%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRA014+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 00:04:30 EDT 2023 % Result : Theorem 14.80s 2.83s % Output : Proof 16.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GRA014+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n018.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Sun Aug 27 04:03:30 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.72/0.96 Prover 1: Preprocessing ... % 1.72/0.96 Prover 4: Preprocessing ... % 2.16/1.00 Prover 3: Preprocessing ... % 2.16/1.00 Prover 2: Preprocessing ... % 2.16/1.00 Prover 0: Preprocessing ... % 2.16/1.00 Prover 5: Preprocessing ... % 2.16/1.00 Prover 6: Preprocessing ... % 2.96/1.10 Prover 5: Constructing countermodel ... % 3.24/1.14 Prover 6: Constructing countermodel ... % 3.24/1.14 Prover 2: Constructing countermodel ... % 3.24/1.14 Prover 1: Constructing countermodel ... % 3.24/1.14 Prover 3: Constructing countermodel ... % 3.24/1.20 Prover 4: Constructing countermodel ... % 3.73/1.22 Prover 1: gave up % 3.73/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.73/1.23 Prover 3: gave up % 3.73/1.23 Prover 0: Proving ... % 3.73/1.24 Prover 7: Preprocessing ... % 3.73/1.24 Prover 6: gave up % 3.73/1.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.73/1.25 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 3.73/1.26 Prover 9: Preprocessing ... % 3.73/1.27 Prover 7: Constructing countermodel ... % 4.17/1.27 Prover 8: Preprocessing ... % 4.17/1.34 Prover 8: Warning: ignoring some quantifiers % 4.17/1.34 Prover 8: Constructing countermodel ... % 4.83/1.37 Prover 8: gave up % 4.83/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.03/1.39 Prover 10: Preprocessing ... % 5.03/1.40 Prover 9: Constructing countermodel ... % 5.03/1.41 Prover 10: Constructing countermodel ... % 14.80/2.82 Prover 10: Found proof (size 1220) % 14.80/2.82 Prover 10: proved (1449ms) % 14.80/2.83 Prover 2: stopped % 14.80/2.83 Prover 7: stopped % 14.80/2.83 Prover 5: stopped % 14.80/2.83 Prover 4: stopped % 14.80/2.83 Prover 0: stopped % 14.80/2.83 Prover 9: stopped % 14.80/2.83 % 14.80/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.80/2.83 % 14.80/2.86 % SZS output start Proof for theBenchmark % 14.80/2.87 Assumptions after simplification: % 14.80/2.87 --------------------------------- % 14.80/2.87 % 14.80/2.87 (goal_to_be_proved) % 14.80/2.87 ~ goal % 14.80/2.88 % 14.80/2.88 (green_clique) % 14.80/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.80/2.88 ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | goal) % 14.80/2.88 % 14.80/2.88 (less_than_transitive) % 14.80/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.80/2.88 ~ less_than(v1, v2) | ~ less_than(v0, v1) | less_than(v0, v2)) % 14.80/2.88 % 14.80/2.88 (ordering) % 14.80/2.88 $i(n6) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & less_than(n5, n6) & % 14.80/2.88 less_than(n4, n5) & less_than(n3, n4) & less_than(n2, n3) & less_than(n1, n2) % 14.80/2.88 % 14.80/2.88 (partition) % 14.80/2.88 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ less_than(v0, v1) | % 14.80/2.88 green(v0, v1) | red(v0, v1)) % 14.80/2.88 % 14.80/2.88 (red_clique) % 14.80/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.80/2.88 ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 14.80/2.88 % 14.80/2.88 Those formulas are unsatisfiable: % 14.80/2.88 --------------------------------- % 14.80/2.88 % 14.80/2.88 Begin of proof % 14.80/2.88 | % 14.80/2.89 | ALPHA: (ordering) implies: % 14.80/2.89 | (1) less_than(n1, n2) % 14.80/2.89 | (2) less_than(n2, n3) % 14.80/2.89 | (3) less_than(n3, n4) % 14.80/2.89 | (4) less_than(n4, n5) % 14.80/2.89 | (5) less_than(n5, n6) % 14.80/2.89 | (6) $i(n1) % 14.80/2.89 | (7) $i(n2) % 14.80/2.89 | (8) $i(n3) % 14.80/2.89 | (9) $i(n4) % 14.80/2.89 | (10) $i(n5) % 14.80/2.89 | (11) $i(n6) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (partition) with n1, n2, simplifying with (1), (6), % 14.80/2.89 | (7) gives: % 14.80/2.89 | (12) green(n1, n2) | red(n1, n2) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (less_than_transitive) with n1, n2, n3, simplifying % 14.80/2.89 | with (1), (2), (6), (7), (8) gives: % 14.80/2.89 | (13) less_than(n1, n3) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (partition) with n2, n3, simplifying with (2), (7), % 14.80/2.89 | (8) gives: % 14.80/2.89 | (14) green(n2, n3) | red(n2, n3) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (less_than_transitive) with n2, n3, n4, simplifying % 14.80/2.89 | with (2), (3), (7), (8), (9) gives: % 14.80/2.89 | (15) less_than(n2, n4) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (partition) with n3, n4, simplifying with (3), (8), % 14.80/2.89 | (9) gives: % 14.80/2.89 | (16) green(n3, n4) | red(n3, n4) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (less_than_transitive) with n3, n4, n5, simplifying % 14.80/2.89 | with (3), (4), (8), (9), (10) gives: % 14.80/2.89 | (17) less_than(n3, n5) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (partition) with n4, n5, simplifying with (4), (9), % 14.80/2.89 | (10) gives: % 14.80/2.89 | (18) green(n4, n5) | red(n4, n5) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (less_than_transitive) with n4, n5, n6, simplifying % 14.80/2.89 | with (4), (5), (9), (10), (11) gives: % 14.80/2.89 | (19) less_than(n4, n6) % 14.80/2.89 | % 14.80/2.89 | GROUND_INST: instantiating (partition) with n5, n6, simplifying with (5), % 14.80/2.89 | (10), (11) gives: % 14.80/2.90 | (20) green(n5, n6) | red(n5, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n1, n3, simplifying with (6), (8), % 14.80/2.90 | (13) gives: % 14.80/2.90 | (21) green(n1, n3) | red(n1, n3) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n1, n2, n4, simplifying % 14.80/2.90 | with (1), (6), (7), (9), (15) gives: % 14.80/2.90 | (22) less_than(n1, n4) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n2, n4, simplifying with (7), (9), % 14.80/2.90 | (15) gives: % 14.80/2.90 | (23) green(n2, n4) | red(n2, n4) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n2, n3, n5, simplifying % 14.80/2.90 | with (2), (7), (8), (10), (17) gives: % 14.80/2.90 | (24) less_than(n2, n5) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n1, n3, n5, simplifying % 14.80/2.90 | with (6), (8), (10), (13), (17) gives: % 14.80/2.90 | (25) less_than(n1, n5) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n3, n5, simplifying with (8), % 14.80/2.90 | (10), (17) gives: % 14.80/2.90 | (26) green(n3, n5) | red(n3, n5) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n3, n4, n6, simplifying % 14.80/2.90 | with (3), (8), (9), (11), (19) gives: % 14.80/2.90 | (27) less_than(n3, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n2, n4, n6, simplifying % 14.80/2.90 | with (7), (9), (11), (15), (19) gives: % 14.80/2.90 | (28) less_than(n2, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n4, n6, simplifying with (9), % 14.80/2.90 | (11), (19) gives: % 14.80/2.90 | (29) green(n4, n6) | red(n4, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n1, n4, simplifying with (6), (9), % 14.80/2.90 | (22) gives: % 14.80/2.90 | (30) green(n1, n4) | red(n1, n4) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n1, n5, simplifying with (6), % 14.80/2.90 | (10), (25) gives: % 14.80/2.90 | (31) green(n1, n5) | red(n1, n5) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n2, n5, simplifying with (7), % 14.80/2.90 | (10), (24) gives: % 14.80/2.90 | (32) green(n2, n5) | red(n2, n5) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n2, n6, simplifying with (7), % 14.80/2.90 | (11), (28) gives: % 14.80/2.90 | (33) green(n2, n6) | red(n2, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (less_than_transitive) with n1, n3, n6, simplifying % 14.80/2.90 | with (6), (8), (11), (13), (27) gives: % 14.80/2.90 | (34) less_than(n1, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n3, n6, simplifying with (8), % 14.80/2.90 | (11), (27) gives: % 14.80/2.90 | (35) green(n3, n6) | red(n3, n6) % 14.80/2.90 | % 14.80/2.90 | GROUND_INST: instantiating (partition) with n1, n6, simplifying with (6), % 14.80/2.90 | (11), (34) gives: % 14.80/2.91 | (36) green(n1, n6) | red(n1, n6) % 14.80/2.91 | % 14.80/2.91 | BETA: splitting (18) gives: % 14.80/2.91 | % 14.80/2.91 | Case 1: % 14.80/2.91 | | % 14.80/2.91 | | (37) green(n4, n5) % 14.80/2.91 | | % 14.80/2.91 | | BETA: splitting (20) gives: % 14.80/2.91 | | % 14.80/2.91 | | Case 1: % 14.80/2.91 | | | % 14.80/2.91 | | | (38) green(n5, n6) % 14.80/2.91 | | | % 14.80/2.91 | | | BETA: splitting (16) gives: % 14.80/2.91 | | | % 14.80/2.91 | | | Case 1: % 14.80/2.91 | | | | % 14.80/2.91 | | | | (39) green(n3, n4) % 14.80/2.91 | | | | % 14.80/2.91 | | | | BETA: splitting (14) gives: % 14.80/2.91 | | | | % 14.80/2.91 | | | | Case 1: % 14.80/2.91 | | | | | % 14.80/2.91 | | | | | (40) green(n2, n3) % 14.80/2.91 | | | | | % 14.80/2.91 | | | | | BETA: splitting (12) gives: % 14.80/2.91 | | | | | % 14.80/2.91 | | | | | Case 1: % 14.80/2.91 | | | | | | % 14.80/2.91 | | | | | | (41) green(n1, n2) % 14.80/2.91 | | | | | | % 14.80/2.91 | | | | | | BETA: splitting (21) gives: % 14.80/2.91 | | | | | | % 14.80/2.91 | | | | | | Case 1: % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | (42) green(n1, n3) % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 14.80/2.91 | | | | | | | simplifying with (6), (7), (8), (40), (41), (42), % 14.80/2.91 | | | | | | | (goal_to_be_proved) gives: % 14.80/2.91 | | | | | | | (43) $false % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | CLOSE: (43) is inconsistent. % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | Case 2: % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | (44) red(n1, n3) % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | BETA: splitting (29) gives: % 14.80/2.91 | | | | | | | % 14.80/2.91 | | | | | | | Case 1: % 14.80/2.91 | | | | | | | | % 14.80/2.91 | | | | | | | | (45) green(n4, n6) % 14.80/2.91 | | | | | | | | % 14.80/2.91 | | | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 14.80/2.91 | | | | | | | | simplifying with (9), (10), (11), (37), (38), (45), % 14.80/2.91 | | | | | | | | (goal_to_be_proved) gives: % 14.80/2.91 | | | | | | | | (46) $false % 14.80/2.91 | | | | | | | | % 14.80/2.91 | | | | | | | | CLOSE: (46) is inconsistent. % 14.80/2.91 | | | | | | | | % 14.80/2.91 | | | | | | | Case 2: % 14.80/2.91 | | | | | | | | % 14.80/2.91 | | | | | | | | (47) red(n4, n6) % 14.80/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (23), (33), (35), (36), % 15.27/2.91 | | | | | | | | (39), (40), (41), (44), (47), (goal_to_be_proved), % 15.27/2.91 | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.91 | | | | | | | | sub-proof #35. % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | End of split % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | End of split % 15.27/2.91 | | | | | | % 15.27/2.91 | | | | | Case 2: % 15.27/2.91 | | | | | | % 15.27/2.91 | | | | | | (48) red(n1, n2) % 15.27/2.91 | | | | | | % 15.27/2.91 | | | | | | BETA: splitting (29) gives: % 15.27/2.91 | | | | | | % 15.27/2.91 | | | | | | Case 1: % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | (49) green(n4, n6) % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.91 | | | | | | | simplifying with (9), (10), (11), (37), (38), (49), % 15.27/2.91 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.91 | | | | | | | (50) $false % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | CLOSE: (50) is inconsistent. % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | Case 2: % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | (51) red(n4, n6) % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | BETA: splitting (23) gives: % 15.27/2.91 | | | | | | | % 15.27/2.91 | | | | | | | Case 1: % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | | (52) green(n2, n4) % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.91 | | | | | | | | simplifying with (7), (8), (9), (39), (40), (52), % 15.27/2.91 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.91 | | | | | | | | (53) $false % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | | CLOSE: (53) is inconsistent. % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | Case 2: % 15.27/2.91 | | | | | | | | % 15.27/2.91 | | | | | | | | (54) red(n2, n4) % 15.27/2.91 | | | | | | | | % 15.27/2.92 | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (11), (30), (31), (32), (33), % 15.27/2.92 | | | | | | | | (37), (38), (48), (51), (54), (goal_to_be_proved), % 15.27/2.92 | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.92 | | | | | | | | sub-proof #33. % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | End of split % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | End of split % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | End of split % 15.27/2.92 | | | | | % 15.27/2.92 | | | | Case 2: % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | (55) red(n2, n3) % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | BETA: splitting (29) gives: % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | Case 1: % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | (56) green(n4, n6) % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.92 | | | | | | simplifying with (9), (10), (11), (37), (38), (56), % 15.27/2.92 | | | | | | (goal_to_be_proved) gives: % 15.27/2.92 | | | | | | (57) $false % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | CLOSE: (57) is inconsistent. % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | Case 2: % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | (58) red(n4, n6) % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | BETA: splitting (26) gives: % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | Case 1: % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | (59) green(n3, n5) % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.92 | | | | | | | simplifying with (8), (9), (10), (37), (39), (59), % 15.27/2.92 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.92 | | | | | | | (60) $false % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | CLOSE: (60) is inconsistent. % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | Case 2: % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | (61) red(n3, n5) % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (23), (32), (33), (37), % 15.27/2.92 | | | | | | | (38), (55), (58), (61), (goal_to_be_proved), % 15.27/2.92 | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.92 | | | | | | | sub-proof #30. % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | End of split % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | End of split % 15.27/2.92 | | | | | % 15.27/2.92 | | | | End of split % 15.27/2.92 | | | | % 15.27/2.92 | | | Case 2: % 15.27/2.92 | | | | % 15.27/2.92 | | | | (62) red(n3, n4) % 15.27/2.92 | | | | % 15.27/2.92 | | | | BETA: splitting (14) gives: % 15.27/2.92 | | | | % 15.27/2.92 | | | | Case 1: % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | (63) green(n2, n3) % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | BETA: splitting (12) gives: % 15.27/2.92 | | | | | % 15.27/2.92 | | | | | Case 1: % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | (64) green(n1, n2) % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | BETA: splitting (21) gives: % 15.27/2.92 | | | | | | % 15.27/2.92 | | | | | | Case 1: % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | (65) green(n1, n3) % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 15.27/2.92 | | | | | | | simplifying with (6), (7), (8), (63), (64), (65), % 15.27/2.92 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.92 | | | | | | | (66) $false % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | CLOSE: (66) is inconsistent. % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | Case 2: % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | (67) red(n1, n3) % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | BETA: splitting (29) gives: % 15.27/2.92 | | | | | | | % 15.27/2.92 | | | | | | | Case 1: % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | (68) green(n4, n6) % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.92 | | | | | | | | simplifying with (9), (10), (11), (37), (38), (68), % 15.27/2.92 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.92 | | | | | | | | (69) $false % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | CLOSE: (69) is inconsistent. % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | Case 2: % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | (70) red(n4, n6) % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | BETA: splitting (26) gives: % 15.27/2.92 | | | | | | | | % 15.27/2.92 | | | | | | | | Case 1: % 15.27/2.92 | | | | | | | | | % 15.27/2.92 | | | | | | | | | (71) green(n3, n5) % 15.27/2.92 | | | | | | | | | % 15.27/2.92 | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (38), (62), (70), (71), % 15.27/2.92 | | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) % 15.27/2.92 | | | | | | | | | are inconsistent by sub-proof #29. % 15.27/2.92 | | | | | | | | | % 15.27/2.92 | | | | | | | | Case 2: % 15.27/2.92 | | | | | | | | | % 15.27/2.92 | | | | | | | | | (72) red(n3, n5) % 15.27/2.92 | | | | | | | | | % 15.27/2.93 | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (31), (37), (62), (67), % 15.27/2.93 | | | | | | | | | (72), (goal_to_be_proved), (green_clique), % 15.27/2.93 | | | | | | | | | (red_clique) are inconsistent by sub-proof #27. % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | End of split % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | End of split % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | End of split % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | Case 2: % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | (73) red(n1, n2) % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | BETA: splitting (21) gives: % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | Case 1: % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | (74) green(n1, n3) % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | BETA: splitting (29) gives: % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | Case 1: % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | (75) green(n4, n6) % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.93 | | | | | | | | simplifying with (9), (10), (11), (37), (38), (75), % 15.27/2.93 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.93 | | | | | | | | (76) $false % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | CLOSE: (76) is inconsistent. % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | Case 2: % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | (77) red(n4, n6) % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (33), (35), (36), (62), % 15.27/2.93 | | | | | | | | (63), (73), (74), (77), (goal_to_be_proved), % 15.27/2.93 | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.93 | | | | | | | | sub-proof #24. % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | End of split % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | Case 2: % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | (78) red(n1, n3) % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | BETA: splitting (29) gives: % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | | Case 1: % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | (79) green(n4, n6) % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.93 | | | | | | | | simplifying with (9), (10), (11), (37), (38), (79), % 15.27/2.93 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.93 | | | | | | | | (80) $false % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | CLOSE: (80) is inconsistent. % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | Case 2: % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | (81) red(n4, n6) % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | | Case 1: % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | | (82) green(n2, n4) % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (30), (31), (32), (37), % 15.27/2.93 | | | | | | | | | (62), (73), (78), (82), (goal_to_be_proved), % 15.27/2.93 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.93 | | | | | | | | | sub-proof #23. % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | Case 2: % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | | (83) red(n2, n4) % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (11), (30), (31), (32), (33), % 15.27/2.93 | | | | | | | | | (37), (38), (73), (81), (83), (goal_to_be_proved), % 15.27/2.93 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.93 | | | | | | | | | sub-proof #33. % 15.27/2.93 | | | | | | | | | % 15.27/2.93 | | | | | | | | End of split % 15.27/2.93 | | | | | | | | % 15.27/2.93 | | | | | | | End of split % 15.27/2.93 | | | | | | | % 15.27/2.93 | | | | | | End of split % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | End of split % 15.27/2.93 | | | | | % 15.27/2.93 | | | | Case 2: % 15.27/2.93 | | | | | % 15.27/2.93 | | | | | (84) red(n2, n3) % 15.27/2.93 | | | | | % 15.27/2.93 | | | | | BETA: splitting (29) gives: % 15.27/2.93 | | | | | % 15.27/2.93 | | | | | Case 1: % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | (85) green(n4, n6) % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | GROUND_INST: instantiating (green_clique) with n4, n5, n6, % 15.27/2.93 | | | | | | simplifying with (9), (10), (11), (37), (38), (85), % 15.27/2.93 | | | | | | (goal_to_be_proved) gives: % 15.27/2.93 | | | | | | (86) $false % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | | CLOSE: (86) is inconsistent. % 15.27/2.93 | | | | | | % 15.27/2.93 | | | | | Case 2: % 15.27/2.93 | | | | | | % 15.27/2.94 | | | | | | (87) red(n4, n6) % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | | BETA: splitting (26) gives: % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | | Case 1: % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | (88) green(n3, n5) % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (38), (62), (87), (88), % 15.27/2.94 | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 15.27/2.94 | | | | | | | inconsistent by sub-proof #29. % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | Case 2: % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | (89) red(n3, n5) % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (23), (32), (33), (37), % 15.27/2.94 | | | | | | | (38), (84), (87), (89), (goal_to_be_proved), % 15.27/2.94 | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.94 | | | | | | | sub-proof #30. % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | End of split % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | End of split % 15.27/2.94 | | | | | % 15.27/2.94 | | | | End of split % 15.27/2.94 | | | | % 15.27/2.94 | | | End of split % 15.27/2.94 | | | % 15.27/2.94 | | Case 2: % 15.27/2.94 | | | % 15.27/2.94 | | | (90) red(n5, n6) % 15.27/2.94 | | | % 15.27/2.94 | | | BETA: splitting (16) gives: % 15.27/2.94 | | | % 15.27/2.94 | | | Case 1: % 15.27/2.94 | | | | % 15.27/2.94 | | | | (91) green(n3, n4) % 15.27/2.94 | | | | % 15.27/2.94 | | | | BETA: splitting (14) gives: % 15.27/2.94 | | | | % 15.27/2.94 | | | | Case 1: % 15.27/2.94 | | | | | % 15.27/2.94 | | | | | (92) green(n2, n3) % 15.27/2.94 | | | | | % 15.27/2.94 | | | | | BETA: splitting (12) gives: % 15.27/2.94 | | | | | % 15.27/2.94 | | | | | Case 1: % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | | (93) green(n1, n2) % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | | BETA: splitting (21) gives: % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | | Case 1: % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | (94) green(n1, n3) % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 15.27/2.94 | | | | | | | simplifying with (6), (7), (8), (92), (93), (94), % 15.27/2.94 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.94 | | | | | | | (95) $false % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | CLOSE: (95) is inconsistent. % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | Case 2: % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | (96) red(n1, n3) % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | BETA: splitting (29) gives: % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | | Case 1: % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | | (97) green(n4, n6) % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | | BETA: splitting (26) gives: % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | | Case 1: % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | | (98) green(n3, n5) % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (32), (33), (35), (36), % 15.27/2.94 | | | | | | | | | (90), (92), (93), (96), (98), (goal_to_be_proved), % 15.27/2.94 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.94 | | | | | | | | | sub-proof #21. % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | Case 2: % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | | (99) red(n3, n5) % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (90), (91), (97), (99), % 15.27/2.94 | | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) % 15.27/2.94 | | | | | | | | | are inconsistent by sub-proof #20. % 15.27/2.94 | | | | | | | | | % 15.27/2.94 | | | | | | | | End of split % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | Case 2: % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | | (100) red(n4, n6) % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (23), (33), (35), (36), % 15.27/2.94 | | | | | | | | (91), (92), (93), (96), (100), (goal_to_be_proved), % 15.27/2.94 | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.94 | | | | | | | | sub-proof #35. % 15.27/2.94 | | | | | | | | % 15.27/2.94 | | | | | | | End of split % 15.27/2.94 | | | | | | | % 15.27/2.94 | | | | | | End of split % 15.27/2.94 | | | | | | % 15.27/2.94 | | | | | Case 2: % 15.27/2.94 | | | | | | % 15.27/2.95 | | | | | | (101) red(n1, n2) % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | | BETA: splitting (29) gives: % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | | Case 1: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | (102) green(n4, n6) % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | BETA: splitting (26) gives: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (103) green(n3, n5) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (104) green(n2, n4) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (32), (33), (37), (90), % 15.27/2.95 | | | | | | | | | (102), (104), (goal_to_be_proved), (green_clique), % 15.27/2.95 | | | | | | | | | (red_clique) are inconsistent by sub-proof #18. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (105) red(n2, n4) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (30), (31), (32), (37), % 15.27/2.95 | | | | | | | | | (92), (101), (103), (105), (goal_to_be_proved), % 15.27/2.95 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.95 | | | | | | | | | sub-proof #17. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | End of split % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (106) red(n3, n5) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (90), (91), (102), (106), % 15.27/2.95 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 15.27/2.95 | | | | | | | | inconsistent by sub-proof #20. % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | End of split % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | Case 2: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | (107) red(n4, n6) % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | BETA: splitting (26) gives: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (108) green(n3, n5) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.95 | | | | | | | | simplifying with (8), (9), (10), (37), (91), (108), % 15.27/2.95 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | (109) $false % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | CLOSE: (109) is inconsistent. % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (110) red(n3, n5) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (111) green(n2, n4) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.95 | | | | | | | | | simplifying with (7), (8), (9), (91), (92), (111), % 15.27/2.95 | | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | | (112) $false % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | CLOSE: (112) is inconsistent. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (113) red(n2, n4) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | BETA: splitting (35) gives: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | (114) green(n3, n6) % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | REF_CLOSE: (7), (8), (9), (11), (33), (92), (107), (113), % 15.27/2.95 | | | | | | | | | | (114), (goal_to_be_proved), (green_clique), % 15.27/2.95 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #37. % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | (115) red(n3, n6) % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n5, n6, % 15.27/2.95 | | | | | | | | | | simplifying with (8), (10), (11), (90), (110), % 15.27/2.95 | | | | | | | | | | (115), (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | | | (116) $false % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | CLOSE: (116) is inconsistent. % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | End of split % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | End of split % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | End of split % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | End of split % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | End of split % 15.27/2.95 | | | | | % 15.27/2.95 | | | | Case 2: % 15.27/2.95 | | | | | % 15.27/2.95 | | | | | (117) red(n2, n3) % 15.27/2.95 | | | | | % 15.27/2.95 | | | | | BETA: splitting (12) gives: % 15.27/2.95 | | | | | % 15.27/2.95 | | | | | Case 1: % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | | (118) green(n1, n2) % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | | BETA: splitting (21) gives: % 15.27/2.95 | | | | | | % 15.27/2.95 | | | | | | Case 1: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | (119) green(n1, n3) % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | BETA: splitting (29) gives: % 15.27/2.95 | | | | | | | % 15.27/2.95 | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (120) green(n4, n6) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | BETA: splitting (26) gives: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (121) green(n3, n5) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.95 | | | | | | | | | simplifying with (8), (9), (10), (37), (91), % 15.27/2.95 | | | | | | | | | (121), (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | | (122) $false % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | CLOSE: (122) is inconsistent. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (123) red(n3, n5) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (90), (91), (120), % 15.27/2.95 | | | | | | | | | (123), (goal_to_be_proved), (green_clique), % 15.27/2.95 | | | | | | | | | (red_clique) are inconsistent by sub-proof #20. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | End of split % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | (124) red(n4, n6) % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | BETA: splitting (26) gives: % 15.27/2.95 | | | | | | | | % 15.27/2.95 | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (125) green(n3, n5) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.95 | | | | | | | | | simplifying with (8), (9), (10), (37), (91), % 15.27/2.95 | | | | | | | | | (125), (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | | (126) $false % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | CLOSE: (126) is inconsistent. % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | (127) red(n3, n5) % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | BETA: splitting (23) gives: % 15.27/2.95 | | | | | | | | | % 15.27/2.95 | | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | (128) green(n2, n4) % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (32), (37), (117), (127), % 15.27/2.95 | | | | | | | | | | (128), (goal_to_be_proved), (green_clique), % 15.27/2.95 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #32. % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | (129) red(n2, n4) % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | BETA: splitting (33) gives: % 15.27/2.95 | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | (130) green(n2, n6) % 15.27/2.95 | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | BETA: splitting (30) gives: % 15.27/2.95 | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | Case 1: % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | | (131) green(n1, n4) % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n3, n4, % 15.27/2.95 | | | | | | | | | | | | simplifying with (6), (8), (9), (91), (119), % 15.27/2.95 | | | | | | | | | | | | (131), (goal_to_be_proved) gives: % 15.27/2.95 | | | | | | | | | | | | (132) $false % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | Case 2: % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.95 | | | | | | | | | | | | (133) red(n1, n4) % 15.27/2.95 | | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (36), (118), (124), (130), % 15.27/2.96 | | | | | | | | | | | | (133), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | | | | | (red_clique) are inconsistent by sub-proof #16. % 15.27/2.96 | | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | | End of split % 15.27/2.96 | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | | (134) red(n2, n6) % 15.27/2.96 | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n4, n6, % 15.27/2.96 | | | | | | | | | | | simplifying with (7), (9), (11), (124), (129), % 15.27/2.96 | | | | | | | | | | | (134), (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | | | | | (135) $false % 15.27/2.96 | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | | CLOSE: (135) is inconsistent. % 15.27/2.96 | | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | End of split % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | End of split % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | End of split % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | End of split % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | Case 2: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (136) red(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | BETA: splitting (26) gives: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (137) green(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.96 | | | | | | | | simplifying with (8), (9), (10), (37), (91), (137), % 15.27/2.96 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | | (138) $false % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | CLOSE: (138) is inconsistent. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (139) red(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (31), (32), (117), (118), (136), % 15.27/2.96 | | | | | | | | (139), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | (red_clique) are inconsistent by sub-proof #14. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | End of split % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | End of split % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | Case 2: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | (140) red(n1, n2) % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | BETA: splitting (21) gives: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | Case 1: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (141) green(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | BETA: splitting (26) gives: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (142) green(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n5, % 15.27/2.96 | | | | | | | | simplifying with (8), (9), (10), (37), (91), (142), % 15.27/2.96 | | | | | | | | (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | | (143) $false % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | CLOSE: (143) is inconsistent. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (144) red(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (145) green(n2, n4) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (32), (37), (117), (144), % 15.27/2.96 | | | | | | | | | (145), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | | (red_clique) are inconsistent by sub-proof #32. % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (146) red(n2, n4) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (30), (91), (140), (141), % 15.27/2.96 | | | | | | | | | (146), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | | (red_clique) are inconsistent by sub-proof #13. % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | End of split % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | End of split % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | Case 2: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (147) red(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 15.27/2.96 | | | | | | | simplifying with (6), (7), (8), (117), (140), (147), % 15.27/2.96 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | (148) $false % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | CLOSE: (148) is inconsistent. % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | End of split % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | End of split % 15.27/2.96 | | | | | % 15.27/2.96 | | | | End of split % 15.27/2.96 | | | | % 15.27/2.96 | | | Case 2: % 15.27/2.96 | | | | % 15.27/2.96 | | | | (149) red(n3, n4) % 15.27/2.96 | | | | % 15.27/2.96 | | | | BETA: splitting (14) gives: % 15.27/2.96 | | | | % 15.27/2.96 | | | | Case 1: % 15.27/2.96 | | | | | % 15.27/2.96 | | | | | (150) green(n2, n3) % 15.27/2.96 | | | | | % 15.27/2.96 | | | | | BETA: splitting (12) gives: % 15.27/2.96 | | | | | % 15.27/2.96 | | | | | Case 1: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | (151) green(n1, n2) % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | BETA: splitting (21) gives: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | Case 1: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (152) green(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 15.27/2.96 | | | | | | | simplifying with (6), (7), (8), (150), (151), (152), % 15.27/2.96 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | (153) $false % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | CLOSE: (153) is inconsistent. % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | Case 2: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (154) red(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | BETA: splitting (26) gives: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (155) green(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (32), (33), (35), (36), % 15.27/2.96 | | | | | | | | (90), (150), (151), (154), (155), % 15.27/2.96 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 15.27/2.96 | | | | | | | | inconsistent by sub-proof #21. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (156) red(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (31), (37), (149), (154), % 15.27/2.96 | | | | | | | | (156), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | (red_clique) are inconsistent by sub-proof #27. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | End of split % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | End of split % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | Case 2: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | (157) red(n1, n2) % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | BETA: splitting (21) gives: % 15.27/2.96 | | | | | | % 15.27/2.96 | | | | | | Case 1: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (158) green(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | BETA: splitting (29) gives: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (159) green(n4, n6) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | BETA: splitting (26) gives: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (160) green(n3, n5) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | BETA: splitting (23) gives: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | (161) green(n2, n4) % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (32), (33), (37), (90), % 15.27/2.96 | | | | | | | | | | (159), (161), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #18. % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | (162) red(n2, n4) % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (30), (31), (32), (37), % 15.27/2.96 | | | | | | | | | | (150), (157), (160), (162), (goal_to_be_proved), % 15.27/2.96 | | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.96 | | | | | | | | | | sub-proof #17. % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | End of split % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (163) red(n3, n5) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | BETA: splitting (35) gives: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | (164) green(n3, n6) % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (33), (36), (150), (157), % 15.27/2.96 | | | | | | | | | | (158), (164), (goal_to_be_proved), (green_clique), % 15.27/2.96 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #25. % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | (165) red(n3, n6) % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n5, n6, % 15.27/2.96 | | | | | | | | | | simplifying with (8), (10), (11), (90), (163), % 15.27/2.96 | | | | | | | | | | (165), (goal_to_be_proved) gives: % 15.27/2.96 | | | | | | | | | | (166) $false % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | | CLOSE: (166) is inconsistent. % 15.27/2.96 | | | | | | | | | | % 15.27/2.96 | | | | | | | | | End of split % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | End of split % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (167) red(n4, n6) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (33), (35), (36), (149), % 15.27/2.96 | | | | | | | | (150), (157), (158), (167), (goal_to_be_proved), % 15.27/2.96 | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.96 | | | | | | | | sub-proof #24. % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | End of split % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | Case 2: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | (168) red(n1, n3) % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | BETA: splitting (26) gives: % 15.27/2.96 | | | | | | | % 15.27/2.96 | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | (169) green(n3, n5) % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | | Case 1: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (170) green(n2, n4) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (30), (31), (32), (37), % 15.27/2.96 | | | | | | | | | (149), (157), (168), (170), (goal_to_be_proved), % 15.27/2.96 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.96 | | | | | | | | | sub-proof #23. % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | (171) red(n2, n4) % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (30), (31), (32), (37), % 15.27/2.96 | | | | | | | | | (150), (157), (169), (171), (goal_to_be_proved), % 15.27/2.96 | | | | | | | | | (green_clique), (red_clique) are inconsistent by % 15.27/2.96 | | | | | | | | | sub-proof #17. % 15.27/2.96 | | | | | | | | | % 15.27/2.96 | | | | | | | | End of split % 15.27/2.96 | | | | | | | | % 15.27/2.96 | | | | | | | Case 2: % 15.27/2.96 | | | | | | | | % 15.27/2.97 | | | | | | | | (172) red(n3, n5) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (31), (37), (149), (168), % 15.27/2.97 | | | | | | | | (172), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | (red_clique) are inconsistent by sub-proof #27. % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | End of split % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | End of split % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | End of split % 15.27/2.97 | | | | | % 15.27/2.97 | | | | Case 2: % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | (173) red(n2, n3) % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | BETA: splitting (12) gives: % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | Case 1: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | (174) green(n1, n2) % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | BETA: splitting (29) gives: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | Case 1: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (175) green(n4, n6) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | BETA: splitting (23) gives: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (176) green(n2, n4) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (32), (33), (37), (90), (175), % 15.27/2.97 | | | | | | | | (176), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | (red_clique) are inconsistent by sub-proof #18. % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (177) red(n2, n4) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n3, n4, % 15.27/2.97 | | | | | | | | simplifying with (7), (8), (9), (149), (173), % 15.27/2.97 | | | | | | | | (177), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | (178) $false % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | CLOSE: (178) is inconsistent. % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | End of split % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | Case 2: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (179) red(n4, n6) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | BETA: splitting (23) gives: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (180) green(n2, n4) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | BETA: splitting (33) gives: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (181) green(n2, n6) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | BETA: splitting (30) gives: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (182) green(n1, n4) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n4, % 15.27/2.97 | | | | | | | | | | simplifying with (6), (7), (9), (174), (180), % 15.27/2.97 | | | | | | | | | | (182), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | | (183) $false % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | CLOSE: (183) is inconsistent. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (184) red(n1, n4) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (36), (174), (179), (181), % 15.27/2.97 | | | | | | | | | | (184), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #16. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | End of split % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (185) red(n2, n6) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (32), (37), (90), (180), % 15.27/2.97 | | | | | | | | | (185), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | | (red_clique) are inconsistent by sub-proof #19. % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | End of split % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (186) red(n2, n4) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n3, n4, % 15.27/2.97 | | | | | | | | simplifying with (7), (8), (9), (149), (173), % 15.27/2.97 | | | | | | | | (186), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | (187) $false % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | CLOSE: (187) is inconsistent. % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | End of split % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | End of split % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | Case 2: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | (188) red(n1, n2) % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | BETA: splitting (21) gives: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | Case 1: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (189) green(n1, n3) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | BETA: splitting (26) gives: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (190) green(n3, n5) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (191) green(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | BETA: splitting (32) gives: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (192) green(n2, n5) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n4, n5, % 15.27/2.97 | | | | | | | | | | simplifying with (7), (9), (10), (37), (191), % 15.27/2.97 | | | | | | | | | | (192), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | | (193) $false % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | CLOSE: (193) is inconsistent. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (194) red(n2, n5) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (31), (188), (189), (190), % 15.27/2.97 | | | | | | | | | | (194), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #12. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | End of split % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (195) red(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n3, n4, % 15.27/2.97 | | | | | | | | | simplifying with (7), (8), (9), (149), (173), % 15.27/2.97 | | | | | | | | | (195), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | (196) $false % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | CLOSE: (196) is inconsistent. % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | End of split % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (197) red(n3, n5) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (198) green(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (32), (37), (173), (197), % 15.27/2.97 | | | | | | | | | (198), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | | (red_clique) are inconsistent by sub-proof #32. % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (199) red(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n3, n4, % 15.27/2.97 | | | | | | | | | simplifying with (7), (8), (9), (149), (173), % 15.27/2.97 | | | | | | | | | (199), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | (200) $false % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | CLOSE: (200) is inconsistent. % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | End of split % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | End of split % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | Case 2: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (201) red(n1, n3) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 15.27/2.97 | | | | | | | simplifying with (6), (7), (8), (173), (188), (201), % 15.27/2.97 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | (202) $false % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | CLOSE: (202) is inconsistent. % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | End of split % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | End of split % 15.27/2.97 | | | | | % 15.27/2.97 | | | | End of split % 15.27/2.97 | | | | % 15.27/2.97 | | | End of split % 15.27/2.97 | | | % 15.27/2.97 | | End of split % 15.27/2.97 | | % 15.27/2.97 | Case 2: % 15.27/2.97 | | % 15.27/2.97 | | (203) red(n4, n5) % 15.27/2.97 | | % 15.27/2.97 | | BETA: splitting (20) gives: % 15.27/2.97 | | % 15.27/2.97 | | Case 1: % 15.27/2.97 | | | % 15.27/2.97 | | | (204) green(n5, n6) % 15.27/2.97 | | | % 15.27/2.97 | | | BETA: splitting (16) gives: % 15.27/2.97 | | | % 15.27/2.97 | | | Case 1: % 15.27/2.97 | | | | % 15.27/2.97 | | | | (205) green(n3, n4) % 15.27/2.97 | | | | % 15.27/2.97 | | | | BETA: splitting (14) gives: % 15.27/2.97 | | | | % 15.27/2.97 | | | | Case 1: % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | (206) green(n2, n3) % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | BETA: splitting (12) gives: % 15.27/2.97 | | | | | % 15.27/2.97 | | | | | Case 1: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | (207) green(n1, n2) % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | BETA: splitting (21) gives: % 15.27/2.97 | | | | | | % 15.27/2.97 | | | | | | Case 1: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (208) green(n1, n3) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 15.27/2.97 | | | | | | | simplifying with (6), (7), (8), (206), (207), (208), % 15.27/2.97 | | | | | | | (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | (209) $false % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | CLOSE: (209) is inconsistent. % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | Case 2: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | (210) red(n1, n3) % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | BETA: splitting (26) gives: % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (211) green(n3, n5) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (23), (32), (203), (205), (206), % 15.27/2.97 | | | | | | | | (211), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | (red_clique) are inconsistent by sub-proof #10. % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | (212) red(n3, n5) % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (213) green(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.97 | | | | | | | | | simplifying with (7), (8), (9), (205), (206), % 15.27/2.97 | | | | | | | | | (213), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | (214) $false % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | CLOSE: (214) is inconsistent. % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | (215) red(n2, n4) % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | BETA: splitting (32) gives: % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 1: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (216) green(n2, n5) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (31), (207), (210), (212), % 15.27/2.97 | | | | | | | | | | (216), (goal_to_be_proved), (green_clique), % 15.27/2.97 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #15. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | Case 2: % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | (217) red(n2, n5) % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n4, n5, % 15.27/2.97 | | | | | | | | | | simplifying with (7), (9), (10), (203), (215), % 15.27/2.97 | | | | | | | | | | (217), (goal_to_be_proved) gives: % 15.27/2.97 | | | | | | | | | | (218) $false % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | | CLOSE: (218) is inconsistent. % 15.27/2.97 | | | | | | | | | | % 15.27/2.97 | | | | | | | | | End of split % 15.27/2.97 | | | | | | | | | % 15.27/2.97 | | | | | | | | End of split % 15.27/2.97 | | | | | | | | % 15.27/2.97 | | | | | | | End of split % 15.27/2.97 | | | | | | | % 15.27/2.97 | | | | | | End of split % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | Case 2: % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | (219) red(n1, n2) % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | BETA: splitting (21) gives: % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | Case 1: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | (220) green(n1, n3) % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | BETA: splitting (23) gives: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | (221) green(n2, n4) % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.98 | | | | | | | | simplifying with (7), (8), (9), (205), (206), % 15.27/2.98 | | | | | | | | (221), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | (222) $false % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | CLOSE: (222) is inconsistent. % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | (223) red(n2, n4) % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (30), (205), (219), (220), (223), % 15.27/2.98 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 15.27/2.98 | | | | | | | | inconsistent by sub-proof #13. % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | End of split % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | Case 2: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | (224) red(n1, n3) % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | BETA: splitting (29) gives: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | (225) green(n4, n6) % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | (226) green(n2, n4) % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.98 | | | | | | | | | simplifying with (7), (8), (9), (205), (206), % 15.27/2.98 | | | | | | | | | (226), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | (227) $false % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | CLOSE: (227) is inconsistent. % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | (228) red(n2, n4) % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | BETA: splitting (35) gives: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | (229) green(n3, n6) % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n6, % 15.27/2.98 | | | | | | | | | | simplifying with (8), (9), (11), (205), (225), % 15.27/2.98 | | | | | | | | | | (229), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | | (230) $false % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | CLOSE: (230) is inconsistent. % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | (231) red(n3, n6) % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | BETA: splitting (30) gives: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | (232) green(n1, n4) % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (36), (224), (225), (231), % 15.27/2.98 | | | | | | | | | | | (232), (goal_to_be_proved), (green_clique), % 15.27/2.98 | | | | | | | | | | | (red_clique) are inconsistent by sub-proof #9. % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | (233) red(n1, n4) % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n4, % 15.27/2.98 | | | | | | | | | | | simplifying with (6), (7), (9), (219), (228), % 15.27/2.98 | | | | | | | | | | | (233), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | | | (234) $false % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | CLOSE: (234) is inconsistent. % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | End of split % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | End of split % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | End of split % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | (235) red(n4, n6) % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | BETA: splitting (23) gives: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | (236) green(n2, n4) % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n4, % 15.27/2.98 | | | | | | | | | simplifying with (7), (8), (9), (205), (206), % 15.27/2.98 | | | | | | | | | (236), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | (237) $false % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | CLOSE: (237) is inconsistent. % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | (238) red(n2, n4) % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | BETA: splitting (33) gives: % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | (239) green(n2, n6) % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | BETA: splitting (32) gives: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | (240) green(n2, n5) % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n5, n6, % 15.27/2.98 | | | | | | | | | | | simplifying with (7), (10), (11), (204), (239), % 15.27/2.98 | | | | | | | | | | | (240), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | | | (241) $false % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | CLOSE: (241) is inconsistent. % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | (242) red(n2, n5) % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n4, n5, % 15.27/2.98 | | | | | | | | | | | simplifying with (7), (9), (10), (203), (238), % 15.27/2.98 | | | | | | | | | | | (242), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | | | (243) $false % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | | CLOSE: (243) is inconsistent. % 15.27/2.98 | | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | End of split % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | (244) red(n2, n6) % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n4, n6, % 15.27/2.98 | | | | | | | | | | simplifying with (7), (9), (11), (235), (238), % 15.27/2.98 | | | | | | | | | | (244), (goal_to_be_proved) gives: % 15.27/2.98 | | | | | | | | | | (245) $false % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | | CLOSE: (245) is inconsistent. % 15.27/2.98 | | | | | | | | | | % 15.27/2.98 | | | | | | | | | End of split % 15.27/2.98 | | | | | | | | | % 15.27/2.98 | | | | | | | | End of split % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | End of split % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | End of split % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | End of split % 15.27/2.98 | | | | | % 15.27/2.98 | | | | Case 2: % 15.27/2.98 | | | | | % 15.27/2.98 | | | | | (246) red(n2, n3) % 15.27/2.98 | | | | | % 15.27/2.98 | | | | | BETA: splitting (12) gives: % 15.27/2.98 | | | | | % 15.27/2.98 | | | | | Case 1: % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | (247) green(n1, n2) % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | BETA: splitting (21) gives: % 15.27/2.98 | | | | | | % 15.27/2.98 | | | | | | Case 1: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | (248) green(n1, n3) % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | BETA: splitting (26) gives: % 15.27/2.98 | | | | | | | % 15.27/2.98 | | | | | | | Case 1: % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | (249) green(n3, n5) % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (31), (203), (205), (248), % 15.27/2.98 | | | | | | | | (249), (goal_to_be_proved), (green_clique), % 15.27/2.98 | | | | | | | | (red_clique) are inconsistent by sub-proof #7. % 15.27/2.98 | | | | | | | | % 15.27/2.98 | | | | | | | Case 2: % 15.27/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | (250) red(n3, n5) % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | BETA: splitting (32) gives: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | Case 1: % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | (251) green(n2, n5) % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | BETA: splitting (31) gives: % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | Case 1: % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | | (252) green(n1, n5) % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n5, % 16.28/2.98 | | | | | | | | | | simplifying with (6), (7), (10), (247), (251), % 16.28/2.98 | | | | | | | | | | (252), (goal_to_be_proved) gives: % 16.28/2.98 | | | | | | | | | | (253) $false % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | | CLOSE: (253) is inconsistent. % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | Case 2: % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | | (254) red(n1, n5) % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (203), (205), (248), % 16.28/2.98 | | | | | | | | | | (254), (goal_to_be_proved), (green_clique), % 16.28/2.98 | | | | | | | | | | (red_clique) are inconsistent by sub-proof #8. % 16.28/2.98 | | | | | | | | | | % 16.28/2.98 | | | | | | | | | End of split % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | Case 2: % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | (255) red(n2, n5) % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | GROUND_INST: instantiating (red_clique) with n2, n3, n5, % 16.28/2.98 | | | | | | | | | simplifying with (7), (8), (10), (246), (250), % 16.28/2.98 | | | | | | | | | (255), (goal_to_be_proved) gives: % 16.28/2.98 | | | | | | | | | (256) $false % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | CLOSE: (256) is inconsistent. % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | End of split % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | End of split % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | Case 2: % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | (257) red(n1, n3) % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | BETA: splitting (26) gives: % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | Case 1: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | (258) green(n3, n5) % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | BETA: splitting (35) gives: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | Case 1: % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | (259) green(n3, n6) % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n5, n6, % 16.28/2.98 | | | | | | | | | simplifying with (8), (10), (11), (204), (258), % 16.28/2.98 | | | | | | | | | (259), (goal_to_be_proved) gives: % 16.28/2.98 | | | | | | | | | (260) $false % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | CLOSE: (260) is inconsistent. % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | Case 2: % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | (261) red(n3, n6) % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (33), (36), (246), (247), % 16.28/2.98 | | | | | | | | | (257), (261), (goal_to_be_proved), (green_clique), % 16.28/2.98 | | | | | | | | | (red_clique) are inconsistent by sub-proof #6. % 16.28/2.98 | | | | | | | | | % 16.28/2.98 | | | | | | | | End of split % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | Case 2: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | (262) red(n3, n5) % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (31), (32), (246), (247), (257), % 16.28/2.98 | | | | | | | | (262), (goal_to_be_proved), (green_clique), % 16.28/2.98 | | | | | | | | (red_clique) are inconsistent by sub-proof #14. % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | End of split % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | End of split % 16.28/2.98 | | | | | | % 16.28/2.98 | | | | | Case 2: % 16.28/2.98 | | | | | | % 16.28/2.98 | | | | | | (263) red(n1, n2) % 16.28/2.98 | | | | | | % 16.28/2.98 | | | | | | BETA: splitting (21) gives: % 16.28/2.98 | | | | | | % 16.28/2.98 | | | | | | Case 1: % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | (264) green(n1, n3) % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | BETA: splitting (26) gives: % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | Case 1: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | (265) green(n3, n5) % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (30), (31), (203), (205), (264), % 16.28/2.98 | | | | | | | | (265), (goal_to_be_proved), (green_clique), % 16.28/2.98 | | | | | | | | (red_clique) are inconsistent by sub-proof #7. % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | Case 2: % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | (266) red(n3, n5) % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (32), (33), (35), (36), % 16.28/2.98 | | | | | | | | (204), (246), (263), (264), (266), % 16.28/2.98 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 16.28/2.98 | | | | | | | | inconsistent by sub-proof #5. % 16.28/2.98 | | | | | | | | % 16.28/2.98 | | | | | | | End of split % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | Case 2: % 16.28/2.98 | | | | | | | % 16.28/2.98 | | | | | | | (267) red(n1, n3) % 16.28/2.98 | | | | | | | % 16.28/2.99 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 16.28/2.99 | | | | | | | simplifying with (6), (7), (8), (246), (263), (267), % 16.28/2.99 | | | | | | | (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | (268) $false % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | CLOSE: (268) is inconsistent. % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | End of split % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | End of split % 16.28/2.99 | | | | | % 16.28/2.99 | | | | End of split % 16.28/2.99 | | | | % 16.28/2.99 | | | Case 2: % 16.28/2.99 | | | | % 16.28/2.99 | | | | (269) red(n3, n4) % 16.28/2.99 | | | | % 16.28/2.99 | | | | BETA: splitting (14) gives: % 16.28/2.99 | | | | % 16.28/2.99 | | | | Case 1: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | (270) green(n2, n3) % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | BETA: splitting (12) gives: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | Case 1: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (271) green(n1, n2) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | BETA: splitting (21) gives: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | Case 1: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (272) green(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | GROUND_INST: instantiating (green_clique) with n1, n2, n3, % 16.28/2.99 | | | | | | | simplifying with (6), (7), (8), (270), (271), (272), % 16.28/2.99 | | | | | | | (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | (273) $false % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | CLOSE: (273) is inconsistent. % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | Case 2: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (274) red(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (275) green(n3, n5) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | BETA: splitting (23) gives: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (276) green(n2, n4) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (30), (269), (271), (274), % 16.28/2.99 | | | | | | | | | (276), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | (red_clique) are inconsistent by sub-proof #4. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (277) red(n2, n4) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (32), (203), (270), (275), % 16.28/2.99 | | | | | | | | | (277), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | (red_clique) are inconsistent by sub-proof #11. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | End of split % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (278) red(n3, n5) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n4, n5, % 16.28/2.99 | | | | | | | | simplifying with (8), (9), (10), (203), (269), % 16.28/2.99 | | | | | | | | (278), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | (279) $false % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | CLOSE: (279) is inconsistent. % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | End of split % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | End of split % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | Case 2: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (280) red(n1, n2) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | BETA: splitting (21) gives: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | Case 1: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (281) green(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (282) green(n3, n5) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | BETA: splitting (32) gives: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (283) green(n2, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n3, n5, % 16.28/2.99 | | | | | | | | | simplifying with (7), (8), (10), (270), (282), % 16.28/2.99 | | | | | | | | | (283), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | | (284) $false % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | CLOSE: (284) is inconsistent. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (285) red(n2, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (31), (280), (281), (282), % 16.28/2.99 | | | | | | | | | (285), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | (red_clique) are inconsistent by sub-proof #12. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | End of split % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (286) red(n3, n5) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n4, n5, % 16.28/2.99 | | | | | | | | simplifying with (8), (9), (10), (203), (269), % 16.28/2.99 | | | | | | | | (286), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | (287) $false % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | CLOSE: (287) is inconsistent. % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | End of split % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | Case 2: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (288) red(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | BETA: splitting (29) gives: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (289) green(n4, n6) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (290) green(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | BETA: splitting (35) gives: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | (291) green(n3, n6) % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n5, n6, % 16.28/2.99 | | | | | | | | | | simplifying with (8), (10), (11), (204), (290), % 16.28/2.99 | | | | | | | | | | (291), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | | | (292) $false % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | CLOSE: (292) is inconsistent. % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | (293) red(n3, n6) % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | BETA: splitting (30) gives: % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | | (294) green(n1, n4) % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (36), (288), (289), (293), % 16.28/2.99 | | | | | | | | | | | (294), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | | | (red_clique) are inconsistent by sub-proof #9. % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | | (295) red(n1, n4) % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n3, n4, % 16.28/2.99 | | | | | | | | | | | simplifying with (6), (8), (9), (269), (288), % 16.28/2.99 | | | | | | | | | | | (295), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | | | | (296) $false % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | | CLOSE: (296) is inconsistent. % 16.28/2.99 | | | | | | | | | | | % 16.28/2.99 | | | | | | | | | | End of split % 16.28/2.99 | | | | | | | | | | % 16.28/2.99 | | | | | | | | | End of split % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (297) red(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n4, n5, % 16.28/2.99 | | | | | | | | | simplifying with (8), (9), (10), (203), (269), % 16.28/2.99 | | | | | | | | | (297), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | | (298) $false % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | CLOSE: (298) is inconsistent. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | End of split % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (299) red(n4, n6) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (300) green(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (204), (269), (299), % 16.28/2.99 | | | | | | | | | (300), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | (red_clique) are inconsistent by sub-proof #29. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (301) red(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n4, n5, % 16.28/2.99 | | | | | | | | | simplifying with (8), (9), (10), (203), (269), % 16.28/2.99 | | | | | | | | | (301), (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | | | (302) $false % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | CLOSE: (302) is inconsistent. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | End of split % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | End of split % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | End of split % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | End of split % 16.28/2.99 | | | | | % 16.28/2.99 | | | | Case 2: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | (303) red(n2, n3) % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | BETA: splitting (12) gives: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | Case 1: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (304) green(n1, n2) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (21), (23), (26), (30), (31), % 16.28/2.99 | | | | | | (203), (269), (303), (304), (goal_to_be_proved), % 16.28/2.99 | | | | | | (green_clique), (red_clique) are inconsistent by % 16.28/2.99 | | | | | | sub-proof #3. % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | Case 2: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (305) red(n1, n2) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | BETA: splitting (21) gives: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | Case 1: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (306) green(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | BETA: splitting (29) gives: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (307) green(n4, n6) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (23), (33), (35), (36), % 16.28/2.99 | | | | | | | | (269), (303), (305), (306), (307), % 16.28/2.99 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 16.28/2.99 | | | | | | | | inconsistent by sub-proof #2. % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | (308) red(n4, n6) % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | | Case 1: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (309) green(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (204), (269), (308), % 16.28/2.99 | | | | | | | | | (309), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | | | (red_clique) are inconsistent by sub-proof #29. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | Case 2: % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | (310) red(n3, n5) % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (32), (33), (35), (36), % 16.28/2.99 | | | | | | | | | (204), (303), (305), (306), (310), % 16.28/2.99 | | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) % 16.28/2.99 | | | | | | | | | are inconsistent by sub-proof #5. % 16.28/2.99 | | | | | | | | | % 16.28/2.99 | | | | | | | | End of split % 16.28/2.99 | | | | | | | | % 16.28/2.99 | | | | | | | End of split % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | Case 2: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (311) red(n1, n3) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 16.28/2.99 | | | | | | | simplifying with (6), (7), (8), (303), (305), (311), % 16.28/2.99 | | | | | | | (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | | (312) $false % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | CLOSE: (312) is inconsistent. % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | End of split % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | End of split % 16.28/2.99 | | | | | % 16.28/2.99 | | | | End of split % 16.28/2.99 | | | | % 16.28/2.99 | | | End of split % 16.28/2.99 | | | % 16.28/2.99 | | Case 2: % 16.28/2.99 | | | % 16.28/2.99 | | | (313) red(n5, n6) % 16.28/2.99 | | | % 16.28/2.99 | | | BETA: splitting (16) gives: % 16.28/2.99 | | | % 16.28/2.99 | | | Case 1: % 16.28/2.99 | | | | % 16.28/2.99 | | | | (314) green(n3, n4) % 16.28/2.99 | | | | % 16.28/2.99 | | | | BETA: splitting (14) gives: % 16.28/2.99 | | | | % 16.28/2.99 | | | | Case 1: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | (315) green(n2, n3) % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | BETA: splitting (29) gives: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | Case 1: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (316) green(n4, n6) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | BETA: splitting (26) gives: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | Case 1: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (317) green(n3, n5) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | REF_CLOSE: (7), (8), (9), (10), (23), (32), (203), (314), (315), % 16.28/2.99 | | | | | | | (317), (goal_to_be_proved), (green_clique), % 16.28/2.99 | | | | | | | (red_clique) are inconsistent by sub-proof #10. % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | Case 2: % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | (318) red(n3, n5) % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | | REF_CLOSE: (8), (9), (10), (11), (35), (313), (314), (316), (318), % 16.28/2.99 | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 16.28/2.99 | | | | | | | inconsistent by sub-proof #20. % 16.28/2.99 | | | | | | | % 16.28/2.99 | | | | | | End of split % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | Case 2: % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | (319) red(n4, n6) % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | GROUND_INST: instantiating (red_clique) with n4, n5, n6, simplifying % 16.28/2.99 | | | | | | with (9), (10), (11), (203), (313), (319), % 16.28/2.99 | | | | | | (goal_to_be_proved) gives: % 16.28/2.99 | | | | | | (320) $false % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | | CLOSE: (320) is inconsistent. % 16.28/2.99 | | | | | | % 16.28/2.99 | | | | | End of split % 16.28/2.99 | | | | | % 16.28/2.99 | | | | Case 2: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | (321) red(n2, n3) % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | BETA: splitting (12) gives: % 16.28/2.99 | | | | | % 16.28/2.99 | | | | | Case 1: % 16.28/2.99 | | | | | | % 16.28/3.00 | | | | | | (322) green(n1, n2) % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | BETA: splitting (21) gives: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | Case 1: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (323) green(n1, n3) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (26), (29), (30), (31), % 16.28/3.00 | | | | | | | (35), (203), (313), (314), (323), (goal_to_be_proved), % 16.28/3.00 | | | | | | | (green_clique), (red_clique) are inconsistent by % 16.28/3.00 | | | | | | | sub-proof #1. % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | Case 2: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (324) red(n1, n3) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | BETA: splitting (29) gives: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | Case 1: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | (325) green(n4, n6) % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | BETA: splitting (35) gives: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | Case 1: % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | (326) green(n3, n6) % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n3, n4, n6, % 16.28/3.00 | | | | | | | | | simplifying with (8), (9), (11), (314), (325), % 16.28/3.00 | | | | | | | | | (326), (goal_to_be_proved) gives: % 16.28/3.00 | | | | | | | | | (327) $false % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | CLOSE: (327) is inconsistent. % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | Case 2: % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | (328) red(n3, n6) % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (33), (36), (321), (322), % 16.28/3.00 | | | | | | | | | (324), (328), (goal_to_be_proved), (green_clique), % 16.28/3.00 | | | | | | | | | (red_clique) are inconsistent by sub-proof #6. % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | End of split % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | Case 2: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | (329) red(n4, n6) % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | GROUND_INST: instantiating (red_clique) with n4, n5, n6, % 16.28/3.00 | | | | | | | | simplifying with (9), (10), (11), (203), (313), % 16.28/3.00 | | | | | | | | (329), (goal_to_be_proved) gives: % 16.28/3.00 | | | | | | | | (330) $false % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | CLOSE: (330) is inconsistent. % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | End of split % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | End of split % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | Case 2: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | (331) red(n1, n2) % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | BETA: splitting (21) gives: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | Case 1: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (332) green(n1, n3) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (26), (29), (30), (31), % 16.28/3.00 | | | | | | | (35), (203), (313), (314), (332), (goal_to_be_proved), % 16.28/3.00 | | | | | | | (green_clique), (red_clique) are inconsistent by % 16.28/3.00 | | | | | | | sub-proof #1. % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | Case 2: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (333) red(n1, n3) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 16.28/3.00 | | | | | | | simplifying with (6), (7), (8), (321), (331), (333), % 16.28/3.00 | | | | | | | (goal_to_be_proved) gives: % 16.28/3.00 | | | | | | | (334) $false % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | CLOSE: (334) is inconsistent. % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | End of split % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | End of split % 16.28/3.00 | | | | | % 16.28/3.00 | | | | End of split % 16.28/3.00 | | | | % 16.28/3.00 | | | Case 2: % 16.28/3.00 | | | | % 16.28/3.00 | | | | (335) red(n3, n4) % 16.28/3.00 | | | | % 16.28/3.00 | | | | BETA: splitting (14) gives: % 16.28/3.00 | | | | % 16.28/3.00 | | | | Case 1: % 16.28/3.00 | | | | | % 16.28/3.00 | | | | | (336) green(n2, n3) % 16.28/3.00 | | | | | % 16.28/3.00 | | | | | BETA: splitting (29) gives: % 16.28/3.00 | | | | | % 16.28/3.00 | | | | | Case 1: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | (337) green(n4, n6) % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | BETA: splitting (26) gives: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | Case 1: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (338) green(n3, n5) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | BETA: splitting (23) gives: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | Case 1: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | (339) green(n2, n4) % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | BETA: splitting (33) gives: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | Case 1: % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | (340) green(n2, n6) % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | GROUND_INST: instantiating (green_clique) with n2, n4, n6, % 16.28/3.00 | | | | | | | | | simplifying with (7), (9), (11), (337), (339), % 16.28/3.00 | | | | | | | | | (340), (goal_to_be_proved) gives: % 16.28/3.00 | | | | | | | | | (341) $false % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | CLOSE: (341) is inconsistent. % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | Case 2: % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | (342) red(n2, n6) % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (32), (313), (336), (338), % 16.28/3.00 | | | | | | | | | (342), (goal_to_be_proved), (green_clique), % 16.28/3.00 | | | | | | | | | (red_clique) are inconsistent by sub-proof #22. % 16.28/3.00 | | | | | | | | | % 16.28/3.00 | | | | | | | | End of split % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | Case 2: % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | (343) red(n2, n4) % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (32), (203), (336), (338), % 16.28/3.00 | | | | | | | | (343), (goal_to_be_proved), (green_clique), % 16.28/3.00 | | | | | | | | (red_clique) are inconsistent by sub-proof #11. % 16.28/3.00 | | | | | | | | % 16.28/3.00 | | | | | | | End of split % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | Case 2: % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | (344) red(n3, n5) % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | GROUND_INST: instantiating (red_clique) with n3, n4, n5, % 16.28/3.00 | | | | | | | simplifying with (8), (9), (10), (203), (335), (344), % 16.28/3.00 | | | | | | | (goal_to_be_proved) gives: % 16.28/3.00 | | | | | | | (345) $false % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | | CLOSE: (345) is inconsistent. % 16.28/3.00 | | | | | | | % 16.28/3.00 | | | | | | End of split % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | Case 2: % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | (346) red(n4, n6) % 16.28/3.00 | | | | | | % 16.28/3.00 | | | | | | GROUND_INST: instantiating (red_clique) with n4, n5, n6, simplifying % 16.28/3.00 | | | | | | with (9), (10), (11), (203), (313), (346), % 16.37/3.00 | | | | | | (goal_to_be_proved) gives: % 16.37/3.00 | | | | | | (347) $false % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | CLOSE: (347) is inconsistent. % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | End of split % 16.37/3.00 | | | | | % 16.37/3.00 | | | | Case 2: % 16.37/3.00 | | | | | % 16.37/3.00 | | | | | (348) red(n2, n3) % 16.37/3.00 | | | | | % 16.37/3.00 | | | | | BETA: splitting (12) gives: % 16.37/3.00 | | | | | % 16.37/3.00 | | | | | Case 1: % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | (349) green(n1, n2) % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (21), (23), (26), (30), (31), % 16.37/3.00 | | | | | | (203), (335), (348), (349), (goal_to_be_proved), % 16.37/3.00 | | | | | | (green_clique), (red_clique) are inconsistent by % 16.37/3.00 | | | | | | sub-proof #3. % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | Case 2: % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | (350) red(n1, n2) % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | BETA: splitting (21) gives: % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | | Case 1: % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | (351) green(n1, n3) % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | BETA: splitting (29) gives: % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | Case 1: % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | | (352) green(n4, n6) % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (11), (23), (33), (35), (36), % 16.37/3.00 | | | | | | | | (335), (348), (350), (351), (352), % 16.37/3.00 | | | | | | | | (goal_to_be_proved), (green_clique), (red_clique) are % 16.37/3.00 | | | | | | | | inconsistent by sub-proof #2. % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | Case 2: % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | | (353) red(n4, n6) % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | | GROUND_INST: instantiating (red_clique) with n4, n5, n6, % 16.37/3.00 | | | | | | | | simplifying with (9), (10), (11), (203), (313), % 16.37/3.00 | | | | | | | | (353), (goal_to_be_proved) gives: % 16.37/3.00 | | | | | | | | (354) $false % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | | CLOSE: (354) is inconsistent. % 16.37/3.00 | | | | | | | | % 16.37/3.00 | | | | | | | End of split % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | Case 2: % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | (355) red(n1, n3) % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | GROUND_INST: instantiating (red_clique) with n1, n2, n3, % 16.37/3.00 | | | | | | | simplifying with (6), (7), (8), (348), (350), (355), % 16.37/3.00 | | | | | | | (goal_to_be_proved) gives: % 16.37/3.00 | | | | | | | (356) $false % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | | CLOSE: (356) is inconsistent. % 16.37/3.00 | | | | | | | % 16.37/3.00 | | | | | | End of split % 16.37/3.00 | | | | | | % 16.37/3.00 | | | | | End of split % 16.37/3.00 | | | | | % 16.37/3.00 | | | | End of split % 16.37/3.00 | | | | % 16.37/3.00 | | | End of split % 16.37/3.00 | | | % 16.37/3.00 | | End of split % 16.37/3.00 | | % 16.37/3.00 | End of split % 16.37/3.00 | % 16.37/3.00 End of proof % 16.37/3.00 % 16.37/3.00 Sub-proof #1 shows that the following formulas are inconsistent: % 16.37/3.00 ---------------------------------------------------------------- % 16.37/3.00 (1) green(n3, n5) | red(n3, n5) % 16.37/3.00 (2) green(n1, n5) | red(n1, n5) % 16.37/3.00 (3) green(n4, n6) | red(n4, n6) % 16.37/3.00 (4) green(n1, n3) % 16.37/3.00 (5) $i(n4) % 16.37/3.00 (6) ~ goal % 16.37/3.00 (7) $i(n5) % 16.37/3.00 (8) green(n3, n4) % 16.37/3.00 (9) green(n1, n4) | red(n1, n4) % 16.37/3.00 (10) $i(n1) % 16.37/3.00 (11) red(n4, n5) % 16.37/3.00 (12) $i(n3) % 16.37/3.00 (13) $i(n6) % 16.37/3.00 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.00 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.37/3.00 (15) red(n5, n6) % 16.37/3.00 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.00 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.37/3.00 goal) % 16.37/3.00 (17) green(n3, n6) | red(n3, n6) % 16.37/3.00 % 16.37/3.00 Begin of proof % 16.37/3.00 | % 16.37/3.00 | BETA: splitting (3) gives: % 16.37/3.00 | % 16.37/3.00 | Case 1: % 16.37/3.00 | | % 16.37/3.00 | | (18) green(n4, n6) % 16.37/3.00 | | % 16.37/3.00 | | BETA: splitting (1) gives: % 16.37/3.00 | | % 16.37/3.00 | | Case 1: % 16.37/3.00 | | | % 16.37/3.00 | | | (19) green(n3, n5) % 16.37/3.00 | | | % 16.37/3.00 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 16.37/3.00 | | | (16), (19) are inconsistent by sub-proof #7. % 16.37/3.00 | | | % 16.37/3.00 | | Case 2: % 16.37/3.00 | | | % 16.37/3.00 | | | (20) red(n3, n5) % 16.37/3.00 | | | % 16.37/3.01 | | | REF_CLOSE: (5), (6), (7), (8), (12), (13), (14), (15), (16), (17), (18), % 16.37/3.01 | | | (20) are inconsistent by sub-proof #20. % 16.37/3.01 | | | % 16.37/3.01 | | End of split % 16.37/3.01 | | % 16.37/3.01 | Case 2: % 16.37/3.01 | | % 16.37/3.01 | | (21) red(n4, n6) % 16.37/3.01 | | % 16.37/3.01 | | GROUND_INST: instantiating (14) with n4, n5, n6, simplifying with (5), (6), % 16.37/3.01 | | (7), (11), (13), (15), (21) gives: % 16.37/3.01 | | (22) $false % 16.37/3.01 | | % 16.37/3.01 | | CLOSE: (22) is inconsistent. % 16.37/3.01 | | % 16.37/3.01 | End of split % 16.37/3.01 | % 16.37/3.01 End of proof % 16.37/3.01 % 16.37/3.01 Sub-proof #2 shows that the following formulas are inconsistent: % 16.37/3.01 ---------------------------------------------------------------- % 16.37/3.01 (1) green(n1, n3) % 16.37/3.01 (2) $i(n2) % 16.37/3.01 (3) red(n3, n4) % 16.37/3.01 (4) red(n2, n3) % 16.37/3.01 (5) green(n2, n4) | red(n2, n4) % 16.37/3.01 (6) $i(n4) % 16.37/3.01 (7) ~ goal % 16.37/3.01 (8) $i(n1) % 16.37/3.01 (9) $i(n3) % 16.37/3.01 (10) $i(n6) % 16.37/3.01 (11) green(n2, n6) | red(n2, n6) % 16.37/3.01 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.01 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.37/3.01 (13) green(n4, n6) % 16.37/3.01 (14) green(n1, n6) | red(n1, n6) % 16.37/3.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.01 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.37/3.01 goal) % 16.37/3.01 (16) red(n1, n2) % 16.37/3.01 (17) green(n3, n6) | red(n3, n6) % 16.37/3.01 % 16.37/3.01 Begin of proof % 16.37/3.01 | % 16.37/3.01 | BETA: splitting (5) gives: % 16.37/3.01 | % 16.37/3.01 | Case 1: % 16.37/3.01 | | % 16.37/3.01 | | (18) green(n2, n4) % 16.37/3.01 | | % 16.37/3.01 | | BETA: splitting (17) gives: % 16.37/3.01 | | % 16.37/3.01 | | Case 1: % 16.37/3.01 | | | % 16.37/3.01 | | | (19) green(n3, n6) % 16.37/3.01 | | | % 16.37/3.01 | | | BETA: splitting (11) gives: % 16.37/3.01 | | | % 16.37/3.01 | | | Case 1: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (20) green(n2, n6) % 16.37/3.01 | | | | % 16.37/3.01 | | | | GROUND_INST: instantiating (15) with n2, n4, n6, simplifying with (2), % 16.37/3.01 | | | | (6), (7), (10), (13), (18), (20) gives: % 16.37/3.01 | | | | (21) $false % 16.37/3.01 | | | | % 16.37/3.01 | | | | CLOSE: (21) is inconsistent. % 16.37/3.01 | | | | % 16.37/3.01 | | | Case 2: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (22) red(n2, n6) % 16.37/3.01 | | | | % 16.37/3.01 | | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (12), (14), (15), (16), (19), % 16.37/3.01 | | | | (22) are inconsistent by sub-proof #26. % 16.37/3.01 | | | | % 16.37/3.01 | | | End of split % 16.37/3.01 | | | % 16.37/3.01 | | Case 2: % 16.37/3.01 | | | % 16.37/3.01 | | | (23) red(n3, n6) % 16.37/3.01 | | | % 16.37/3.01 | | | BETA: splitting (11) gives: % 16.37/3.01 | | | % 16.37/3.01 | | | Case 1: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (24) green(n2, n6) % 16.37/3.01 | | | | % 16.37/3.01 | | | | GROUND_INST: instantiating (15) with n2, n4, n6, simplifying with (2), % 16.37/3.01 | | | | (6), (7), (10), (13), (18), (24) gives: % 16.37/3.01 | | | | (25) $false % 16.37/3.01 | | | | % 16.37/3.01 | | | | CLOSE: (25) is inconsistent. % 16.37/3.01 | | | | % 16.37/3.01 | | | Case 2: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (26) red(n2, n6) % 16.37/3.01 | | | | % 16.37/3.01 | | | | GROUND_INST: instantiating (12) with n2, n3, n6, simplifying with (2), % 16.37/3.01 | | | | (4), (7), (9), (10), (23), (26) gives: % 16.37/3.01 | | | | (27) $false % 16.37/3.01 | | | | % 16.37/3.01 | | | | CLOSE: (27) is inconsistent. % 16.37/3.01 | | | | % 16.37/3.01 | | | End of split % 16.37/3.01 | | | % 16.37/3.01 | | End of split % 16.37/3.01 | | % 16.37/3.01 | Case 2: % 16.37/3.01 | | % 16.37/3.01 | | (28) red(n2, n4) % 16.37/3.01 | | % 16.37/3.01 | | GROUND_INST: instantiating (12) with n2, n3, n4, simplifying with (2), (3), % 16.37/3.01 | | (4), (6), (7), (9), (28) gives: % 16.37/3.01 | | (29) $false % 16.37/3.01 | | % 16.37/3.01 | | CLOSE: (29) is inconsistent. % 16.37/3.01 | | % 16.37/3.01 | End of split % 16.37/3.01 | % 16.37/3.01 End of proof % 16.37/3.01 % 16.37/3.01 Sub-proof #3 shows that the following formulas are inconsistent: % 16.37/3.01 ---------------------------------------------------------------- % 16.37/3.01 (1) green(n3, n5) | red(n3, n5) % 16.37/3.01 (2) green(n1, n5) | red(n1, n5) % 16.37/3.01 (3) $i(n2) % 16.37/3.01 (4) red(n3, n4) % 16.37/3.01 (5) red(n2, n3) % 16.37/3.01 (6) green(n2, n4) | red(n2, n4) % 16.37/3.01 (7) $i(n4) % 16.37/3.01 (8) ~ goal % 16.37/3.01 (9) $i(n5) % 16.37/3.01 (10) green(n1, n4) | red(n1, n4) % 16.37/3.01 (11) $i(n1) % 16.37/3.01 (12) red(n4, n5) % 16.37/3.01 (13) $i(n3) % 16.37/3.01 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.01 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.37/3.01 (15) green(n1, n2) % 16.37/3.01 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.37/3.01 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.37/3.01 goal) % 16.37/3.01 (17) green(n1, n3) | red(n1, n3) % 16.37/3.01 % 16.37/3.01 Begin of proof % 16.37/3.01 | % 16.37/3.01 | BETA: splitting (17) gives: % 16.37/3.01 | % 16.37/3.01 | Case 1: % 16.37/3.01 | | % 16.37/3.01 | | (18) green(n1, n3) % 16.37/3.01 | | % 16.37/3.01 | | BETA: splitting (1) gives: % 16.37/3.01 | | % 16.37/3.01 | | Case 1: % 16.37/3.01 | | | % 16.37/3.01 | | | (19) green(n3, n5) % 16.37/3.01 | | | % 16.37/3.01 | | | BETA: splitting (6) gives: % 16.37/3.01 | | | % 16.37/3.01 | | | Case 1: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (20) green(n2, n4) % 16.37/3.01 | | | | % 16.37/3.01 | | | | BETA: splitting (2) gives: % 16.37/3.01 | | | | % 16.37/3.01 | | | | Case 1: % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | (21) green(n1, n5) % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | GROUND_INST: instantiating (16) with n1, n3, n5, simplifying with (8), % 16.37/3.01 | | | | | (9), (11), (13), (18), (19), (21) gives: % 16.37/3.01 | | | | | (22) $false % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | CLOSE: (22) is inconsistent. % 16.37/3.01 | | | | | % 16.37/3.01 | | | | Case 2: % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | (23) red(n1, n5) % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | BETA: splitting (10) gives: % 16.37/3.01 | | | | | % 16.37/3.01 | | | | | Case 1: % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | (24) green(n1, n4) % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | GROUND_INST: instantiating (16) with n1, n2, n4, simplifying with % 16.37/3.01 | | | | | | (3), (7), (8), (11), (15), (20), (24) gives: % 16.37/3.01 | | | | | | (25) $false % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | CLOSE: (25) is inconsistent. % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | Case 2: % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | (26) red(n1, n4) % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | GROUND_INST: instantiating (14) with n1, n4, n5, simplifying with % 16.37/3.01 | | | | | | (7), (8), (9), (11), (12), (23), (26) gives: % 16.37/3.01 | | | | | | (27) $false % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | | CLOSE: (27) is inconsistent. % 16.37/3.01 | | | | | | % 16.37/3.01 | | | | | End of split % 16.37/3.01 | | | | | % 16.37/3.01 | | | | End of split % 16.37/3.01 | | | | % 16.37/3.01 | | | Case 2: % 16.37/3.01 | | | | % 16.37/3.01 | | | | (28) red(n2, n4) % 16.37/3.01 | | | | % 16.37/3.01 | | | | GROUND_INST: instantiating (14) with n2, n3, n4, simplifying with (3), % 16.37/3.01 | | | | (4), (5), (7), (8), (13), (28) gives: % 16.37/3.01 | | | | (29) $false % 16.37/3.01 | | | | % 16.37/3.01 | | | | CLOSE: (29) is inconsistent. % 16.37/3.01 | | | | % 16.37/3.01 | | | End of split % 16.37/3.01 | | | % 16.37/3.01 | | Case 2: % 16.37/3.01 | | | % 16.37/3.01 | | | (30) red(n3, n5) % 16.37/3.01 | | | % 16.37/3.01 | | | GROUND_INST: instantiating (14) with n3, n4, n5, simplifying with (4), % 16.37/3.01 | | | (7), (8), (9), (12), (13), (30) gives: % 16.37/3.01 | | | (31) $false % 16.37/3.01 | | | % 16.37/3.01 | | | CLOSE: (31) is inconsistent. % 16.37/3.01 | | | % 16.37/3.01 | | End of split % 16.37/3.01 | | % 16.37/3.01 | Case 2: % 16.37/3.01 | | % 16.37/3.01 | | (32) red(n1, n3) % 16.37/3.01 | | % 16.37/3.01 | | BETA: splitting (6) gives: % 16.37/3.01 | | % 16.37/3.01 | | Case 1: % 16.37/3.01 | | | % 16.37/3.01 | | | (33) green(n2, n4) % 16.37/3.01 | | | % 16.37/3.01 | | | REF_CLOSE: (3), (4), (7), (8), (10), (11), (13), (14), (15), (16), (32), % 16.37/3.01 | | | (33) are inconsistent by sub-proof #4. % 16.37/3.01 | | | % 16.37/3.01 | | Case 2: % 16.37/3.01 | | | % 16.37/3.01 | | | (34) red(n2, n4) % 16.37/3.01 | | | % 16.37/3.01 | | | GROUND_INST: instantiating (14) with n2, n3, n4, simplifying with (3), % 16.37/3.01 | | | (4), (5), (7), (8), (13), (34) gives: % 16.37/3.01 | | | (35) $false % 16.37/3.01 | | | % 16.37/3.01 | | | CLOSE: (35) is inconsistent. % 16.37/3.01 | | | % 16.37/3.01 | | End of split % 16.37/3.01 | | % 16.37/3.01 | End of split % 16.37/3.01 | % 16.37/3.01 End of proof % 16.37/3.01 % 16.37/3.01 Sub-proof #4 shows that the following formulas are inconsistent: % 16.37/3.01 ---------------------------------------------------------------- % 16.37/3.01 (1) $i(n2) % 16.37/3.01 (2) red(n3, n4) % 16.37/3.01 (3) $i(n4) % 16.37/3.01 (4) red(n1, n3) % 16.37/3.02 (5) ~ goal % 16.37/3.02 (6) green(n1, n4) | red(n1, n4) % 16.45/3.02 (7) $i(n1) % 16.45/3.02 (8) $i(n3) % 16.45/3.02 (9) green(n2, n4) % 16.45/3.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.02 (11) green(n1, n2) % 16.45/3.02 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.02 goal) % 16.45/3.02 % 16.45/3.02 Begin of proof % 16.45/3.02 | % 16.45/3.02 | BETA: splitting (6) gives: % 16.45/3.02 | % 16.45/3.02 | Case 1: % 16.45/3.02 | | % 16.45/3.02 | | (13) green(n1, n4) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (12) with n1, n2, n4, simplifying with (1), (3), % 16.45/3.02 | | (5), (7), (9), (11), (13) gives: % 16.45/3.02 | | (14) $false % 16.45/3.02 | | % 16.45/3.02 | | CLOSE: (14) is inconsistent. % 16.45/3.02 | | % 16.45/3.02 | Case 2: % 16.45/3.02 | | % 16.45/3.02 | | (15) red(n1, n4) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (10) with n1, n3, n4, simplifying with (2), (3), % 16.45/3.02 | | (4), (5), (7), (8), (15) gives: % 16.45/3.02 | | (16) $false % 16.45/3.02 | | % 16.45/3.02 | | CLOSE: (16) is inconsistent. % 16.45/3.02 | | % 16.45/3.02 | End of split % 16.45/3.02 | % 16.45/3.02 End of proof % 16.45/3.02 % 16.45/3.02 Sub-proof #5 shows that the following formulas are inconsistent: % 16.45/3.02 ---------------------------------------------------------------- % 16.45/3.02 (1) green(n2, n5) | red(n2, n5) % 16.45/3.02 (2) green(n1, n3) % 16.45/3.02 (3) $i(n2) % 16.45/3.02 (4) red(n2, n3) % 16.45/3.02 (5) red(n3, n5) % 16.45/3.02 (6) ~ goal % 16.45/3.02 (7) green(n5, n6) % 16.45/3.02 (8) $i(n5) % 16.45/3.02 (9) $i(n1) % 16.45/3.02 (10) $i(n3) % 16.45/3.02 (11) $i(n6) % 16.45/3.02 (12) green(n2, n6) | red(n2, n6) % 16.45/3.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.02 (14) green(n1, n6) | red(n1, n6) % 16.45/3.02 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.02 goal) % 16.45/3.02 (16) red(n1, n2) % 16.45/3.02 (17) green(n3, n6) | red(n3, n6) % 16.45/3.02 % 16.45/3.02 Begin of proof % 16.45/3.02 | % 16.45/3.02 | BETA: splitting (17) gives: % 16.45/3.02 | % 16.45/3.02 | Case 1: % 16.45/3.02 | | % 16.45/3.02 | | (18) green(n3, n6) % 16.45/3.02 | | % 16.45/3.02 | | BETA: splitting (12) gives: % 16.45/3.02 | | % 16.45/3.02 | | Case 1: % 16.45/3.02 | | | % 16.45/3.02 | | | (19) green(n2, n6) % 16.45/3.02 | | | % 16.45/3.02 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (13), (15), (19) % 16.45/3.02 | | | are inconsistent by sub-proof #31. % 16.45/3.02 | | | % 16.45/3.02 | | Case 2: % 16.45/3.02 | | | % 16.45/3.02 | | | (20) red(n2, n6) % 16.45/3.02 | | | % 16.45/3.02 | | | REF_CLOSE: (2), (3), (6), (9), (10), (11), (13), (14), (15), (16), (18), % 16.45/3.02 | | | (20) are inconsistent by sub-proof #26. % 16.45/3.02 | | | % 16.45/3.02 | | End of split % 16.45/3.02 | | % 16.45/3.02 | Case 2: % 16.45/3.02 | | % 16.45/3.02 | | (21) red(n3, n6) % 16.45/3.02 | | % 16.45/3.02 | | BETA: splitting (12) gives: % 16.45/3.02 | | % 16.45/3.02 | | Case 1: % 16.45/3.02 | | | % 16.45/3.02 | | | (22) green(n2, n6) % 16.45/3.02 | | | % 16.45/3.02 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (13), (15), (22) % 16.45/3.02 | | | are inconsistent by sub-proof #31. % 16.45/3.02 | | | % 16.45/3.02 | | Case 2: % 16.45/3.02 | | | % 16.45/3.02 | | | (23) red(n2, n6) % 16.45/3.02 | | | % 16.45/3.02 | | | GROUND_INST: instantiating (13) with n2, n3, n6, simplifying with (3), % 16.45/3.02 | | | (4), (6), (10), (11), (21), (23) gives: % 16.45/3.02 | | | (24) $false % 16.45/3.02 | | | % 16.45/3.02 | | | CLOSE: (24) is inconsistent. % 16.45/3.02 | | | % 16.45/3.02 | | End of split % 16.45/3.02 | | % 16.45/3.02 | End of split % 16.45/3.02 | % 16.45/3.02 End of proof % 16.45/3.02 % 16.45/3.02 Sub-proof #6 shows that the following formulas are inconsistent: % 16.45/3.02 ---------------------------------------------------------------- % 16.45/3.02 (1) $i(n2) % 16.45/3.02 (2) red(n2, n3) % 16.45/3.02 (3) red(n1, n3) % 16.45/3.02 (4) ~ goal % 16.45/3.02 (5) $i(n1) % 16.45/3.02 (6) $i(n3) % 16.45/3.02 (7) $i(n6) % 16.45/3.02 (8) green(n2, n6) | red(n2, n6) % 16.45/3.02 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.02 (10) red(n3, n6) % 16.45/3.02 (11) green(n1, n2) % 16.45/3.02 (12) green(n1, n6) | red(n1, n6) % 16.45/3.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.02 goal) % 16.45/3.02 % 16.45/3.02 Begin of proof % 16.45/3.02 | % 16.45/3.02 | BETA: splitting (8) gives: % 16.45/3.02 | % 16.45/3.02 | Case 1: % 16.45/3.02 | | % 16.45/3.02 | | (14) green(n2, n6) % 16.45/3.02 | | % 16.45/3.02 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14) % 16.45/3.02 | | are inconsistent by sub-proof #36. % 16.45/3.02 | | % 16.45/3.02 | Case 2: % 16.45/3.02 | | % 16.45/3.02 | | (15) red(n2, n6) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (9) with n2, n3, n6, simplifying with (1), (2), % 16.45/3.02 | | (4), (6), (7), (10), (15) gives: % 16.45/3.02 | | (16) $false % 16.45/3.02 | | % 16.45/3.02 | | CLOSE: (16) is inconsistent. % 16.45/3.02 | | % 16.45/3.02 | End of split % 16.45/3.02 | % 16.45/3.02 End of proof % 16.45/3.02 % 16.45/3.02 Sub-proof #7 shows that the following formulas are inconsistent: % 16.45/3.02 ---------------------------------------------------------------- % 16.45/3.02 (1) green(n1, n5) | red(n1, n5) % 16.45/3.02 (2) green(n1, n3) % 16.45/3.02 (3) $i(n4) % 16.45/3.02 (4) ~ goal % 16.45/3.02 (5) $i(n5) % 16.45/3.02 (6) green(n3, n4) % 16.45/3.02 (7) green(n1, n4) | red(n1, n4) % 16.45/3.02 (8) $i(n1) % 16.45/3.02 (9) red(n4, n5) % 16.45/3.02 (10) green(n3, n5) % 16.45/3.02 (11) $i(n3) % 16.45/3.02 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.02 goal) % 16.45/3.02 % 16.45/3.02 Begin of proof % 16.45/3.02 | % 16.45/3.02 | BETA: splitting (1) gives: % 16.45/3.02 | % 16.45/3.02 | Case 1: % 16.45/3.02 | | % 16.45/3.02 | | (14) green(n1, n5) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (13) with n1, n3, n5, simplifying with (2), (4), % 16.45/3.02 | | (5), (8), (10), (11), (14) gives: % 16.45/3.02 | | (15) $false % 16.45/3.02 | | % 16.45/3.02 | | CLOSE: (15) is inconsistent. % 16.45/3.02 | | % 16.45/3.02 | Case 2: % 16.45/3.02 | | % 16.45/3.02 | | (16) red(n1, n5) % 16.45/3.02 | | % 16.45/3.02 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16) % 16.45/3.02 | | are inconsistent by sub-proof #8. % 16.45/3.02 | | % 16.45/3.02 | End of split % 16.45/3.02 | % 16.45/3.02 End of proof % 16.45/3.02 % 16.45/3.02 Sub-proof #8 shows that the following formulas are inconsistent: % 16.45/3.02 ---------------------------------------------------------------- % 16.45/3.02 (1) red(n1, n5) % 16.45/3.02 (2) green(n1, n3) % 16.45/3.02 (3) $i(n4) % 16.45/3.02 (4) ~ goal % 16.45/3.02 (5) $i(n5) % 16.45/3.02 (6) green(n3, n4) % 16.45/3.02 (7) green(n1, n4) | red(n1, n4) % 16.45/3.02 (8) $i(n1) % 16.45/3.02 (9) red(n4, n5) % 16.45/3.02 (10) $i(n3) % 16.45/3.02 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.02 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.02 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.02 goal) % 16.45/3.02 % 16.45/3.02 Begin of proof % 16.45/3.02 | % 16.45/3.02 | BETA: splitting (7) gives: % 16.45/3.02 | % 16.45/3.02 | Case 1: % 16.45/3.02 | | % 16.45/3.02 | | (13) green(n1, n4) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (12) with n1, n3, n4, simplifying with (2), (3), % 16.45/3.02 | | (4), (6), (8), (10), (13) gives: % 16.45/3.02 | | (14) $false % 16.45/3.02 | | % 16.45/3.02 | | CLOSE: (14) is inconsistent. % 16.45/3.02 | | % 16.45/3.02 | Case 2: % 16.45/3.02 | | % 16.45/3.02 | | (15) red(n1, n4) % 16.45/3.02 | | % 16.45/3.02 | | GROUND_INST: instantiating (11) with n1, n4, n5, simplifying with (1), (3), % 16.45/3.02 | | (4), (5), (8), (9), (15) gives: % 16.45/3.03 | | (16) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (16) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #9 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) $i(n4) % 16.45/3.03 (2) red(n1, n3) % 16.45/3.03 (3) ~ goal % 16.45/3.03 (4) green(n1, n4) % 16.45/3.03 (5) $i(n1) % 16.45/3.03 (6) $i(n3) % 16.45/3.03 (7) $i(n6) % 16.45/3.03 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.03 (9) red(n3, n6) % 16.45/3.03 (10) green(n4, n6) % 16.45/3.03 (11) green(n1, n6) | red(n1, n6) % 16.45/3.03 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.03 goal) % 16.45/3.03 % 16.45/3.03 Begin of proof % 16.45/3.03 | % 16.45/3.03 | BETA: splitting (11) gives: % 16.45/3.03 | % 16.45/3.03 | Case 1: % 16.45/3.03 | | % 16.45/3.03 | | (13) green(n1, n6) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (12) with n1, n4, n6, simplifying with (1), (3), % 16.45/3.03 | | (4), (5), (7), (10), (13) gives: % 16.45/3.03 | | (14) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (14) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | Case 2: % 16.45/3.03 | | % 16.45/3.03 | | (15) red(n1, n6) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (8) with n1, n3, n6, simplifying with (2), (3), % 16.45/3.03 | | (5), (6), (7), (9), (15) gives: % 16.45/3.03 | | (16) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (16) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #10 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) green(n2, n5) | red(n2, n5) % 16.45/3.03 (2) $i(n2) % 16.45/3.03 (3) green(n2, n4) | red(n2, n4) % 16.45/3.03 (4) $i(n4) % 16.45/3.03 (5) ~ goal % 16.45/3.03 (6) $i(n5) % 16.45/3.03 (7) green(n3, n4) % 16.45/3.03 (8) red(n4, n5) % 16.45/3.03 (9) green(n3, n5) % 16.45/3.03 (10) $i(n3) % 16.45/3.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.03 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.03 goal) % 16.45/3.03 (13) green(n2, n3) % 16.45/3.03 % 16.45/3.03 Begin of proof % 16.45/3.03 | % 16.45/3.03 | BETA: splitting (3) gives: % 16.45/3.03 | % 16.45/3.03 | Case 1: % 16.45/3.03 | | % 16.45/3.03 | | (14) green(n2, n4) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (12) with n2, n3, n4, simplifying with (2), (4), % 16.45/3.03 | | (5), (7), (10), (13), (14) gives: % 16.45/3.03 | | (15) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (15) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | Case 2: % 16.45/3.03 | | % 16.45/3.03 | | (16) red(n2, n4) % 16.45/3.03 | | % 16.45/3.03 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16) % 16.45/3.03 | | are inconsistent by sub-proof #11. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #11 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) green(n2, n5) | red(n2, n5) % 16.45/3.03 (2) $i(n2) % 16.45/3.03 (3) $i(n4) % 16.45/3.03 (4) ~ goal % 16.45/3.03 (5) $i(n5) % 16.45/3.03 (6) red(n4, n5) % 16.45/3.03 (7) green(n3, n5) % 16.45/3.03 (8) $i(n3) % 16.45/3.03 (9) red(n2, n4) % 16.45/3.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.03 goal) % 16.45/3.03 (12) green(n2, n3) % 16.45/3.03 % 16.45/3.03 Begin of proof % 16.45/3.03 | % 16.45/3.03 | BETA: splitting (1) gives: % 16.45/3.03 | % 16.45/3.03 | Case 1: % 16.45/3.03 | | % 16.45/3.03 | | (13) green(n2, n5) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (11) with n2, n3, n5, simplifying with (2), (4), % 16.45/3.03 | | (5), (7), (8), (12), (13) gives: % 16.45/3.03 | | (14) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (14) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | Case 2: % 16.45/3.03 | | % 16.45/3.03 | | (15) red(n2, n5) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (10) with n2, n4, n5, simplifying with (2), (3), % 16.45/3.03 | | (4), (5), (6), (9), (15) gives: % 16.45/3.03 | | (16) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (16) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #12 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) green(n1, n5) | red(n1, n5) % 16.45/3.03 (2) green(n1, n3) % 16.45/3.03 (3) $i(n2) % 16.45/3.03 (4) ~ goal % 16.45/3.03 (5) $i(n5) % 16.45/3.03 (6) $i(n1) % 16.45/3.03 (7) green(n3, n5) % 16.45/3.03 (8) $i(n3) % 16.45/3.03 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.03 (10) red(n2, n5) % 16.45/3.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.03 goal) % 16.45/3.03 (12) red(n1, n2) % 16.45/3.03 % 16.45/3.03 Begin of proof % 16.45/3.03 | % 16.45/3.03 | BETA: splitting (1) gives: % 16.45/3.03 | % 16.45/3.03 | Case 1: % 16.45/3.03 | | % 16.45/3.03 | | (13) green(n1, n5) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (11) with n1, n3, n5, simplifying with (2), (4), % 16.45/3.03 | | (5), (6), (7), (8), (13) gives: % 16.45/3.03 | | (14) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (14) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | Case 2: % 16.45/3.03 | | % 16.45/3.03 | | (15) red(n1, n5) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (9) with n1, n2, n5, simplifying with (3), (4), % 16.45/3.03 | | (5), (6), (10), (12), (15) gives: % 16.45/3.03 | | (16) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (16) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #13 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) green(n1, n3) % 16.45/3.03 (2) $i(n2) % 16.45/3.03 (3) $i(n4) % 16.45/3.03 (4) ~ goal % 16.45/3.03 (5) green(n3, n4) % 16.45/3.03 (6) green(n1, n4) | red(n1, n4) % 16.45/3.03 (7) $i(n1) % 16.45/3.03 (8) $i(n3) % 16.45/3.03 (9) red(n2, n4) % 16.45/3.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.03 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.03 goal) % 16.45/3.03 (12) red(n1, n2) % 16.45/3.03 % 16.45/3.03 Begin of proof % 16.45/3.03 | % 16.45/3.03 | BETA: splitting (6) gives: % 16.45/3.03 | % 16.45/3.03 | Case 1: % 16.45/3.03 | | % 16.45/3.03 | | (13) green(n1, n4) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (11) with n1, n3, n4, simplifying with (1), (3), % 16.45/3.03 | | (4), (5), (7), (8), (13) gives: % 16.45/3.03 | | (14) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (14) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | Case 2: % 16.45/3.03 | | % 16.45/3.03 | | (15) red(n1, n4) % 16.45/3.03 | | % 16.45/3.03 | | GROUND_INST: instantiating (10) with n1, n2, n4, simplifying with (2), (3), % 16.45/3.03 | | (4), (7), (9), (12), (15) gives: % 16.45/3.03 | | (16) $false % 16.45/3.03 | | % 16.45/3.03 | | CLOSE: (16) is inconsistent. % 16.45/3.03 | | % 16.45/3.03 | End of split % 16.45/3.03 | % 16.45/3.03 End of proof % 16.45/3.03 % 16.45/3.03 Sub-proof #14 shows that the following formulas are inconsistent: % 16.45/3.03 ---------------------------------------------------------------- % 16.45/3.03 (1) green(n1, n5) | red(n1, n5) % 16.45/3.03 (2) green(n2, n5) | red(n2, n5) % 16.45/3.03 (3) $i(n2) % 16.45/3.03 (4) red(n2, n3) % 16.45/3.03 (5) red(n1, n3) % 16.45/3.03 (6) red(n3, n5) % 16.45/3.03 (7) ~ goal % 16.45/3.03 (8) $i(n5) % 16.45/3.03 (9) $i(n1) % 16.45/3.03 (10) $i(n3) % 16.45/3.04 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (12) green(n1, n2) % 16.45/3.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (2) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (14) green(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14) % 16.45/3.04 | | are inconsistent by sub-proof #15. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (15) red(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (11) with n2, n3, n5, simplifying with (3), (4), % 16.45/3.04 | | (6), (7), (8), (10), (15) gives: % 16.45/3.04 | | (16) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (16) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #15 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) green(n1, n5) | red(n1, n5) % 16.45/3.04 (2) $i(n2) % 16.45/3.04 (3) red(n1, n3) % 16.45/3.04 (4) red(n3, n5) % 16.45/3.04 (5) ~ goal % 16.45/3.04 (6) green(n2, n5) % 16.45/3.04 (7) $i(n5) % 16.45/3.04 (8) $i(n1) % 16.45/3.04 (9) $i(n3) % 16.45/3.04 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (11) green(n1, n2) % 16.45/3.04 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (1) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (13) green(n1, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (12) with n1, n2, n5, simplifying with (2), (5), % 16.45/3.04 | | (6), (7), (8), (11), (13) gives: % 16.45/3.04 | | (14) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (14) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (15) red(n1, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (10) with n1, n3, n5, simplifying with (3), (4), % 16.45/3.04 | | (5), (7), (8), (9), (15) gives: % 16.45/3.04 | | (16) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (16) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #16 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) $i(n2) % 16.45/3.04 (2) $i(n4) % 16.45/3.04 (3) ~ goal % 16.45/3.04 (4) red(n1, n4) % 16.45/3.04 (5) $i(n1) % 16.45/3.04 (6) green(n2, n6) % 16.45/3.04 (7) $i(n6) % 16.45/3.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (9) green(n1, n2) % 16.45/3.04 (10) green(n1, n6) | red(n1, n6) % 16.45/3.04 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 (12) red(n4, n6) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (10) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (13) green(n1, n6) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (11) with n1, n2, n6, simplifying with (1), (3), % 16.45/3.04 | | (5), (6), (7), (9), (13) gives: % 16.45/3.04 | | (14) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (14) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (15) red(n1, n6) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (8) with n1, n4, n6, simplifying with (2), (3), % 16.45/3.04 | | (4), (5), (7), (12), (15) gives: % 16.45/3.04 | | (16) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (16) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #17 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) green(n1, n5) | red(n1, n5) % 16.45/3.04 (2) green(n2, n5) | red(n2, n5) % 16.45/3.04 (3) $i(n2) % 16.45/3.04 (4) $i(n4) % 16.45/3.04 (5) ~ goal % 16.45/3.04 (6) $i(n5) % 16.45/3.04 (7) green(n1, n4) | red(n1, n4) % 16.45/3.04 (8) $i(n1) % 16.45/3.04 (9) green(n3, n5) % 16.45/3.04 (10) $i(n3) % 16.45/3.04 (11) red(n2, n4) % 16.45/3.04 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (13) green(n4, n5) % 16.45/3.04 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 (15) red(n1, n2) % 16.45/3.04 (16) green(n2, n3) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (2) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (17) green(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (14) with n2, n3, n5, simplifying with (3), (5), % 16.45/3.04 | | (6), (9), (10), (16), (17) gives: % 16.45/3.04 | | (18) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (18) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (19) red(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), (15), % 16.45/3.04 | | (19) are inconsistent by sub-proof #34. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #18 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) green(n2, n5) | red(n2, n5) % 16.45/3.04 (2) $i(n2) % 16.45/3.04 (3) $i(n4) % 16.45/3.04 (4) ~ goal % 16.45/3.04 (5) $i(n5) % 16.45/3.04 (6) green(n2, n4) % 16.45/3.04 (7) $i(n6) % 16.45/3.04 (8) green(n2, n6) | red(n2, n6) % 16.45/3.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (10) green(n4, n5) % 16.45/3.04 (11) red(n5, n6) % 16.45/3.04 (12) green(n4, n6) % 16.45/3.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (8) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (14) green(n2, n6) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (13) with n2, n4, n6, simplifying with (2), (3), % 16.45/3.04 | | (4), (6), (7), (12), (14) gives: % 16.45/3.04 | | (15) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (15) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (16) red(n2, n6) % 16.45/3.04 | | % 16.45/3.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (16) % 16.45/3.04 | | are inconsistent by sub-proof #19. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #19 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) green(n2, n5) | red(n2, n5) % 16.45/3.04 (2) $i(n2) % 16.45/3.04 (3) $i(n4) % 16.45/3.04 (4) ~ goal % 16.45/3.04 (5) $i(n5) % 16.45/3.04 (6) red(n2, n6) % 16.45/3.04 (7) green(n2, n4) % 16.45/3.04 (8) $i(n6) % 16.45/3.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (10) green(n4, n5) % 16.45/3.04 (11) red(n5, n6) % 16.45/3.04 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (1) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (13) green(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (12) with n2, n4, n5, simplifying with (2), (3), % 16.45/3.04 | | (4), (5), (7), (10), (13) gives: % 16.45/3.04 | | (14) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (14) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (15) red(n2, n5) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (9) with n2, n5, n6, simplifying with (2), (4), % 16.45/3.04 | | (5), (6), (8), (11), (15) gives: % 16.45/3.04 | | (16) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (16) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #20 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) $i(n4) % 16.45/3.04 (2) red(n3, n5) % 16.45/3.04 (3) ~ goal % 16.45/3.04 (4) $i(n5) % 16.45/3.04 (5) green(n3, n4) % 16.45/3.04 (6) $i(n3) % 16.45/3.04 (7) $i(n6) % 16.45/3.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.04 (9) red(n5, n6) % 16.45/3.04 (10) green(n4, n6) % 16.45/3.04 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.04 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.04 goal) % 16.45/3.04 (12) green(n3, n6) | red(n3, n6) % 16.45/3.04 % 16.45/3.04 Begin of proof % 16.45/3.04 | % 16.45/3.04 | BETA: splitting (12) gives: % 16.45/3.04 | % 16.45/3.04 | Case 1: % 16.45/3.04 | | % 16.45/3.04 | | (13) green(n3, n6) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (11) with n3, n4, n6, simplifying with (1), (3), % 16.45/3.04 | | (5), (6), (7), (10), (13) gives: % 16.45/3.04 | | (14) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (14) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | Case 2: % 16.45/3.04 | | % 16.45/3.04 | | (15) red(n3, n6) % 16.45/3.04 | | % 16.45/3.04 | | GROUND_INST: instantiating (8) with n3, n5, n6, simplifying with (2), (3), % 16.45/3.04 | | (4), (6), (7), (9), (15) gives: % 16.45/3.04 | | (16) $false % 16.45/3.04 | | % 16.45/3.04 | | CLOSE: (16) is inconsistent. % 16.45/3.04 | | % 16.45/3.04 | End of split % 16.45/3.04 | % 16.45/3.04 End of proof % 16.45/3.04 % 16.45/3.04 Sub-proof #21 shows that the following formulas are inconsistent: % 16.45/3.04 ---------------------------------------------------------------- % 16.45/3.04 (1) green(n2, n5) | red(n2, n5) % 16.45/3.04 (2) $i(n2) % 16.45/3.04 (3) red(n1, n3) % 16.45/3.04 (4) ~ goal % 16.45/3.04 (5) $i(n5) % 16.45/3.04 (6) $i(n1) % 16.45/3.04 (7) green(n3, n5) % 16.45/3.04 (8) $i(n3) % 16.45/3.04 (9) $i(n6) % 16.45/3.05 (10) green(n2, n6) | red(n2, n6) % 16.45/3.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (12) red(n5, n6) % 16.45/3.05 (13) green(n1, n2) % 16.45/3.05 (14) green(n1, n6) | red(n1, n6) % 16.45/3.05 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (16) green(n3, n6) | red(n3, n6) % 16.45/3.05 (17) green(n2, n3) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (16) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (18) green(n3, n6) % 16.45/3.05 | | % 16.45/3.05 | | BETA: splitting (10) gives: % 16.45/3.05 | | % 16.45/3.05 | | Case 1: % 16.45/3.05 | | | % 16.45/3.05 | | | (19) green(n2, n6) % 16.45/3.05 | | | % 16.45/3.05 | | | GROUND_INST: instantiating (15) with n2, n3, n6, simplifying with (2), % 16.45/3.05 | | | (4), (8), (9), (17), (18), (19) gives: % 16.45/3.05 | | | (20) $false % 16.45/3.05 | | | % 16.45/3.05 | | | CLOSE: (20) is inconsistent. % 16.45/3.05 | | | % 16.45/3.05 | | Case 2: % 16.45/3.05 | | | % 16.45/3.05 | | | (21) red(n2, n6) % 16.45/3.05 | | | % 16.45/3.05 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (15), (17), (21) % 16.45/3.05 | | | are inconsistent by sub-proof #22. % 16.45/3.05 | | | % 16.45/3.05 | | End of split % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (22) red(n3, n6) % 16.45/3.05 | | % 16.45/3.05 | | BETA: splitting (10) gives: % 16.45/3.05 | | % 16.45/3.05 | | Case 1: % 16.45/3.05 | | | % 16.45/3.05 | | | (23) green(n2, n6) % 16.45/3.05 | | | % 16.45/3.05 | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (11), (13), (14), (15), (22), % 16.45/3.05 | | | (23) are inconsistent by sub-proof #36. % 16.45/3.05 | | | % 16.45/3.05 | | Case 2: % 16.45/3.05 | | | % 16.45/3.05 | | | (24) red(n2, n6) % 16.45/3.05 | | | % 16.45/3.05 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (15), (17), (24) % 16.45/3.05 | | | are inconsistent by sub-proof #22. % 16.45/3.05 | | | % 16.45/3.05 | | End of split % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #22 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n2, n5) | red(n2, n5) % 16.45/3.05 (2) $i(n2) % 16.45/3.05 (3) ~ goal % 16.45/3.05 (4) $i(n5) % 16.45/3.05 (5) red(n2, n6) % 16.45/3.05 (6) green(n3, n5) % 16.45/3.05 (7) $i(n3) % 16.45/3.05 (8) $i(n6) % 16.45/3.05 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (10) red(n5, n6) % 16.45/3.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (12) green(n2, n3) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (1) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (13) green(n2, n5) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (11) with n2, n3, n5, simplifying with (2), (3), % 16.45/3.05 | | (4), (6), (7), (12), (13) gives: % 16.45/3.05 | | (14) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (14) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (15) red(n2, n5) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (9) with n2, n5, n6, simplifying with (2), (3), % 16.45/3.05 | | (4), (5), (8), (10), (15) gives: % 16.45/3.05 | | (16) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (16) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #23 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n1, n5) | red(n1, n5) % 16.45/3.05 (2) green(n2, n5) | red(n2, n5) % 16.45/3.05 (3) $i(n2) % 16.45/3.05 (4) red(n3, n4) % 16.45/3.05 (5) $i(n4) % 16.45/3.05 (6) red(n1, n3) % 16.45/3.05 (7) ~ goal % 16.45/3.05 (8) $i(n5) % 16.45/3.05 (9) green(n1, n4) | red(n1, n4) % 16.45/3.05 (10) $i(n1) % 16.45/3.05 (11) $i(n3) % 16.45/3.05 (12) green(n2, n4) % 16.45/3.05 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (14) green(n4, n5) % 16.45/3.05 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (16) red(n1, n2) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (2) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (17) green(n2, n5) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (15) with n2, n4, n5, simplifying with (3), (5), % 16.45/3.05 | | (7), (8), (12), (14), (17) gives: % 16.45/3.05 | | (18) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (18) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (19) red(n2, n5) % 16.45/3.05 | | % 16.45/3.05 | | BETA: splitting (1) gives: % 16.45/3.05 | | % 16.45/3.05 | | Case 1: % 16.45/3.05 | | | % 16.45/3.05 | | | (20) green(n1, n5) % 16.45/3.05 | | | % 16.45/3.05 | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15), % 16.45/3.05 | | | (20) are inconsistent by sub-proof #28. % 16.45/3.05 | | | % 16.45/3.05 | | Case 2: % 16.45/3.05 | | | % 16.45/3.05 | | | (21) red(n1, n5) % 16.45/3.05 | | | % 16.45/3.05 | | | GROUND_INST: instantiating (13) with n1, n2, n5, simplifying with (3), % 16.45/3.05 | | | (7), (8), (10), (16), (19), (21) gives: % 16.45/3.05 | | | (22) $false % 16.45/3.05 | | | % 16.45/3.05 | | | CLOSE: (22) is inconsistent. % 16.45/3.05 | | | % 16.45/3.05 | | End of split % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #24 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n1, n3) % 16.45/3.05 (2) $i(n2) % 16.45/3.05 (3) red(n3, n4) % 16.45/3.05 (4) $i(n4) % 16.45/3.05 (5) ~ goal % 16.45/3.05 (6) $i(n1) % 16.45/3.05 (7) $i(n3) % 16.45/3.05 (8) $i(n6) % 16.45/3.05 (9) green(n2, n6) | red(n2, n6) % 16.45/3.05 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (11) green(n1, n6) | red(n1, n6) % 16.45/3.05 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (13) red(n4, n6) % 16.45/3.05 (14) red(n1, n2) % 16.45/3.05 (15) green(n3, n6) | red(n3, n6) % 16.45/3.05 (16) green(n2, n3) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (15) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (17) green(n3, n6) % 16.45/3.05 | | % 16.45/3.05 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (14), (16), % 16.45/3.05 | | (17) are inconsistent by sub-proof #25. % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (18) red(n3, n6) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (10) with n3, n4, n6, simplifying with (3), (4), % 16.45/3.05 | | (5), (7), (8), (13), (18) gives: % 16.45/3.05 | | (19) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (19) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #25 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n3, n6) % 16.45/3.05 (2) green(n1, n3) % 16.45/3.05 (3) $i(n2) % 16.45/3.05 (4) ~ goal % 16.45/3.05 (5) $i(n1) % 16.45/3.05 (6) $i(n3) % 16.45/3.05 (7) $i(n6) % 16.45/3.05 (8) green(n2, n6) | red(n2, n6) % 16.45/3.05 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (10) green(n1, n6) | red(n1, n6) % 16.45/3.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (12) red(n1, n2) % 16.45/3.05 (13) green(n2, n3) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (8) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (14) green(n2, n6) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (11) with n2, n3, n6, simplifying with (1), (3), % 16.45/3.05 | | (4), (6), (7), (13), (14) gives: % 16.45/3.05 | | (15) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (15) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (16) red(n2, n6) % 16.45/3.05 | | % 16.45/3.05 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (16) % 16.45/3.05 | | are inconsistent by sub-proof #26. % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #26 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n3, n6) % 16.45/3.05 (2) green(n1, n3) % 16.45/3.05 (3) $i(n2) % 16.45/3.05 (4) ~ goal % 16.45/3.05 (5) $i(n1) % 16.45/3.05 (6) red(n2, n6) % 16.45/3.05 (7) $i(n3) % 16.45/3.05 (8) $i(n6) % 16.45/3.05 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.05 (10) green(n1, n6) | red(n1, n6) % 16.45/3.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.05 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.05 goal) % 16.45/3.05 (12) red(n1, n2) % 16.45/3.05 % 16.45/3.05 Begin of proof % 16.45/3.05 | % 16.45/3.05 | BETA: splitting (10) gives: % 16.45/3.05 | % 16.45/3.05 | Case 1: % 16.45/3.05 | | % 16.45/3.05 | | (13) green(n1, n6) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (11) with n1, n3, n6, simplifying with (1), (2), % 16.45/3.05 | | (4), (5), (7), (8), (13) gives: % 16.45/3.05 | | (14) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (14) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | Case 2: % 16.45/3.05 | | % 16.45/3.05 | | (15) red(n1, n6) % 16.45/3.05 | | % 16.45/3.05 | | GROUND_INST: instantiating (9) with n1, n2, n6, simplifying with (3), (4), % 16.45/3.05 | | (5), (6), (8), (12), (15) gives: % 16.45/3.05 | | (16) $false % 16.45/3.05 | | % 16.45/3.05 | | CLOSE: (16) is inconsistent. % 16.45/3.05 | | % 16.45/3.05 | End of split % 16.45/3.05 | % 16.45/3.05 End of proof % 16.45/3.05 % 16.45/3.05 Sub-proof #27 shows that the following formulas are inconsistent: % 16.45/3.05 ---------------------------------------------------------------- % 16.45/3.05 (1) green(n1, n5) | red(n1, n5) % 16.45/3.05 (2) red(n3, n4) % 16.45/3.05 (3) $i(n4) % 16.45/3.05 (4) red(n1, n3) % 16.45/3.05 (5) red(n3, n5) % 16.45/3.05 (6) ~ goal % 16.45/3.05 (7) $i(n5) % 16.45/3.05 (8) green(n1, n4) | red(n1, n4) % 16.45/3.05 (9) $i(n1) % 16.45/3.05 (10) $i(n3) % 16.45/3.06 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (12) green(n4, n5) % 16.45/3.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (1) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (14) green(n1, n5) % 16.45/3.06 | | % 16.45/3.06 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14) % 16.45/3.06 | | are inconsistent by sub-proof #28. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (15) red(n1, n5) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (11) with n1, n3, n5, simplifying with (4), (5), % 16.45/3.06 | | (6), (7), (9), (10), (15) gives: % 16.45/3.06 | | (16) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (16) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #28 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) red(n3, n4) % 16.45/3.06 (2) $i(n4) % 16.45/3.06 (3) red(n1, n3) % 16.45/3.06 (4) ~ goal % 16.45/3.06 (5) $i(n5) % 16.45/3.06 (6) green(n1, n4) | red(n1, n4) % 16.45/3.06 (7) $i(n1) % 16.45/3.06 (8) green(n1, n5) % 16.45/3.06 (9) $i(n3) % 16.45/3.06 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (11) green(n4, n5) % 16.45/3.06 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (6) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (13) green(n1, n4) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (12) with n1, n4, n5, simplifying with (2), (4), % 16.45/3.06 | | (5), (7), (8), (11), (13) gives: % 16.45/3.06 | | (14) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (14) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (15) red(n1, n4) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (10) with n1, n3, n4, simplifying with (1), (2), % 16.45/3.06 | | (3), (4), (7), (9), (15) gives: % 16.45/3.06 | | (16) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (16) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #29 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) red(n3, n4) % 16.45/3.06 (2) $i(n4) % 16.45/3.06 (3) ~ goal % 16.45/3.06 (4) green(n5, n6) % 16.45/3.06 (5) $i(n5) % 16.45/3.06 (6) green(n3, n5) % 16.45/3.06 (7) $i(n3) % 16.45/3.06 (8) $i(n6) % 16.45/3.06 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 (11) red(n4, n6) % 16.45/3.06 (12) green(n3, n6) | red(n3, n6) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (12) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (13) green(n3, n6) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (10) with n3, n5, n6, simplifying with (3), (4), % 16.45/3.06 | | (5), (6), (7), (8), (13) gives: % 16.45/3.06 | | (14) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (14) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (15) red(n3, n6) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (9) with n3, n4, n6, simplifying with (1), (2), % 16.45/3.06 | | (3), (7), (8), (11), (15) gives: % 16.45/3.06 | | (16) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (16) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #30 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) green(n2, n5) | red(n2, n5) % 16.45/3.06 (2) $i(n2) % 16.45/3.06 (3) red(n2, n3) % 16.45/3.06 (4) green(n2, n4) | red(n2, n4) % 16.45/3.06 (5) $i(n4) % 16.45/3.06 (6) red(n3, n5) % 16.45/3.06 (7) ~ goal % 16.45/3.06 (8) green(n5, n6) % 16.45/3.06 (9) $i(n5) % 16.45/3.06 (10) $i(n3) % 16.45/3.06 (11) $i(n6) % 16.45/3.06 (12) green(n2, n6) | red(n2, n6) % 16.45/3.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (14) green(n4, n5) % 16.45/3.06 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 (16) red(n4, n6) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (4) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (17) green(n2, n4) % 16.45/3.06 | | % 16.45/3.06 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (13), (14), (15), (17) % 16.45/3.06 | | are inconsistent by sub-proof #32. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (18) red(n2, n4) % 16.45/3.06 | | % 16.45/3.06 | | BETA: splitting (12) gives: % 16.45/3.06 | | % 16.45/3.06 | | Case 1: % 16.45/3.06 | | | % 16.45/3.06 | | | (19) green(n2, n6) % 16.45/3.06 | | | % 16.45/3.06 | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (13), (15), (19) % 16.45/3.06 | | | are inconsistent by sub-proof #31. % 16.45/3.06 | | | % 16.45/3.06 | | Case 2: % 16.45/3.06 | | | % 16.45/3.06 | | | (20) red(n2, n6) % 16.45/3.06 | | | % 16.45/3.06 | | | GROUND_INST: instantiating (13) with n2, n4, n6, simplifying with (2), % 16.45/3.06 | | | (5), (7), (11), (16), (18), (20) gives: % 16.45/3.06 | | | (21) $false % 16.45/3.06 | | | % 16.45/3.06 | | | CLOSE: (21) is inconsistent. % 16.45/3.06 | | | % 16.45/3.06 | | End of split % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #31 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) green(n2, n5) | red(n2, n5) % 16.45/3.06 (2) $i(n2) % 16.45/3.06 (3) red(n2, n3) % 16.45/3.06 (4) red(n3, n5) % 16.45/3.06 (5) ~ goal % 16.45/3.06 (6) green(n5, n6) % 16.45/3.06 (7) $i(n5) % 16.45/3.06 (8) green(n2, n6) % 16.45/3.06 (9) $i(n3) % 16.45/3.06 (10) $i(n6) % 16.45/3.06 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (1) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (13) green(n2, n5) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (12) with n2, n5, n6, simplifying with (2), (5), % 16.45/3.06 | | (6), (7), (8), (10), (13) gives: % 16.45/3.06 | | (14) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (14) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (15) red(n2, n5) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (11) with n2, n3, n5, simplifying with (2), (3), % 16.45/3.06 | | (4), (5), (7), (9), (15) gives: % 16.45/3.06 | | (16) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (16) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #32 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) green(n2, n5) | red(n2, n5) % 16.45/3.06 (2) $i(n2) % 16.45/3.06 (3) red(n2, n3) % 16.45/3.06 (4) $i(n4) % 16.45/3.06 (5) red(n3, n5) % 16.45/3.06 (6) ~ goal % 16.45/3.06 (7) $i(n5) % 16.45/3.06 (8) $i(n3) % 16.45/3.06 (9) green(n2, n4) % 16.45/3.06 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (11) green(n4, n5) % 16.45/3.06 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (1) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (13) green(n2, n5) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (12) with n2, n4, n5, simplifying with (2), (4), % 16.45/3.06 | | (6), (7), (9), (11), (13) gives: % 16.45/3.06 | | (14) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (14) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | Case 2: % 16.45/3.06 | | % 16.45/3.06 | | (15) red(n2, n5) % 16.45/3.06 | | % 16.45/3.06 | | GROUND_INST: instantiating (10) with n2, n3, n5, simplifying with (2), (3), % 16.45/3.06 | | (5), (6), (7), (8), (15) gives: % 16.45/3.06 | | (16) $false % 16.45/3.06 | | % 16.45/3.06 | | CLOSE: (16) is inconsistent. % 16.45/3.06 | | % 16.45/3.06 | End of split % 16.45/3.06 | % 16.45/3.06 End of proof % 16.45/3.06 % 16.45/3.06 Sub-proof #33 shows that the following formulas are inconsistent: % 16.45/3.06 ---------------------------------------------------------------- % 16.45/3.06 (1) green(n1, n5) | red(n1, n5) % 16.45/3.06 (2) green(n2, n5) | red(n2, n5) % 16.45/3.06 (3) $i(n2) % 16.45/3.06 (4) $i(n4) % 16.45/3.06 (5) ~ goal % 16.45/3.06 (6) green(n5, n6) % 16.45/3.06 (7) $i(n5) % 16.45/3.06 (8) green(n1, n4) | red(n1, n4) % 16.45/3.06 (9) $i(n1) % 16.45/3.06 (10) $i(n6) % 16.45/3.06 (11) green(n2, n6) | red(n2, n6) % 16.45/3.06 (12) red(n2, n4) % 16.45/3.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.06 (14) green(n4, n5) % 16.45/3.06 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.06 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.06 goal) % 16.45/3.06 (16) red(n4, n6) % 16.45/3.06 (17) red(n1, n2) % 16.45/3.06 % 16.45/3.06 Begin of proof % 16.45/3.06 | % 16.45/3.06 | BETA: splitting (11) gives: % 16.45/3.06 | % 16.45/3.06 | Case 1: % 16.45/3.06 | | % 16.45/3.06 | | (18) green(n2, n6) % 16.45/3.06 | | % 16.45/3.06 | | BETA: splitting (2) gives: % 16.45/3.06 | | % 16.45/3.06 | | Case 1: % 16.45/3.06 | | | % 16.45/3.06 | | | (19) green(n2, n5) % 16.45/3.06 | | | % 16.45/3.06 | | | GROUND_INST: instantiating (15) with n2, n5, n6, simplifying with (3), % 16.45/3.06 | | | (5), (6), (7), (10), (18), (19) gives: % 16.45/3.06 | | | (20) $false % 16.45/3.06 | | | % 16.45/3.06 | | | CLOSE: (20) is inconsistent. % 16.45/3.06 | | | % 16.45/3.07 | | Case 2: % 16.45/3.07 | | | % 16.45/3.07 | | | (21) red(n2, n5) % 16.45/3.07 | | | % 16.45/3.07 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (12), (13), (14), (15), % 16.45/3.07 | | | (17), (21) are inconsistent by sub-proof #34. % 16.45/3.07 | | | % 16.45/3.07 | | End of split % 16.45/3.07 | | % 16.45/3.07 | Case 2: % 16.45/3.07 | | % 16.45/3.07 | | (22) red(n2, n6) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (13) with n2, n4, n6, simplifying with (3), (4), % 16.45/3.07 | | (5), (10), (12), (16), (22) gives: % 16.45/3.07 | | (23) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (23) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | End of split % 16.45/3.07 | % 16.45/3.07 End of proof % 16.45/3.07 % 16.45/3.07 Sub-proof #34 shows that the following formulas are inconsistent: % 16.45/3.07 ---------------------------------------------------------------- % 16.45/3.07 (1) green(n1, n5) | red(n1, n5) % 16.45/3.07 (2) $i(n2) % 16.45/3.07 (3) $i(n4) % 16.45/3.07 (4) ~ goal % 16.45/3.07 (5) $i(n5) % 16.45/3.07 (6) green(n1, n4) | red(n1, n4) % 16.45/3.07 (7) $i(n1) % 16.45/3.07 (8) red(n2, n4) % 16.45/3.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.07 (10) green(n4, n5) % 16.45/3.07 (11) red(n2, n5) % 16.45/3.07 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.07 goal) % 16.45/3.07 (13) red(n1, n2) % 16.45/3.07 % 16.45/3.07 Begin of proof % 16.45/3.07 | % 16.45/3.07 | BETA: splitting (1) gives: % 16.45/3.07 | % 16.45/3.07 | Case 1: % 16.45/3.07 | | % 16.45/3.07 | | (14) green(n1, n5) % 16.45/3.07 | | % 16.45/3.07 | | BETA: splitting (6) gives: % 16.45/3.07 | | % 16.45/3.07 | | Case 1: % 16.45/3.07 | | | % 16.45/3.07 | | | (15) green(n1, n4) % 16.45/3.07 | | | % 16.45/3.07 | | | GROUND_INST: instantiating (12) with n1, n4, n5, simplifying with (3), % 16.45/3.07 | | | (4), (5), (7), (10), (14), (15) gives: % 16.45/3.07 | | | (16) $false % 16.45/3.07 | | | % 16.45/3.07 | | | CLOSE: (16) is inconsistent. % 16.45/3.07 | | | % 16.45/3.07 | | Case 2: % 16.45/3.07 | | | % 16.45/3.07 | | | (17) red(n1, n4) % 16.45/3.07 | | | % 16.45/3.07 | | | GROUND_INST: instantiating (9) with n1, n2, n4, simplifying with (2), (3), % 16.45/3.07 | | | (4), (7), (8), (13), (17) gives: % 16.45/3.07 | | | (18) $false % 16.45/3.07 | | | % 16.45/3.07 | | | CLOSE: (18) is inconsistent. % 16.45/3.07 | | | % 16.45/3.07 | | End of split % 16.45/3.07 | | % 16.45/3.07 | Case 2: % 16.45/3.07 | | % 16.45/3.07 | | (19) red(n1, n5) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (9) with n1, n2, n5, simplifying with (2), (4), % 16.45/3.07 | | (5), (7), (11), (13), (19) gives: % 16.45/3.07 | | (20) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (20) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | End of split % 16.45/3.07 | % 16.45/3.07 End of proof % 16.45/3.07 % 16.45/3.07 Sub-proof #35 shows that the following formulas are inconsistent: % 16.45/3.07 ---------------------------------------------------------------- % 16.45/3.07 (1) $i(n2) % 16.45/3.07 (2) green(n2, n4) | red(n2, n4) % 16.45/3.07 (3) $i(n4) % 16.45/3.07 (4) red(n1, n3) % 16.45/3.07 (5) ~ goal % 16.45/3.07 (6) green(n3, n4) % 16.45/3.07 (7) $i(n1) % 16.45/3.07 (8) $i(n3) % 16.45/3.07 (9) $i(n6) % 16.45/3.07 (10) green(n2, n6) | red(n2, n6) % 16.45/3.07 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.07 (12) green(n1, n2) % 16.45/3.07 (13) green(n1, n6) | red(n1, n6) % 16.45/3.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.07 goal) % 16.45/3.07 (15) red(n4, n6) % 16.45/3.07 (16) green(n3, n6) | red(n3, n6) % 16.45/3.07 (17) green(n2, n3) % 16.45/3.07 % 16.45/3.07 Begin of proof % 16.45/3.07 | % 16.45/3.07 | BETA: splitting (2) gives: % 16.45/3.07 | % 16.45/3.07 | Case 1: % 16.45/3.07 | | % 16.45/3.07 | | (18) green(n2, n4) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (14) with n2, n3, n4, simplifying with (1), (3), % 16.45/3.07 | | (5), (6), (8), (17), (18) gives: % 16.45/3.07 | | (19) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (19) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | Case 2: % 16.45/3.07 | | % 16.45/3.07 | | (20) red(n2, n4) % 16.45/3.07 | | % 16.45/3.07 | | BETA: splitting (16) gives: % 16.45/3.07 | | % 16.45/3.07 | | Case 1: % 16.45/3.07 | | | % 16.45/3.07 | | | (21) green(n3, n6) % 16.45/3.07 | | | % 16.45/3.07 | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (14), (15), (17), (20), % 16.45/3.07 | | | (21) are inconsistent by sub-proof #37. % 16.45/3.07 | | | % 16.45/3.07 | | Case 2: % 16.45/3.07 | | | % 16.45/3.07 | | | (22) red(n3, n6) % 16.45/3.07 | | | % 16.45/3.07 | | | BETA: splitting (10) gives: % 16.45/3.07 | | | % 16.45/3.07 | | | Case 1: % 16.45/3.07 | | | | % 16.45/3.07 | | | | (23) green(n2, n6) % 16.45/3.07 | | | | % 16.45/3.07 | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11), (12), (13), (14), (22), % 16.45/3.07 | | | | (23) are inconsistent by sub-proof #36. % 16.45/3.07 | | | | % 16.45/3.07 | | | Case 2: % 16.45/3.07 | | | | % 16.45/3.07 | | | | (24) red(n2, n6) % 16.45/3.07 | | | | % 16.45/3.07 | | | | GROUND_INST: instantiating (11) with n2, n4, n6, simplifying with (1), % 16.45/3.07 | | | | (3), (5), (9), (15), (20), (24) gives: % 16.45/3.07 | | | | (25) $false % 16.45/3.07 | | | | % 16.45/3.07 | | | | CLOSE: (25) is inconsistent. % 16.45/3.07 | | | | % 16.45/3.07 | | | End of split % 16.45/3.07 | | | % 16.45/3.07 | | End of split % 16.45/3.07 | | % 16.45/3.07 | End of split % 16.45/3.07 | % 16.45/3.07 End of proof % 16.45/3.07 % 16.45/3.07 Sub-proof #36 shows that the following formulas are inconsistent: % 16.45/3.07 ---------------------------------------------------------------- % 16.45/3.07 (1) $i(n2) % 16.45/3.07 (2) red(n1, n3) % 16.45/3.07 (3) ~ goal % 16.45/3.07 (4) $i(n1) % 16.45/3.07 (5) green(n2, n6) % 16.45/3.07 (6) $i(n3) % 16.45/3.07 (7) $i(n6) % 16.45/3.07 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.07 (9) red(n3, n6) % 16.45/3.07 (10) green(n1, n2) % 16.45/3.07 (11) green(n1, n6) | red(n1, n6) % 16.45/3.07 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.07 goal) % 16.45/3.07 % 16.45/3.07 Begin of proof % 16.45/3.07 | % 16.45/3.07 | BETA: splitting (11) gives: % 16.45/3.07 | % 16.45/3.07 | Case 1: % 16.45/3.07 | | % 16.45/3.07 | | (13) green(n1, n6) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (12) with n1, n2, n6, simplifying with (1), (3), % 16.45/3.07 | | (4), (5), (7), (10), (13) gives: % 16.45/3.07 | | (14) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (14) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | Case 2: % 16.45/3.07 | | % 16.45/3.07 | | (15) red(n1, n6) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (8) with n1, n3, n6, simplifying with (2), (3), % 16.45/3.07 | | (4), (6), (7), (9), (15) gives: % 16.45/3.07 | | (16) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (16) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | End of split % 16.45/3.07 | % 16.45/3.07 End of proof % 16.45/3.07 % 16.45/3.07 Sub-proof #37 shows that the following formulas are inconsistent: % 16.45/3.07 ---------------------------------------------------------------- % 16.45/3.07 (1) green(n3, n6) % 16.45/3.07 (2) $i(n2) % 16.45/3.07 (3) $i(n4) % 16.45/3.07 (4) ~ goal % 16.45/3.07 (5) $i(n3) % 16.45/3.07 (6) $i(n6) % 16.45/3.07 (7) green(n2, n6) | red(n2, n6) % 16.45/3.07 (8) red(n2, n4) % 16.45/3.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ red(v1, v2) | ~ red(v0, v2) | ~ red(v0, v1) | goal) % 16.45/3.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 16.45/3.07 $i(v0) | ~ green(v1, v2) | ~ green(v0, v2) | ~ green(v0, v1) | % 16.45/3.07 goal) % 16.45/3.07 (11) red(n4, n6) % 16.45/3.07 (12) green(n2, n3) % 16.45/3.07 % 16.45/3.07 Begin of proof % 16.45/3.07 | % 16.45/3.07 | BETA: splitting (7) gives: % 16.45/3.07 | % 16.45/3.07 | Case 1: % 16.45/3.07 | | % 16.45/3.07 | | (13) green(n2, n6) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (10) with n2, n3, n6, simplifying with (1), (2), % 16.45/3.07 | | (4), (5), (6), (12), (13) gives: % 16.45/3.07 | | (14) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (14) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | Case 2: % 16.45/3.07 | | % 16.45/3.07 | | (15) red(n2, n6) % 16.45/3.07 | | % 16.45/3.07 | | GROUND_INST: instantiating (9) with n2, n4, n6, simplifying with (2), (3), % 16.45/3.07 | | (4), (6), (8), (11), (15) gives: % 16.45/3.07 | | (16) $false % 16.45/3.07 | | % 16.45/3.07 | | CLOSE: (16) is inconsistent. % 16.45/3.07 | | % 16.45/3.07 | End of split % 16.45/3.07 | % 16.45/3.07 End of proof % 16.45/3.07 % SZS output end Proof for theBenchmark % 16.45/3.07 % 16.45/3.07 2466ms %------------------------------------------------------------------------------