36 Prover 5: Proving ... % 4.90/1.36 Prover 6: Proving ... % 4.90/1.36 Prover 4: Constructing countermodel ... % 4.90/1.37 Prover 0: Proving ... % 4.90/1.37 Prover 3: Constructing countermodel ... % 5.80/1.48 Prover 2: Proving ... % 6.24/1.55 Prover 3: gave up % 6.24/1.55 Prover 1: gave up % 6.52/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.52/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.52/1.59 Prover 7: Preprocessing ... % 6.52/1.59 Prover 8: Preprocessing ... % 7.11/1.66 Prover 8: Warning: ignoring some quantifiers % 7.11/1.66 Prover 8: Constructing countermodel ... % 7.42/1.69 Prover 7: Warning: ignoring some quantifiers % 7.42/1.70 Prover 7: Constructing countermodel ... % 8.22/1.81 Prover 8: gave up % 8.22/1.82 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.68/1.85 Prover 9: Preprocessing ... % 8.77/1.88 Prover 7: Found proof (size 50) % 8.77/1.88 Prover 7: proved (328ms) % 8.77/1.88 Prover 4: stopped % 8.77/1.88 Prover 2: stopped % 8.77/1.88 Prover 0: stopped % 8.77/1.88 Prover 6: stopped % 8.77/1.88 Prover 5: stopped % 9.11/1.92 Prover 9: Warning: ignoring some quantifiers % 9.11/1.92 Prover 9: Constructing countermodel ... % 9.11/1.92 Prover 9: stopped % 9.11/1.92 % 9.11/1.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.11/1.92 % 9.11/1.93 % SZS output start Proof for theBenchmark % 9.11/1.94 Assumptions after simplification: % 9.11/1.94 --------------------------------- % 9.11/1.94 % 9.11/1.94 (formula_10) % 9.31/1.95 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~ (g(v0) = v1)) % 9.31/1.95 % 9.31/1.95 (formula_11) % 9.31/1.96 Array[Int,Int](arr) & Set(s0) & Set(s1) & ? [v0: int] : ? [v1: int] : (g(i1) % 9.31/1.96 = v0 & select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s0, v1) = s1) % 9.31/1.96 % 9.31/1.96 (formula_12) % 9.31/1.96 Set(s0) & Set(s1) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & sup(s0) = v1 % 9.31/1.96 & sup(s1) = v0) % 9.31/1.96 % 9.31/1.96 (formula_2) % 9.31/1.96 ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | ~ % 9.31/1.96 (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0, v2)) & % 9.31/1.96 ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | ~ % 9.31/1.96 (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v2) | member(v0, v3)) % 9.31/1.96 % 9.31/1.96 (formula_6) % 9.31/1.96 ! [v0: Set] : ! [v1: int] : ( ~ (sup(v0) = v1) | ~ Set(v0) | member(v1, % 9.31/1.96 v0)) % 9.31/1.96 % 9.31/1.96 (formula_7) % 9.31/1.97 ! [v0: Set] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, $difference(v1, % 9.31/1.97 v2))) | ~ (sup(v0) = v2) | ~ Set(v0) | ~ member(v1, v0)) % 9.31/1.97 % 9.31/1.97 (formula_8) % 9.31/1.97 ! [v0: Set] : ! [v1: int] : ! [v2: Set] : ( ~ (insert(v0, v1) = v2) | ~ % 9.31/1.97 Set(v0) | ? [v3: int] : ? [v4: int] : ((v4 = v1 & sup(v2) = v1) | % 9.31/1.97 ($lesseq(v1, v3) & sup(v0) = v3))) % 9.31/1.97 % 9.31/1.97 (formula_9) % 9.31/1.97 Array[Int,Int](arr) & Set(s0) & ? [v0: int] : (sup(s0) = v0 & ! [v1: int] : % 9.31/1.97 ! [v2: int] : ( ~ ($lesseq(v0, v2)) | ~ ($lesseq(1, v1)) | ~ % 9.31/1.97 (select:(Array[Int,Int]*Int)>Int(arr, v1) = v2))) % 9.31/1.97 % 9.31/1.97 (function-axioms) % 9.31/1.98 ! [v0: Array[Int,Int]] : ! [v1: Array[Int,Int]] : ! [v2: int] : ! [v3: % 9.31/1.98 int] : ! [v4: Array[Int,Int]] : (v1 = v0 | ~ % 9.31/1.98 (store:(Array[Int,Int]*Int*Int)>Array[Int,Int](v4, v3, v2) = v1) | ~ % 9.31/1.98 (store:(Array[Int,Int]*Int*Int)>Array[Int,Int](v4, v3, v2) = v0)) & ! [v0: % 9.31/1.98 int] : ! [v1: int] : ! [v2: int] : ! [v3: Array[Int,Int]] : (v1 = v0 | ~ % 9.31/1.98 (select:(Array[Int,Int]*Int)>Int(v3, v2) = v1) | ~ % 9.31/1.98 (select:(Array[Int,Int]*Int)>Int(v3, v2) = v0)) & ! [v0: Set] : ! [v1: % 9.31/1.98 Set] : ! [v2: int] : ! [v3: Set] : (v1 = v0 | ~ (delete(v3, v2) = v1) | % 9.31/1.98 ~ (delete(v3, v2) = v0)) & ! [v0: Set] : ! [v1: Set] : ! [v2: int] : ! % 9.31/1.98 [v3: Set] : (v1 = v0 | ~ (insert(v3, v2) = v1) | ~ (insert(v3, v2) = v0)) & % 9.31/1.98 ! [v0: Array[Int,Int]] : ! [v1: Array[Int,Int]] : ! [v2: int] : (v1 = v0 | % 9.31/1.98 ~ (const:(Int)>Array[Int,Int](v2) = v1) | ~ (const:(Int)>Array[Int,Int](v2) % 9.31/1.98 = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (g(v2) % 9.31/1.98 = v1) | ~ (g(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Set] : % 9.31/1.98 (v1 = v0 | ~ (sup(v2) = v1) | ~ (sup(v2) = v0)) % 9.31/1.98 % 9.31/1.98 Further assumptions not needed in the proof: % 9.31/1.98 -------------------------------------------- % 9.31/1.98 formula_1, formula_13, formula_14, formula_15, formula_16, formula_3, formula_4, % 9.31/1.98 formula_5 % 9.31/1.98 % 9.31/1.98 Those formulas are unsatisfiable: % 9.31/1.98 --------------------------------- % 9.31/1.98 % 9.31/1.98 Begin of proof % 9.31/1.98 | % 9.31/1.98 | ALPHA: (formula_2) implies: % 9.31/1.98 | (1) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | % 9.31/1.98 | ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v2) | member(v0, % 9.31/1.98 | v3)) % 9.31/1.98 | (2) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | % 9.31/1.98 | ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0, % 9.31/1.98 | v2)) % 9.31/1.98 | % 9.31/1.98 | ALPHA: (formula_9) implies: % 9.31/1.98 | (3) ? [v0: int] : (sup(s0) = v0 & ! [v1: int] : ! [v2: int] : ( ~ % 9.31/1.98 | ($lesseq(v0, v2)) | ~ ($lesseq(1, v1)) | ~ % 9.31/1.98 | (select:(Array[Int,Int]*Int)>Int(arr, v1) = v2))) % 9.31/1.98 | % 9.31/1.98 | ALPHA: (formula_11) implies: % 9.31/1.98 | (4) ? [v0: int] : ? [v1: int] : (g(i1) = v0 & % 9.31/1.98 | select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s0, v1) = s1) % 9.31/1.99 | % 9.31/1.99 | ALPHA: (formula_12) implies: % 9.31/1.99 | (5) Set(s1) % 9.31/1.99 | (6) Set(s0) % 9.31/1.99 | (7) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & sup(s0) = v1 & sup(s1) = % 9.31/1.99 | v0) % 9.31/1.99 | % 9.31/1.99 | ALPHA: (function-axioms) implies: % 9.31/1.99 | (8) ! [v0: int] : ! [v1: int] : ! [v2: Set] : (v1 = v0 | ~ (sup(v2) = % 9.31/1.99 | v1) | ~ (sup(v2) = v0)) % 9.31/1.99 | % 9.31/1.99 | DELTA: instantiating (4) with fresh symbols all_20_0, all_20_1 gives: % 9.31/1.99 | (9) g(i1) = all_20_1 & select:(Array[Int,Int]*Int)>Int(arr, all_20_1) = % 9.31/1.99 | all_20_0 & insert(s0, all_20_0) = s1 % 9.31/1.99 | % 9.31/1.99 | ALPHA: (9) implies: % 9.31/1.99 | (10) insert(s0, all_20_0) = s1 % 9.31/1.99 | (11) select:(Array[Int,Int]*Int)>Int(arr, all_20_1) = all_20_0 % 9.31/1.99 | (12) g(i1) = all_20_1 % 9.31/1.99 | % 9.31/1.99 | DELTA: instantiating (7) with fresh symbols all_22_0, all_22_1 gives: % 9.31/1.99 | (13) ~ (all_22_0 = all_22_1) & sup(s0) = all_22_0 & sup(s1) = all_22_1 % 9.31/1.99 | % 9.31/1.99 | ALPHA: (13) implies: % 9.31/1.99 | (14) ~ (all_22_0 = all_22_1) % 9.31/1.99 | (15) sup(s1) = all_22_1 % 9.31/1.99 | (16) sup(s0) = all_22_0 % 9.31/1.99 | % 9.31/1.99 | DELTA: instantiating (3) with fresh symbol all_24_0 gives: % 9.31/1.99 | (17) sup(s0) = all_24_0 & ! [v0: int] : ! [v1: int] : ( ~ % 9.31/1.99 | ($lesseq(all_24_0, v1)) | ~ ($lesseq(1, v0)) | ~ % 9.31/1.99 | (select:(Array[Int,Int]*Int)>Int(arr, v0) = v1)) % 9.31/1.99 | % 9.31/1.99 | ALPHA: (17) implies: % 9.31/1.99 | (18) sup(s0) = all_24_0 % 9.31/1.99 | (19) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(all_24_0, v1)) | ~ % 9.31/1.99 | ($lesseq(1, v0)) | ~ (select:(Array[Int,Int]*Int)>Int(arr, v0) = % 9.31/1.99 | v1)) % 9.31/1.99 | % 9.31/2.00 | GROUND_INST: instantiating (8) with all_22_0, all_24_0, s0, simplifying with % 9.31/2.00 | (16), (18) gives: % 9.31/2.00 | (20) all_24_0 = all_22_0 % 9.31/2.00 | % 9.31/2.00 | GROUND_INST: instantiating (19) with all_20_1, all_20_0, simplifying with (11) % 9.31/2.00 | gives: % 9.31/2.00 | (21) ~ ($lesseq(all_24_0, all_20_0)) | ~ ($lesseq(1, all_20_1)) % 9.31/2.00 | % 9.31/2.00 | GROUND_INST: instantiating (formula_10) with i1, all_20_1, simplifying with % 9.31/2.00 | (12) gives: % 9.31/2.00 | (22) $lesseq(1, all_20_1) % 9.31/2.00 | % 9.31/2.00 | BETA: splitting (21) gives: % 9.31/2.00 | % 9.31/2.00 | Case 1: % 9.31/2.00 | | % 9.31/2.00 | | (23) $lesseq(1, $difference(all_24_0, all_20_0)) % 9.31/2.00 | | % 9.31/2.00 | | REDUCE: (20), (23) imply: % 9.31/2.00 | | (24) $lesseq(1, $difference(all_22_0, all_20_0)) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (formula_8) with s0, all_20_0, s1, simplifying % 9.31/2.00 | | with (6), (10) gives: % 9.31/2.00 | | (25) ? [v0: int] : ? [v1: int] : ((v1 = all_20_0 & sup(s1) = all_20_0) % 9.31/2.00 | | | ($lesseq(all_20_0, v0) & sup(s0) = v0)) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (formula_6) with s1, all_22_1, simplifying with % 9.31/2.00 | | (5), (15) gives: % 9.31/2.00 | | (26) member(all_22_1, s1) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (formula_6) with s0, all_22_0, simplifying with % 9.31/2.00 | | (6), (16) gives: % 9.31/2.00 | | (27) member(all_22_0, s0) % 9.31/2.00 | | % 9.31/2.00 | | DELTA: instantiating (25) with fresh symbols all_48_0, all_48_1 gives: % 9.31/2.00 | | (28) (all_48_0 = all_20_0 & sup(s1) = all_20_0) | ($lesseq(all_20_0, % 9.31/2.00 | | all_48_1) & sup(s0) = all_48_1) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (2) with all_22_1, all_20_0, s0, s1, simplifying % 9.31/2.00 | | with (6), (10), (26) gives: % 9.31/2.00 | | (29) all_22_1 = all_20_0 | member(all_22_1, s0) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (1) with all_22_0, all_20_0, s0, s1, simplifying % 9.31/2.00 | | with (6), (10), (27) gives: % 9.31/2.00 | | (30) all_22_0 = all_20_0 | member(all_22_0, s1) % 9.31/2.00 | | % 9.31/2.00 | | GROUND_INST: instantiating (formula_7) with s1, all_22_0, all_22_1, % 9.31/2.00 | | simplifying with (5), (15) gives: % 9.31/2.00 | | (31) ~ ($lesseq(1, $difference(all_22_0, all_22_1))) | ~ % 9.31/2.00 | | member(all_22_0, s1) % 9.31/2.00 | | % 9.31/2.00 | | BETA: splitting (30) gives: % 9.31/2.00 | | % 9.31/2.00 | | Case 1: % 9.31/2.00 | | | % 9.31/2.00 | | | (32) member(all_22_0, s1) % 9.31/2.00 | | | % 9.31/2.00 | | | BETA: splitting (31) gives: % 9.31/2.00 | | | % 9.31/2.00 | | | Case 1: % 9.31/2.00 | | | | % 9.31/2.01 | | | | (33) ~ member(all_22_0, s1) % 9.31/2.01 | | | | % 9.31/2.01 | | | | PRED_UNIFY: (32), (33) imply: % 9.31/2.01 | | | | (34) $false % 9.31/2.01 | | | | % 9.31/2.01 | | | | CLOSE: (34) is inconsistent. % 9.31/2.01 | | | | % 9.31/2.01 | | | Case 2: % 9.31/2.01 | | | | % 9.31/2.01 | | | | (35) $lesseq(all_22_0, all_22_1) % 9.31/2.01 | | | | % 9.31/2.01 | | | | STRENGTHEN: (14), (35) imply: % 9.31/2.01 | | | | (36) $lesseq(1, $difference(all_22_1, all_22_0)) % 9.31/2.01 | | | | % 9.31/2.01 | | | | BETA: splitting (28) gives: % 9.31/2.01 | | | | % 9.31/2.01 | | | | Case 1: % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | (37) all_48_0 = all_20_0 & sup(s1) = all_20_0 % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | ALPHA: (37) implies: % 9.31/2.01 | | | | | (38) sup(s1) = all_20_0 % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | GROUND_INST: instantiating (8) with all_20_0, all_22_1, s1, % 9.31/2.01 | | | | | simplifying with (15), (38) gives: % 9.31/2.01 | | | | | (39) all_22_1 = all_20_0 % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | REDUCE: (36), (39) imply: % 9.31/2.01 | | | | | (40) $lesseq(1, $difference(all_20_0, all_22_0)) % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | COMBINE_INEQS: (24), (40) imply: % 9.31/2.01 | | | | | (41) $false % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | CLOSE: (41) is inconsistent. % 9.31/2.01 | | | | | % 9.31/2.01 | | | | Case 2: % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | (42) $lesseq(all_20_0, all_48_1) & sup(s0) = all_48_1 % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | ALPHA: (42) implies: % 9.31/2.01 | | | | | (43) sup(s0) = all_48_1 % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | BETA: splitting (29) gives: % 9.31/2.01 | | | | | % 9.31/2.01 | | | | | Case 1: % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | (44) member(all_22_1, s0) % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | GROUND_INST: instantiating (8) with all_22_0, all_48_1, s0, % 9.31/2.01 | | | | | | simplifying with (16), (43) gives: % 9.31/2.01 | | | | | | (45) all_48_1 = all_22_0 % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | GROUND_INST: instantiating (formula_7) with s0, all_22_1, all_22_0, % 9.31/2.01 | | | | | | simplifying with (6), (16), (44) gives: % 9.31/2.01 | | | | | | (46) $lesseq(all_22_1, all_22_0) % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | COMBINE_INEQS: (36), (46) imply: % 9.31/2.01 | | | | | | (47) $false % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | CLOSE: (47) is inconsistent. % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | Case 2: % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | (48) all_22_1 = all_20_0 % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | REDUCE: (36), (48) imply: % 9.31/2.01 | | | | | | (49) $lesseq(1, $difference(all_20_0, all_22_0)) % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | COMBINE_INEQS: (24), (49) imply: % 9.31/2.01 | | | | | | (50) $false % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | | CLOSE: (50) is inconsistent. % 9.31/2.01 | | | | | | % 9.31/2.01 | | | | | End of split % 9.31/2.01 | | | | | % 9.31/2.01 | | | | End of split % 9.31/2.01 | | | | % 9.31/2.01 | | | End of split % 9.31/2.01 | | | % 9.31/2.01 | | Case 2: % 9.31/2.01 | | | % 9.31/2.01 | | | (51) all_22_0 = all_20_0 % 9.31/2.01 | | | % 9.31/2.01 | | | REDUCE: (24), (51) imply: % 9.31/2.01 | | | (52) $false % 9.31/2.01 | | | % 9.31/2.01 | | | CLOSE: (52) is inconsistent. % 9.31/2.01 | | | % 9.31/2.01 | | End of split % 9.31/2.01 | | % 9.31/2.01 | Case 2: % 9.31/2.01 | | % 9.31/2.01 | | (53) $lesseq(all_20_1, 0) % 9.31/2.01 | | % 9.31/2.01 | | COMBINE_INEQS: (22), (53) imply: % 9.31/2.01 | | (54) $false % 9.31/2.01 | | % 9.31/2.01 | | CLOSE: (54) is inconsistent. % 9.31/2.01 | | % 9.31/2.01 | End of split % 9.31/2.01 | % 9.31/2.01 End of proof % 9.31/2.01 % SZS output end Proof for theBenchmark % 9.31/2.01 % 9.31/2.01 1407ms %------------------------------------------------------------------------------