%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO189+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:03 EDT 2023 % Result : Theorem 15.67s 2.82s % Output : Proof 16.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO189+2 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 22:00:14 EDT 2023 % 0.12/0.33 % CPUTime : % 0.47/0.60 ________ _____ % 0.47/0.60 ___ __ \_________(_)________________________________ % 0.47/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.47/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.47/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.47/0.60 % 0.47/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.47/0.60 (2023-06-19) % 0.47/0.60 % 0.47/0.60 (c) Philipp Rümmer, 2009-2023 % 0.47/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.47/0.60 Amanda Stjerna. % 0.47/0.60 Free software under BSD-3-Clause. % 0.47/0.60 % 0.47/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.47/0.60 % 0.47/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.47/0.61 Running up to 7 provers in parallel. % 0.47/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.47/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.47/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.47/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.47/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.47/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.47/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/1.06 Prover 4: Preprocessing ... % 2.59/1.06 Prover 1: Preprocessing ... % 2.69/1.11 Prover 3: Preprocessing ... % 2.69/1.11 Prover 5: Preprocessing ... % 2.69/1.11 Prover 6: Preprocessing ... % 2.69/1.11 Prover 0: Preprocessing ... % 2.69/1.12 Prover 2: Preprocessing ... % 4.16/1.31 Prover 6: Constructing countermodel ... % 4.16/1.31 Prover 2: Proving ... % 4.16/1.32 Prover 5: Proving ... % 4.16/1.32 Prover 3: Constructing countermodel ... % 4.16/1.34 Prover 1: Constructing countermodel ... % 4.67/1.40 Prover 4: Constructing countermodel ... % 5.08/1.42 Prover 0: Proving ... % 5.42/1.46 Prover 6: gave up % 5.42/1.47 Prover 3: gave up % 5.42/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.42/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.42/1.49 Prover 1: gave up % 5.42/1.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.42/1.51 Prover 8: Preprocessing ... % 5.42/1.53 Prover 7: Preprocessing ... % 6.06/1.55 Prover 9: Preprocessing ... % 6.06/1.56 Prover 7: Warning: ignoring some quantifiers % 6.39/1.59 Prover 7: Constructing countermodel ... % 6.39/1.61 Prover 8: Warning: ignoring some quantifiers % 6.39/1.62 Prover 8: Constructing countermodel ... % 7.47/1.73 Prover 8: gave up % 7.47/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.72/1.76 Prover 10: Preprocessing ... % 7.72/1.81 Prover 10: Warning: ignoring some quantifiers % 7.72/1.81 Prover 10: Constructing countermodel ... % 7.72/1.82 Prover 9: Constructing countermodel ... % 8.29/1.86 Prover 7: gave up % 8.60/1.87 Prover 10: gave up % 8.60/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.60/1.89 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.60/1.89 Prover 11: Preprocessing ... % 8.60/1.93 Prover 12: Preprocessing ... % 9.29/2.01 Prover 12: Proving ... % 9.75/2.05 Prover 11: Constructing countermodel ... % 11.76/2.32 Prover 11: gave up % 11.76/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.07/2.33 Prover 13: Preprocessing ... % 12.77/2.41 Prover 13: Warning: ignoring some quantifiers % 12.77/2.42 Prover 13: Constructing countermodel ... % 14.42/2.63 Prover 13: gave up % 14.53/2.65 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 14.53/2.66 Prover 14: Preprocessing ... % 15.67/2.79 Prover 14: Proving ... % 15.67/2.82 Prover 4: Found proof (size 276) % 15.67/2.82 Prover 4: proved (2198ms) % 15.67/2.82 Prover 9: stopped % 15.67/2.82 Prover 2: stopped % 15.67/2.82 Prover 5: stopped % 15.67/2.82 Prover 0: stopped % 15.67/2.82 Prover 14: stopped % 15.67/2.82 Prover 12: stopped % 15.67/2.82 % 15.67/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.67/2.82 % 15.67/2.84 % SZS output start Proof for theBenchmark % 15.67/2.85 Assumptions after simplification: % 15.67/2.85 --------------------------------- % 15.67/2.85 % 15.67/2.85 (apart1) % 16.21/2.87 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 16.21/2.87 % 16.21/2.87 (ceq2) % 16.21/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.21/2.87 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 16.21/2.87 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 16.21/2.87 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 16.21/2.87 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 16.21/2.87 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.21/2.87 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.21/2.87 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 16.21/2.88 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.21/2.88 apart_point_and_line(v0, v2) = 0) % 16.21/2.88 % 16.21/2.88 (con) % 16.21/2.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 16.21/2.88 $i] : ( ~ (v4 = 0) & line_connecting(v0, v2) = v5 & line_connecting(v0, v1) % 16.21/2.88 = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v1, v5) = 0 % 16.21/2.88 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & % 16.21/2.88 distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.21/2.88 % 16.21/2.88 (con1) % 16.21/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.21/2.88 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~ % 16.21/2.88 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 16.21/2.88 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & % 16.21/2.88 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 16.21/2.88 % 16.21/2.88 (cu1) % 16.28/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.28/2.89 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.28/2.89 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.28/2.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 16.28/2.89 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 16.28/2.89 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 16.28/2.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 16.28/2.89 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 16.28/2.89 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 16.28/2.89 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 16.28/2.89 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 16.28/2.89 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 16.28/2.89 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.28/2.89 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 16.28/2.89 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 16.28/2.89 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 16.28/2.89 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 16.28/2.89 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 16.28/2.89 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 16.28/2.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 16.28/2.89 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 16.28/2.89 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.28/2.89 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 16.28/2.89 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 16.28/2.89 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 16.28/2.89 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 16.28/2.89 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 16.28/2.89 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 16.28/2.89 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.28/2.89 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 16.28/2.89 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 16.28/2.89 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 16.28/2.89 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.28/2.89 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 16.28/2.89 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.28/2.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 16.28/2.89 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 16.28/2.89 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 16.28/2.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.28/2.89 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 16.28/2.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 16.28/2.89 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 16.28/2.89 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 16.28/2.89 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 16.28/2.89 % 16.28/2.89 (function-axioms) % 16.28/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.28/2.89 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.28/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.28/2.89 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.28/2.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.28/2.89 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.28/2.89 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.28/2.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.28/2.89 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.28/2.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.28/2.89 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.28/2.89 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.28/2.89 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.28/2.89 (distinct_points(v3, v2) = v0)) % 16.28/2.89 % 16.28/2.89 Further assumptions not needed in the proof: % 16.28/2.89 -------------------------------------------- % 16.28/2.89 apart2, apart3, apart4, apart5, apart6, ceq1, ceq3, con2 % 16.28/2.89 % 16.28/2.89 Those formulas are unsatisfiable: % 16.28/2.89 --------------------------------- % 16.28/2.89 % 16.28/2.89 Begin of proof % 16.28/2.90 | % 16.28/2.90 | ALPHA: (cu1) implies: % 16.28/2.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.28/2.90 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.28/2.90 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 16.28/2.90 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3) % 16.28/2.90 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, % 16.28/2.90 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | % 16.28/2.90 | v5 = 0 | v4 = 0))) % 16.28/2.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.28/2.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 16.28/2.90 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.28/2.90 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 16.28/2.90 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 16.28/2.90 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 16.28/2.90 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 16.28/2.90 | | v8 = 0))) % 16.28/2.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.28/2.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.28/2.90 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.28/2.90 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 16.28/2.90 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 16.28/2.90 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 16.28/2.90 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 16.28/2.90 | | v8 = 0))) % 16.28/2.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.28/2.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.28/2.90 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 16.28/2.90 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 16.28/2.90 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 16.28/2.90 | apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & % 16.28/2.90 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 16.28/2.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.28/2.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.28/2.90 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 16.28/2.90 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.28/2.90 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 16.28/2.90 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 16.28/2.90 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 16.28/2.90 | % 16.28/2.90 | ALPHA: (ceq2) implies: % 16.28/2.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.28/2.90 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 16.28/2.90 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 16.28/2.90 | v2) = 0) % 16.28/2.90 | % 16.28/2.90 | ALPHA: (function-axioms) implies: % 16.28/2.90 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.28/2.90 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.28/2.90 | (distinct_points(v3, v2) = v0)) % 16.28/2.91 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.28/2.91 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.28/2.91 | (apart_point_and_line(v3, v2) = v0)) % 16.28/2.91 | % 16.28/2.91 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2, % 16.28/2.91 | all_15_3, all_15_4, all_15_5 gives: % 16.28/2.91 | (9) ~ (all_15_1 = 0) & line_connecting(all_15_5, all_15_3) = all_15_0 & % 16.28/2.91 | line_connecting(all_15_5, all_15_4) = all_15_2 & % 16.28/2.91 | apart_point_and_line(all_15_3, all_15_2) = all_15_1 & % 16.28/2.91 | apart_point_and_line(all_15_4, all_15_0) = 0 & % 16.28/2.91 | distinct_points(all_15_4, all_15_3) = 0 & distinct_points(all_15_5, % 16.28/2.91 | all_15_3) = 0 & distinct_points(all_15_5, all_15_4) = 0 & % 16.28/2.91 | $i(all_15_0) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & % 16.28/2.91 | $i(all_15_5) % 16.28/2.91 | % 16.28/2.91 | ALPHA: (9) implies: % 16.28/2.91 | (10) ~ (all_15_1 = 0) % 16.28/2.91 | (11) $i(all_15_5) % 16.28/2.91 | (12) $i(all_15_4) % 16.28/2.91 | (13) $i(all_15_3) % 16.28/2.91 | (14) $i(all_15_2) % 16.28/2.91 | (15) $i(all_15_0) % 16.28/2.91 | (16) distinct_points(all_15_5, all_15_4) = 0 % 16.28/2.91 | (17) distinct_points(all_15_5, all_15_3) = 0 % 16.28/2.91 | (18) distinct_points(all_15_4, all_15_3) = 0 % 16.28/2.91 | (19) apart_point_and_line(all_15_4, all_15_0) = 0 % 16.28/2.91 | (20) apart_point_and_line(all_15_3, all_15_2) = all_15_1 % 16.28/2.91 | (21) line_connecting(all_15_5, all_15_4) = all_15_2 % 16.28/2.91 | (22) line_connecting(all_15_5, all_15_3) = all_15_0 % 16.28/2.91 | % 16.28/2.91 | GROUND_INST: instantiating (5) with all_15_4, all_15_3, all_15_2, all_15_2, % 16.28/2.91 | all_15_1, all_15_1, simplifying with (12), (13), (14), (18), (20) % 16.28/2.91 | gives: % 16.28/2.91 | (23) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.28/2.91 | (apart_point_and_line(all_15_4, all_15_2) = v2 & % 16.28/2.91 | apart_point_and_line(all_15_4, all_15_2) = v1 & % 16.28/2.91 | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 16.28/2.91 | = 0)) % 16.28/2.91 | % 16.42/2.91 | GROUND_INST: instantiating (5) with all_15_5, all_15_3, all_15_2, all_15_2, % 16.42/2.91 | all_15_1, all_15_1, simplifying with (11), (13), (14), (17), (20) % 16.42/2.91 | gives: % 16.42/2.91 | (24) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.42/2.91 | (apart_point_and_line(all_15_5, all_15_2) = v2 & % 16.42/2.91 | apart_point_and_line(all_15_5, all_15_2) = v1 & % 16.42/2.91 | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 16.42/2.91 | = 0)) % 16.42/2.91 | % 16.42/2.91 | GROUND_INST: instantiating (3) with all_15_3, all_15_3, all_15_2, all_15_2, % 16.42/2.91 | all_15_1, all_15_1, simplifying with (13), (14), (20) gives: % 16.42/2.91 | (25) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 16.42/2.91 | any] : (apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.42/2.91 | apart_point_and_line(all_15_3, all_15_2) = v2 & % 16.42/2.91 | distinct_lines(all_15_2, all_15_2) = v1 & distinct_points(all_15_3, % 16.42/2.91 | all_15_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.42/2.91 | % 16.42/2.91 | GROUND_INST: instantiating (con1) with all_15_5, all_15_3, all_15_4, all_15_0, % 16.42/2.91 | simplifying with (11), (12), (13), (19), (22) gives: % 16.42/2.91 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.42/2.91 | (distinct_points(all_15_4, all_15_3) = v2 & distinct_points(all_15_4, % 16.42/2.91 | all_15_5) = v1 & distinct_points(all_15_5, all_15_3) = v0 & ( ~ % 16.42/2.91 | (v0 = 0) | (v2 = 0 & v1 = 0))) % 16.42/2.91 | % 16.42/2.91 | DELTA: instantiating (26) with fresh symbols all_22_0, all_22_1, all_22_2 % 16.42/2.91 | gives: % 16.42/2.91 | (27) distinct_points(all_15_4, all_15_3) = all_22_0 & % 16.42/2.91 | distinct_points(all_15_4, all_15_5) = all_22_1 & % 16.42/2.91 | distinct_points(all_15_5, all_15_3) = all_22_2 & ( ~ (all_22_2 = 0) | % 16.42/2.91 | (all_22_0 = 0 & all_22_1 = 0)) % 16.42/2.91 | % 16.42/2.91 | ALPHA: (27) implies: % 16.42/2.91 | (28) distinct_points(all_15_5, all_15_3) = all_22_2 % 16.42/2.91 | (29) distinct_points(all_15_4, all_15_5) = all_22_1 % 16.42/2.92 | (30) distinct_points(all_15_4, all_15_3) = all_22_0 % 16.42/2.92 | (31) ~ (all_22_2 = 0) | (all_22_0 = 0 & all_22_1 = 0) % 16.42/2.92 | % 16.42/2.92 | BETA: splitting (24) gives: % 16.42/2.92 | % 16.42/2.92 | Case 1: % 16.42/2.92 | | % 16.42/2.92 | | (32) all_15_1 = 0 % 16.42/2.92 | | % 16.42/2.92 | | REDUCE: (10), (32) imply: % 16.42/2.92 | | (33) $false % 16.42/2.92 | | % 16.42/2.92 | | CLOSE: (33) is inconsistent. % 16.42/2.92 | | % 16.42/2.92 | Case 2: % 16.42/2.92 | | % 16.42/2.92 | | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.42/2.92 | | (apart_point_and_line(all_15_5, all_15_2) = v2 & % 16.42/2.92 | | apart_point_and_line(all_15_5, all_15_2) = v1 & % 16.42/2.92 | | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 16.42/2.92 | | v1 = 0)) % 16.42/2.92 | | % 16.42/2.92 | | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1, all_28_2 % 16.42/2.92 | | gives: % 16.42/2.92 | | (35) apart_point_and_line(all_15_5, all_15_2) = all_28_0 & % 16.42/2.92 | | apart_point_and_line(all_15_5, all_15_2) = all_28_1 & % 16.42/2.92 | | distinct_lines(all_15_2, all_15_2) = all_28_2 & ( ~ (all_28_2 = 0) | % 16.42/2.92 | | all_28_0 = 0 | all_28_1 = 0) % 16.42/2.92 | | % 16.42/2.92 | | ALPHA: (35) implies: % 16.42/2.92 | | (36) apart_point_and_line(all_15_5, all_15_2) = all_28_1 % 16.42/2.92 | | (37) apart_point_and_line(all_15_5, all_15_2) = all_28_0 % 16.42/2.92 | | % 16.42/2.92 | | BETA: splitting (23) gives: % 16.42/2.92 | | % 16.42/2.92 | | Case 1: % 16.42/2.92 | | | % 16.42/2.92 | | | (38) all_15_1 = 0 % 16.42/2.92 | | | % 16.42/2.92 | | | REDUCE: (10), (38) imply: % 16.42/2.92 | | | (39) $false % 16.42/2.92 | | | % 16.42/2.92 | | | CLOSE: (39) is inconsistent. % 16.42/2.92 | | | % 16.42/2.92 | | Case 2: % 16.42/2.92 | | | % 16.42/2.92 | | | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.42/2.92 | | | (apart_point_and_line(all_15_4, all_15_2) = v2 & % 16.42/2.92 | | | apart_point_and_line(all_15_4, all_15_2) = v1 & % 16.42/2.92 | | | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 16.42/2.92 | | | | v1 = 0)) % 16.42/2.92 | | | % 16.42/2.92 | | | DELTA: instantiating (40) with fresh symbols all_33_0, all_33_1, all_33_2 % 16.42/2.92 | | | gives: % 16.42/2.92 | | | (41) apart_point_and_line(all_15_4, all_15_2) = all_33_0 & % 16.42/2.92 | | | apart_point_and_line(all_15_4, all_15_2) = all_33_1 & % 16.42/2.92 | | | distinct_lines(all_15_2, all_15_2) = all_33_2 & ( ~ (all_33_2 = 0) % 16.42/2.92 | | | | all_33_0 = 0 | all_33_1 = 0) % 16.42/2.92 | | | % 16.42/2.92 | | | ALPHA: (41) implies: % 16.42/2.92 | | | (42) apart_point_and_line(all_15_4, all_15_2) = all_33_1 % 16.42/2.92 | | | (43) apart_point_and_line(all_15_4, all_15_2) = all_33_0 % 16.42/2.92 | | | % 16.42/2.92 | | | BETA: splitting (25) gives: % 16.42/2.92 | | | % 16.42/2.92 | | | Case 1: % 16.42/2.92 | | | | % 16.42/2.92 | | | | (44) all_15_1 = 0 % 16.42/2.92 | | | | % 16.42/2.92 | | | | REDUCE: (10), (44) imply: % 16.42/2.92 | | | | (45) $false % 16.42/2.92 | | | | % 16.42/2.92 | | | | CLOSE: (45) is inconsistent. % 16.42/2.92 | | | | % 16.42/2.92 | | | Case 2: % 16.42/2.92 | | | | % 16.42/2.92 | | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.42/2.92 | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.42/2.92 | | | | apart_point_and_line(all_15_3, all_15_2) = v2 & % 16.42/2.92 | | | | distinct_lines(all_15_2, all_15_2) = v1 & % 16.42/2.92 | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v1 = 0) | ~ % 16.42/2.92 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.42/2.92 | | | | % 16.42/2.92 | | | | DELTA: instantiating (46) with fresh symbols all_38_0, all_38_1, % 16.42/2.92 | | | | all_38_2, all_38_3 gives: % 16.42/2.92 | | | | (47) apart_point_and_line(all_15_3, all_15_2) = all_38_0 & % 16.42/2.92 | | | | apart_point_and_line(all_15_3, all_15_2) = all_38_1 & % 16.42/2.92 | | | | distinct_lines(all_15_2, all_15_2) = all_38_2 & % 16.42/2.92 | | | | distinct_points(all_15_3, all_15_3) = all_38_3 & ( ~ (all_38_2 = % 16.42/2.92 | | | | 0) | ~ (all_38_3 = 0) | all_38_0 = 0 | all_38_1 = 0) % 16.42/2.92 | | | | % 16.42/2.92 | | | | ALPHA: (47) implies: % 16.42/2.92 | | | | (48) apart_point_and_line(all_15_3, all_15_2) = all_38_1 % 16.42/2.92 | | | | (49) apart_point_and_line(all_15_3, all_15_2) = all_38_0 % 16.42/2.92 | | | | % 16.42/2.92 | | | | GROUND_INST: instantiating (7) with 0, all_22_2, all_15_3, all_15_5, % 16.42/2.92 | | | | simplifying with (17), (28) gives: % 16.42/2.92 | | | | (50) all_22_2 = 0 % 16.42/2.92 | | | | % 16.42/2.92 | | | | GROUND_INST: instantiating (7) with 0, all_22_0, all_15_3, all_15_4, % 16.42/2.92 | | | | simplifying with (18), (30) gives: % 16.42/2.92 | | | | (51) all_22_0 = 0 % 16.42/2.92 | | | | % 16.42/2.92 | | | | GROUND_INST: instantiating (8) with all_28_1, all_28_0, all_15_2, % 16.42/2.92 | | | | all_15_5, simplifying with (36), (37) gives: % 16.48/2.92 | | | | (52) all_28_0 = all_28_1 % 16.48/2.92 | | | | % 16.48/2.92 | | | | GROUND_INST: instantiating (8) with all_33_1, all_33_0, all_15_2, % 16.48/2.92 | | | | all_15_4, simplifying with (42), (43) gives: % 16.48/2.92 | | | | (53) all_33_0 = all_33_1 % 16.48/2.92 | | | | % 16.48/2.93 | | | | GROUND_INST: instantiating (8) with all_15_1, all_38_0, all_15_2, % 16.48/2.93 | | | | all_15_3, simplifying with (20), (49) gives: % 16.48/2.93 | | | | (54) all_38_0 = all_15_1 % 16.48/2.93 | | | | % 16.48/2.93 | | | | GROUND_INST: instantiating (8) with all_38_1, all_38_0, all_15_2, % 16.48/2.93 | | | | all_15_3, simplifying with (48), (49) gives: % 16.48/2.93 | | | | (55) all_38_0 = all_38_1 % 16.48/2.93 | | | | % 16.48/2.93 | | | | COMBINE_EQS: (54), (55) imply: % 16.48/2.93 | | | | (56) all_38_1 = all_15_1 % 16.48/2.93 | | | | % 16.48/2.93 | | | | BETA: splitting (31) gives: % 16.48/2.93 | | | | % 16.48/2.93 | | | | Case 1: % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | (57) ~ (all_22_2 = 0) % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | REDUCE: (50), (57) imply: % 16.48/2.93 | | | | | (58) $false % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | CLOSE: (58) is inconsistent. % 16.48/2.93 | | | | | % 16.48/2.93 | | | | Case 2: % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | (59) all_22_0 = 0 & all_22_1 = 0 % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | ALPHA: (59) implies: % 16.48/2.93 | | | | | (60) all_22_1 = 0 % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | REDUCE: (29), (60) imply: % 16.48/2.93 | | | | | (61) distinct_points(all_15_4, all_15_5) = 0 % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | GROUND_INST: instantiating (3) with all_15_5, all_15_5, all_15_2, % 16.48/2.93 | | | | | all_15_2, all_28_1, all_28_1, simplifying with (11), % 16.48/2.93 | | | | | (14), (36) gives: % 16.48/2.93 | | | | | (62) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.48/2.93 | | | | | [v3: any] : (apart_point_and_line(all_15_5, all_15_2) = v3 & % 16.48/2.93 | | | | | apart_point_and_line(all_15_5, all_15_2) = v2 & % 16.48/2.93 | | | | | distinct_lines(all_15_2, all_15_2) = v1 & % 16.48/2.93 | | | | | distinct_points(all_15_5, all_15_5) = v0 & ( ~ (v1 = 0) | ~ % 16.48/2.93 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | GROUND_INST: instantiating (6) with all_15_4, all_15_0, all_15_2, % 16.48/2.93 | | | | | all_33_1, simplifying with (12), (14), (15), (19), (42) % 16.48/2.93 | | | | | gives: % 16.48/2.93 | | | | | (63) all_33_1 = 0 | distinct_lines(all_15_0, all_15_2) = 0 % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | GROUND_INST: instantiating (3) with all_15_4, all_15_4, all_15_2, % 16.48/2.93 | | | | | all_15_2, all_33_1, all_33_1, simplifying with (12), % 16.48/2.93 | | | | | (14), (42) gives: % 16.48/2.93 | | | | | (64) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.48/2.93 | | | | | [v3: any] : (apart_point_and_line(all_15_4, all_15_2) = v3 & % 16.48/2.93 | | | | | apart_point_and_line(all_15_4, all_15_2) = v2 & % 16.48/2.93 | | | | | distinct_lines(all_15_2, all_15_2) = v1 & % 16.48/2.93 | | | | | distinct_points(all_15_4, all_15_4) = v0 & ( ~ (v1 = 0) | ~ % 16.48/2.93 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | BETA: splitting (63) gives: % 16.48/2.93 | | | | | % 16.48/2.93 | | | | | Case 1: % 16.48/2.93 | | | | | | % 16.48/2.93 | | | | | | (65) distinct_lines(all_15_0, all_15_2) = 0 % 16.48/2.93 | | | | | | % 16.48/2.93 | | | | | | GROUND_INST: instantiating (4) with all_15_3, all_15_3, all_15_0, % 16.48/2.93 | | | | | | all_15_2, all_15_1, all_15_1, simplifying with (13), % 16.48/2.93 | | | | | | (14), (15), (20), (65) gives: % 16.48/2.93 | | | | | | (66) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.93 | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 & % 16.48/2.93 | | | | | | apart_point_and_line(all_15_3, all_15_0) = v1 & % 16.48/2.93 | | | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v0 = 0) | % 16.48/2.93 | | | | | | v2 = 0 | v1 = 0)) % 16.48/2.93 | | | | | | % 16.48/2.93 | | | | | | GROUND_INST: instantiating (4) with all_15_3, all_15_4, all_15_0, % 16.48/2.93 | | | | | | all_15_2, all_15_1, all_33_1, simplifying with (12), % 16.48/2.93 | | | | | | (13), (14), (15), (20), (42), (65) gives: % 16.48/2.93 | | | | | | (67) all_33_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] : % 16.48/2.93 | | | | | | ? [v2: any] : (apart_point_and_line(all_15_3, all_15_0) = v1 % 16.48/2.93 | | | | | | & apart_point_and_line(all_15_4, all_15_0) = v2 & % 16.48/2.93 | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~ (v0 = 0) | % 16.48/2.93 | | | | | | v2 = 0 | v1 = 0)) % 16.48/2.93 | | | | | | % 16.48/2.93 | | | | | | GROUND_INST: instantiating (4) with all_15_3, all_15_5, all_15_0, % 16.48/2.93 | | | | | | all_15_2, all_15_1, all_28_1, simplifying with (11), % 16.48/2.93 | | | | | | (13), (14), (15), (20), (36), (65) gives: % 16.48/2.94 | | | | | | (68) all_28_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] : % 16.48/2.94 | | | | | | ? [v2: any] : (apart_point_and_line(all_15_3, all_15_0) = v1 % 16.48/2.94 | | | | | | & apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.94 | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ (v0 = 0) | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | GROUND_INST: instantiating (4) with all_15_5, all_15_5, all_15_0, % 16.48/2.94 | | | | | | all_15_2, all_28_1, all_28_1, simplifying with (11), % 16.48/2.94 | | | | | | (14), (15), (36), (65) gives: % 16.48/2.94 | | | | | | (69) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.94 | | | | | | (apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = v1 & % 16.48/2.94 | | | | | | distinct_points(all_15_5, all_15_5) = v0 & ( ~ (v0 = 0) | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | GROUND_INST: instantiating (1) with all_15_4, all_15_3, all_15_0, % 16.48/2.94 | | | | | | all_15_2, simplifying with (12), (13), (14), (15), % 16.48/2.94 | | | | | | (18), (65) gives: % 16.48/2.94 | | | | | | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.48/2.94 | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_0) = v0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_2) = v1 & (v3 = 0 | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0 | v0 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | GROUND_INST: instantiating (1) with all_15_4, all_15_5, all_15_0, % 16.48/2.94 | | | | | | all_15_2, simplifying with (11), (12), (14), (15), % 16.48/2.94 | | | | | | (61), (65) gives: % 16.48/2.94 | | | | | | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.48/2.94 | | | | | | (apart_point_and_line(all_15_4, all_15_0) = v0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_2) = v1 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_2) = v3 & (v3 = 0 | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0 | v0 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_3, all_15_0, % 16.48/2.94 | | | | | | all_15_2, simplifying with (11), (13), (14), (15), % 16.48/2.94 | | | | | | (17), (65) gives: % 16.48/2.94 | | | | | | (72) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.48/2.94 | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = v0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & (v3 = 0 | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0 | v0 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_4, all_15_0, % 16.48/2.94 | | | | | | all_15_2, simplifying with (11), (12), (14), (15), % 16.48/2.94 | | | | | | (16), (65) gives: % 16.48/2.94 | | | | | | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.48/2.94 | | | | | | (apart_point_and_line(all_15_4, all_15_0) = v2 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_2) = v3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = v0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & (v3 = 0 | % 16.48/2.94 | | | | | | v2 = 0 | v1 = 0 | v0 = 0)) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | DELTA: instantiating (73) with fresh symbols all_73_0, all_73_1, % 16.48/2.94 | | | | | | all_73_2, all_73_3 gives: % 16.48/2.94 | | | | | | (74) apart_point_and_line(all_15_4, all_15_0) = all_73_1 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_2) = all_73_0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = all_73_3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_2) = all_73_2 & % 16.48/2.94 | | | | | | (all_73_0 = 0 | all_73_1 = 0 | all_73_2 = 0 | all_73_3 = 0) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | ALPHA: (74) implies: % 16.48/2.94 | | | | | | (75) apart_point_and_line(all_15_5, all_15_2) = all_73_2 % 16.48/2.94 | | | | | | (76) apart_point_and_line(all_15_5, all_15_0) = all_73_3 % 16.48/2.94 | | | | | | (77) apart_point_and_line(all_15_4, all_15_2) = all_73_0 % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | DELTA: instantiating (72) with fresh symbols all_75_0, all_75_1, % 16.48/2.94 | | | | | | all_75_2, all_75_3 gives: % 16.48/2.94 | | | | | | (78) apart_point_and_line(all_15_3, all_15_0) = all_75_1 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_3, all_15_2) = all_75_0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_0) = all_75_3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_5, all_15_2) = all_75_2 & % 16.48/2.94 | | | | | | (all_75_0 = 0 | all_75_1 = 0 | all_75_2 = 0 | all_75_3 = 0) % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | ALPHA: (78) implies: % 16.48/2.94 | | | | | | (79) apart_point_and_line(all_15_5, all_15_2) = all_75_2 % 16.48/2.94 | | | | | | (80) apart_point_and_line(all_15_5, all_15_0) = all_75_3 % 16.48/2.94 | | | | | | (81) apart_point_and_line(all_15_3, all_15_2) = all_75_0 % 16.48/2.94 | | | | | | (82) apart_point_and_line(all_15_3, all_15_0) = all_75_1 % 16.48/2.94 | | | | | | (83) all_75_0 = 0 | all_75_1 = 0 | all_75_2 = 0 | all_75_3 = 0 % 16.48/2.94 | | | | | | % 16.48/2.94 | | | | | | DELTA: instantiating (70) with fresh symbols all_77_0, all_77_1, % 16.48/2.94 | | | | | | all_77_2, all_77_3 gives: % 16.48/2.94 | | | | | | (84) apart_point_and_line(all_15_3, all_15_0) = all_77_1 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_3, all_15_2) = all_77_0 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_0) = all_77_3 & % 16.48/2.94 | | | | | | apart_point_and_line(all_15_4, all_15_2) = all_77_2 & % 16.48/2.95 | | | | | | (all_77_0 = 0 | all_77_1 = 0 | all_77_2 = 0 | all_77_3 = 0) % 16.48/2.95 | | | | | | % 16.48/2.95 | | | | | | ALPHA: (84) implies: % 16.48/2.95 | | | | | | (85) apart_point_and_line(all_15_4, all_15_2) = all_77_2 % 16.48/2.95 | | | | | | (86) apart_point_and_line(all_15_3, all_15_2) = all_77_0 % 16.48/2.95 | | | | | | (87) apart_point_and_line(all_15_3, all_15_0) = all_77_1 % 16.48/2.95 | | | | | | % 16.48/2.95 | | | | | | DELTA: instantiating (71) with fresh symbols all_79_0, all_79_1, % 16.48/2.95 | | | | | | all_79_2, all_79_3 gives: % 16.48/2.95 | | | | | | (88) apart_point_and_line(all_15_4, all_15_0) = all_79_3 & % 16.48/2.95 | | | | | | apart_point_and_line(all_15_4, all_15_2) = all_79_2 & % 16.48/2.95 | | | | | | apart_point_and_line(all_15_5, all_15_0) = all_79_1 & % 16.48/2.95 | | | | | | apart_point_and_line(all_15_5, all_15_2) = all_79_0 & % 16.48/2.95 | | | | | | (all_79_0 = 0 | all_79_1 = 0 | all_79_2 = 0 | all_79_3 = 0) % 16.48/2.95 | | | | | | % 16.48/2.95 | | | | | | ALPHA: (88) implies: % 16.48/2.95 | | | | | | (89) apart_point_and_line(all_15_5, all_15_2) = all_79_0 % 16.48/2.95 | | | | | | (90) apart_point_and_line(all_15_5, all_15_0) = all_79_1 % 16.48/2.95 | | | | | | (91) apart_point_and_line(all_15_4, all_15_2) = all_79_2 % 16.48/2.95 | | | | | | % 16.48/2.95 | | | | | | BETA: splitting (66) gives: % 16.48/2.95 | | | | | | % 16.48/2.95 | | | | | | Case 1: % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | (92) all_15_1 = 0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | REDUCE: (10), (92) imply: % 16.48/2.95 | | | | | | | (93) $false % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | CLOSE: (93) is inconsistent. % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | Case 2: % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | (94) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.95 | | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 & % 16.48/2.95 | | | | | | | apart_point_and_line(all_15_3, all_15_0) = v1 & % 16.48/2.95 | | | | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v0 = 0) % 16.48/2.95 | | | | | | | | v2 = 0 | v1 = 0)) % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | DELTA: instantiating (94) with fresh symbols all_85_0, all_85_1, % 16.48/2.95 | | | | | | | all_85_2 gives: % 16.48/2.95 | | | | | | | (95) apart_point_and_line(all_15_3, all_15_0) = all_85_0 & % 16.48/2.95 | | | | | | | apart_point_and_line(all_15_3, all_15_0) = all_85_1 & % 16.48/2.95 | | | | | | | distinct_points(all_15_3, all_15_3) = all_85_2 & ( ~ % 16.48/2.95 | | | | | | | (all_85_2 = 0) | all_85_0 = 0 | all_85_1 = 0) % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | ALPHA: (95) implies: % 16.48/2.95 | | | | | | | (96) distinct_points(all_15_3, all_15_3) = all_85_2 % 16.48/2.95 | | | | | | | (97) apart_point_and_line(all_15_3, all_15_0) = all_85_1 % 16.48/2.95 | | | | | | | (98) apart_point_and_line(all_15_3, all_15_0) = all_85_0 % 16.48/2.95 | | | | | | | (99) ~ (all_85_2 = 0) | all_85_0 = 0 | all_85_1 = 0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_28_1, all_75_2, all_15_2, % 16.48/2.95 | | | | | | | all_15_5, simplifying with (36), (79) gives: % 16.48/2.95 | | | | | | | (100) all_75_2 = all_28_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_75_2, all_79_0, all_15_2, % 16.48/2.95 | | | | | | | all_15_5, simplifying with (79), (89) gives: % 16.48/2.95 | | | | | | | (101) all_79_0 = all_75_2 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_73_2, all_79_0, all_15_2, % 16.48/2.95 | | | | | | | all_15_5, simplifying with (75), (89) gives: % 16.48/2.95 | | | | | | | (102) all_79_0 = all_73_2 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_75_3, all_79_1, all_15_0, % 16.48/2.95 | | | | | | | all_15_5, simplifying with (80), (90) gives: % 16.48/2.95 | | | | | | | (103) all_79_1 = all_75_3 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_73_3, all_79_1, all_15_0, % 16.48/2.95 | | | | | | | all_15_5, simplifying with (76), (90) gives: % 16.48/2.95 | | | | | | | (104) all_79_1 = all_73_3 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_33_1, all_77_2, all_15_2, % 16.48/2.95 | | | | | | | all_15_4, simplifying with (42), (85) gives: % 16.48/2.95 | | | | | | | (105) all_77_2 = all_33_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_77_2, all_79_2, all_15_2, % 16.48/2.95 | | | | | | | all_15_4, simplifying with (85), (91) gives: % 16.48/2.95 | | | | | | | (106) all_79_2 = all_77_2 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_73_0, all_79_2, all_15_2, % 16.48/2.95 | | | | | | | all_15_4, simplifying with (77), (91) gives: % 16.48/2.95 | | | | | | | (107) all_79_2 = all_73_0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_15_1, all_77_0, all_15_2, % 16.48/2.95 | | | | | | | all_15_3, simplifying with (20), (86) gives: % 16.48/2.95 | | | | | | | (108) all_77_0 = all_15_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_75_0, all_77_0, all_15_2, % 16.48/2.95 | | | | | | | all_15_3, simplifying with (81), (86) gives: % 16.48/2.95 | | | | | | | (109) all_77_0 = all_75_0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_77_1, all_85_1, all_15_0, % 16.48/2.95 | | | | | | | all_15_3, simplifying with (87), (97) gives: % 16.48/2.95 | | | | | | | (110) all_85_1 = all_77_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_85_1, all_85_0, all_15_0, % 16.48/2.95 | | | | | | | all_15_3, simplifying with (97), (98) gives: % 16.48/2.95 | | | | | | | (111) all_85_0 = all_85_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | GROUND_INST: instantiating (8) with all_75_1, all_85_0, all_15_0, % 16.48/2.95 | | | | | | | all_15_3, simplifying with (82), (98) gives: % 16.48/2.95 | | | | | | | (112) all_85_0 = all_75_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (111), (112) imply: % 16.48/2.95 | | | | | | | (113) all_85_1 = all_75_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (113) implies: % 16.48/2.95 | | | | | | | (114) all_85_1 = all_75_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (110), (114) imply: % 16.48/2.95 | | | | | | | (115) all_77_1 = all_75_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (115) implies: % 16.48/2.95 | | | | | | | (116) all_77_1 = all_75_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (101), (102) imply: % 16.48/2.95 | | | | | | | (117) all_75_2 = all_73_2 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (117) implies: % 16.48/2.95 | | | | | | | (118) all_75_2 = all_73_2 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (103), (104) imply: % 16.48/2.95 | | | | | | | (119) all_75_3 = all_73_3 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (119) implies: % 16.48/2.95 | | | | | | | (120) all_75_3 = all_73_3 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (106), (107) imply: % 16.48/2.95 | | | | | | | (121) all_77_2 = all_73_0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (121) implies: % 16.48/2.95 | | | | | | | (122) all_77_2 = all_73_0 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (108), (109) imply: % 16.48/2.95 | | | | | | | (123) all_75_0 = all_15_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | SIMP: (123) implies: % 16.48/2.95 | | | | | | | (124) all_75_0 = all_15_1 % 16.48/2.95 | | | | | | | % 16.48/2.95 | | | | | | | COMBINE_EQS: (105), (122) imply: % 16.48/2.96 | | | | | | | (125) all_73_0 = all_33_1 % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | COMBINE_EQS: (100), (118) imply: % 16.48/2.96 | | | | | | | (126) all_73_2 = all_28_1 % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | GROUND_INST: instantiating (5) with all_15_5, all_15_3, all_15_2, % 16.48/2.96 | | | | | | | all_15_0, all_15_1, all_75_1, simplifying with (11), % 16.48/2.96 | | | | | | | (13), (14), (15), (17), (20), (82) gives: % 16.48/2.96 | | | | | | | (127) all_75_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] % 16.48/2.96 | | | | | | | : ? [v2: any] : (apart_point_and_line(all_15_5, % 16.48/2.96 | | | | | | | all_15_0) = v2 & apart_point_and_line(all_15_5, % 16.48/2.96 | | | | | | | all_15_2) = v1 & distinct_lines(all_15_2, all_15_0) = % 16.48/2.96 | | | | | | | v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | GROUND_INST: instantiating (3) with all_15_5, all_15_3, all_15_2, % 16.48/2.96 | | | | | | | all_15_0, all_28_1, all_75_1, simplifying with (11), % 16.48/2.96 | | | | | | | (13), (14), (15), (36), (82) gives: % 16.48/2.96 | | | | | | | (128) all_75_1 = 0 | all_28_1 = 0 | ? [v0: any] : ? [v1: any] % 16.48/2.96 | | | | | | | : ? [v2: any] : ? [v3: any] : % 16.48/2.96 | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.48/2.96 | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.96 | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.96 | | | | | | | distinct_points(all_15_5, all_15_3) = v0 & ( ~ (v1 = 0) % 16.48/2.96 | | | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | GROUND_INST: instantiating (2) with all_15_3, all_15_5, all_15_2, % 16.48/2.96 | | | | | | | all_15_0, all_75_1, all_28_1, simplifying with (11), % 16.48/2.96 | | | | | | | (13), (14), (15), (36), (82) gives: % 16.48/2.96 | | | | | | | (129) all_75_1 = 0 | all_28_1 = 0 | ? [v0: any] : ? [v1: any] % 16.48/2.96 | | | | | | | : ? [v2: any] : ? [v3: any] : % 16.48/2.96 | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v2 & % 16.48/2.96 | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v3 & % 16.48/2.96 | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.96 | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ (v1 = 0) % 16.48/2.96 | | | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | GROUND_INST: instantiating (3) with all_15_3, all_15_3, all_15_0, % 16.48/2.96 | | | | | | | all_15_0, all_75_1, all_75_1, simplifying with (13), % 16.48/2.96 | | | | | | | (15), (82) gives: % 16.48/2.96 | | | | | | | (130) all_75_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 16.48/2.96 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_15_3, % 16.48/2.96 | | | | | | | all_15_0) = v3 & apart_point_and_line(all_15_3, % 16.48/2.96 | | | | | | | all_15_0) = v2 & distinct_lines(all_15_0, all_15_0) = % 16.48/2.96 | | | | | | | v1 & distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v1 % 16.48/2.96 | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | BETA: splitting (64) gives: % 16.48/2.96 | | | | | | | % 16.48/2.96 | | | | | | | Case 1: % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | (131) all_33_1 = 0 % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | REDUCE: (42), (131) imply: % 16.48/2.96 | | | | | | | | (132) apart_point_and_line(all_15_4, all_15_2) = 0 % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | REF_CLOSE: (7), (11), (12), (16), (21), (132), (apart1), (con1) % 16.48/2.96 | | | | | | | | are inconsistent by sub-proof #1. % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | Case 2: % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | (133) ~ (all_33_1 = 0) % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | BETA: splitting (67) gives: % 16.48/2.96 | | | | | | | | % 16.48/2.96 | | | | | | | | Case 1: % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | (134) all_33_1 = 0 % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | REDUCE: (133), (134) imply: % 16.48/2.96 | | | | | | | | | (135) $false % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | CLOSE: (135) is inconsistent. % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | Case 2: % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | (136) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 16.48/2.96 | | | | | | | | | any] : (apart_point_and_line(all_15_3, all_15_0) = % 16.48/2.96 | | | | | | | | | v1 & apart_point_and_line(all_15_4, all_15_0) = v2 % 16.48/2.96 | | | | | | | | | & distinct_points(all_15_3, all_15_4) = v0 & ( ~ % 16.48/2.96 | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | BETA: splitting (136) gives: % 16.48/2.96 | | | | | | | | | % 16.48/2.96 | | | | | | | | | Case 1: % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | (137) all_15_1 = 0 % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | REDUCE: (10), (137) imply: % 16.48/2.96 | | | | | | | | | | (138) $false % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | CLOSE: (138) is inconsistent. % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | Case 2: % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.96 | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v1 & % 16.48/2.96 | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 & % 16.48/2.96 | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~ % 16.48/2.96 | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_111_0, % 16.48/2.96 | | | | | | | | | | all_111_1, all_111_2 gives: % 16.48/2.96 | | | | | | | | | | (140) apart_point_and_line(all_15_3, all_15_0) = % 16.48/2.96 | | | | | | | | | | all_111_1 & apart_point_and_line(all_15_4, % 16.48/2.96 | | | | | | | | | | all_15_0) = all_111_0 & distinct_points(all_15_3, % 16.48/2.96 | | | | | | | | | | all_15_4) = all_111_2 & ( ~ (all_111_2 = 0) | % 16.48/2.96 | | | | | | | | | | all_111_0 = 0 | all_111_1 = 0) % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | ALPHA: (140) implies: % 16.48/2.96 | | | | | | | | | | (141) apart_point_and_line(all_15_3, all_15_0) = % 16.48/2.96 | | | | | | | | | | all_111_1 % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | GROUND_INST: instantiating (8) with all_75_1, all_111_1, % 16.48/2.96 | | | | | | | | | | all_15_0, all_15_3, simplifying with (82), (141) % 16.48/2.96 | | | | | | | | | | gives: % 16.48/2.96 | | | | | | | | | | (142) all_111_1 = all_75_1 % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | BETA: splitting (62) gives: % 16.48/2.96 | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | Case 1: % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | (143) all_28_1 = 0 % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | REDUCE: (36), (143) imply: % 16.48/2.96 | | | | | | | | | | | (144) apart_point_and_line(all_15_5, all_15_2) = 0 % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, % 16.48/2.96 | | | | | | | | | | | all_15_5, all_15_2, simplifying with (11), (12), % 16.48/2.96 | | | | | | | | | | | (21), (144) gives: % 16.48/2.96 | | | | | | | | | | | (145) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.96 | | | | | | | | | | | (distinct_points(all_15_5, all_15_4) = v2 & % 16.48/2.96 | | | | | | | | | | | distinct_points(all_15_5, all_15_4) = v0 & % 16.48/2.96 | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = v1 & ( ~ % 16.48/2.96 | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0))) % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | DELTA: instantiating (145) with fresh symbols all_134_0, % 16.48/2.96 | | | | | | | | | | | all_134_1, all_134_2 gives: % 16.48/2.96 | | | | | | | | | | | (146) distinct_points(all_15_5, all_15_4) = all_134_0 & % 16.48/2.96 | | | | | | | | | | | distinct_points(all_15_5, all_15_4) = all_134_2 & % 16.48/2.96 | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = all_134_1 & % 16.48/2.96 | | | | | | | | | | | ( ~ (all_134_2 = 0) | (all_134_0 = 0 & all_134_1 = % 16.48/2.96 | | | | | | | | | | | 0)) % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | ALPHA: (146) implies: % 16.48/2.96 | | | | | | | | | | | (147) distinct_points(all_15_5, all_15_5) = all_134_1 % 16.48/2.96 | | | | | | | | | | | (148) distinct_points(all_15_5, all_15_4) = all_134_2 % 16.48/2.96 | | | | | | | | | | | (149) distinct_points(all_15_5, all_15_4) = all_134_0 % 16.48/2.96 | | | | | | | | | | | (150) ~ (all_134_2 = 0) | (all_134_0 = 0 & all_134_1 = % 16.48/2.96 | | | | | | | | | | | 0) % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_134_0, all_15_4, % 16.48/2.96 | | | | | | | | | | | all_15_5, simplifying with (16), (149) gives: % 16.48/2.96 | | | | | | | | | | | (151) all_134_0 = 0 % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_134_2, all_134_0, % 16.48/2.96 | | | | | | | | | | | all_15_4, all_15_5, simplifying with (148), (149) % 16.48/2.96 | | | | | | | | | | | gives: % 16.48/2.96 | | | | | | | | | | | (152) all_134_0 = all_134_2 % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | COMBINE_EQS: (151), (152) imply: % 16.48/2.96 | | | | | | | | | | | (153) all_134_2 = 0 % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | BETA: splitting (150) gives: % 16.48/2.96 | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | Case 1: % 16.48/2.96 | | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | | (154) ~ (all_134_2 = 0) % 16.48/2.96 | | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | | REDUCE: (153), (154) imply: % 16.48/2.96 | | | | | | | | | | | | (155) $false % 16.48/2.96 | | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 16.48/2.96 | | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | Case 2: % 16.48/2.96 | | | | | | | | | | | | % 16.48/2.96 | | | | | | | | | | | | (156) all_134_0 = 0 & all_134_1 = 0 % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | ALPHA: (156) implies: % 16.48/2.97 | | | | | | | | | | | | (157) all_134_1 = 0 % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | REDUCE: (147), (157) imply: % 16.48/2.97 | | | | | | | | | | | | (158) distinct_points(all_15_5, all_15_5) = 0 % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying % 16.48/2.97 | | | | | | | | | | | | with (11), (158) gives: % 16.48/2.97 | | | | | | | | | | | | (159) $false % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | End of split % 16.48/2.97 | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | (160) ~ (all_28_1 = 0) % 16.48/2.97 | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | BETA: splitting (68) gives: % 16.48/2.97 | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | (161) all_28_1 = 0 % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | REDUCE: (160), (161) imply: % 16.48/2.97 | | | | | | | | | | | | (162) $false % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | (163) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.48/2.97 | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_3, % 16.48/2.97 | | | | | | | | | | | | all_15_0) = v1 & % 16.48/2.97 | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.97 | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ % 16.48/2.97 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | BETA: splitting (163) gives: % 16.48/2.97 | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | (164) all_15_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | REDUCE: (10), (164) imply: % 16.48/2.97 | | | | | | | | | | | | | (165) $false % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | (166) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.97 | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v1 & % 16.48/2.97 | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.97 | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ % 16.48/2.97 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | DELTA: instantiating (166) with fresh symbols all_147_0, % 16.48/2.97 | | | | | | | | | | | | | all_147_1, all_147_2 gives: % 16.48/2.97 | | | | | | | | | | | | | (167) apart_point_and_line(all_15_3, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | all_147_1 & apart_point_and_line(all_15_5, % 16.48/2.97 | | | | | | | | | | | | | all_15_0) = all_147_0 & % 16.48/2.97 | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = all_147_2 & % 16.48/2.97 | | | | | | | | | | | | | ( ~ (all_147_2 = 0) | all_147_0 = 0 | all_147_1 = % 16.48/2.97 | | | | | | | | | | | | | 0) % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | ALPHA: (167) implies: % 16.48/2.97 | | | | | | | | | | | | | (168) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | all_147_0 % 16.48/2.97 | | | | | | | | | | | | | (169) apart_point_and_line(all_15_3, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | all_147_1 % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_73_3, all_147_0, % 16.48/2.97 | | | | | | | | | | | | | all_15_0, all_15_5, simplifying with (76), (168) % 16.48/2.97 | | | | | | | | | | | | | gives: % 16.48/2.97 | | | | | | | | | | | | | (170) all_147_0 = all_73_3 % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_75_1, all_147_1, % 16.48/2.97 | | | | | | | | | | | | | all_15_0, all_15_3, simplifying with (82), (169) % 16.48/2.97 | | | | | | | | | | | | | gives: % 16.48/2.97 | | | | | | | | | | | | | (171) all_147_1 = all_75_1 % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | BETA: splitting (69) gives: % 16.48/2.97 | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | (172) all_28_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | REDUCE: (160), (172) imply: % 16.48/2.97 | | | | | | | | | | | | | | (173) $false % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.97 | | | | | | | | | | | | | | (apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.97 | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v1 & % 16.48/2.97 | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = v0 & ( ~ % 16.48/2.97 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_160_0, % 16.48/2.97 | | | | | | | | | | | | | | all_160_1, all_160_2 gives: % 16.48/2.97 | | | | | | | | | | | | | | (175) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | | all_160_0 & apart_point_and_line(all_15_5, % 16.48/2.97 | | | | | | | | | | | | | | all_15_0) = all_160_1 & % 16.48/2.97 | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = all_160_2 & % 16.48/2.97 | | | | | | | | | | | | | | ( ~ (all_160_2 = 0) | all_160_0 = 0 | all_160_1 = % 16.48/2.97 | | | | | | | | | | | | | | 0) % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | ALPHA: (175) implies: % 16.48/2.97 | | | | | | | | | | | | | | (176) distinct_points(all_15_5, all_15_5) = all_160_2 % 16.48/2.97 | | | | | | | | | | | | | | (177) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | | all_160_1 % 16.48/2.97 | | | | | | | | | | | | | | (178) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.97 | | | | | | | | | | | | | | all_160_0 % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_73_3, all_160_0, % 16.48/2.97 | | | | | | | | | | | | | | all_15_0, all_15_5, simplifying with (76), (178) % 16.48/2.97 | | | | | | | | | | | | | | gives: % 16.48/2.97 | | | | | | | | | | | | | | (179) all_160_0 = all_73_3 % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_160_1, all_160_0, % 16.48/2.97 | | | | | | | | | | | | | | all_15_0, all_15_5, simplifying with (177), (178) % 16.48/2.97 | | | | | | | | | | | | | | gives: % 16.48/2.97 | | | | | | | | | | | | | | (180) all_160_0 = all_160_1 % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | COMBINE_EQS: (179), (180) imply: % 16.48/2.97 | | | | | | | | | | | | | | (181) all_160_1 = all_73_3 % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | BETA: splitting (83) gives: % 16.48/2.97 | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | (182) all_75_0 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | COMBINE_EQS: (124), (182) imply: % 16.48/2.97 | | | | | | | | | | | | | | | (183) all_15_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | REDUCE: (10), (183) imply: % 16.48/2.97 | | | | | | | | | | | | | | | (184) $false % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | (185) ~ (all_75_0 = 0) % 16.48/2.97 | | | | | | | | | | | | | | | (186) all_75_1 = 0 | all_75_2 = 0 | all_75_3 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 16.48/2.97 | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | (187) ~ (all_85_2 = 0) % 16.48/2.97 | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | (188) all_75_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | REDUCE: (82), (188) imply: % 16.48/2.97 | | | | | | | | | | | | | | | | | (189) apart_point_and_line(all_15_3, all_15_0) = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_3, % 16.48/2.97 | | | | | | | | | | | | | | | | | all_15_3, all_15_0, simplifying with (11), (13), % 16.48/2.97 | | | | | | | | | | | | | | | | | (22), (189) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.97 | | | | | | | | | | | | | | | | | (distinct_points(all_15_3, all_15_3) = v2 & % 16.48/2.97 | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v1 & % 16.48/2.97 | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = v0 & ( ~ % 16.48/2.97 | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0))) % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_199_0, % 16.48/2.97 | | | | | | | | | | | | | | | | | all_199_1, all_199_2 gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | (191) distinct_points(all_15_3, all_15_3) = all_199_0 & % 16.48/2.97 | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = all_199_1 & % 16.48/2.97 | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = all_199_2 & % 16.48/2.97 | | | | | | | | | | | | | | | | | ( ~ (all_199_2 = 0) | (all_199_0 = 0 & all_199_1 = % 16.48/2.97 | | | | | | | | | | | | | | | | | 0)) % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 16.48/2.97 | | | | | | | | | | | | | | | | | (192) distinct_points(all_15_5, all_15_3) = all_199_2 % 16.48/2.97 | | | | | | | | | | | | | | | | | (193) distinct_points(all_15_3, all_15_3) = all_199_0 % 16.48/2.97 | | | | | | | | | | | | | | | | | (194) ~ (all_199_2 = 0) | (all_199_0 = 0 & all_199_1 = % 16.48/2.97 | | | | | | | | | | | | | | | | | 0) % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_199_2, all_15_3, % 16.48/2.97 | | | | | | | | | | | | | | | | | all_15_5, simplifying with (17), (192) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | (195) all_199_2 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_85_2, all_199_0, % 16.48/2.97 | | | | | | | | | | | | | | | | | all_15_3, all_15_3, simplifying with (96), (193) % 16.48/2.97 | | | | | | | | | | | | | | | | | gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | (196) all_199_0 = all_85_2 % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | (197) ~ (all_199_2 = 0) % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | REDUCE: (195), (197) imply: % 16.48/2.97 | | | | | | | | | | | | | | | | | | (198) $false % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | (199) all_199_0 = 0 & all_199_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 16.48/2.97 | | | | | | | | | | | | | | | | | | (200) all_199_0 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (200) imply: % 16.48/2.97 | | | | | | | | | | | | | | | | | | (201) all_85_2 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | REDUCE: (187), (201) imply: % 16.48/2.97 | | | | | | | | | | | | | | | | | | (202) $false % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | End of split % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | (203) ~ (all_75_1 = 0) % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | (204) all_75_1 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | REDUCE: (203), (204) imply: % 16.48/2.97 | | | | | | | | | | | | | | | | | | (205) $false % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | (206) all_75_2 = 0 | all_75_3 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 16.48/2.97 | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.97 | | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | | (207) all_75_2 = 0 % 16.48/2.97 | | | | | | | | | | | | | | | | | | | % 16.48/2.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (207) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (208) all_28_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | SIMP: (208) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (209) all_28_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | REDUCE: (160), (209) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (210) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (211) all_75_3 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (212) ~ (all_75_2 = 0) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (211) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (213) all_73_3 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | SIMP: (213) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (214) all_73_3 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | REDUCE: (76), (214) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | (215) apart_point_and_line(all_15_5, all_15_0) = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | (216) all_75_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (216) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | (217) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | (218) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_5, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | all_15_0) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | (219) all_75_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (219) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | (220) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | (221) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | (222) all_75_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (222) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | (223) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | (224) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (225) all_15_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (225) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (226) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (227) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_238_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_238_1, all_238_2 gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (228) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_238_0 & apart_point_and_line(all_15_5, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = all_238_1 & distinct_lines(all_15_2, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_238_2 & ( ~ (all_238_2 = 0) | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_238_0 = 0 | all_238_1 = 0) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | (229) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | all_238_0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_28_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (230) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (231) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_15_3, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_253_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_253_1, all_253_2, all_253_3 gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (233) apart_point_and_line(all_15_3, all_15_2) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_253_1 & apart_point_and_line(all_15_5, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_253_0 & distinct_lines(all_15_2, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_253_2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = all_253_3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_253_2 = 0) | ~ (all_253_3 = 0) | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_253_0 = 0 | all_253_1 = 0) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | (234) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | all_253_0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_28_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (235) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (237) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_15_3, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = v3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = v0 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_268_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_268_1, all_268_2, all_268_3 gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (238) apart_point_and_line(all_15_3, all_15_2) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_268_0 & apart_point_and_line(all_15_5, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_268_1 & distinct_lines(all_15_2, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_268_2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = all_268_3 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_268_2 = 0) | ~ (all_268_3 = 0) | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_268_0 = 0 | all_268_1 = 0) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (239) distinct_points(all_15_5, all_15_3) = all_268_3 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (240) apart_point_and_line(all_15_5, all_15_0) = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_268_1 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_268_3, all_15_3, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_5, simplifying with (17), (239) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_268_3 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_238_0, all_253_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0, all_15_5, simplifying with (229), (234) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_253_0 = all_238_0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_253_0, all_268_1, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0, all_15_5, simplifying with (234), (240) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_268_1 = all_253_0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_268_1, all_15_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_5, simplifying with (215), (240) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_268_1 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (244) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_253_0 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (245) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_253_0 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (246) imply: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_238_0 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (247) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_238_0 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_3, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_5, all_15_0, simplifying with (11), (13), % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (22), (215) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (distinct_points(all_15_5, all_15_3) = v2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = v0 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = v1 & ( ~ % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0))) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_279_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_279_1, all_279_2 gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (250) distinct_points(all_15_5, all_15_3) = all_279_0 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_3) = all_279_2 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_5, all_15_5) = all_279_1 & % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_279_2 = 0) | (all_279_0 = 0 & all_279_1 = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | 0)) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (251) distinct_points(all_15_5, all_15_5) = all_279_1 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (252) distinct_points(all_15_5, all_15_3) = all_279_2 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (253) distinct_points(all_15_5, all_15_3) = all_279_0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_279_2 = 0) | (all_279_0 = 0 & all_279_1 = % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | 0) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_160_2, all_279_1, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_5, all_15_5, simplifying with (176), (251) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_279_1 = all_160_2 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_279_0, all_15_3, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_5, simplifying with (17), (253) gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_279_0 = 0 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_279_2, all_279_0, % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_3, all_15_5, simplifying with (252), (253) % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_279_0 = all_279_2 % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_279_2 = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (259) ~ (all_279_2 = 0) % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (259) imply: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (260) $false % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent. % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_279_0 = 0 & all_279_1 = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_279_1 = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (262) imply: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_160_2 = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (263) imply: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (264) distinct_points(all_15_5, all_15_5) = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | with (11), (264) gives: % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (265) $false % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | Case 2: % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | (266) all_85_2 = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | REDUCE: (96), (266) imply: % 16.48/2.99 | | | | | | | | | | | | | | | | (267) distinct_points(all_15_3, all_15_3) = 0 % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_3, simplifying % 16.48/2.99 | | | | | | | | | | | | | | | | with (13), (267) gives: % 16.48/2.99 | | | | | | | | | | | | | | | | (268) $false % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. % 16.48/2.99 | | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | | % 16.48/2.99 | | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | | % 16.48/2.99 | | | | | | | | | End of split % 16.48/2.99 | | | | | | | | | % 16.48/2.99 | | | | | | | | End of split % 16.48/2.99 | | | | | | | | % 16.48/2.99 | | | | | | | End of split % 16.48/2.99 | | | | | | | % 16.48/2.99 | | | | | | End of split % 16.48/2.99 | | | | | | % 16.48/2.99 | | | | | Case 2: % 16.48/2.99 | | | | | | % 16.48/2.99 | | | | | | (269) all_33_1 = 0 % 16.48/2.99 | | | | | | % 16.48/2.99 | | | | | | REDUCE: (42), (269) imply: % 16.48/2.99 | | | | | | (270) apart_point_and_line(all_15_4, all_15_2) = 0 % 16.48/2.99 | | | | | | % 16.48/2.99 | | | | | | REF_CLOSE: (7), (11), (12), (16), (21), (270), (apart1), (con1) are % 16.48/2.99 | | | | | | inconsistent by sub-proof #1. % 16.48/2.99 | | | | | | % 16.48/2.99 | | | | | End of split % 16.48/2.99 | | | | | % 16.48/2.99 | | | | End of split % 16.48/2.99 | | | | % 16.48/2.99 | | | End of split % 16.48/2.99 | | | % 16.48/2.99 | | End of split % 16.48/2.99 | | % 16.48/2.99 | End of split % 16.48/2.99 | % 16.48/2.99 End of proof % 16.48/2.99 % 16.48/2.99 Sub-proof #1 shows that the following formulas are inconsistent: % 16.48/2.99 ---------------------------------------------------------------- % 16.48/2.99 (1) line_connecting(all_15_5, all_15_4) = all_15_2 % 16.48/2.99 (2) $i(all_15_4) % 16.48/2.99 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.48/2.99 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) % 16.48/2.99 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 16.48/2.99 [v6: any] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = % 16.48/2.99 v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = % 16.48/2.99 0)))) % 16.48/2.99 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.48/2.99 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.48/2.99 (distinct_points(v3, v2) = v0)) % 16.48/2.99 (5) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 16.48/2.99 (6) distinct_points(all_15_5, all_15_4) = 0 % 16.48/2.99 (7) $i(all_15_5) % 16.48/2.99 (8) apart_point_and_line(all_15_4, all_15_2) = 0 % 16.48/2.99 % 16.48/2.99 Begin of proof % 16.48/2.99 | % 16.48/2.99 | GROUND_INST: instantiating (3) with all_15_5, all_15_4, all_15_4, all_15_2, % 16.48/2.99 | simplifying with (1), (2), (7), (8) gives: % 16.48/2.99 | (9) ? [v0: any] : ? [v1: any] : ? [v2: any] : (distinct_points(all_15_4, % 16.48/2.99 | all_15_4) = v2 & distinct_points(all_15_4, all_15_5) = v1 & % 16.48/2.99 | distinct_points(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 & % 16.48/2.99 | v1 = 0))) % 16.48/2.99 | % 16.48/2.99 | DELTA: instantiating (9) with fresh symbols all_103_0, all_103_1, all_103_2 % 16.48/2.99 | gives: % 16.48/2.99 | (10) distinct_points(all_15_4, all_15_4) = all_103_0 & % 16.48/2.99 | distinct_points(all_15_4, all_15_5) = all_103_1 & % 16.48/2.99 | distinct_points(all_15_5, all_15_4) = all_103_2 & ( ~ (all_103_2 = 0) % 16.48/2.99 | | (all_103_0 = 0 & all_103_1 = 0)) % 16.48/2.99 | % 16.48/2.99 | ALPHA: (10) implies: % 16.48/2.99 | (11) distinct_points(all_15_5, all_15_4) = all_103_2 % 16.48/2.99 | (12) distinct_points(all_15_4, all_15_4) = all_103_0 % 16.48/2.99 | (13) ~ (all_103_2 = 0) | (all_103_0 = 0 & all_103_1 = 0) % 16.48/2.99 | % 16.48/2.99 | GROUND_INST: instantiating (4) with 0, all_103_2, all_15_4, all_15_5, % 16.48/2.99 | simplifying with (6), (11) gives: % 16.48/2.99 | (14) all_103_2 = 0 % 16.48/2.99 | % 16.48/2.99 | BETA: splitting (13) gives: % 16.48/2.99 | % 16.48/2.99 | Case 1: % 16.48/2.99 | | % 16.48/2.99 | | (15) ~ (all_103_2 = 0) % 16.48/2.99 | | % 16.48/2.99 | | REDUCE: (14), (15) imply: % 16.48/2.99 | | (16) $false % 16.48/2.99 | | % 16.48/2.99 | | CLOSE: (16) is inconsistent. % 16.48/2.99 | | % 16.48/2.99 | Case 2: % 16.48/2.99 | | % 16.48/2.99 | | (17) all_103_0 = 0 & all_103_1 = 0 % 16.48/2.99 | | % 16.48/2.99 | | ALPHA: (17) implies: % 16.48/2.99 | | (18) all_103_0 = 0 % 16.48/2.99 | | % 16.48/2.99 | | REDUCE: (12), (18) imply: % 16.48/2.99 | | (19) distinct_points(all_15_4, all_15_4) = 0 % 16.48/2.99 | | % 16.48/2.99 | | GROUND_INST: instantiating (5) with all_15_4, simplifying with (2), (19) % 16.48/2.99 | | gives: % 16.48/2.99 | | (20) $false % 16.48/2.99 | | % 16.48/2.99 | | CLOSE: (20) is inconsistent. % 16.48/2.99 | | % 16.48/2.99 | End of split % 16.48/2.99 | % 16.48/2.99 End of proof % 16.48/2.99 % SZS output end Proof for theBenchmark % 16.48/2.99 % 16.48/2.99 2392ms %------------------------------------------------------------------------------