%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET372+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.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 : Thu Aug 31 15:24:47 EDT 2023 % Result : Theorem 8.71s 1.97s % Output : Proof 9.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET372+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n016.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 09:20:27 EDT 2023 % 0.12/0.33 % 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. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.07 Prover 1: Preprocessing ... % 2.63/1.07 Prover 4: Preprocessing ... % 2.63/1.11 Prover 2: Preprocessing ... % 2.63/1.11 Prover 3: Preprocessing ... % 2.63/1.11 Prover 6: Preprocessing ... % 2.63/1.11 Prover 5: Preprocessing ... % 2.63/1.11 Prover 0: Preprocessing ... % 4.75/1.45 Prover 6: Proving ... % 4.75/1.47 Prover 1: Constructing countermodel ... % 4.75/1.47 Prover 2: Proving ... % 4.75/1.48 Prover 5: Proving ... % 4.75/1.48 Prover 3: Constructing countermodel ... % 4.75/1.53 Prover 0: Proving ... % 4.75/1.54 Prover 4: Constructing countermodel ... % 8.71/1.97 Prover 3: proved (1345ms) % 8.71/1.97 % 8.71/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.71/1.97 % 8.71/1.97 Prover 2: stopped % 9.06/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.06/1.97 Prover 1: Found proof (size 105) % 9.06/1.97 Prover 1: proved (1354ms) % 9.06/1.97 Prover 5: stopped % 9.06/1.97 Prover 0: stopped % 9.06/1.97 Prover 6: stopped % 9.06/1.97 Prover 4: stopped % 9.06/1.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.06/2.00 Prover 7: Preprocessing ... % 9.06/2.00 Prover 8: Preprocessing ... % 9.06/2.02 Prover 7: stopped % 9.43/2.07 Prover 8: Warning: ignoring some quantifiers % 9.56/2.07 Prover 8: Constructing countermodel ... % 9.56/2.08 Prover 8: stopped % 9.56/2.08 % 9.56/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.56/2.08 % 9.56/2.09 % SZS output start Proof for theBenchmark % 9.56/2.10 Assumptions after simplification: % 9.56/2.10 --------------------------------- % 9.56/2.10 % 9.56/2.10 (equal_set) % 9.56/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 9.56/2.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 9.56/2.13 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 9.56/2.13 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.56/2.13 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 9.56/2.13 % 9.56/2.13 (intersection) % 9.56/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.56/2.13 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 9.56/2.13 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 9.56/2.13 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 9.56/2.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 9.56/2.13 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 9.56/2.13 0 & member(v0, v1) = 0)) % 9.56/2.13 % 9.56/2.13 (power_set) % 9.56/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.56/2.14 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 9.56/2.14 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 9.56/2.14 : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) % 9.56/2.14 | ~ $i(v0) | subset(v0, v1) = 0) % 9.56/2.14 % 9.56/2.14 (subset) % 9.56/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 9.56/2.14 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 9.56/2.14 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 9.56/2.14 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 9.56/2.14 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 9.56/2.14 % 9.56/2.14 (thI21) % 9.56/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.56/2.14 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & intersection(v4, v5) = v6 % 9.56/2.14 & intersection(v0, v1) = v2 & power_set(v2) = v3 & power_set(v1) = v5 & % 9.56/2.14 power_set(v0) = v4 & equal_set(v3, v6) = v7 & $i(v6) & $i(v5) & $i(v4) & % 9.56/2.14 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.56/2.15 % 9.56/2.15 (function-axioms) % 9.56/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.56/2.16 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 9.56/2.16 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.56/2.16 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 9.56/2.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 9.56/2.16 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.56/2.16 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 9.56/2.16 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.56/2.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 9.56/2.16 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.56/2.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 9.56/2.16 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.56/2.16 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.56/2.16 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 9.56/2.16 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 9.56/2.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 9.56/2.16 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.56/2.16 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 9.56/2.16 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 9.56/2.16 (power_set(v2) = v0)) % 9.56/2.16 % 9.56/2.16 Further assumptions not needed in the proof: % 9.56/2.16 -------------------------------------------- % 9.56/2.16 difference, empty_set, product, singleton, sum, union, unordered_pair % 9.56/2.16 % 9.56/2.16 Those formulas are unsatisfiable: % 9.56/2.16 --------------------------------- % 9.56/2.16 % 9.56/2.16 Begin of proof % 9.56/2.16 | % 9.56/2.16 | ALPHA: (subset) implies: % 9.56/2.16 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 9.56/2.16 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 9.56/2.16 | member(v2, v1) = 0)) % 9.56/2.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 9.56/2.16 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 9.56/2.16 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 9.56/2.16 | % 9.56/2.16 | ALPHA: (equal_set) implies: % 9.56/2.16 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 9.56/2.16 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.56/2.16 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 9.56/2.16 | 0)))) % 9.56/2.16 | % 9.56/2.16 | ALPHA: (power_set) implies: % 9.56/2.16 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ % 9.56/2.16 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) % 9.56/2.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.56/2.17 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ % 9.56/2.17 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 9.56/2.17 | % 9.56/2.17 | ALPHA: (intersection) implies: % 9.56/2.17 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.56/2.17 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 9.56/2.17 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 9.56/2.17 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.56/2.17 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 9.56/2.17 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.56/2.17 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 9.56/2.17 | 0)))) % 9.56/2.17 | % 9.56/2.17 | ALPHA: (function-axioms) implies: % 9.56/2.17 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.56/2.17 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.56/2.17 | = v0)) % 9.56/2.17 | % 9.56/2.17 | DELTA: instantiating (thI21) with fresh symbols all_15_0, all_15_1, all_15_2, % 9.56/2.17 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 9.56/2.17 | (9) ~ (all_15_0 = 0) & intersection(all_15_3, all_15_2) = all_15_1 & % 9.56/2.17 | intersection(all_15_7, all_15_6) = all_15_5 & power_set(all_15_5) = % 9.56/2.17 | all_15_4 & power_set(all_15_6) = all_15_2 & power_set(all_15_7) = % 9.56/2.17 | all_15_3 & equal_set(all_15_4, all_15_1) = all_15_0 & $i(all_15_1) & % 9.56/2.17 | $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & % 9.56/2.17 | $i(all_15_6) & $i(all_15_7) % 9.56/2.17 | % 9.56/2.17 | ALPHA: (9) implies: % 9.56/2.17 | (10) ~ (all_15_0 = 0) % 9.56/2.17 | (11) $i(all_15_7) % 9.56/2.17 | (12) $i(all_15_6) % 9.56/2.17 | (13) $i(all_15_5) % 9.56/2.17 | (14) $i(all_15_4) % 9.56/2.17 | (15) $i(all_15_3) % 9.56/2.17 | (16) $i(all_15_2) % 9.56/2.17 | (17) $i(all_15_1) % 9.56/2.17 | (18) equal_set(all_15_4, all_15_1) = all_15_0 % 9.56/2.17 | (19) power_set(all_15_7) = all_15_3 % 9.56/2.17 | (20) power_set(all_15_6) = all_15_2 % 9.56/2.17 | (21) power_set(all_15_5) = all_15_4 % 9.56/2.17 | (22) intersection(all_15_7, all_15_6) = all_15_5 % 9.56/2.17 | (23) intersection(all_15_3, all_15_2) = all_15_1 % 9.56/2.17 | % 9.56/2.18 | GROUND_INST: instantiating (3) with all_15_4, all_15_1, all_15_0, simplifying % 9.56/2.18 | with (14), (17), (18) gives: % 9.56/2.18 | (24) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 9.56/2.18 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | % 9.56/2.18 | ~ (v0 = 0))) % 9.56/2.18 | % 9.56/2.18 | BETA: splitting (24) gives: % 9.56/2.18 | % 9.56/2.18 | Case 1: % 9.56/2.18 | | % 9.56/2.18 | | (25) all_15_0 = 0 % 9.56/2.18 | | % 9.56/2.18 | | REDUCE: (10), (25) imply: % 9.56/2.18 | | (26) $false % 9.56/2.18 | | % 9.56/2.18 | | CLOSE: (26) is inconsistent. % 9.56/2.18 | | % 9.56/2.18 | Case 2: % 9.56/2.18 | | % 9.56/2.18 | | (27) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 & % 9.56/2.18 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.56/2.18 | | % 9.56/2.18 | | DELTA: instantiating (27) with fresh symbols all_24_0, all_24_1 gives: % 9.56/2.18 | | (28) subset(all_15_1, all_15_4) = all_24_0 & subset(all_15_4, all_15_1) = % 9.56/2.18 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 9.56/2.18 | | % 9.56/2.18 | | ALPHA: (28) implies: % 9.56/2.18 | | (29) subset(all_15_4, all_15_1) = all_24_1 % 9.56/2.18 | | (30) subset(all_15_1, all_15_4) = all_24_0 % 9.56/2.18 | | (31) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 9.56/2.18 | | % 9.56/2.18 | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_24_1, % 9.56/2.18 | | simplifying with (14), (17), (29) gives: % 9.56/2.18 | | (32) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.56/2.18 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 9.56/2.18 | | % 9.56/2.18 | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_24_0, % 9.56/2.18 | | simplifying with (14), (17), (30) gives: % 9.56/2.18 | | (33) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.56/2.18 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 9.56/2.18 | | % 9.56/2.18 | | BETA: splitting (31) gives: % 9.56/2.18 | | % 9.56/2.18 | | Case 1: % 9.56/2.18 | | | % 9.56/2.18 | | | (34) ~ (all_24_0 = 0) % 9.56/2.18 | | | % 9.56/2.18 | | | BETA: splitting (33) gives: % 9.56/2.18 | | | % 9.56/2.18 | | | Case 1: % 9.56/2.18 | | | | % 9.56/2.18 | | | | (35) all_24_0 = 0 % 9.56/2.18 | | | | % 9.56/2.18 | | | | REDUCE: (34), (35) imply: % 9.56/2.18 | | | | (36) $false % 9.56/2.18 | | | | % 9.56/2.18 | | | | CLOSE: (36) is inconsistent. % 9.56/2.18 | | | | % 9.56/2.18 | | | Case 2: % 9.56/2.18 | | | | % 9.56/2.18 | | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 9.56/2.19 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 9.56/2.19 | | | | % 9.56/2.19 | | | | DELTA: instantiating (37) with fresh symbols all_37_0, all_37_1 gives: % 9.56/2.19 | | | | (38) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 9.56/2.19 | | | | member(all_37_1, all_15_4) = all_37_0 & $i(all_37_1) % 9.56/2.19 | | | | % 9.56/2.19 | | | | ALPHA: (38) implies: % 9.56/2.19 | | | | (39) ~ (all_37_0 = 0) % 9.56/2.19 | | | | (40) $i(all_37_1) % 9.56/2.19 | | | | (41) member(all_37_1, all_15_4) = all_37_0 % 9.56/2.19 | | | | (42) member(all_37_1, all_15_1) = 0 % 9.56/2.19 | | | | % 9.56/2.19 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_5, all_15_4, % 9.56/2.19 | | | | all_37_0, simplifying with (13), (21), (40), (41) gives: % 9.56/2.19 | | | | (43) all_37_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, % 9.56/2.19 | | | | all_15_5) = v0) % 9.56/2.19 | | | | % 9.56/2.19 | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_3, all_15_2, % 9.56/2.19 | | | | all_15_1, simplifying with (15), (16), (23), (40), (42) % 9.56/2.19 | | | | gives: % 9.56/2.19 | | | | (44) member(all_37_1, all_15_2) = 0 & member(all_37_1, all_15_3) = 0 % 9.56/2.19 | | | | % 9.56/2.19 | | | | ALPHA: (44) implies: % 9.56/2.19 | | | | (45) member(all_37_1, all_15_3) = 0 % 9.56/2.19 | | | | (46) member(all_37_1, all_15_2) = 0 % 9.56/2.19 | | | | % 9.56/2.19 | | | | BETA: splitting (43) gives: % 9.56/2.19 | | | | % 9.56/2.19 | | | | Case 1: % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | (47) all_37_0 = 0 % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | REDUCE: (39), (47) imply: % 9.56/2.19 | | | | | (48) $false % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | CLOSE: (48) is inconsistent. % 9.56/2.19 | | | | | % 9.56/2.19 | | | | Case 2: % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_5) = v0) % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | DELTA: instantiating (49) with fresh symbol all_49_0 gives: % 9.56/2.19 | | | | | (50) ~ (all_49_0 = 0) & subset(all_37_1, all_15_5) = all_49_0 % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | ALPHA: (50) implies: % 9.56/2.19 | | | | | (51) ~ (all_49_0 = 0) % 9.56/2.19 | | | | | (52) subset(all_37_1, all_15_5) = all_49_0 % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_7, all_15_3, % 9.56/2.19 | | | | | simplifying with (11), (19), (40), (45) gives: % 9.56/2.19 | | | | | (53) subset(all_37_1, all_15_7) = 0 % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_6, all_15_2, % 9.56/2.19 | | | | | simplifying with (12), (20), (40), (46) gives: % 9.56/2.19 | | | | | (54) subset(all_37_1, all_15_6) = 0 % 9.56/2.19 | | | | | % 9.56/2.19 | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_5, all_49_0, % 9.56/2.19 | | | | | simplifying with (13), (40), (52) gives: % 9.56/2.20 | | | | | (55) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.56/2.20 | | | | | member(v0, all_37_1) = 0 & member(v0, all_15_5) = v1 & % 9.56/2.20 | | | | | $i(v0)) % 9.56/2.20 | | | | | % 9.56/2.20 | | | | | BETA: splitting (55) gives: % 9.56/2.20 | | | | | % 9.56/2.20 | | | | | Case 1: % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | (56) all_49_0 = 0 % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | REDUCE: (51), (56) imply: % 9.56/2.20 | | | | | | (57) $false % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | CLOSE: (57) is inconsistent. % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | Case 2: % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | (58) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 9.56/2.20 | | | | | | all_37_1) = 0 & member(v0, all_15_5) = v1 & $i(v0)) % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | DELTA: instantiating (58) with fresh symbols all_61_0, all_61_1 % 9.56/2.20 | | | | | | gives: % 9.56/2.20 | | | | | | (59) ~ (all_61_0 = 0) & member(all_61_1, all_37_1) = 0 & % 9.56/2.20 | | | | | | member(all_61_1, all_15_5) = all_61_0 & $i(all_61_1) % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | ALPHA: (59) implies: % 9.56/2.20 | | | | | | (60) ~ (all_61_0 = 0) % 9.56/2.20 | | | | | | (61) $i(all_61_1) % 9.56/2.20 | | | | | | (62) member(all_61_1, all_15_5) = all_61_0 % 9.56/2.20 | | | | | | (63) member(all_61_1, all_37_1) = 0 % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | GROUND_INST: instantiating (7) with all_61_1, all_15_7, all_15_6, % 9.56/2.20 | | | | | | all_15_5, all_61_0, simplifying with (11), (12), (22), % 9.56/2.20 | | | | | | (61), (62) gives: % 9.56/2.20 | | | | | | (64) all_61_0 = 0 | ? [v0: any] : ? [v1: any] : % 9.56/2.20 | | | | | | (member(all_61_1, all_15_6) = v1 & member(all_61_1, % 9.56/2.20 | | | | | | all_15_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_7, simplifying % 9.56/2.20 | | | | | | with (11), (40), (53) gives: % 9.56/2.20 | | | | | | (65) ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) | ~ $i(v0) | % 9.56/2.20 | | | | | | member(v0, all_15_7) = 0) % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_6, simplifying % 9.56/2.20 | | | | | | with (12), (40), (54) gives: % 9.56/2.20 | | | | | | (66) ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) | ~ $i(v0) | % 9.56/2.20 | | | | | | member(v0, all_15_6) = 0) % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | GROUND_INST: instantiating (66) with all_61_1, simplifying with % 9.56/2.20 | | | | | | (61), (63) gives: % 9.56/2.20 | | | | | | (67) member(all_61_1, all_15_6) = 0 % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | GROUND_INST: instantiating (65) with all_61_1, simplifying with % 9.56/2.20 | | | | | | (61), (63) gives: % 9.56/2.20 | | | | | | (68) member(all_61_1, all_15_7) = 0 % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | BETA: splitting (64) gives: % 9.56/2.20 | | | | | | % 9.56/2.20 | | | | | | Case 1: % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | | (69) all_61_0 = 0 % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | | REDUCE: (60), (69) imply: % 9.56/2.20 | | | | | | | (70) $false % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | | CLOSE: (70) is inconsistent. % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | Case 2: % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | | (71) ? [v0: any] : ? [v1: any] : (member(all_61_1, all_15_6) % 9.56/2.20 | | | | | | | = v1 & member(all_61_1, all_15_7) = v0 & ( ~ (v1 = 0) | % 9.56/2.20 | | | | | | | ~ (v0 = 0))) % 9.56/2.20 | | | | | | | % 9.56/2.20 | | | | | | | DELTA: instantiating (71) with fresh symbols all_76_0, all_76_1 % 9.56/2.20 | | | | | | | gives: % 9.56/2.21 | | | | | | | (72) member(all_61_1, all_15_6) = all_76_0 & member(all_61_1, % 9.56/2.21 | | | | | | | all_15_7) = all_76_1 & ( ~ (all_76_0 = 0) | ~ (all_76_1 % 9.56/2.21 | | | | | | | = 0)) % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | | ALPHA: (72) implies: % 9.56/2.21 | | | | | | | (73) member(all_61_1, all_15_7) = all_76_1 % 9.56/2.21 | | | | | | | (74) member(all_61_1, all_15_6) = all_76_0 % 9.56/2.21 | | | | | | | (75) ~ (all_76_0 = 0) | ~ (all_76_1 = 0) % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | | GROUND_INST: instantiating (8) with 0, all_76_1, all_15_7, % 9.56/2.21 | | | | | | | all_61_1, simplifying with (68), (73) gives: % 9.56/2.21 | | | | | | | (76) all_76_1 = 0 % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | | GROUND_INST: instantiating (8) with 0, all_76_0, all_15_6, % 9.56/2.21 | | | | | | | all_61_1, simplifying with (67), (74) gives: % 9.56/2.21 | | | | | | | (77) all_76_0 = 0 % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | | BETA: splitting (75) gives: % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | | Case 1: % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | (78) ~ (all_76_0 = 0) % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | REDUCE: (77), (78) imply: % 9.56/2.21 | | | | | | | | (79) $false % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | CLOSE: (79) is inconsistent. % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | Case 2: % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | (80) ~ (all_76_1 = 0) % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | REDUCE: (76), (80) imply: % 9.56/2.21 | | | | | | | | (81) $false % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | | CLOSE: (81) is inconsistent. % 9.56/2.21 | | | | | | | | % 9.56/2.21 | | | | | | | End of split % 9.56/2.21 | | | | | | | % 9.56/2.21 | | | | | | End of split % 9.56/2.21 | | | | | | % 9.56/2.21 | | | | | End of split % 9.56/2.21 | | | | | % 9.56/2.21 | | | | End of split % 9.56/2.21 | | | | % 9.56/2.21 | | | End of split % 9.56/2.21 | | | % 9.56/2.21 | | Case 2: % 9.56/2.21 | | | % 9.56/2.21 | | | (82) ~ (all_24_1 = 0) % 9.56/2.21 | | | % 9.56/2.21 | | | BETA: splitting (32) gives: % 9.56/2.21 | | | % 9.56/2.21 | | | Case 1: % 9.56/2.21 | | | | % 9.56/2.21 | | | | (83) all_24_1 = 0 % 9.56/2.21 | | | | % 9.56/2.21 | | | | REDUCE: (82), (83) imply: % 9.56/2.21 | | | | (84) $false % 9.56/2.21 | | | | % 9.56/2.21 | | | | CLOSE: (84) is inconsistent. % 9.56/2.21 | | | | % 9.56/2.21 | | | Case 2: % 9.56/2.21 | | | | % 9.56/2.21 | | | | (85) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 9.56/2.21 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 9.56/2.21 | | | | % 9.56/2.21 | | | | DELTA: instantiating (85) with fresh symbols all_37_0, all_37_1 gives: % 9.56/2.21 | | | | (86) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 9.56/2.21 | | | | member(all_37_1, all_15_4) = 0 & $i(all_37_1) % 9.56/2.21 | | | | % 9.56/2.21 | | | | ALPHA: (86) implies: % 9.56/2.21 | | | | (87) ~ (all_37_0 = 0) % 9.56/2.21 | | | | (88) $i(all_37_1) % 9.56/2.21 | | | | (89) member(all_37_1, all_15_4) = 0 % 9.56/2.21 | | | | (90) member(all_37_1, all_15_1) = all_37_0 % 9.56/2.21 | | | | % 9.56/2.21 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4, % 9.56/2.21 | | | | simplifying with (13), (21), (88), (89) gives: % 9.56/2.21 | | | | (91) subset(all_37_1, all_15_5) = 0 % 9.56/2.21 | | | | % 9.56/2.21 | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_3, all_15_2, % 9.56/2.21 | | | | all_15_1, all_37_0, simplifying with (15), (16), (23), % 9.56/2.21 | | | | (88), (90) gives: % 9.56/2.22 | | | | (92) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 9.56/2.22 | | | | all_15_2) = v1 & member(all_37_1, all_15_3) = v0 & ( ~ (v1 = % 9.56/2.22 | | | | 0) | ~ (v0 = 0))) % 9.56/2.22 | | | | % 9.56/2.22 | | | | BETA: splitting (92) gives: % 9.56/2.22 | | | | % 9.56/2.22 | | | | Case 1: % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | (93) all_37_0 = 0 % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | REDUCE: (87), (93) imply: % 9.56/2.22 | | | | | (94) $false % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | CLOSE: (94) is inconsistent. % 9.56/2.22 | | | | | % 9.56/2.22 | | | | Case 2: % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | (95) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = v1 % 9.56/2.22 | | | | | & member(all_37_1, all_15_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 9.56/2.22 | | | | | 0))) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | DELTA: instantiating (95) with fresh symbols all_50_0, all_50_1 gives: % 9.56/2.22 | | | | | (96) member(all_37_1, all_15_2) = all_50_0 & member(all_37_1, % 9.56/2.22 | | | | | all_15_3) = all_50_1 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = % 9.56/2.22 | | | | | 0)) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | ALPHA: (96) implies: % 9.56/2.22 | | | | | (97) member(all_37_1, all_15_3) = all_50_1 % 9.56/2.22 | | | | | (98) member(all_37_1, all_15_2) = all_50_0 % 9.56/2.22 | | | | | (99) ~ (all_50_0 = 0) | ~ (all_50_1 = 0) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_7, all_15_3, % 9.56/2.22 | | | | | all_50_1, simplifying with (11), (19), (88), (97) gives: % 9.56/2.22 | | | | | (100) all_50_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, % 9.56/2.22 | | | | | all_15_7) = v0) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_2, % 9.56/2.22 | | | | | all_50_0, simplifying with (12), (20), (88), (98) gives: % 9.56/2.22 | | | | | (101) all_50_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, % 9.56/2.22 | | | | | all_15_6) = v0) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | GROUND_INST: instantiating (1) with all_37_1, all_15_5, simplifying % 9.56/2.22 | | | | | with (13), (88), (91) gives: % 9.56/2.22 | | | | | (102) ! [v0: $i] : ( ~ (member(v0, all_37_1) = 0) | ~ $i(v0) | % 9.56/2.22 | | | | | member(v0, all_15_5) = 0) % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | BETA: splitting (99) gives: % 9.56/2.22 | | | | | % 9.56/2.22 | | | | | Case 1: % 9.56/2.22 | | | | | | % 9.56/2.22 | | | | | | (103) ~ (all_50_0 = 0) % 9.56/2.22 | | | | | | % 9.56/2.22 | | | | | | BETA: splitting (101) gives: % 9.56/2.22 | | | | | | % 9.56/2.22 | | | | | | Case 1: % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | (104) all_50_0 = 0 % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | REDUCE: (103), (104) imply: % 9.56/2.22 | | | | | | | (105) $false % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | CLOSE: (105) is inconsistent. % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | Case 2: % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | (106) ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_6) % 9.56/2.22 | | | | | | | = v0) % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | DELTA: instantiating (106) with fresh symbol all_66_0 gives: % 9.56/2.22 | | | | | | | (107) ~ (all_66_0 = 0) & subset(all_37_1, all_15_6) = all_66_0 % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | ALPHA: (107) implies: % 9.56/2.22 | | | | | | | (108) ~ (all_66_0 = 0) % 9.56/2.22 | | | | | | | (109) subset(all_37_1, all_15_6) = all_66_0 % 9.56/2.22 | | | | | | | % 9.56/2.22 | | | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_6, all_66_0, % 9.56/2.22 | | | | | | | simplifying with (12), (88), (109) gives: % 9.56/2.22 | | | | | | | (110) all_66_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 9.56/2.22 | | | | | | | & member(v0, all_37_1) = 0 & member(v0, all_15_6) = v1 % 9.56/2.23 | | | | | | | & $i(v0)) % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | BETA: splitting (110) gives: % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | Case 1: % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | (111) all_66_0 = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | REDUCE: (108), (111) imply: % 9.56/2.23 | | | | | | | | (112) $false % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | CLOSE: (112) is inconsistent. % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | Case 2: % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | (113) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 9.56/2.23 | | | | | | | | all_37_1) = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | DELTA: instantiating (113) with fresh symbols all_79_0, all_79_1 % 9.56/2.23 | | | | | | | | gives: % 9.56/2.23 | | | | | | | | (114) ~ (all_79_0 = 0) & member(all_79_1, all_37_1) = 0 & % 9.56/2.23 | | | | | | | | member(all_79_1, all_15_6) = all_79_0 & $i(all_79_1) % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | ALPHA: (114) implies: % 9.56/2.23 | | | | | | | | (115) ~ (all_79_0 = 0) % 9.56/2.23 | | | | | | | | (116) $i(all_79_1) % 9.56/2.23 | | | | | | | | (117) member(all_79_1, all_15_6) = all_79_0 % 9.56/2.23 | | | | | | | | (118) member(all_79_1, all_37_1) = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | GROUND_INST: instantiating (102) with all_79_1, simplifying with % 9.56/2.23 | | | | | | | | (116), (118) gives: % 9.56/2.23 | | | | | | | | (119) member(all_79_1, all_15_5) = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | GROUND_INST: instantiating (6) with all_79_1, all_15_7, % 9.56/2.23 | | | | | | | | all_15_6, all_15_5, simplifying with (11), (12), % 9.56/2.23 | | | | | | | | (22), (116), (119) gives: % 9.56/2.23 | | | | | | | | (120) member(all_79_1, all_15_6) = 0 & member(all_79_1, % 9.56/2.23 | | | | | | | | all_15_7) = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | ALPHA: (120) implies: % 9.56/2.23 | | | | | | | | (121) member(all_79_1, all_15_6) = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | GROUND_INST: instantiating (8) with all_79_0, 0, all_15_6, % 9.56/2.23 | | | | | | | | all_79_1, simplifying with (117), (121) gives: % 9.56/2.23 | | | | | | | | (122) all_79_0 = 0 % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | REDUCE: (115), (122) imply: % 9.56/2.23 | | | | | | | | (123) $false % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | | CLOSE: (123) is inconsistent. % 9.56/2.23 | | | | | | | | % 9.56/2.23 | | | | | | | End of split % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | End of split % 9.56/2.23 | | | | | | % 9.56/2.23 | | | | | Case 2: % 9.56/2.23 | | | | | | % 9.56/2.23 | | | | | | (124) ~ (all_50_1 = 0) % 9.56/2.23 | | | | | | % 9.56/2.23 | | | | | | BETA: splitting (100) gives: % 9.56/2.23 | | | | | | % 9.56/2.23 | | | | | | Case 1: % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | (125) all_50_1 = 0 % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | REDUCE: (124), (125) imply: % 9.56/2.23 | | | | | | | (126) $false % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | CLOSE: (126) is inconsistent. % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | Case 2: % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | (127) ? [v0: int] : ( ~ (v0 = 0) & subset(all_37_1, all_15_7) % 9.56/2.23 | | | | | | | = v0) % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | DELTA: instantiating (127) with fresh symbol all_66_0 gives: % 9.56/2.23 | | | | | | | (128) ~ (all_66_0 = 0) & subset(all_37_1, all_15_7) = all_66_0 % 9.56/2.23 | | | | | | | % 9.56/2.23 | | | | | | | ALPHA: (128) implies: % 9.56/2.23 | | | | | | | (129) ~ (all_66_0 = 0) % 9.56/2.24 | | | | | | | (130) subset(all_37_1, all_15_7) = all_66_0 % 9.56/2.24 | | | | | | | % 9.56/2.24 | | | | | | | GROUND_INST: instantiating (2) with all_37_1, all_15_7, all_66_0, % 9.56/2.24 | | | | | | | simplifying with (11), (88), (130) gives: % 9.56/2.24 | | | | | | | (131) all_66_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 9.56/2.24 | | | | | | | & member(v0, all_37_1) = 0 & member(v0, all_15_7) = v1 % 9.56/2.24 | | | | | | | & $i(v0)) % 9.56/2.24 | | | | | | | % 9.56/2.24 | | | | | | | BETA: splitting (131) gives: % 9.56/2.24 | | | | | | | % 9.56/2.24 | | | | | | | Case 1: % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | (132) all_66_0 = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | REDUCE: (129), (132) imply: % 9.56/2.24 | | | | | | | | (133) $false % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | CLOSE: (133) is inconsistent. % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | Case 2: % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | (134) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 9.56/2.24 | | | | | | | | all_37_1) = 0 & member(v0, all_15_7) = v1 & $i(v0)) % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | DELTA: instantiating (134) with fresh symbols all_78_0, all_78_1 % 9.56/2.24 | | | | | | | | gives: % 9.56/2.24 | | | | | | | | (135) ~ (all_78_0 = 0) & member(all_78_1, all_37_1) = 0 & % 9.56/2.24 | | | | | | | | member(all_78_1, all_15_7) = all_78_0 & $i(all_78_1) % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | ALPHA: (135) implies: % 9.56/2.24 | | | | | | | | (136) ~ (all_78_0 = 0) % 9.56/2.24 | | | | | | | | (137) $i(all_78_1) % 9.56/2.24 | | | | | | | | (138) member(all_78_1, all_15_7) = all_78_0 % 9.56/2.24 | | | | | | | | (139) member(all_78_1, all_37_1) = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | GROUND_INST: instantiating (102) with all_78_1, simplifying with % 9.56/2.24 | | | | | | | | (137), (139) gives: % 9.56/2.24 | | | | | | | | (140) member(all_78_1, all_15_5) = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | GROUND_INST: instantiating (6) with all_78_1, all_15_7, % 9.56/2.24 | | | | | | | | all_15_6, all_15_5, simplifying with (11), (12), % 9.56/2.24 | | | | | | | | (22), (137), (140) gives: % 9.56/2.24 | | | | | | | | (141) member(all_78_1, all_15_6) = 0 & member(all_78_1, % 9.56/2.24 | | | | | | | | all_15_7) = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | ALPHA: (141) implies: % 9.56/2.24 | | | | | | | | (142) member(all_78_1, all_15_7) = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | GROUND_INST: instantiating (8) with all_78_0, 0, all_15_7, % 9.56/2.24 | | | | | | | | all_78_1, simplifying with (138), (142) gives: % 9.56/2.24 | | | | | | | | (143) all_78_0 = 0 % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | REDUCE: (136), (143) imply: % 9.56/2.24 | | | | | | | | (144) $false % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | | CLOSE: (144) is inconsistent. % 9.56/2.24 | | | | | | | | % 9.56/2.24 | | | | | | | End of split % 9.56/2.24 | | | | | | | % 9.56/2.24 | | | | | | End of split % 9.56/2.24 | | | | | | % 9.56/2.24 | | | | | End of split % 9.56/2.24 | | | | | % 9.56/2.24 | | | | End of split % 9.56/2.24 | | | | % 9.56/2.24 | | | End of split % 9.56/2.24 | | | % 9.56/2.24 | | End of split % 9.56/2.24 | | % 9.56/2.24 | End of split % 9.56/2.24 | % 9.56/2.24 End of proof % 9.56/2.24 % SZS output end Proof for theBenchmark % 9.56/2.24 % 9.56/2.24 1646ms %------------------------------------------------------------------------------