%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW679_1 : TPTP v8.1.2. Released v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.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 : Fri Sep 1 00:51:06 EDT 2023 % Result : Theorem 5.89s 1.55s % Output : Proof 7.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWW679_1 : TPTP v8.1.2. Released v6.4.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 19:47:12 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.88/1.10 Prover 4: Preprocessing ... % 2.88/1.11 Prover 1: Preprocessing ... % 2.88/1.13 Prover 5: Preprocessing ... % 2.88/1.13 Prover 6: Preprocessing ... % 2.88/1.13 Prover 2: Preprocessing ... % 2.88/1.13 Prover 3: Preprocessing ... % 2.88/1.13 Prover 0: Preprocessing ... % 5.02/1.42 Prover 1: Constructing countermodel ... % 5.02/1.42 Prover 3: Constructing countermodel ... % 5.02/1.42 Prover 6: Proving ... % 5.20/1.49 Prover 5: Proving ... % 5.20/1.50 Prover 4: Constructing countermodel ... % 5.89/1.53 Prover 0: Proving ... % 5.89/1.55 Prover 2: Proving ... % 5.89/1.55 Prover 3: proved (915ms) % 5.89/1.55 % 5.89/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.89/1.55 % 5.89/1.56 Prover 5: stopped % 5.89/1.56 Prover 6: stopped % 5.89/1.56 Prover 0: stopped % 5.89/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.89/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.89/1.56 Prover 2: stopped % 5.89/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.89/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.89/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.41/1.60 Prover 13: Preprocessing ... % 6.41/1.61 Prover 8: Preprocessing ... % 6.41/1.62 Prover 10: Preprocessing ... % 6.41/1.62 Prover 7: Preprocessing ... % 6.41/1.63 Prover 11: Preprocessing ... % 7.02/1.69 Prover 1: Found proof (size 27) % 7.02/1.69 Prover 1: proved (1058ms) % 7.02/1.70 Prover 4: stopped % 7.23/1.72 Prover 10: Warning: ignoring some quantifiers % 7.40/1.72 Prover 10: Constructing countermodel ... % 7.40/1.73 Prover 8: Warning: ignoring some quantifiers % 7.40/1.73 Prover 10: stopped % 7.40/1.73 Prover 8: Constructing countermodel ... % 7.40/1.74 Prover 8: stopped % 7.40/1.74 Prover 7: Warning: ignoring some quantifiers % 7.40/1.75 Prover 7: Constructing countermodel ... % 7.40/1.75 Prover 7: stopped % 7.40/1.75 Prover 13: Warning: ignoring some quantifiers % 7.40/1.76 Prover 13: Constructing countermodel ... % 7.40/1.77 Prover 13: stopped % 7.40/1.78 Prover 11: Constructing countermodel ... % 7.40/1.78 Prover 11: stopped % 7.40/1.78 % 7.40/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.40/1.78 % 7.40/1.79 % SZS output start Proof for theBenchmark % 7.40/1.79 Assumptions after simplification: % 7.40/1.79 --------------------------------- % 7.40/1.79 % 7.40/1.79 (formula_006) % 7.40/1.82 Tree(empty:Tree) & ! [v0: Tree] : ! [v1: int] : (v1 = 0 | ~ (searchtree(v0) % 7.40/1.82 = v1) | ~ Tree(v0) | ( ~ (v0 = empty:Tree) & ? [v2: Tree] : ? [v3: any] % 7.40/1.82 : ? [v4: Tree] : ? [v5: any] : ? [v6: int] : (searchtree(v4) = v5 & % 7.40/1.82 searchtree(v2) = v3 & val:(Tree)>Int(v0) = v6 & left:(Tree)>Tree(v0) = % 7.40/1.82 v2 & right:(Tree)>Tree(v0) = v4 & Tree(v4) & Tree(v2) & ( ~ (v5 = 0) | % 7.40/1.82 ~ (v3 = 0) | ? [v7: int] : ($lesseq(v7, v6) & in(v7, v4) = 0) | ? % 7.40/1.82 [v7: int] : ($lesseq(1, $difference(v7, v6)) & in(v7, v2) = 0))))) & % 7.40/1.82 ! [v0: Tree] : (v0 = empty:Tree | ~ (searchtree(v0) = 0) | ~ Tree(v0) | ? % 7.40/1.82 [v1: Tree] : ? [v2: Tree] : ? [v3: int] : (searchtree(v2) = 0 & % 7.40/1.82 searchtree(v1) = 0 & val:(Tree)>Int(v0) = v3 & left:(Tree)>Tree(v0) = v1 & % 7.40/1.82 right:(Tree)>Tree(v0) = v2 & Tree(v2) & Tree(v1) & ! [v4: int] : ( ~ % 7.40/1.82 ($lesseq(v4, v3)) | ~ (in(v4, v2) = 0)) & ! [v4: int] : ( ~ % 7.40/1.82 ($lesseq(1, $difference(v4, v3))) | ~ (in(v4, v1) = 0)))) % 7.40/1.82 % 7.40/1.82 (formula_007) % 7.40/1.82 Tree(empty:Tree) & ? [v0: Tree] : ? [v1: int] : ? [v2: int] : ? [v3: Tree] % 7.40/1.82 : ? [v4: Tree] : ( ~ (v2 = v1) & ~ (v0 = empty:Tree) & searchtree(v0) = 0 & % 7.40/1.82 val:(Tree)>Int(v0) = v2 & left:(Tree)>Tree(v0) = v3 & right:(Tree)>Tree(v0) % 7.40/1.82 = v4 & Tree(v4) & Tree(v3) & Tree(v0) & (($lesseq(1, $difference(v1, v2)) & % 7.40/1.82 ~ (searchtree(v4) = 0)) | ($lesseq(1, $difference(v2, v1)) & ~ % 7.40/1.82 (searchtree(v3) = 0)))) % 7.40/1.82 % 7.40/1.82 (function-axioms) % 7.40/1.82 ! [v0: Tree] : ! [v1: Tree] : ! [v2: Tree] : ! [v3: Tree] : ! [v4: int] : % 7.40/1.82 (v1 = v0 | ~ (node:(Int*Tree*Tree)>Tree(v4, v3, v2) = v1) | ~ % 7.40/1.82 (node:(Int*Tree*Tree)>Tree(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 7.40/1.82 ! [v1: MultipleValueBool] : ! [v2: Tree] : ! [v3: int] : (v1 = v0 | ~ % 7.40/1.82 (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 7.40/1.82 [v1: MultipleValueBool] : ! [v2: Tree] : (v1 = v0 | ~ (searchtree(v2) = v1) % 7.40/1.82 | ~ (searchtree(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Tree] : % 7.40/1.82 (v1 = v0 | ~ (val:(Tree)>Int(v2) = v1) | ~ (val:(Tree)>Int(v2) = v0)) & ! % 7.40/1.82 [v0: Tree] : ! [v1: Tree] : ! [v2: Tree] : (v1 = v0 | ~ % 7.40/1.82 (left:(Tree)>Tree(v2) = v1) | ~ (left:(Tree)>Tree(v2) = v0)) & ! [v0: % 7.40/1.82 Tree] : ! [v1: Tree] : ! [v2: Tree] : (v1 = v0 | ~ (right:(Tree)>Tree(v2) % 7.40/1.82 = v1) | ~ (right:(Tree)>Tree(v2) = v0)) % 7.40/1.83 % 7.40/1.83 Further assumptions not needed in the proof: % 7.40/1.83 -------------------------------------------- % 7.40/1.83 formula, formula_001, formula_002, formula_003, formula_004, formula_005 % 7.40/1.83 % 7.40/1.83 Those formulas are unsatisfiable: % 7.40/1.83 --------------------------------- % 7.40/1.83 % 7.40/1.83 Begin of proof % 7.40/1.83 | % 7.40/1.83 | ALPHA: (formula_006) implies: % 7.40/1.83 | (1) ! [v0: Tree] : (v0 = empty:Tree | ~ (searchtree(v0) = 0) | ~ % 7.40/1.83 | Tree(v0) | ? [v1: Tree] : ? [v2: Tree] : ? [v3: int] : % 7.40/1.83 | (searchtree(v2) = 0 & searchtree(v1) = 0 & val:(Tree)>Int(v0) = v3 & % 7.40/1.83 | left:(Tree)>Tree(v0) = v1 & right:(Tree)>Tree(v0) = v2 & Tree(v2) & % 7.40/1.83 | Tree(v1) & ! [v4: int] : ( ~ ($lesseq(v4, v3)) | ~ (in(v4, v2) = % 7.40/1.83 | 0)) & ! [v4: int] : ( ~ ($lesseq(1, $difference(v4, v3))) | ~ % 7.40/1.83 | (in(v4, v1) = 0)))) % 7.40/1.83 | % 7.40/1.83 | ALPHA: (formula_007) implies: % 7.40/1.83 | (2) ? [v0: Tree] : ? [v1: int] : ? [v2: int] : ? [v3: Tree] : ? [v4: % 7.40/1.83 | Tree] : ( ~ (v2 = v1) & ~ (v0 = empty:Tree) & searchtree(v0) = 0 & % 7.40/1.83 | val:(Tree)>Int(v0) = v2 & left:(Tree)>Tree(v0) = v3 & % 7.40/1.83 | right:(Tree)>Tree(v0) = v4 & Tree(v4) & Tree(v3) & Tree(v0) & % 7.40/1.83 | (($lesseq(1, $difference(v1, v2)) & ~ (searchtree(v4) = 0)) | % 7.40/1.83 | ($lesseq(1, $difference(v2, v1)) & ~ (searchtree(v3) = 0)))) % 7.40/1.83 | % 7.40/1.83 | ALPHA: (function-axioms) implies: % 7.40/1.83 | (3) ! [v0: Tree] : ! [v1: Tree] : ! [v2: Tree] : (v1 = v0 | ~ % 7.40/1.83 | (right:(Tree)>Tree(v2) = v1) | ~ (right:(Tree)>Tree(v2) = v0)) % 7.40/1.83 | (4) ! [v0: Tree] : ! [v1: Tree] : ! [v2: Tree] : (v1 = v0 | ~ % 7.40/1.83 | (left:(Tree)>Tree(v2) = v1) | ~ (left:(Tree)>Tree(v2) = v0)) % 7.40/1.83 | % 7.40/1.83 | DELTA: instantiating (2) with fresh symbols all_13_0, all_13_1, all_13_2, % 7.40/1.83 | all_13_3, all_13_4 gives: % 7.40/1.84 | (5) ~ (all_13_2 = all_13_3) & ~ (all_13_4 = empty:Tree) & % 7.40/1.84 | searchtree(all_13_4) = 0 & val:(Tree)>Int(all_13_4) = all_13_2 & % 7.40/1.84 | left:(Tree)>Tree(all_13_4) = all_13_1 & right:(Tree)>Tree(all_13_4) = % 7.40/1.84 | all_13_0 & Tree(all_13_0) & Tree(all_13_1) & Tree(all_13_4) & % 7.40/1.84 | (($lesseq(1, $difference(all_13_3, all_13_2)) & ~ % 7.40/1.84 | (searchtree(all_13_0) = 0)) | ($lesseq(1, $difference(all_13_2, % 7.40/1.84 | all_13_3)) & ~ (searchtree(all_13_1) = 0))) % 7.40/1.84 | % 7.40/1.84 | ALPHA: (5) implies: % 7.40/1.84 | (6) ~ (all_13_4 = empty:Tree) % 7.40/1.84 | (7) Tree(all_13_4) % 7.40/1.84 | (8) right:(Tree)>Tree(all_13_4) = all_13_0 % 7.40/1.84 | (9) left:(Tree)>Tree(all_13_4) = all_13_1 % 7.40/1.84 | (10) searchtree(all_13_4) = 0 % 7.40/1.84 | (11) ($lesseq(1, $difference(all_13_3, all_13_2)) & ~ % 7.40/1.84 | (searchtree(all_13_0) = 0)) | ($lesseq(1, $difference(all_13_2, % 7.40/1.84 | all_13_3)) & ~ (searchtree(all_13_1) = 0)) % 7.40/1.84 | % 7.40/1.84 | GROUND_INST: instantiating (1) with all_13_4, simplifying with (7), (10) % 7.40/1.84 | gives: % 7.40/1.84 | (12) all_13_4 = empty:Tree | ? [v0: Tree] : ? [v1: Tree] : ? [v2: int] : % 7.40/1.84 | (searchtree(v1) = 0 & searchtree(v0) = 0 & val:(Tree)>Int(all_13_4) = % 7.40/1.84 | v2 & left:(Tree)>Tree(all_13_4) = v0 & right:(Tree)>Tree(all_13_4) = % 7.40/1.84 | v1 & Tree(v1) & Tree(v0) & ! [v3: int] : ( ~ ($lesseq(v3, v2)) | ~ % 7.40/1.84 | (in(v3, v1) = 0)) & ! [v3: int] : ( ~ ($lesseq(1, $difference(v3, % 7.40/1.84 | v2))) | ~ (in(v3, v0) = 0))) % 7.40/1.84 | % 7.40/1.84 | BETA: splitting (11) gives: % 7.40/1.84 | % 7.40/1.84 | Case 1: % 7.40/1.84 | | % 7.40/1.84 | | (13) $lesseq(1, $difference(all_13_3, all_13_2)) & ~ % 7.40/1.84 | | (searchtree(all_13_0) = 0) % 7.40/1.84 | | % 7.40/1.84 | | ALPHA: (13) implies: % 7.40/1.84 | | (14) ~ (searchtree(all_13_0) = 0) % 7.40/1.84 | | % 7.40/1.84 | | BETA: splitting (12) gives: % 7.40/1.84 | | % 7.40/1.84 | | Case 1: % 7.40/1.84 | | | % 7.40/1.84 | | | (15) all_13_4 = empty:Tree % 7.40/1.84 | | | % 7.40/1.84 | | | REDUCE: (6), (15) imply: % 7.40/1.84 | | | (16) $false % 7.40/1.84 | | | % 7.40/1.84 | | | CLOSE: (16) is inconsistent. % 7.40/1.84 | | | % 7.40/1.84 | | Case 2: % 7.40/1.84 | | | % 7.40/1.85 | | | (17) ? [v0: Tree] : ? [v1: Tree] : ? [v2: int] : (searchtree(v1) = 0 % 7.40/1.85 | | | & searchtree(v0) = 0 & val:(Tree)>Int(all_13_4) = v2 & % 7.40/1.85 | | | left:(Tree)>Tree(all_13_4) = v0 & right:(Tree)>Tree(all_13_4) = % 7.40/1.85 | | | v1 & Tree(v1) & Tree(v0) & ! [v3: int] : ( ~ ($lesseq(v3, v2)) % 7.40/1.85 | | | | ~ (in(v3, v1) = 0)) & ! [v3: int] : ( ~ ($lesseq(1, % 7.40/1.85 | | | $difference(v3, v2))) | ~ (in(v3, v0) = 0))) % 7.40/1.85 | | | % 7.40/1.85 | | | DELTA: instantiating (17) with fresh symbols all_27_0, all_27_1, all_27_2 % 7.40/1.85 | | | gives: % 7.40/1.85 | | | (18) searchtree(all_27_1) = 0 & searchtree(all_27_2) = 0 & % 7.40/1.85 | | | val:(Tree)>Int(all_13_4) = all_27_0 & left:(Tree)>Tree(all_13_4) = % 7.40/1.85 | | | all_27_2 & right:(Tree)>Tree(all_13_4) = all_27_1 & Tree(all_27_1) % 7.40/1.85 | | | & Tree(all_27_2) & ! [v0: int] : ( ~ ($lesseq(v0, all_27_0)) | ~ % 7.40/1.85 | | | (in(v0, all_27_1) = 0)) & ! [v0: int] : ( ~ ($lesseq(1, % 7.40/1.85 | | | $difference(v0, all_27_0))) | ~ (in(v0, all_27_2) = 0)) % 7.40/1.85 | | | % 7.40/1.85 | | | ALPHA: (18) implies: % 7.40/1.85 | | | (19) right:(Tree)>Tree(all_13_4) = all_27_1 % 7.40/1.85 | | | (20) searchtree(all_27_1) = 0 % 7.40/1.85 | | | % 7.40/1.85 | | | GROUND_INST: instantiating (3) with all_13_0, all_27_1, all_13_4, % 7.40/1.85 | | | simplifying with (8), (19) gives: % 7.40/1.85 | | | (21) all_27_1 = all_13_0 % 7.40/1.85 | | | % 7.40/1.85 | | | REDUCE: (20), (21) imply: % 7.40/1.85 | | | (22) searchtree(all_13_0) = 0 % 7.40/1.85 | | | % 7.40/1.85 | | | PRED_UNIFY: (14), (22) imply: % 7.40/1.85 | | | (23) $false % 7.40/1.85 | | | % 7.40/1.85 | | | CLOSE: (23) is inconsistent. % 7.40/1.85 | | | % 7.40/1.85 | | End of split % 7.40/1.85 | | % 7.40/1.85 | Case 2: % 7.40/1.85 | | % 7.40/1.85 | | (24) $lesseq(1, $difference(all_13_2, all_13_3)) & ~ % 7.40/1.85 | | (searchtree(all_13_1) = 0) % 7.40/1.85 | | % 7.40/1.85 | | ALPHA: (24) implies: % 7.40/1.85 | | (25) ~ (searchtree(all_13_1) = 0) % 7.40/1.85 | | % 7.40/1.85 | | BETA: splitting (12) gives: % 7.40/1.85 | | % 7.40/1.85 | | Case 1: % 7.40/1.85 | | | % 7.40/1.85 | | | (26) all_13_4 = empty:Tree % 7.40/1.85 | | | % 7.40/1.85 | | | REDUCE: (6), (26) imply: % 7.40/1.85 | | | (27) $false % 7.40/1.85 | | | % 7.40/1.85 | | | CLOSE: (27) is inconsistent. % 7.40/1.85 | | | % 7.40/1.85 | | Case 2: % 7.40/1.85 | | | % 7.40/1.85 | | | (28) ? [v0: Tree] : ? [v1: Tree] : ? [v2: int] : (searchtree(v1) = 0 % 7.40/1.85 | | | & searchtree(v0) = 0 & val:(Tree)>Int(all_13_4) = v2 & % 7.40/1.85 | | | left:(Tree)>Tree(all_13_4) = v0 & right:(Tree)>Tree(all_13_4) = % 7.40/1.85 | | | v1 & Tree(v1) & Tree(v0) & ! [v3: int] : ( ~ ($lesseq(v3, v2)) % 7.40/1.85 | | | | ~ (in(v3, v1) = 0)) & ! [v3: int] : ( ~ ($lesseq(1, % 7.40/1.85 | | | $difference(v3, v2))) | ~ (in(v3, v0) = 0))) % 7.40/1.85 | | | % 7.40/1.85 | | | DELTA: instantiating (28) with fresh symbols all_27_0, all_27_1, all_27_2 % 7.40/1.85 | | | gives: % 7.40/1.85 | | | (29) searchtree(all_27_1) = 0 & searchtree(all_27_2) = 0 & % 7.40/1.85 | | | val:(Tree)>Int(all_13_4) = all_27_0 & left:(Tree)>Tree(all_13_4) = % 7.40/1.85 | | | all_27_2 & right:(Tree)>Tree(all_13_4) = all_27_1 & Tree(all_27_1) % 7.40/1.85 | | | & Tree(all_27_2) & ! [v0: int] : ( ~ ($lesseq(v0, all_27_0)) | ~ % 7.40/1.85 | | | (in(v0, all_27_1) = 0)) & ! [v0: int] : ( ~ ($lesseq(1, % 7.40/1.85 | | | $difference(v0, all_27_0))) | ~ (in(v0, all_27_2) = 0)) % 7.40/1.85 | | | % 7.40/1.85 | | | ALPHA: (29) implies: % 7.40/1.85 | | | (30) left:(Tree)>Tree(all_13_4) = all_27_2 % 7.40/1.85 | | | (31) searchtree(all_27_2) = 0 % 7.40/1.85 | | | % 7.40/1.85 | | | GROUND_INST: instantiating (4) with all_13_1, all_27_2, all_13_4, % 7.40/1.85 | | | simplifying with (9), (30) gives: % 7.40/1.85 | | | (32) all_27_2 = all_13_1 % 7.40/1.85 | | | % 7.40/1.85 | | | REDUCE: (31), (32) imply: % 7.40/1.85 | | | (33) searchtree(all_13_1) = 0 % 7.40/1.85 | | | % 7.40/1.85 | | | PRED_UNIFY: (25), (33) imply: % 7.40/1.85 | | | (34) $false % 7.40/1.85 | | | % 7.40/1.85 | | | CLOSE: (34) is inconsistent. % 7.40/1.85 | | | % 7.40/1.85 | | End of split % 7.40/1.85 | | % 7.40/1.85 | End of split % 7.40/1.85 | % 7.40/1.85 End of proof % 7.40/1.85 % SZS output end Proof for theBenchmark % 7.40/1.85 % 7.40/1.85 1238ms %------------------------------------------------------------------------------