%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT053+1 : TPTP v9.3.0. Released v2.4.0. % 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:27 AM UTC 2026 % Result : Theorem 7.66s 1.80s % Output : Proof 10.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT053+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.38 % Computer : n016.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Mon Sep 7 13:27:47 UTC 2026 % 0.11/0.38 % CPUTime : % 0.11/0.40 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.64/0.74 ________ _____ % 0.64/0.74 ___ __ \_________(_)________________________________ % 0.64/0.74 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.64/0.74 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.64/0.74 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.64/0.74 % 0.64/0.74 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.64/0.74 (2023-06-19) % 0.64/0.74 % 0.64/0.74 (c) Philipp Rümmer, 2009-2023 % 0.64/0.74 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.64/0.74 Amanda Stjerna. % 0.64/0.74 Free software under BSD-3-Clause. % 0.64/0.74 % 0.64/0.74 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.64/0.74 % 0.64/0.74 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.64/0.76 Running up to 7 provers in parallel. % 0.64/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.87/1.12 Prover 1: Preprocessing ... % 2.61/1.15 Prover 4: Preprocessing ... % 3.10/1.23 Prover 6: Preprocessing ... % 3.10/1.23 Prover 2: Preprocessing ... % 3.10/1.24 Prover 3: Preprocessing ... % 3.10/1.24 Prover 0: Preprocessing ... % 3.10/1.24 Prover 5: Preprocessing ... % 4.59/1.43 Prover 5: Proving ... % 4.59/1.43 Prover 2: Proving ... % 4.59/1.48 Prover 1: Constructing countermodel ... % 5.35/1.52 Prover 3: Constructing countermodel ... % 5.35/1.58 Prover 6: Constructing countermodel ... % 6.18/1.60 Prover 4: Constructing countermodel ... % 6.93/1.74 Prover 0: Proving ... % 6.93/1.79 Prover 3: proved (1024ms) % 6.93/1.80 % 7.66/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.66/1.80 % 7.66/1.80 Prover 6: stopped % 7.66/1.80 Prover 5: stopped % 7.66/1.80 Prover 2: stopped % 7.66/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.66/1.81 Prover 0: stopped % 7.66/1.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.66/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.66/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.66/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.66/1.83 Prover 7: Preprocessing ... % 7.66/1.84 Prover 10: Preprocessing ... % 7.66/1.86 Prover 7: Warning: ignoring some quantifiers % 7.66/1.88 Prover 7: Constructing countermodel ... % 7.66/1.88 Prover 13: Preprocessing ... % 7.66/1.89 Prover 8: Preprocessing ... % 7.66/1.89 Prover 11: Preprocessing ... % 8.46/1.92 Prover 10: Warning: ignoring some quantifiers % 8.46/1.94 Prover 10: Constructing countermodel ... % 8.46/1.94 Prover 13: Warning: ignoring some quantifiers % 8.46/1.95 Prover 13: Constructing countermodel ... % 8.46/1.98 Prover 1: Found proof (size 81) % 8.46/1.98 Prover 1: proved (1207ms) % 8.46/1.98 Prover 4: stopped % 8.46/1.98 Prover 10: stopped % 8.46/1.98 Prover 13: stopped % 8.46/1.98 Prover 11: stopped % 8.46/1.99 Prover 7: stopped % 8.46/2.01 Prover 8: Warning: ignoring some quantifiers % 8.46/2.02 Prover 8: Constructing countermodel ... % 9.35/2.04 Prover 8: stopped % 9.35/2.04 % 9.35/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.35/2.04 % 9.35/2.06 % SZS output start Proof for theBenchmark % 9.35/2.06 Assumptions after simplification: % 9.35/2.06 --------------------------------- % 9.35/2.06 % 9.35/2.06 (definition_2) % 9.35/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.35/2.13 (dissimilar(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 9.35/2.13 any] : ? [v5: any] : ? [v6: any] : (organization(v0) = v4 & % 9.35/2.13 is_aligned(v0, v2) = v6 & is_aligned(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ % 9.35/2.13 (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))))) & ! [v0: $i] : ! % 9.35/2.13 [v1: $i] : ! [v2: $i] : ( ~ (dissimilar(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 9.35/2.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (organization(v0) = 0 & % 9.35/2.13 is_aligned(v0, v2) = v4 & is_aligned(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 % 9.35/2.13 = 0)) & (v4 = 0 | v3 = 0))) % 9.35/2.13 % 9.35/2.13 (lemma_7) % 9.85/2.13 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 9.85/2.13 (dissimilar(v0, v2, v1) = v4 & dissimilar(v0, v1, v2) = v3 & $i(v2) & $i(v1) & % 9.85/2.13 $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 9.85/2.13 % 9.85/2.13 (function-axioms) % 9.85/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.85/2.15 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (dissimilar(v4, v3, v2) = v1) | ~ % 9.85/2.15 (dissimilar(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.85/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.85/2.15 (is_aligned(v3, v2) = v1) | ~ (is_aligned(v3, v2) = v0)) & ! [v0: % 9.85/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.85/2.15 : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) % 9.85/2.15 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.85/2.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 9.85/2.15 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.85/2.15 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ % 9.85/2.15 (smaller_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.85/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (smaller(v3, % 9.85/2.15 v2) = v1) | ~ (smaller(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.85/2.15 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (organization(v2) = v1) % 9.85/2.15 | ~ (organization(v2) = v0)) % 9.85/2.15 % 9.85/2.15 Further assumptions not needed in the proof: % 9.85/2.15 -------------------------------------------- % 9.85/2.15 definition_greater_or_equal, definition_smaller, definition_smaller_or_equal, % 9.85/2.15 meaning_postulate_greater_comparable, meaning_postulate_greater_strict, % 9.85/2.15 meaning_postulate_greater_transitive % 9.85/2.15 % 9.85/2.15 Those formulas are unsatisfiable: % 9.85/2.15 --------------------------------- % 9.85/2.15 % 9.85/2.15 Begin of proof % 9.85/2.15 | % 9.85/2.15 | ALPHA: (definition_2) implies: % 9.85/2.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (dissimilar(v0, v1, v2) = % 9.85/2.16 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 9.85/2.16 | any] : (organization(v0) = 0 & is_aligned(v0, v2) = v4 & % 9.85/2.16 | is_aligned(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | % 9.85/2.16 | v3 = 0))) % 9.85/2.17 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.85/2.17 | (dissimilar(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.85/2.17 | ? [v4: any] : ? [v5: any] : ? [v6: any] : (organization(v0) = v4 & % 9.85/2.17 | is_aligned(v0, v2) = v6 & is_aligned(v0, v1) = v5 & ( ~ (v4 = 0) | % 9.85/2.17 | (( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))))) % 9.85/2.17 | % 9.85/2.17 | ALPHA: (function-axioms) implies: % 9.85/2.17 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.85/2.17 | (v1 = v0 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0)) % 9.85/2.17 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.85/2.17 | ! [v3: $i] : (v1 = v0 | ~ (is_aligned(v3, v2) = v1) | ~ % 9.85/2.17 | (is_aligned(v3, v2) = v0)) % 9.85/2.17 | % 9.85/2.17 | DELTA: instantiating (lemma_7) with fresh symbols all_10_0, all_10_1, % 9.85/2.17 | all_10_2, all_10_3, all_10_4 gives: % 9.85/2.18 | (5) dissimilar(all_10_4, all_10_2, all_10_3) = all_10_0 & % 9.85/2.18 | dissimilar(all_10_4, all_10_3, all_10_2) = all_10_1 & $i(all_10_2) & % 9.85/2.18 | $i(all_10_3) & $i(all_10_4) & ((all_10_0 = 0 & ~ (all_10_1 = 0)) | % 9.85/2.18 | (all_10_1 = 0 & ~ (all_10_0 = 0))) % 9.85/2.18 | % 9.85/2.18 | ALPHA: (5) implies: % 9.85/2.18 | (6) $i(all_10_4) % 9.85/2.18 | (7) $i(all_10_3) % 9.85/2.18 | (8) $i(all_10_2) % 9.85/2.18 | (9) dissimilar(all_10_4, all_10_3, all_10_2) = all_10_1 % 9.85/2.18 | (10) dissimilar(all_10_4, all_10_2, all_10_3) = all_10_0 % 9.85/2.18 | (11) (all_10_0 = 0 & ~ (all_10_1 = 0)) | (all_10_1 = 0 & ~ (all_10_0 = % 9.85/2.18 | 0)) % 9.85/2.18 | % 9.85/2.18 | GROUND_INST: instantiating (2) with all_10_4, all_10_3, all_10_2, all_10_1, % 9.85/2.19 | simplifying with (6), (7), (8), (9) gives: % 9.85/2.19 | (12) all_10_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.85/2.19 | (organization(all_10_4) = v0 & is_aligned(all_10_4, all_10_2) = v2 & % 9.85/2.19 | is_aligned(all_10_4, all_10_3) = v1 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | % 9.85/2.19 | v1 = 0) & ( ~ (v1 = 0) | v2 = 0)))) % 9.85/2.19 | % 9.85/2.19 | GROUND_INST: instantiating (2) with all_10_4, all_10_2, all_10_3, all_10_0, % 9.85/2.19 | simplifying with (6), (7), (8), (10) gives: % 9.85/2.19 | (13) all_10_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.85/2.19 | (organization(all_10_4) = v0 & is_aligned(all_10_4, all_10_2) = v1 & % 9.85/2.19 | is_aligned(all_10_4, all_10_3) = v2 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | % 9.85/2.19 | v1 = 0) & ( ~ (v1 = 0) | v2 = 0)))) % 9.85/2.19 | % 9.85/2.19 | BETA: splitting (11) gives: % 9.85/2.19 | % 9.85/2.19 | Case 1: % 9.85/2.19 | | % 9.85/2.19 | | (14) all_10_0 = 0 & ~ (all_10_1 = 0) % 9.85/2.19 | | % 9.85/2.19 | | ALPHA: (14) implies: % 9.85/2.19 | | (15) all_10_0 = 0 % 9.85/2.20 | | (16) ~ (all_10_1 = 0) % 9.85/2.20 | | % 9.85/2.20 | | REDUCE: (10), (15) imply: % 9.85/2.20 | | (17) dissimilar(all_10_4, all_10_2, all_10_3) = 0 % 9.85/2.20 | | % 10.16/2.20 | | BETA: splitting (12) gives: % 10.16/2.20 | | % 10.16/2.20 | | Case 1: % 10.16/2.20 | | | % 10.16/2.20 | | | (18) all_10_1 = 0 % 10.16/2.20 | | | % 10.16/2.20 | | | REDUCE: (16), (18) imply: % 10.16/2.20 | | | (19) $false % 10.16/2.20 | | | % 10.16/2.20 | | | CLOSE: (19) is inconsistent. % 10.16/2.20 | | | % 10.16/2.20 | | Case 2: % 10.16/2.20 | | | % 10.16/2.20 | | | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 10.16/2.20 | | | (organization(all_10_4) = v0 & is_aligned(all_10_4, all_10_2) = v2 % 10.16/2.20 | | | & is_aligned(all_10_4, all_10_3) = v1 & ( ~ (v0 = 0) | (( ~ (v2 % 10.16/2.20 | | | = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0)))) % 10.16/2.20 | | | % 10.16/2.20 | | | DELTA: instantiating (20) with fresh symbols all_23_0, all_23_1, all_23_2 % 10.16/2.20 | | | gives: % 10.16/2.20 | | | (21) organization(all_10_4) = all_23_2 & is_aligned(all_10_4, all_10_2) % 10.16/2.20 | | | = all_23_0 & is_aligned(all_10_4, all_10_3) = all_23_1 & ( ~ % 10.16/2.20 | | | (all_23_2 = 0) | (( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ % 10.16/2.20 | | | (all_23_1 = 0) | all_23_0 = 0))) % 10.16/2.20 | | | % 10.16/2.20 | | | ALPHA: (21) implies: % 10.16/2.21 | | | (22) is_aligned(all_10_4, all_10_3) = all_23_1 % 10.16/2.21 | | | (23) is_aligned(all_10_4, all_10_2) = all_23_0 % 10.16/2.21 | | | (24) organization(all_10_4) = all_23_2 % 10.16/2.21 | | | (25) ~ (all_23_2 = 0) | (( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ % 10.16/2.21 | | | (all_23_1 = 0) | all_23_0 = 0)) % 10.16/2.21 | | | % 10.16/2.21 | | | GROUND_INST: instantiating (1) with all_10_4, all_10_2, all_10_3, % 10.16/2.21 | | | simplifying with (6), (7), (8), (17) gives: % 10.16/2.21 | | | (26) ? [v0: any] : ? [v1: any] : (organization(all_10_4) = 0 & % 10.16/2.21 | | | is_aligned(all_10_4, all_10_2) = v0 & is_aligned(all_10_4, % 10.16/2.21 | | | all_10_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = % 10.16/2.21 | | | 0)) % 10.16/2.21 | | | % 10.16/2.21 | | | DELTA: instantiating (26) with fresh symbols all_30_0, all_30_1 gives: % 10.16/2.21 | | | (27) organization(all_10_4) = 0 & is_aligned(all_10_4, all_10_2) = % 10.16/2.21 | | | all_30_1 & is_aligned(all_10_4, all_10_3) = all_30_0 & ( ~ % 10.16/2.21 | | | (all_30_0 = 0) | ~ (all_30_1 = 0)) & (all_30_0 = 0 | all_30_1 = % 10.16/2.21 | | | 0) % 10.16/2.21 | | | % 10.16/2.21 | | | ALPHA: (27) implies: % 10.16/2.21 | | | (28) is_aligned(all_10_4, all_10_3) = all_30_0 % 10.16/2.21 | | | (29) is_aligned(all_10_4, all_10_2) = all_30_1 % 10.16/2.21 | | | (30) organization(all_10_4) = 0 % 10.16/2.21 | | | (31) all_30_0 = 0 | all_30_1 = 0 % 10.16/2.21 | | | (32) ~ (all_30_0 = 0) | ~ (all_30_1 = 0) % 10.16/2.21 | | | % 10.16/2.21 | | | GROUND_INST: instantiating (4) with all_23_1, all_30_0, all_10_3, % 10.16/2.22 | | | all_10_4, simplifying with (22), (28) gives: % 10.16/2.22 | | | (33) all_30_0 = all_23_1 % 10.16/2.22 | | | % 10.16/2.22 | | | GROUND_INST: instantiating (4) with all_23_0, all_30_1, all_10_2, % 10.16/2.22 | | | all_10_4, simplifying with (23), (29) gives: % 10.16/2.22 | | | (34) all_30_1 = all_23_0 % 10.16/2.22 | | | % 10.16/2.22 | | | GROUND_INST: instantiating (3) with all_23_2, 0, all_10_4, simplifying % 10.16/2.22 | | | with (24), (30) gives: % 10.16/2.22 | | | (35) all_23_2 = 0 % 10.16/2.22 | | | % 10.16/2.22 | | | BETA: splitting (25) gives: % 10.16/2.22 | | | % 10.16/2.22 | | | Case 1: % 10.16/2.22 | | | | % 10.16/2.22 | | | | (36) ~ (all_23_2 = 0) % 10.16/2.22 | | | | % 10.16/2.22 | | | | REDUCE: (35), (36) imply: % 10.16/2.22 | | | | (37) $false % 10.16/2.22 | | | | % 10.16/2.22 | | | | CLOSE: (37) is inconsistent. % 10.16/2.22 | | | | % 10.16/2.22 | | | Case 2: % 10.16/2.22 | | | | % 10.16/2.22 | | | | (38) ( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ (all_23_1 = 0) | % 10.16/2.22 | | | | all_23_0 = 0) % 10.16/2.22 | | | | % 10.16/2.22 | | | | ALPHA: (38) implies: % 10.16/2.22 | | | | (39) ~ (all_23_1 = 0) | all_23_0 = 0 % 10.16/2.22 | | | | (40) ~ (all_23_0 = 0) | all_23_1 = 0 % 10.16/2.22 | | | | % 10.16/2.22 | | | | BETA: splitting (31) gives: % 10.16/2.22 | | | | % 10.16/2.22 | | | | Case 1: % 10.16/2.22 | | | | | % 10.16/2.22 | | | | | (41) all_30_0 = 0 % 10.16/2.22 | | | | | % 10.16/2.22 | | | | | COMBINE_EQS: (33), (41) imply: % 10.16/2.22 | | | | | (42) all_23_1 = 0 % 10.16/2.22 | | | | | % 10.16/2.22 | | | | | BETA: splitting (32) gives: % 10.16/2.22 | | | | | % 10.16/2.22 | | | | | Case 1: % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | (43) ~ (all_30_0 = 0) % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | REDUCE: (41), (43) imply: % 10.16/2.22 | | | | | | (44) $false % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | CLOSE: (44) is inconsistent. % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | Case 2: % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | (45) ~ (all_30_1 = 0) % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | REDUCE: (34), (45) imply: % 10.16/2.22 | | | | | | (46) ~ (all_23_0 = 0) % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | BETA: splitting (39) gives: % 10.16/2.22 | | | | | | % 10.16/2.22 | | | | | | Case 1: % 10.16/2.22 | | | | | | | % 10.16/2.22 | | | | | | | (47) ~ (all_23_1 = 0) % 10.16/2.22 | | | | | | | % 10.16/2.22 | | | | | | | REDUCE: (42), (47) imply: % 10.16/2.22 | | | | | | | (48) $false % 10.16/2.22 | | | | | | | % 10.16/2.22 | | | | | | | CLOSE: (48) is inconsistent. % 10.16/2.22 | | | | | | | % 10.16/2.22 | | | | | | Case 2: % 10.16/2.22 | | | | | | | % 10.16/2.23 | | | | | | | (49) all_23_0 = 0 % 10.16/2.23 | | | | | | | % 10.16/2.23 | | | | | | | REDUCE: (46), (49) imply: % 10.16/2.23 | | | | | | | (50) $false % 10.16/2.23 | | | | | | | % 10.16/2.23 | | | | | | | CLOSE: (50) is inconsistent. % 10.16/2.23 | | | | | | | % 10.16/2.23 | | | | | | End of split % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | End of split % 10.16/2.23 | | | | | % 10.16/2.23 | | | | Case 2: % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | (51) all_30_1 = 0 % 10.16/2.23 | | | | | (52) ~ (all_30_0 = 0) % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | COMBINE_EQS: (34), (51) imply: % 10.16/2.23 | | | | | (53) all_23_0 = 0 % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | SIMP: (53) implies: % 10.16/2.23 | | | | | (54) all_23_0 = 0 % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | REDUCE: (33), (52) imply: % 10.16/2.23 | | | | | (55) ~ (all_23_1 = 0) % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | BETA: splitting (40) gives: % 10.16/2.23 | | | | | % 10.16/2.23 | | | | | Case 1: % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | (56) ~ (all_23_0 = 0) % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | REDUCE: (54), (56) imply: % 10.16/2.23 | | | | | | (57) $false % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | CLOSE: (57) is inconsistent. % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | Case 2: % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | (58) all_23_1 = 0 % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | REDUCE: (55), (58) imply: % 10.16/2.23 | | | | | | (59) $false % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | | CLOSE: (59) is inconsistent. % 10.16/2.23 | | | | | | % 10.16/2.23 | | | | | End of split % 10.16/2.23 | | | | | % 10.16/2.23 | | | | End of split % 10.16/2.23 | | | | % 10.16/2.23 | | | End of split % 10.16/2.23 | | | % 10.16/2.23 | | End of split % 10.16/2.23 | | % 10.16/2.23 | Case 2: % 10.16/2.23 | | % 10.16/2.23 | | (60) all_10_1 = 0 & ~ (all_10_0 = 0) % 10.16/2.23 | | % 10.16/2.23 | | ALPHA: (60) implies: % 10.16/2.23 | | (61) all_10_1 = 0 % 10.16/2.23 | | (62) ~ (all_10_0 = 0) % 10.16/2.23 | | % 10.16/2.23 | | REDUCE: (9), (61) imply: % 10.16/2.23 | | (63) dissimilar(all_10_4, all_10_3, all_10_2) = 0 % 10.16/2.23 | | % 10.16/2.23 | | BETA: splitting (13) gives: % 10.16/2.23 | | % 10.16/2.23 | | Case 1: % 10.16/2.23 | | | % 10.16/2.23 | | | (64) all_10_0 = 0 % 10.16/2.23 | | | % 10.16/2.23 | | | REDUCE: (62), (64) imply: % 10.16/2.23 | | | (65) $false % 10.16/2.23 | | | % 10.16/2.23 | | | CLOSE: (65) is inconsistent. % 10.16/2.23 | | | % 10.16/2.23 | | Case 2: % 10.16/2.23 | | | % 10.16/2.24 | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 10.16/2.24 | | | (organization(all_10_4) = v0 & is_aligned(all_10_4, all_10_2) = v1 % 10.16/2.24 | | | & is_aligned(all_10_4, all_10_3) = v2 & ( ~ (v0 = 0) | (( ~ (v2 % 10.16/2.24 | | | = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0)))) % 10.16/2.24 | | | % 10.16/2.24 | | | DELTA: instantiating (66) with fresh symbols all_23_0, all_23_1, all_23_2 % 10.16/2.24 | | | gives: % 10.16/2.24 | | | (67) organization(all_10_4) = all_23_2 & is_aligned(all_10_4, all_10_2) % 10.16/2.24 | | | = all_23_1 & is_aligned(all_10_4, all_10_3) = all_23_0 & ( ~ % 10.16/2.24 | | | (all_23_2 = 0) | (( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ % 10.16/2.24 | | | (all_23_1 = 0) | all_23_0 = 0))) % 10.16/2.24 | | | % 10.16/2.24 | | | ALPHA: (67) implies: % 10.16/2.24 | | | (68) is_aligned(all_10_4, all_10_3) = all_23_0 % 10.16/2.24 | | | (69) is_aligned(all_10_4, all_10_2) = all_23_1 % 10.16/2.24 | | | (70) organization(all_10_4) = all_23_2 % 10.16/2.24 | | | (71) ~ (all_23_2 = 0) | (( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ % 10.16/2.24 | | | (all_23_1 = 0) | all_23_0 = 0)) % 10.16/2.24 | | | % 10.16/2.24 | | | GROUND_INST: instantiating (1) with all_10_4, all_10_3, all_10_2, % 10.16/2.24 | | | simplifying with (6), (7), (8), (63) gives: % 10.16/2.24 | | | (72) ? [v0: any] : ? [v1: any] : (organization(all_10_4) = 0 & % 10.16/2.24 | | | is_aligned(all_10_4, all_10_2) = v1 & is_aligned(all_10_4, % 10.16/2.24 | | | all_10_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = % 10.16/2.24 | | | 0)) % 10.16/2.24 | | | % 10.16/2.24 | | | DELTA: instantiating (72) with fresh symbols all_30_0, all_30_1 gives: % 10.16/2.24 | | | (73) organization(all_10_4) = 0 & is_aligned(all_10_4, all_10_2) = % 10.16/2.24 | | | all_30_0 & is_aligned(all_10_4, all_10_3) = all_30_1 & ( ~ % 10.16/2.24 | | | (all_30_0 = 0) | ~ (all_30_1 = 0)) & (all_30_0 = 0 | all_30_1 = % 10.16/2.24 | | | 0) % 10.16/2.24 | | | % 10.16/2.24 | | | ALPHA: (73) implies: % 10.16/2.24 | | | (74) is_aligned(all_10_4, all_10_3) = all_30_1 % 10.16/2.24 | | | (75) is_aligned(all_10_4, all_10_2) = all_30_0 % 10.16/2.25 | | | (76) organization(all_10_4) = 0 % 10.16/2.25 | | | (77) all_30_0 = 0 | all_30_1 = 0 % 10.16/2.25 | | | (78) ~ (all_30_0 = 0) | ~ (all_30_1 = 0) % 10.16/2.25 | | | % 10.16/2.25 | | | GROUND_INST: instantiating (4) with all_23_0, all_30_1, all_10_3, % 10.16/2.25 | | | all_10_4, simplifying with (68), (74) gives: % 10.16/2.25 | | | (79) all_30_1 = all_23_0 % 10.16/2.25 | | | % 10.16/2.25 | | | GROUND_INST: instantiating (4) with all_23_1, all_30_0, all_10_2, % 10.16/2.25 | | | all_10_4, simplifying with (69), (75) gives: % 10.16/2.25 | | | (80) all_30_0 = all_23_1 % 10.16/2.25 | | | % 10.16/2.25 | | | GROUND_INST: instantiating (3) with all_23_2, 0, all_10_4, simplifying % 10.16/2.25 | | | with (70), (76) gives: % 10.16/2.25 | | | (81) all_23_2 = 0 % 10.16/2.25 | | | % 10.16/2.25 | | | BETA: splitting (71) gives: % 10.16/2.25 | | | % 10.16/2.25 | | | Case 1: % 10.16/2.25 | | | | % 10.16/2.25 | | | | (82) ~ (all_23_2 = 0) % 10.16/2.25 | | | | % 10.16/2.25 | | | | REDUCE: (81), (82) imply: % 10.16/2.25 | | | | (83) $false % 10.16/2.25 | | | | % 10.16/2.25 | | | | CLOSE: (83) is inconsistent. % 10.16/2.25 | | | | % 10.16/2.25 | | | Case 2: % 10.16/2.25 | | | | % 10.16/2.25 | | | | (84) ( ~ (all_23_0 = 0) | all_23_1 = 0) & ( ~ (all_23_1 = 0) | % 10.16/2.25 | | | | all_23_0 = 0) % 10.16/2.25 | | | | % 10.16/2.25 | | | | ALPHA: (84) implies: % 10.16/2.25 | | | | (85) ~ (all_23_1 = 0) | all_23_0 = 0 % 10.16/2.25 | | | | (86) ~ (all_23_0 = 0) | all_23_1 = 0 % 10.16/2.25 | | | | % 10.16/2.25 | | | | BETA: splitting (77) gives: % 10.16/2.25 | | | | % 10.16/2.25 | | | | Case 1: % 10.16/2.25 | | | | | % 10.16/2.25 | | | | | (87) all_30_0 = 0 % 10.16/2.25 | | | | | % 10.16/2.25 | | | | | COMBINE_EQS: (80), (87) imply: % 10.16/2.25 | | | | | (88) all_23_1 = 0 % 10.16/2.25 | | | | | % 10.16/2.25 | | | | | BETA: splitting (78) gives: % 10.16/2.25 | | | | | % 10.16/2.25 | | | | | Case 1: % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | (89) ~ (all_30_0 = 0) % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | REDUCE: (87), (89) imply: % 10.16/2.25 | | | | | | (90) $false % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | CLOSE: (90) is inconsistent. % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | Case 2: % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | (91) ~ (all_30_1 = 0) % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | REDUCE: (79), (91) imply: % 10.16/2.25 | | | | | | (92) ~ (all_23_0 = 0) % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | BETA: splitting (85) gives: % 10.16/2.25 | | | | | | % 10.16/2.25 | | | | | | Case 1: % 10.16/2.25 | | | | | | | % 10.16/2.26 | | | | | | | (93) ~ (all_23_1 = 0) % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | | REDUCE: (88), (93) imply: % 10.16/2.26 | | | | | | | (94) $false % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | | CLOSE: (94) is inconsistent. % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | Case 2: % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | | (95) all_23_0 = 0 % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | | REDUCE: (92), (95) imply: % 10.16/2.26 | | | | | | | (96) $false % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | | CLOSE: (96) is inconsistent. % 10.16/2.26 | | | | | | | % 10.16/2.26 | | | | | | End of split % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | End of split % 10.16/2.26 | | | | | % 10.16/2.26 | | | | Case 2: % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | (97) all_30_1 = 0 % 10.16/2.26 | | | | | (98) ~ (all_30_0 = 0) % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | COMBINE_EQS: (79), (97) imply: % 10.16/2.26 | | | | | (99) all_23_0 = 0 % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | SIMP: (99) implies: % 10.16/2.26 | | | | | (100) all_23_0 = 0 % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | REDUCE: (80), (98) imply: % 10.16/2.26 | | | | | (101) ~ (all_23_1 = 0) % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | BETA: splitting (86) gives: % 10.16/2.26 | | | | | % 10.16/2.26 | | | | | Case 1: % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | (102) ~ (all_23_0 = 0) % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | REDUCE: (100), (102) imply: % 10.16/2.26 | | | | | | (103) $false % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | CLOSE: (103) is inconsistent. % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | Case 2: % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | (104) all_23_1 = 0 % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | REDUCE: (101), (104) imply: % 10.16/2.26 | | | | | | (105) $false % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | | CLOSE: (105) is inconsistent. % 10.16/2.26 | | | | | | % 10.16/2.26 | | | | | End of split % 10.16/2.26 | | | | | % 10.16/2.26 | | | | End of split % 10.16/2.26 | | | | % 10.16/2.26 | | | End of split % 10.16/2.26 | | | % 10.16/2.26 | | End of split % 10.16/2.26 | | % 10.16/2.26 | End of split % 10.16/2.26 | % 10.16/2.26 End of proof % 10.16/2.26 % SZS output end Proof for theBenchmark % 10.16/2.26 % 10.16/2.26 1521ms %------------------------------------------------------------------------------