%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO199+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 23:22:11 EDT 2023 % Result : Theorem 54.90s 8.01s % Output : Proof 55.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO199+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 21:16:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.59/0.66 ________ _____ % 0.59/0.66 ___ __ \_________(_)________________________________ % 0.59/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.59/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.59/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.59/0.66 % 0.59/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.59/0.66 (2023-06-19) % 0.59/0.66 % 0.59/0.66 (c) Philipp Rümmer, 2009-2023 % 0.59/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.59/0.66 Amanda Stjerna. % 0.59/0.66 Free software under BSD-3-Clause. % 0.59/0.66 % 0.59/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.59/0.66 % 0.59/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.68 Running up to 7 provers in parallel. % 0.59/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.59/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.59/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.59/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.59/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.59/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.59/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.75/1.13 Prover 4: Preprocessing ... % 2.75/1.13 Prover 1: Preprocessing ... % 2.75/1.16 Prover 6: Preprocessing ... % 2.75/1.16 Prover 2: Preprocessing ... % 2.75/1.16 Prover 5: Preprocessing ... % 2.75/1.16 Prover 3: Preprocessing ... % 2.75/1.16 Prover 0: Preprocessing ... % 4.58/1.40 Prover 5: Proving ... % 4.58/1.40 Prover 2: Proving ... % 4.58/1.42 Prover 6: Constructing countermodel ... % 5.03/1.45 Prover 3: Constructing countermodel ... % 5.03/1.45 Prover 1: Constructing countermodel ... % 5.53/1.53 Prover 3: gave up % 5.53/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.53/1.54 Prover 1: gave up % 5.53/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.83/1.56 Prover 0: Proving ... % 5.83/1.56 Prover 6: gave up % 5.83/1.57 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.83/1.57 Prover 4: Constructing countermodel ... % 5.83/1.57 Prover 7: Preprocessing ... % 5.83/1.59 Prover 8: Preprocessing ... % 5.83/1.59 Prover 9: Preprocessing ... % 6.47/1.65 Prover 7: Warning: ignoring some quantifiers % 6.47/1.66 Prover 7: Constructing countermodel ... % 6.81/1.69 Prover 8: Warning: ignoring some quantifiers % 6.81/1.71 Prover 8: Constructing countermodel ... % 7.35/1.77 Prover 8: gave up % 7.35/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.35/1.78 Prover 9: Constructing countermodel ... % 7.35/1.83 Prover 10: Preprocessing ... % 7.35/1.86 Prover 10: Warning: ignoring some quantifiers % 7.35/1.87 Prover 10: Constructing countermodel ... % 7.35/1.87 Prover 7: gave up % 7.94/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.94/1.90 Prover 11: Preprocessing ... % 8.43/1.93 Prover 10: gave up % 8.43/1.95 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.43/1.97 Prover 12: Preprocessing ... % 9.66/2.10 Prover 11: Constructing countermodel ... % 9.66/2.11 Prover 12: Proving ... % 33.15/5.18 Prover 12: stopped % 33.15/5.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 33.58/5.23 Prover 13: Preprocessing ... % 33.93/5.25 Prover 13: Warning: ignoring some quantifiers % 33.93/5.26 Prover 13: Constructing countermodel ... % 34.61/5.35 Prover 13: gave up % 34.61/5.36 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 34.61/5.37 Prover 14: Preprocessing ... % 35.41/5.45 Prover 14: Proving ... % 54.17/7.92 Prover 2: stopped % 54.17/7.95 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181 % 54.17/7.96 Prover 15: Preprocessing ... % 54.17/7.98 Prover 4: Found proof (size 319) % 54.17/7.98 Prover 4: proved (7283ms) % 54.17/7.98 Prover 9: stopped % 54.17/7.98 Prover 0: stopped % 54.17/7.98 Prover 5: stopped % 54.90/7.98 Prover 11: stopped % 54.90/7.98 Prover 14: stopped % 54.90/8.00 Prover 15: Proving ... % 54.90/8.00 Prover 15: stopped % 54.90/8.00 % 54.90/8.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 54.90/8.01 % 54.90/8.02 % SZS output start Proof for theBenchmark % 54.90/8.03 Assumptions after simplification: % 54.90/8.03 --------------------------------- % 54.90/8.03 % 54.90/8.03 (apart3) % 55.20/8.05 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 55.20/8.05 % 55.20/8.05 (ax6) % 55.20/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 55.20/8.06 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 55.20/8.06 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 55.20/8.06 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 55.20/8.06 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 55.20/8.06 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.20/8.06 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 55.20/8.06 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 55.20/8.06 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.20/8.06 convergent_lines(v1, v2) = 0) % 55.20/8.06 % 55.20/8.06 (ceq1) % 55.20/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 55.20/8.06 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 55.20/8.06 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 55.20/8.06 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 55.20/8.06 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 55.20/8.06 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 55.20/8.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 55.20/8.06 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 55.20/8.06 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 55.20/8.06 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 55.20/8.06 % 55.20/8.06 (ceq3) % 55.20/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 55.20/8.06 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 55.20/8.06 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 55.20/8.06 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 55.20/8.06 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 55.20/8.06 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.20/8.06 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 55.20/8.06 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 55.20/8.06 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.20/8.06 convergent_lines(v0, v2) = 0) % 55.20/8.06 % 55.20/8.06 (ci3) % 55.20/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 55.20/8.07 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 55.20/8.07 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 55.20/8.07 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 55.20/8.07 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 55.20/8.07 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 55.20/8.07 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 55.20/8.07 % 55.20/8.07 (ci4) % 55.20/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 55.20/8.07 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 55.20/8.07 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 55.20/8.07 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 55.20/8.07 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 55.20/8.07 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 55.20/8.07 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 55.20/8.07 % 55.20/8.07 (con) % 55.20/8.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 55.20/8.07 $i] : ( ~ (v4 = 0) & intersection_point(v1, v0) = v5 & % 55.20/8.07 intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v2) = 0 & % 55.20/8.07 apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & % 55.20/8.07 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v5) & % 55.20/8.07 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 55.20/8.07 % 55.20/8.07 (cu1) % 55.20/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 55.20/8.08 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 55.20/8.08 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 55.20/8.08 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 55.20/8.08 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 55.20/8.08 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 55.20/8.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 55.20/8.08 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 55.20/8.08 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 55.20/8.08 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 55.20/8.08 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 55.20/8.08 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 55.20/8.08 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.20/8.08 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 55.20/8.08 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 55.20/8.08 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 55.20/8.08 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 55.20/8.08 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 55.20/8.08 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 55.20/8.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 55.20/8.08 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 55.20/8.08 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 55.20/8.08 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 55.20/8.08 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 55.20/8.08 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 55.20/8.08 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 55.20/8.08 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 55.20/8.08 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 55.20/8.08 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 55.20/8.08 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 55.20/8.08 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 55.20/8.08 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 55.20/8.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 55.20/8.08 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 55.20/8.08 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 55.20/8.08 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 55.20/8.08 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 55.20/8.08 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 55.20/8.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.20/8.08 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 55.20/8.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 55.20/8.08 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 55.20/8.08 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 55.20/8.08 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 55.20/8.08 % 55.20/8.08 (function-axioms) % 55.20/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.20/8.08 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 55.20/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.20/8.08 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 55.20/8.08 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 55.20/8.08 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 55.20/8.08 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.20/8.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.20/8.08 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 55.20/8.08 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 55.20/8.08 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 55.20/8.08 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 55.20/8.08 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 55.20/8.08 (distinct_points(v3, v2) = v0)) % 55.20/8.08 % 55.20/8.08 Further assumptions not needed in the proof: % 55.20/8.08 -------------------------------------------- % 55.20/8.08 apart1, apart2, apart4, apart5, ceq2, ci1, ci2 % 55.20/8.08 % 55.20/8.08 Those formulas are unsatisfiable: % 55.20/8.08 --------------------------------- % 55.20/8.08 % 55.20/8.08 Begin of proof % 55.20/8.08 | % 55.20/8.08 | ALPHA: (ax6) implies: % 55.20/8.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 55.20/8.08 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 55.20/8.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 55.20/8.08 | % 55.20/8.08 | ALPHA: (ci3) implies: % 55.20/8.08 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 55.20/8.08 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 55.20/8.09 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 55.20/8.09 | & $i(v2))) % 55.20/8.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 55.20/8.09 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 55.20/8.09 | (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & % 55.20/8.09 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 55.20/8.09 | % 55.20/8.09 | ALPHA: (ci4) implies: % 55.20/8.09 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 55.20/8.09 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 55.20/8.09 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 55.20/8.09 | & $i(v2))) % 55.20/8.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 55.20/8.09 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 55.20/8.09 | (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & % 55.20/8.09 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 55.20/8.09 | % 55.20/8.09 | ALPHA: (cu1) implies: % 55.20/8.09 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 55.20/8.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 55.20/8.09 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 55.20/8.09 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 55.20/8.09 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 55.20/8.09 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 55.20/8.09 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 55.20/8.09 | | v8 = 0))) % 55.20/8.09 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 55.20/8.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 55.20/8.09 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 55.20/8.09 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 55.20/8.09 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 55.20/8.09 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 55.20/8.09 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 55.20/8.09 | | v8 = 0))) % 55.20/8.09 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 55.20/8.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 55.20/8.09 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 55.20/8.09 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 55.20/8.09 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 55.20/8.09 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 55.20/8.09 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 55.20/8.09 | % 55.20/8.09 | ALPHA: (ceq1) implies: % 55.20/8.09 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 55.20/8.09 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 55.20/8.09 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.20/8.09 | distinct_points(v0, v2) = 0) % 55.20/8.09 | % 55.20/8.09 | ALPHA: (ceq3) implies: % 55.20/8.09 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 55.20/8.09 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 55.20/8.09 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 55.20/8.09 | % 55.20/8.09 | ALPHA: (function-axioms) implies: % 55.20/8.09 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 55.20/8.09 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 55.20/8.09 | (distinct_lines(v3, v2) = v0)) % 55.20/8.09 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 55.20/8.09 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 55.20/8.09 | (convergent_lines(v3, v2) = v0)) % 55.20/8.09 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 55.20/8.09 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 55.20/8.09 | (apart_point_and_line(v3, v2) = v0)) % 55.20/8.09 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.20/8.09 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 55.20/8.09 | v0)) % 55.20/8.09 | % 55.20/8.09 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 55.20/8.09 | all_17_3, all_17_4, all_17_5 gives: % 55.20/8.10 | (15) ~ (all_17_1 = 0) & intersection_point(all_17_4, all_17_5) = all_17_0 % 55.20/8.10 | & intersection_point(all_17_5, all_17_4) = all_17_2 & % 55.20/8.10 | apart_point_and_line(all_17_0, all_17_3) = 0 & % 55.20/8.10 | apart_point_and_line(all_17_2, all_17_3) = all_17_1 & % 55.20/8.10 | convergent_lines(all_17_3, all_17_4) = 0 & convergent_lines(all_17_5, % 55.20/8.10 | all_17_3) = 0 & convergent_lines(all_17_5, all_17_4) = 0 & % 55.20/8.10 | $i(all_17_0) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & % 55.20/8.10 | $i(all_17_5) % 55.20/8.10 | % 55.20/8.10 | ALPHA: (15) implies: % 55.20/8.10 | (16) ~ (all_17_1 = 0) % 55.20/8.10 | (17) $i(all_17_5) % 55.20/8.10 | (18) $i(all_17_4) % 55.20/8.10 | (19) $i(all_17_3) % 55.20/8.10 | (20) $i(all_17_2) % 55.20/8.10 | (21) $i(all_17_0) % 55.20/8.10 | (22) convergent_lines(all_17_5, all_17_4) = 0 % 55.20/8.10 | (23) convergent_lines(all_17_5, all_17_3) = 0 % 55.20/8.10 | (24) convergent_lines(all_17_3, all_17_4) = 0 % 55.20/8.10 | (25) apart_point_and_line(all_17_2, all_17_3) = all_17_1 % 55.20/8.10 | (26) apart_point_and_line(all_17_0, all_17_3) = 0 % 55.20/8.10 | (27) intersection_point(all_17_5, all_17_4) = all_17_2 % 55.20/8.10 | (28) intersection_point(all_17_4, all_17_5) = all_17_0 % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (17), % 55.20/8.10 | (18), (22) gives: % 55.20/8.10 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_5, all_17_4) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_4) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (17), % 55.20/8.10 | (18), (22) gives: % 55.20/8.10 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_5, all_17_4) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (4) with all_17_5, all_17_3, simplifying with (17), % 55.20/8.10 | (19), (23) gives: % 55.20/8.10 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_5, all_17_3) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_3) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (2) with all_17_5, all_17_3, simplifying with (17), % 55.20/8.10 | (19), (23) gives: % 55.20/8.10 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_5, all_17_3) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (4) with all_17_3, all_17_4, simplifying with (18), % 55.20/8.10 | (19), (24) gives: % 55.20/8.10 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_3, all_17_4) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_4) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (2) with all_17_3, all_17_4, simplifying with (18), % 55.20/8.10 | (19), (24) gives: % 55.20/8.10 | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 55.20/8.10 | intersection_point(all_17_3, all_17_4) = v0 & % 55.20/8.10 | apart_point_and_line(v0, all_17_3) = v1 & $i(v0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (7) with all_17_2, all_17_2, all_17_3, all_17_3, % 55.20/8.10 | all_17_1, all_17_1, simplifying with (19), (20), (25) gives: % 55.20/8.10 | (35) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 55.20/8.10 | any] : (apart_point_and_line(all_17_2, all_17_3) = v3 & % 55.20/8.10 | apart_point_and_line(all_17_2, all_17_3) = v2 & % 55.20/8.10 | distinct_lines(all_17_3, all_17_3) = v1 & distinct_points(all_17_2, % 55.20/8.10 | all_17_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (9) with all_17_0, all_17_3, all_17_2, all_17_1, % 55.20/8.10 | simplifying with (19), (20), (21), (25), (26) gives: % 55.20/8.10 | (36) all_17_1 = 0 | distinct_points(all_17_0, all_17_2) = 0 % 55.20/8.10 | % 55.20/8.10 | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying % 55.20/8.10 | with (17), (18), (27) gives: % 55.20/8.10 | (37) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 55.20/8.10 | all_17_4) = v1 & convergent_lines(all_17_5, all_17_4) = v0 & ( ~ % 55.20/8.10 | (v1 = 0) | ~ (v0 = 0))) % 55.20/8.11 | % 55.20/8.11 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying % 55.20/8.11 | with (17), (18), (27) gives: % 55.20/8.11 | (38) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 55.20/8.11 | all_17_5) = v1 & convergent_lines(all_17_5, all_17_4) = v0 & ( ~ % 55.20/8.11 | (v1 = 0) | ~ (v0 = 0))) % 55.20/8.11 | % 55.20/8.11 | GROUND_INST: instantiating (5) with all_17_4, all_17_5, all_17_0, simplifying % 55.20/8.11 | with (17), (18), (28) gives: % 55.20/8.11 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_0, % 55.20/8.11 | all_17_5) = v1 & convergent_lines(all_17_4, all_17_5) = v0 & ( ~ % 55.20/8.11 | (v1 = 0) | ~ (v0 = 0))) % 55.20/8.11 | % 55.20/8.11 | GROUND_INST: instantiating (3) with all_17_4, all_17_5, all_17_0, simplifying % 55.20/8.11 | with (17), (18), (28) gives: % 55.20/8.11 | (40) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_0, % 55.20/8.11 | all_17_4) = v1 & convergent_lines(all_17_4, all_17_5) = v0 & ( ~ % 55.20/8.11 | (v1 = 0) | ~ (v0 = 0))) % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (40) with fresh symbols all_24_0, all_24_1 gives: % 55.20/8.11 | (41) apart_point_and_line(all_17_0, all_17_4) = all_24_0 & % 55.20/8.11 | convergent_lines(all_17_4, all_17_5) = all_24_1 & ( ~ (all_24_0 = 0) | % 55.20/8.11 | ~ (all_24_1 = 0)) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (41) implies: % 55.20/8.11 | (42) convergent_lines(all_17_4, all_17_5) = all_24_1 % 55.20/8.11 | (43) apart_point_and_line(all_17_0, all_17_4) = all_24_0 % 55.20/8.11 | (44) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (39) with fresh symbols all_26_0, all_26_1 gives: % 55.20/8.11 | (45) apart_point_and_line(all_17_0, all_17_5) = all_26_0 & % 55.20/8.11 | convergent_lines(all_17_4, all_17_5) = all_26_1 & ( ~ (all_26_0 = 0) | % 55.20/8.11 | ~ (all_26_1 = 0)) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (45) implies: % 55.20/8.11 | (46) convergent_lines(all_17_4, all_17_5) = all_26_1 % 55.20/8.11 | (47) apart_point_and_line(all_17_0, all_17_5) = all_26_0 % 55.20/8.11 | (48) ~ (all_26_0 = 0) | ~ (all_26_1 = 0) % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1 gives: % 55.20/8.11 | (49) ~ (all_28_0 = 0) & intersection_point(all_17_3, all_17_4) = all_28_1 % 55.20/8.11 | & apart_point_and_line(all_28_1, all_17_3) = all_28_0 & $i(all_28_1) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (49) implies: % 55.20/8.11 | (50) ~ (all_28_0 = 0) % 55.20/8.11 | (51) apart_point_and_line(all_28_1, all_17_3) = all_28_0 % 55.20/8.11 | (52) intersection_point(all_17_3, all_17_4) = all_28_1 % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (33) with fresh symbols all_30_0, all_30_1 gives: % 55.20/8.11 | (53) ~ (all_30_0 = 0) & intersection_point(all_17_3, all_17_4) = all_30_1 % 55.20/8.11 | & apart_point_and_line(all_30_1, all_17_4) = all_30_0 & $i(all_30_1) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (53) implies: % 55.20/8.11 | (54) ~ (all_30_0 = 0) % 55.20/8.11 | (55) $i(all_30_1) % 55.20/8.11 | (56) apart_point_and_line(all_30_1, all_17_4) = all_30_0 % 55.20/8.11 | (57) intersection_point(all_17_3, all_17_4) = all_30_1 % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1 gives: % 55.20/8.11 | (58) ~ (all_32_0 = 0) & intersection_point(all_17_5, all_17_3) = all_32_1 % 55.20/8.11 | & apart_point_and_line(all_32_1, all_17_5) = all_32_0 & $i(all_32_1) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (58) implies: % 55.20/8.11 | (59) ~ (all_32_0 = 0) % 55.20/8.11 | (60) apart_point_and_line(all_32_1, all_17_5) = all_32_0 % 55.20/8.11 | (61) intersection_point(all_17_5, all_17_3) = all_32_1 % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (30) with fresh symbols all_34_0, all_34_1 gives: % 55.20/8.11 | (62) ~ (all_34_0 = 0) & intersection_point(all_17_5, all_17_4) = all_34_1 % 55.20/8.11 | & apart_point_and_line(all_34_1, all_17_5) = all_34_0 & $i(all_34_1) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (62) implies: % 55.20/8.11 | (63) $i(all_34_1) % 55.20/8.11 | (64) apart_point_and_line(all_34_1, all_17_5) = all_34_0 % 55.20/8.11 | (65) intersection_point(all_17_5, all_17_4) = all_34_1 % 55.20/8.11 | % 55.20/8.11 | DELTA: instantiating (38) with fresh symbols all_36_0, all_36_1 gives: % 55.20/8.11 | (66) apart_point_and_line(all_17_2, all_17_5) = all_36_0 & % 55.20/8.11 | convergent_lines(all_17_5, all_17_4) = all_36_1 & ( ~ (all_36_0 = 0) | % 55.20/8.11 | ~ (all_36_1 = 0)) % 55.20/8.11 | % 55.20/8.11 | ALPHA: (66) implies: % 55.54/8.11 | (67) convergent_lines(all_17_5, all_17_4) = all_36_1 % 55.54/8.11 | (68) apart_point_and_line(all_17_2, all_17_5) = all_36_0 % 55.54/8.11 | (69) ~ (all_36_0 = 0) | ~ (all_36_1 = 0) % 55.54/8.11 | % 55.54/8.11 | DELTA: instantiating (37) with fresh symbols all_38_0, all_38_1 gives: % 55.54/8.11 | (70) apart_point_and_line(all_17_2, all_17_4) = all_38_0 & % 55.54/8.11 | convergent_lines(all_17_5, all_17_4) = all_38_1 & ( ~ (all_38_0 = 0) | % 55.54/8.11 | ~ (all_38_1 = 0)) % 55.54/8.11 | % 55.54/8.11 | ALPHA: (70) implies: % 55.54/8.11 | (71) convergent_lines(all_17_5, all_17_4) = all_38_1 % 55.54/8.11 | (72) apart_point_and_line(all_17_2, all_17_4) = all_38_0 % 55.54/8.11 | (73) ~ (all_38_0 = 0) | ~ (all_38_1 = 0) % 55.54/8.11 | % 55.54/8.11 | DELTA: instantiating (29) with fresh symbols all_40_0, all_40_1 gives: % 55.54/8.11 | (74) ~ (all_40_0 = 0) & intersection_point(all_17_5, all_17_4) = all_40_1 % 55.54/8.11 | & apart_point_and_line(all_40_1, all_17_4) = all_40_0 & $i(all_40_1) % 55.54/8.11 | % 55.54/8.11 | ALPHA: (74) implies: % 55.54/8.11 | (75) ~ (all_40_0 = 0) % 55.54/8.12 | (76) apart_point_and_line(all_40_1, all_17_4) = all_40_0 % 55.54/8.12 | (77) intersection_point(all_17_5, all_17_4) = all_40_1 % 55.54/8.12 | % 55.54/8.12 | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives: % 55.54/8.12 | (78) ~ (all_42_0 = 0) & intersection_point(all_17_5, all_17_3) = all_42_1 % 55.54/8.12 | & apart_point_and_line(all_42_1, all_17_3) = all_42_0 & $i(all_42_1) % 55.54/8.12 | % 55.54/8.12 | ALPHA: (78) implies: % 55.54/8.12 | (79) $i(all_42_1) % 55.54/8.12 | (80) intersection_point(all_17_5, all_17_3) = all_42_1 % 55.54/8.12 | % 55.54/8.12 | BETA: splitting (36) gives: % 55.54/8.12 | % 55.54/8.12 | Case 1: % 55.54/8.12 | | % 55.54/8.12 | | (81) distinct_points(all_17_0, all_17_2) = 0 % 55.54/8.12 | | % 55.54/8.12 | | BETA: splitting (35) gives: % 55.54/8.12 | | % 55.54/8.12 | | Case 1: % 55.54/8.12 | | | % 55.54/8.12 | | | (82) all_17_1 = 0 % 55.54/8.12 | | | % 55.54/8.12 | | | REDUCE: (16), (82) imply: % 55.54/8.12 | | | (83) $false % 55.54/8.12 | | | % 55.54/8.12 | | | CLOSE: (83) is inconsistent. % 55.54/8.12 | | | % 55.54/8.12 | | Case 2: % 55.54/8.12 | | | % 55.54/8.12 | | | (84) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 55.54/8.12 | | | (apart_point_and_line(all_17_2, all_17_3) = v3 & % 55.54/8.12 | | | apart_point_and_line(all_17_2, all_17_3) = v2 & % 55.54/8.12 | | | distinct_lines(all_17_3, all_17_3) = v1 & % 55.54/8.12 | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | ~ (v0 % 55.54/8.12 | | | = 0) | v3 = 0 | v2 = 0)) % 55.54/8.12 | | | % 55.54/8.12 | | | DELTA: instantiating (84) with fresh symbols all_52_0, all_52_1, all_52_2, % 55.54/8.12 | | | all_52_3 gives: % 55.54/8.12 | | | (85) apart_point_and_line(all_17_2, all_17_3) = all_52_0 & % 55.54/8.12 | | | apart_point_and_line(all_17_2, all_17_3) = all_52_1 & % 55.54/8.12 | | | distinct_lines(all_17_3, all_17_3) = all_52_2 & % 55.54/8.12 | | | distinct_points(all_17_2, all_17_2) = all_52_3 & ( ~ (all_52_2 = % 55.54/8.12 | | | 0) | ~ (all_52_3 = 0) | all_52_0 = 0 | all_52_1 = 0) % 55.54/8.12 | | | % 55.54/8.12 | | | ALPHA: (85) implies: % 55.54/8.12 | | | (86) apart_point_and_line(all_17_2, all_17_3) = all_52_1 % 55.54/8.12 | | | (87) apart_point_and_line(all_17_2, all_17_3) = all_52_0 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (12) with 0, all_38_1, all_17_4, all_17_5, % 55.54/8.12 | | | simplifying with (22), (71) gives: % 55.54/8.12 | | | (88) all_38_1 = 0 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (12) with all_36_1, all_38_1, all_17_4, % 55.54/8.12 | | | all_17_5, simplifying with (67), (71) gives: % 55.54/8.12 | | | (89) all_38_1 = all_36_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (12) with all_24_1, all_26_1, all_17_5, % 55.54/8.12 | | | all_17_4, simplifying with (42), (46) gives: % 55.54/8.12 | | | (90) all_26_1 = all_24_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (13) with all_17_1, all_52_0, all_17_3, % 55.54/8.12 | | | all_17_2, simplifying with (25), (87) gives: % 55.54/8.12 | | | (91) all_52_0 = all_17_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (13) with all_52_1, all_52_0, all_17_3, % 55.54/8.12 | | | all_17_2, simplifying with (86), (87) gives: % 55.54/8.12 | | | (92) all_52_0 = all_52_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (14) with all_17_2, all_40_1, all_17_4, % 55.54/8.12 | | | all_17_5, simplifying with (27), (77) gives: % 55.54/8.12 | | | (93) all_40_1 = all_17_2 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (14) with all_34_1, all_40_1, all_17_4, % 55.54/8.12 | | | all_17_5, simplifying with (65), (77) gives: % 55.54/8.12 | | | (94) all_40_1 = all_34_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (14) with all_32_1, all_42_1, all_17_3, % 55.54/8.12 | | | all_17_5, simplifying with (61), (80) gives: % 55.54/8.12 | | | (95) all_42_1 = all_32_1 % 55.54/8.12 | | | % 55.54/8.12 | | | GROUND_INST: instantiating (14) with all_28_1, all_30_1, all_17_4, % 55.54/8.12 | | | all_17_3, simplifying with (52), (57) gives: % 55.54/8.12 | | | (96) all_30_1 = all_28_1 % 55.54/8.12 | | | % 55.54/8.12 | | | COMBINE_EQS: (91), (92) imply: % 55.54/8.12 | | | (97) all_52_1 = all_17_1 % 55.54/8.12 | | | % 55.54/8.12 | | | COMBINE_EQS: (93), (94) imply: % 55.54/8.12 | | | (98) all_34_1 = all_17_2 % 55.54/8.12 | | | % 55.54/8.12 | | | SIMP: (98) implies: % 55.54/8.12 | | | (99) all_34_1 = all_17_2 % 55.54/8.12 | | | % 55.54/8.12 | | | COMBINE_EQS: (88), (89) imply: % 55.54/8.12 | | | (100) all_36_1 = 0 % 55.54/8.12 | | | % 55.54/8.12 | | | REDUCE: (76), (93) imply: % 55.54/8.12 | | | (101) apart_point_and_line(all_17_2, all_17_4) = all_40_0 % 55.54/8.12 | | | % 55.54/8.12 | | | REDUCE: (64), (99) imply: % 55.54/8.12 | | | (102) apart_point_and_line(all_17_2, all_17_5) = all_34_0 % 55.54/8.12 | | | % 55.54/8.13 | | | REDUCE: (56), (96) imply: % 55.54/8.13 | | | (103) apart_point_and_line(all_28_1, all_17_4) = all_30_0 % 55.54/8.13 | | | % 55.54/8.13 | | | REDUCE: (79), (95) imply: % 55.54/8.13 | | | (104) $i(all_32_1) % 55.54/8.13 | | | % 55.54/8.13 | | | REDUCE: (55), (96) imply: % 55.54/8.13 | | | (105) $i(all_28_1) % 55.54/8.13 | | | % 55.54/8.13 | | | BETA: splitting (69) gives: % 55.54/8.13 | | | % 55.54/8.13 | | | Case 1: % 55.54/8.13 | | | | % 55.54/8.13 | | | | (106) ~ (all_36_0 = 0) % 55.54/8.13 | | | | % 55.54/8.13 | | | | BETA: splitting (73) gives: % 55.54/8.13 | | | | % 55.54/8.13 | | | | Case 1: % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (13) with all_36_0, all_34_0, all_17_5, % 55.54/8.13 | | | | | all_17_2, simplifying with (68), (102) gives: % 55.54/8.13 | | | | | (107) all_36_0 = all_34_0 % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (13) with all_38_0, all_40_0, all_17_4, % 55.54/8.13 | | | | | all_17_2, simplifying with (72), (101) gives: % 55.54/8.13 | | | | | (108) all_40_0 = all_38_0 % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | REDUCE: (75), (108) imply: % 55.54/8.13 | | | | | (109) ~ (all_38_0 = 0) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | REDUCE: (106), (107) imply: % 55.54/8.13 | | | | | (110) ~ (all_34_0 = 0) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (1) with all_17_5, all_17_4, all_17_5, % 55.54/8.13 | | | | | all_24_1, simplifying with (17), (18), (22), (42) gives: % 55.54/8.13 | | | | | (111) all_24_1 = 0 | convergent_lines(all_17_5, all_17_5) = 0 % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_3, % 55.54/8.13 | | | | | all_17_5, all_17_1, all_34_0, simplifying with (17), % 55.54/8.13 | | | | | (19), (20), (21), (25), (81), (102) gives: % 55.54/8.13 | | | | | (112) all_34_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : (apart_point_and_line(all_17_0, all_17_3) = v1 % 55.54/8.13 | | | | | & apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.13 | | | | | distinct_lines(all_17_3, all_17_5) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_3, % 55.54/8.13 | | | | | all_17_4, all_17_1, all_38_0, simplifying with (18), % 55.54/8.13 | | | | | (19), (20), (21), (25), (72), (81) gives: % 55.54/8.13 | | | | | (113) all_38_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : (apart_point_and_line(all_17_0, all_17_3) = v1 % 55.54/8.13 | | | | | & apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.13 | | | | | distinct_lines(all_17_3, all_17_4) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_3, all_38_0, all_17_1, simplifying with (18), % 55.54/8.13 | | | | | (19), (20), (21), (25), (72), (81) gives: % 55.54/8.13 | | | | | (114) all_38_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : (apart_point_and_line(all_17_0, all_17_3) = v2 % 55.54/8.13 | | | | | & apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.13 | | | | | distinct_lines(all_17_4, all_17_3) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_4, all_38_0, all_38_0, simplifying with (18), % 55.54/8.13 | | | | | (20), (21), (72), (81) gives: % 55.54/8.13 | | | | | (115) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.13 | | | | | (apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.13 | | | | | apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.13 | | | | | distinct_lines(all_17_4, all_17_4) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_5, % 55.54/8.13 | | | | | all_17_4, all_34_0, all_38_0, simplifying with (17), % 55.54/8.13 | | | | | (18), (20), (21), (72), (81), (102) gives: % 55.54/8.13 | | | | | (116) all_38_0 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : (apart_point_and_line(all_17_0, all_17_4) = v2 % 55.54/8.13 | | | | | & apart_point_and_line(all_17_0, all_17_5) = v1 & % 55.54/8.13 | | | | | distinct_lines(all_17_5, all_17_4) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_5, all_38_0, all_34_0, simplifying with (17), % 55.54/8.13 | | | | | (18), (20), (21), (72), (81), (102) gives: % 55.54/8.13 | | | | | (117) all_38_0 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : (apart_point_and_line(all_17_0, all_17_4) = v1 % 55.54/8.13 | | | | | & apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.13 | | | | | distinct_lines(all_17_4, all_17_5) = v0 & ( ~ (v0 = 0) | v2 % 55.54/8.13 | | | | | = 0 | v1 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (7) with all_17_2, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_5, all_38_0, all_34_0, simplifying with (17), % 55.54/8.13 | | | | | (18), (20), (72), (102) gives: % 55.54/8.13 | | | | | (118) all_38_0 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_2, % 55.54/8.13 | | | | | all_17_4) = v3 & apart_point_and_line(all_17_2, all_17_5) % 55.54/8.13 | | | | | = v2 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.13 | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | % 55.54/8.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (6) with all_17_2, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_5, all_34_0, all_38_0, simplifying with (17), % 55.54/8.13 | | | | | (18), (20), (72), (102) gives: % 55.54/8.13 | | | | | (119) all_38_0 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_2, % 55.54/8.13 | | | | | all_17_4) = v2 & apart_point_and_line(all_17_2, all_17_5) % 55.54/8.13 | | | | | = v3 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.13 | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | % 55.54/8.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.13 | | | | | % 55.54/8.13 | | | | | GROUND_INST: instantiating (7) with all_28_1, all_17_2, all_17_4, % 55.54/8.13 | | | | | all_17_5, all_30_0, all_34_0, simplifying with (17), % 55.54/8.13 | | | | | (18), (20), (102), (103), (105) gives: % 55.54/8.13 | | | | | (120) all_34_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_28_1, % 55.54/8.13 | | | | | all_17_5) = v2 & apart_point_and_line(all_17_2, all_17_4) % 55.54/8.13 | | | | | = v3 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.13 | | | | | distinct_points(all_28_1, all_17_2) = v0 & ( ~ (v1 = 0) | % 55.54/8.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (6) with all_17_2, all_28_1, all_17_4, % 55.54/8.14 | | | | | all_17_5, all_34_0, all_30_0, simplifying with (17), % 55.54/8.14 | | | | | (18), (20), (102), (103), (105) gives: % 55.54/8.14 | | | | | (121) all_34_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_28_1, % 55.54/8.14 | | | | | all_17_5) = v3 & apart_point_and_line(all_17_2, all_17_4) % 55.54/8.14 | | | | | = v2 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (7) with all_17_2, all_28_1, all_17_5, % 55.54/8.14 | | | | | all_17_3, all_34_0, all_28_0, simplifying with (17), % 55.54/8.14 | | | | | (19), (20), (51), (102), (105) gives: % 55.54/8.14 | | | | | (122) all_34_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_28_1, % 55.54/8.14 | | | | | all_17_5) = v3 & apart_point_and_line(all_17_2, all_17_3) % 55.54/8.14 | | | | | = v2 & distinct_lines(all_17_5, all_17_3) = v1 & % 55.54/8.14 | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (7) with all_28_1, all_32_1, all_17_4, % 55.54/8.14 | | | | | all_17_5, all_30_0, all_32_0, simplifying with (17), % 55.54/8.14 | | | | | (18), (60), (103), (104), (105) gives: % 55.54/8.14 | | | | | (123) all_32_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.14 | | | | | all_17_4) = v3 & apart_point_and_line(all_28_1, all_17_5) % 55.54/8.14 | | | | | = v2 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | distinct_points(all_28_1, all_32_1) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (6) with all_32_1, all_28_1, all_17_4, % 55.54/8.14 | | | | | all_17_5, all_32_0, all_30_0, simplifying with (17), % 55.54/8.14 | | | | | (18), (60), (103), (104), (105) gives: % 55.54/8.14 | | | | | (124) all_32_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.14 | | | | | all_17_4) = v2 & apart_point_and_line(all_28_1, all_17_5) % 55.54/8.14 | | | | | = v3 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | distinct_points(all_32_1, all_28_1) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (7) with all_17_2, all_32_1, all_17_4, % 55.54/8.14 | | | | | all_17_5, all_38_0, all_32_0, simplifying with (17), % 55.54/8.14 | | | | | (18), (20), (60), (72), (104) gives: % 55.54/8.14 | | | | | (125) all_38_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.14 | | | | | all_17_4) = v3 & apart_point_and_line(all_17_2, all_17_5) % 55.54/8.14 | | | | | = v2 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | distinct_points(all_17_2, all_32_1) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | GROUND_INST: instantiating (6) with all_32_1, all_17_2, all_17_4, % 55.54/8.14 | | | | | all_17_5, all_32_0, all_38_0, simplifying with (17), % 55.54/8.14 | | | | | (18), (20), (60), (72), (104) gives: % 55.54/8.14 | | | | | (126) all_38_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : % 55.54/8.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.14 | | | | | all_17_4) = v2 & apart_point_and_line(all_17_2, all_17_5) % 55.54/8.14 | | | | | = v3 & distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | distinct_points(all_32_1, all_17_2) = v0 & ( ~ (v1 = 0) | % 55.54/8.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | BETA: splitting (115) gives: % 55.54/8.14 | | | | | % 55.54/8.14 | | | | | Case 1: % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | (127) all_38_0 = 0 % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | REDUCE: (109), (127) imply: % 55.54/8.14 | | | | | | (128) $false % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | CLOSE: (128) is inconsistent. % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | Case 2: % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | (129) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.14 | | | | | | (apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.14 | | | | | | apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.14 | | | | | | distinct_lines(all_17_4, all_17_4) = v0 & ( ~ (v0 = 0) | % 55.54/8.14 | | | | | | v2 = 0 | v1 = 0)) % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | DELTA: instantiating (129) with fresh symbols all_86_0, all_86_1, % 55.54/8.14 | | | | | | all_86_2 gives: % 55.54/8.14 | | | | | | (130) apart_point_and_line(all_17_0, all_17_4) = all_86_0 & % 55.54/8.14 | | | | | | apart_point_and_line(all_17_0, all_17_4) = all_86_1 & % 55.54/8.14 | | | | | | distinct_lines(all_17_4, all_17_4) = all_86_2 & ( ~ % 55.54/8.14 | | | | | | (all_86_2 = 0) | all_86_0 = 0 | all_86_1 = 0) % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | ALPHA: (130) implies: % 55.54/8.14 | | | | | | (131) apart_point_and_line(all_17_0, all_17_4) = all_86_1 % 55.54/8.14 | | | | | | (132) apart_point_and_line(all_17_0, all_17_4) = all_86_0 % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | BETA: splitting (113) gives: % 55.54/8.14 | | | | | | % 55.54/8.14 | | | | | | Case 1: % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | (133) all_38_0 = 0 % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | REDUCE: (109), (133) imply: % 55.54/8.14 | | | | | | | (134) $false % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | CLOSE: (134) is inconsistent. % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | Case 2: % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | (135) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 55.54/8.14 | | | | | | | : (apart_point_and_line(all_17_0, all_17_3) = v1 & % 55.54/8.14 | | | | | | | apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.14 | | | | | | | distinct_lines(all_17_3, all_17_4) = v0 & ( ~ (v0 = 0) % 55.54/8.14 | | | | | | | | v2 = 0 | v1 = 0)) % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | BETA: splitting (114) gives: % 55.54/8.14 | | | | | | | % 55.54/8.14 | | | | | | | Case 1: % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | (136) all_38_0 = 0 % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | REDUCE: (109), (136) imply: % 55.54/8.14 | | | | | | | | (137) $false % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | CLOSE: (137) is inconsistent. % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | Case 2: % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | (138) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 55.54/8.14 | | | | | | | | any] : (apart_point_and_line(all_17_0, all_17_3) = v2 % 55.54/8.14 | | | | | | | | & apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.14 | | | | | | | | distinct_lines(all_17_4, all_17_3) = v0 & ( ~ (v0 = % 55.54/8.14 | | | | | | | | 0) | v2 = 0 | v1 = 0)) % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | BETA: splitting (116) gives: % 55.54/8.14 | | | | | | | | % 55.54/8.14 | | | | | | | | Case 1: % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | (139) all_38_0 = 0 % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | REDUCE: (109), (139) imply: % 55.54/8.14 | | | | | | | | | (140) $false % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | CLOSE: (140) is inconsistent. % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | Case 2: % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | (141) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 55.54/8.14 | | | | | | | | | any] : (apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.14 | | | | | | | | | v2 & apart_point_and_line(all_17_0, all_17_5) = v1 % 55.54/8.14 | | | | | | | | | & distinct_lines(all_17_5, all_17_4) = v0 & ( ~ (v0 % 55.54/8.14 | | | | | | | | | = 0) | v2 = 0 | v1 = 0)) % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | BETA: splitting (119) gives: % 55.54/8.14 | | | | | | | | | % 55.54/8.14 | | | | | | | | | Case 1: % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | (142) all_38_0 = 0 % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | REDUCE: (109), (142) imply: % 55.54/8.14 | | | | | | | | | | (143) $false % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | CLOSE: (143) is inconsistent. % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | Case 2: % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | (144) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.14 | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.14 | | | | | | | | | | (apart_point_and_line(all_17_2, all_17_4) = v2 & % 55.54/8.14 | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v3 & % 55.54/8.14 | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ % 55.54/8.14 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | BETA: splitting (118) gives: % 55.54/8.14 | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | Case 1: % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | (145) all_38_0 = 0 % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | REDUCE: (109), (145) imply: % 55.54/8.14 | | | | | | | | | | | (146) $false % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | CLOSE: (146) is inconsistent. % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | Case 2: % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | (147) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.14 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.14 | | | | | | | | | | | (apart_point_and_line(all_17_2, all_17_4) = v3 & % 55.54/8.14 | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v2 & % 55.54/8.14 | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.14 | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ % 55.54/8.14 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | BETA: splitting (117) gives: % 55.54/8.14 | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | Case 1: % 55.54/8.14 | | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | | (148) all_38_0 = 0 % 55.54/8.14 | | | | | | | | | | | | % 55.54/8.14 | | | | | | | | | | | | REDUCE: (109), (148) imply: % 55.54/8.15 | | | | | | | | | | | | (149) $false % 55.54/8.15 | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | (150) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.15 | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | all_17_4) = v1 & % 55.54/8.15 | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.15 | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | BETA: splitting (135) gives: % 55.54/8.15 | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | (151) all_17_1 = 0 % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | REDUCE: (16), (151) imply: % 55.54/8.15 | | | | | | | | | | | | | (152) $false % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.15 | | | | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_3) = v1 & % 55.54/8.15 | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.15 | | | | | | | | | | | | | distinct_lines(all_17_3, all_17_4) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_141_0, % 55.54/8.15 | | | | | | | | | | | | | all_141_1, all_141_2 gives: % 55.54/8.15 | | | | | | | | | | | | | (154) apart_point_and_line(all_17_0, all_17_3) = % 55.54/8.15 | | | | | | | | | | | | | all_141_1 & apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | | all_17_4) = all_141_0 & distinct_lines(all_17_3, % 55.54/8.15 | | | | | | | | | | | | | all_17_4) = all_141_2 & ( ~ (all_141_2 = 0) | % 55.54/8.15 | | | | | | | | | | | | | all_141_0 = 0 | all_141_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | ALPHA: (154) implies: % 55.54/8.15 | | | | | | | | | | | | | (155) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | all_141_0 % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | BETA: splitting (138) gives: % 55.54/8.15 | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | (156) all_17_1 = 0 % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | REDUCE: (16), (156) imply: % 55.54/8.15 | | | | | | | | | | | | | | (157) $false % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | (158) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.15 | | | | | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_3) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_3) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | DELTA: instantiating (158) with fresh symbols all_146_0, % 55.54/8.15 | | | | | | | | | | | | | | all_146_1, all_146_2 gives: % 55.54/8.15 | | | | | | | | | | | | | | (159) apart_point_and_line(all_17_0, all_17_3) = % 55.54/8.15 | | | | | | | | | | | | | | all_146_0 & apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | | | all_17_4) = all_146_1 & distinct_lines(all_17_4, % 55.54/8.15 | | | | | | | | | | | | | | all_17_3) = all_146_2 & ( ~ (all_146_2 = 0) | % 55.54/8.15 | | | | | | | | | | | | | | all_146_0 = 0 | all_146_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | ALPHA: (159) implies: % 55.54/8.15 | | | | | | | | | | | | | | (160) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | all_146_1 % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | BETA: splitting (141) gives: % 55.54/8.15 | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | (161) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | REDUCE: (110), (161) imply: % 55.54/8.15 | | | | | | | | | | | | | | | (162) $false % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | (163) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.15 | | | | | | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_4) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | distinct_lines(all_17_5, all_17_4) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_151_0, % 55.54/8.15 | | | | | | | | | | | | | | | all_151_1, all_151_2 gives: % 55.54/8.15 | | | | | | | | | | | | | | | (164) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | all_151_0 & apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | | | | all_17_5) = all_151_1 & distinct_lines(all_17_5, % 55.54/8.15 | | | | | | | | | | | | | | | all_17_4) = all_151_2 & ( ~ (all_151_2 = 0) | % 55.54/8.15 | | | | | | | | | | | | | | | all_151_0 = 0 | all_151_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | ALPHA: (164) implies: % 55.54/8.15 | | | | | | | | | | | | | | | (165) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | all_151_0 % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | BETA: splitting (144) gives: % 55.54/8.15 | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | (166) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | REDUCE: (110), (166) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | (167) $false % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | (168) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_2, % 55.54/8.15 | | | | | | | | | | | | | | | | all_17_4) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v3 & % 55.54/8.15 | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | DELTA: instantiating (168) with fresh symbols all_161_0, % 55.54/8.15 | | | | | | | | | | | | | | | | all_161_1, all_161_2, all_161_3 gives: % 55.54/8.15 | | | | | | | | | | | | | | | | (169) apart_point_and_line(all_17_2, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | | all_161_1 & apart_point_and_line(all_17_2, % 55.54/8.15 | | | | | | | | | | | | | | | | all_17_5) = all_161_0 & distinct_lines(all_17_4, % 55.54/8.15 | | | | | | | | | | | | | | | | all_17_5) = all_161_2 & % 55.54/8.15 | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = all_161_3 & % 55.54/8.15 | | | | | | | | | | | | | | | | ( ~ (all_161_2 = 0) | ~ (all_161_3 = 0) | % 55.54/8.15 | | | | | | | | | | | | | | | | all_161_0 = 0 | all_161_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 55.54/8.15 | | | | | | | | | | | | | | | | (170) distinct_lines(all_17_4, all_17_5) = all_161_2 % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | (171) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | REDUCE: (110), (171) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | (172) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | (173) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_2, % 55.54/8.15 | | | | | | | | | | | | | | | | | all_17_4) = v3 & % 55.54/8.15 | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | DELTA: instantiating (173) with fresh symbols all_171_0, % 55.54/8.15 | | | | | | | | | | | | | | | | | all_171_1, all_171_2, all_171_3 gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | (174) apart_point_and_line(all_17_2, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | | | all_171_0 & apart_point_and_line(all_17_2, % 55.54/8.15 | | | | | | | | | | | | | | | | | all_17_5) = all_171_1 & distinct_lines(all_17_4, % 55.54/8.15 | | | | | | | | | | | | | | | | | all_17_5) = all_171_2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = all_171_3 & % 55.54/8.15 | | | | | | | | | | | | | | | | | ( ~ (all_171_2 = 0) | ~ (all_171_3 = 0) | % 55.54/8.15 | | | | | | | | | | | | | | | | | all_171_0 = 0 | all_171_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 55.54/8.15 | | | | | | | | | | | | | | | | | (175) distinct_lines(all_17_4, all_17_5) = all_171_2 % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | (176) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | REDUCE: (110), (176) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | | (177) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | (178) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.15 | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_4) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | DELTA: instantiating (178) with fresh symbols all_176_0, % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_176_1, all_176_2 gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | (179) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_176_1 & apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_17_5) = all_176_0 & distinct_lines(all_17_4, % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_17_5) = all_176_2 & ( ~ (all_176_2 = 0) | % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_176_0 = 0 | all_176_1 = 0) % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | ALPHA: (179) implies: % 55.54/8.15 | | | | | | | | | | | | | | | | | | (180) distinct_lines(all_17_4, all_17_5) = all_176_2 % 55.54/8.15 | | | | | | | | | | | | | | | | | | (181) apart_point_and_line(all_17_0, all_17_5) = % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_176_0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | (182) apart_point_and_line(all_17_0, all_17_4) = % 55.54/8.15 | | | | | | | | | | | | | | | | | | all_176_1 % 55.54/8.15 | | | | | | | | | | | | | | | | | | (183) ~ (all_176_2 = 0) | all_176_0 = 0 | all_176_1 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | (184) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (184) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | (185) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | (186) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_17_0, % 55.54/8.15 | | | | | | | | | | | | | | | | | | | all_17_3) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_3, all_17_5) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | (187) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (187) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | (188) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | (189) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_28_1, all_17_5) = v3 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_4) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | (190) all_34_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (190) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | (191) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | (192) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_28_1, all_17_5) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_4) = v3 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_17_2) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | (193) all_38_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (193) imply: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | (194) $false % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | (195) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_17_4) = v2 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v3 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_17_2) = v0 & ( ~ % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | | (196) all_38_0 = 0 % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (196) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | (197) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | (198) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_17_4) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_32_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | (199) all_32_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (199) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | (200) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | (201) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_17_4) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_28_1, all_17_5) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_32_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_32_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (202) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | (203) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_17_4) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_28_1, all_17_5) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_28_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_34_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (205) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (206) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_28_1, all_17_5) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_3) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_5, all_17_3) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_17_1 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (208) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_3) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_5) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_3, all_17_5) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (210) with fresh symbols all_452_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_1, all_452_2 gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) apart_point_and_line(all_17_0, all_17_3) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_1 & apart_point_and_line(all_17_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_452_0 & distinct_lines(all_17_3, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_452_2 & ( ~ (all_452_2 = 0) | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_0 = 0 | all_452_1 = 0) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) apart_point_and_line(all_17_0, all_17_5) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_30_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (213) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_28_1, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_4) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (215) with fresh symbols all_552_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_552_1, all_552_2, all_552_3 gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) apart_point_and_line(all_28_1, all_17_5) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_552_0 & apart_point_and_line(all_17_2, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = all_552_1 & distinct_lines(all_17_4, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_552_2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = all_552_3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_552_2 = 0) | ~ (all_552_3 = 0) | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_552_0 = 0 | all_552_1 = 0) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) distinct_lines(all_17_4, all_17_5) = all_552_2 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_30_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (218) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_28_1, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_4) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_17_2) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (220) with fresh symbols all_557_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_557_1, all_557_2, all_557_3 gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) apart_point_and_line(all_28_1, all_17_5) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_557_1 & apart_point_and_line(all_17_2, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = all_557_0 & distinct_lines(all_17_4, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_557_2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_17_2) = all_557_3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_557_2 = 0) | ~ (all_557_3 = 0) | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_557_0 = 0 | all_557_1 = 0) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) distinct_lines(all_17_4, all_17_5) = all_557_2 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_32_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (223) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_17_2) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (225) with fresh symbols all_587_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_587_1, all_587_2, all_587_3 gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) apart_point_and_line(all_32_1, all_17_4) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_587_1 & apart_point_and_line(all_17_2, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_587_0 & distinct_lines(all_17_4, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_587_2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_17_2) = all_587_3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_587_2 = 0) | ~ (all_587_3 = 0) | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_587_0 = 0 | all_587_1 = 0) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) distinct_lines(all_17_4, all_17_5) = all_587_2 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_32_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (228) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = v3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_32_1) = v0 & ( ~ % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_592_0, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_592_1, all_592_2, all_592_3 gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) apart_point_and_line(all_32_1, all_17_4) = % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_592_0 & apart_point_and_line(all_17_2, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_592_1 & distinct_lines(all_17_4, % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_592_2 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_32_1) = all_592_3 & % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_592_2 = 0) | ~ (all_592_3 = 0) | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_592_0 = 0 | all_592_1 = 0) % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) distinct_lines(all_17_4, all_17_5) = all_592_2 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_30_0 = 0 % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (233) imply: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) $false % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.54/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = v3 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_28_1, all_17_5) = v2 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_32_1) = v0 & ( ~ % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_707_0, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_707_1, all_707_2, all_707_3 gives: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) apart_point_and_line(all_32_1, all_17_4) = % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_707_0 & apart_point_and_line(all_28_1, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_707_1 & distinct_lines(all_17_4, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_707_2 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_28_1, all_32_1) = all_707_3 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_707_2 = 0) | ~ (all_707_3 = 0) | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_707_0 = 0 | all_707_1 = 0) % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) distinct_lines(all_17_4, all_17_5) = all_707_2 % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_30_0 = 0 % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (238) imply: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) $false % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent. % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4) = v2 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_28_1, all_17_5) = v3 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_5) = v1 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_28_1) = v0 & ( ~ % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (240) with fresh symbols all_712_0, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_712_1, all_712_2, all_712_3 gives: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) apart_point_and_line(all_32_1, all_17_4) = % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_712_1 & apart_point_and_line(all_28_1, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_712_0 & distinct_lines(all_17_4, % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_712_2 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_28_1) = all_712_3 & % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_712_2 = 0) | ~ (all_712_3 = 0) | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_712_0 = 0 | all_712_1 = 0) % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) distinct_lines(all_17_4, all_17_5) = all_712_2 % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_28_0 = 0 % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (243) imply: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) $false % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent. % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_176_2, all_552_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (180), (217) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_552_2 = all_176_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_552_2, all_557_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (217), (222) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_557_2 = all_552_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_557_2, all_587_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (222), (227) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_587_2 = all_557_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_587_2, all_707_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (227), (237) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_707_2 = all_587_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_171_2, all_707_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (175), (237) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_707_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_592_2, all_712_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (232), (242) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_712_2 = all_592_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_176_2, all_712_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (180), (242) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_712_2 = all_176_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_161_2, all_712_2, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_4, simplifying with (170), (242) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_712_2 = all_161_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_26_0, all_452_0, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_0, simplifying with (47), (212) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_452_0 = all_26_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_176_0, all_452_0, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_0, simplifying with (181), (212) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_452_0 = all_176_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_24_0, all_146_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (43), (160) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_146_1 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_86_0, all_146_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (132), (160) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_146_1 = all_86_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_151_0, all_176_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (165), (182) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_176_1 = all_151_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_146_1, all_176_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (160), (182) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_176_1 = all_146_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_141_0, all_176_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (155), (182) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_176_1 = all_141_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_86_1, all_176_1, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_0, simplifying with (131), (182) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_176_1 = all_86_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (251) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_592_2 = all_176_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (252) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_592_2 = all_161_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (249) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_587_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_587_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (262) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_176_2 = all_161_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (265) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_176_2 = all_161_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (264) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_557_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (267) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_557_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (268) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_552_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (269) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_552_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (270) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_176_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_176_2 = all_171_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (254) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_176_0 = all_26_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (258) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_151_0 = all_146_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (260) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_151_0 = all_86_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (259) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_151_0 = all_141_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (272) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_171_2 = all_161_2 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (276) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_141_0 = all_86_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (276) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_146_1 = all_141_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_146_1 = all_141_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (280) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_141_0 = all_86_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_141_0 = all_86_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (256) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_86_0 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (282) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_86_0 = all_86_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_86_0 = all_86_1 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (285) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_86_1 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (286) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_141_0 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (287) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_151_0 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (288) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_176_1 = all_24_0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_17_5, all_17_4, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_161_2, simplifying with (17), (18), % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (22), (170) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_161_2 = 0 | convergent_lines(all_17_5, % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_24_0 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_26_0 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) ~ (all_176_2 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (293) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) ~ (all_161_2 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) convergent_lines(all_17_5, all_17_5) = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_5, simplifying % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (17), (295) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) $false % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_161_2 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (294), (297) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) $false % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_176_0 = 0 | all_176_1 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_176_0 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (300) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_26_0 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_26_0 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (302) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) $false % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_176_1 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (304) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_24_0 = 0 % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (305) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) $false % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) ~ (all_26_1 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (307) imply: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_24_1 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (111), (308), (apart3) are inconsistent by % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_24_1 = 0) % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (111), (309), (apart3) are inconsistent by % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | | % 55.79/8.17 | | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | | % 55.79/8.17 | | | | | | | | | End of split % 55.79/8.17 | | | | | | | | | % 55.79/8.17 | | | | | | | | End of split % 55.79/8.17 | | | | | | | | % 55.79/8.17 | | | | | | | End of split % 55.79/8.17 | | | | | | | % 55.79/8.17 | | | | | | End of split % 55.79/8.17 | | | | | | % 55.79/8.17 | | | | | End of split % 55.79/8.17 | | | | | % 55.79/8.18 | | | | Case 2: % 55.79/8.18 | | | | | % 55.79/8.18 | | | | | (310) ~ (all_38_1 = 0) % 55.79/8.18 | | | | | % 55.79/8.18 | | | | | REDUCE: (88), (310) imply: % 55.79/8.18 | | | | | (311) $false % 55.79/8.18 | | | | | % 55.79/8.18 | | | | | CLOSE: (311) is inconsistent. % 55.79/8.18 | | | | | % 55.79/8.18 | | | | End of split % 55.79/8.18 | | | | % 55.79/8.18 | | | Case 2: % 55.79/8.18 | | | | % 55.79/8.18 | | | | (312) ~ (all_36_1 = 0) % 55.79/8.18 | | | | % 55.79/8.18 | | | | REDUCE: (100), (312) imply: % 55.79/8.18 | | | | (313) $false % 55.79/8.18 | | | | % 55.79/8.18 | | | | CLOSE: (313) is inconsistent. % 55.79/8.18 | | | | % 55.79/8.18 | | | End of split % 55.79/8.18 | | | % 55.79/8.18 | | End of split % 55.79/8.18 | | % 55.79/8.18 | Case 2: % 55.79/8.18 | | % 55.79/8.18 | | (314) all_17_1 = 0 % 55.79/8.18 | | % 55.79/8.18 | | REDUCE: (16), (314) imply: % 55.79/8.18 | | (315) $false % 55.79/8.18 | | % 55.79/8.18 | | CLOSE: (315) is inconsistent. % 55.79/8.18 | | % 55.79/8.18 | End of split % 55.79/8.18 | % 55.79/8.18 End of proof % 55.79/8.18 % 55.79/8.18 Sub-proof #1 shows that the following formulas are inconsistent: % 55.79/8.18 ---------------------------------------------------------------- % 55.79/8.18 (1) all_24_1 = 0 | convergent_lines(all_17_5, all_17_5) = 0 % 55.79/8.18 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 55.79/8.18 (3) $i(all_17_5) % 55.79/8.18 (4) ~ (all_24_1 = 0) % 55.79/8.18 % 55.79/8.18 Begin of proof % 55.79/8.18 | % 55.79/8.18 | BETA: splitting (1) gives: % 55.79/8.18 | % 55.79/8.18 | Case 1: % 55.79/8.18 | | % 55.79/8.18 | | (5) convergent_lines(all_17_5, all_17_5) = 0 % 55.79/8.18 | | % 55.79/8.18 | | GROUND_INST: instantiating (2) with all_17_5, simplifying with (3), (5) % 55.79/8.18 | | gives: % 55.79/8.18 | | (6) $false % 55.79/8.18 | | % 55.79/8.18 | | CLOSE: (6) is inconsistent. % 55.79/8.18 | | % 55.79/8.18 | Case 2: % 55.79/8.18 | | % 55.79/8.18 | | (7) all_24_1 = 0 % 55.79/8.18 | | % 55.79/8.18 | | REDUCE: (4), (7) imply: % 55.79/8.18 | | (8) $false % 55.79/8.18 | | % 55.79/8.18 | | CLOSE: (8) is inconsistent. % 55.79/8.18 | | % 55.79/8.18 | End of split % 55.79/8.18 | % 55.79/8.18 End of proof % 55.79/8.18 % SZS output end Proof for theBenchmark % 55.79/8.18 % 55.79/8.18 7513ms %------------------------------------------------------------------------------