%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO188+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 : n021.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 23:22:01 EDT 2023 % Result : Theorem 15.91s 2.87s % Output : Proof 26.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO188+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.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 22:40:14 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.34/1.06 Prover 4: Preprocessing ... % 2.34/1.07 Prover 1: Preprocessing ... % 2.86/1.10 Prover 0: Preprocessing ... % 2.86/1.10 Prover 5: Preprocessing ... % 2.86/1.10 Prover 3: Preprocessing ... % 2.86/1.10 Prover 6: Preprocessing ... % 2.86/1.10 Prover 2: Preprocessing ... % 4.28/1.34 Prover 2: Proving ... % 4.28/1.34 Prover 5: Proving ... % 4.28/1.36 Prover 6: Constructing countermodel ... % 4.28/1.36 Prover 3: Constructing countermodel ... % 4.28/1.36 Prover 1: Constructing countermodel ... % 5.25/1.47 Prover 3: gave up % 5.25/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.25/1.47 Prover 1: gave up % 5.25/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.25/1.48 Prover 4: Constructing countermodel ... % 5.25/1.50 Prover 7: Preprocessing ... % 5.93/1.51 Prover 6: gave up % 5.93/1.52 Prover 8: Preprocessing ... % 5.93/1.52 Prover 0: Proving ... % 5.93/1.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.93/1.54 Prover 7: Warning: ignoring some quantifiers % 5.93/1.55 Prover 7: Constructing countermodel ... % 5.93/1.55 Prover 9: Preprocessing ... % 6.49/1.60 Prover 8: Warning: ignoring some quantifiers % 6.49/1.62 Prover 8: Constructing countermodel ... % 7.16/1.68 Prover 8: gave up % 7.23/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.38/1.71 Prover 10: Preprocessing ... % 7.38/1.72 Prover 7: gave up % 7.38/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.38/1.73 Prover 9: Constructing countermodel ... % 7.38/1.74 Prover 11: Preprocessing ... % 7.38/1.76 Prover 10: Warning: ignoring some quantifiers % 7.38/1.76 Prover 10: Constructing countermodel ... % 7.75/1.83 Prover 10: gave up % 7.75/1.83 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 7.75/1.87 Prover 12: Preprocessing ... % 8.63/1.91 Prover 11: Constructing countermodel ... % 9.29/2.02 Prover 12: Proving ... % 15.91/2.86 Prover 9: proved (1337ms) % 15.91/2.86 % 15.91/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.91/2.87 % 15.91/2.87 Prover 12: stopped % 15.91/2.87 Prover 0: stopped % 15.91/2.87 Prover 2: stopped % 15.91/2.87 Prover 5: stopped % 15.91/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.91/2.87 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.91/2.87 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.91/2.88 Prover 16: Preprocessing ... % 15.91/2.88 Prover 13: Preprocessing ... % 15.91/2.89 Prover 19: Preprocessing ... % 15.91/2.91 Prover 16: Warning: ignoring some quantifiers % 15.91/2.91 Prover 13: Warning: ignoring some quantifiers % 15.91/2.91 Prover 16: Constructing countermodel ... % 15.91/2.91 Prover 13: Constructing countermodel ... % 16.48/2.95 Prover 19: Warning: ignoring some quantifiers % 16.48/2.96 Prover 19: Constructing countermodel ... % 16.48/2.99 Prover 19: gave up % 16.48/3.00 Prover 13: gave up % 17.08/3.08 Prover 16: gave up % 25.68/4.62 Prover 4: Found proof (size 580) % 25.68/4.62 Prover 4: proved (3999ms) % 25.68/4.63 Prover 11: stopped % 25.68/4.63 % 25.68/4.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.68/4.63 % 25.90/4.68 % SZS output start Proof for theBenchmark % 25.90/4.69 Assumptions after simplification: % 25.90/4.69 --------------------------------- % 25.90/4.69 % 25.90/4.69 (apart1) % 26.24/4.75 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 26.24/4.75 % 26.24/4.75 (apart4) % 26.24/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.24/4.76 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 26.24/4.76 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 26.24/4.76 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.24/4.76 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 26.24/4.76 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.76 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.24/4.77 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 26.24/4.77 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.77 distinct_points(v1, v2) = 0) % 26.24/4.77 % 26.24/4.77 (ceq2) % 26.24/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.24/4.77 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 26.24/4.77 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 26.24/4.77 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 26.24/4.77 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 26.24/4.77 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.77 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.24/4.77 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 26.24/4.77 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.77 apart_point_and_line(v0, v2) = 0) % 26.24/4.77 % 26.24/4.77 (ci1) % 26.24/4.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.24/4.78 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.24/4.78 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 26.24/4.78 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.24/4.78 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 26.24/4.78 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 26.24/4.78 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 26.24/4.78 % 26.24/4.78 (ci2) % 26.24/4.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.24/4.78 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.24/4.78 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 26.24/4.78 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.24/4.78 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 26.24/4.78 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 26.24/4.78 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 26.24/4.78 % 26.37/4.78 (con) % 26.37/4.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 26.37/4.79 $i] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1) % 26.37/4.79 = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, v5) = 0 % 26.37/4.79 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & % 26.37/4.79 distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.37/4.79 % 26.37/4.79 (cu1) % 26.37/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 26.37/4.80 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 26.37/4.80 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.37/4.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.37/4.80 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 26.37/4.80 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.37/4.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.37/4.80 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 26.37/4.80 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 26.37/4.80 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 26.37/4.80 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 26.37/4.80 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 26.37/4.80 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.37/4.80 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.37/4.80 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.37/4.80 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 26.37/4.80 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.37/4.80 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.37/4.80 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 26.37/4.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.37/4.80 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 26.37/4.80 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.37/4.80 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 26.37/4.80 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 26.37/4.80 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 26.37/4.80 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 26.37/4.80 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.37/4.80 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.37/4.80 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.37/4.80 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.37/4.80 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 26.37/4.80 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 26.37/4.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 26.37/4.80 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 26.37/4.80 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.37/4.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.37/4.80 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 26.37/4.80 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.37/4.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.37/4.80 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 26.37/4.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 26.37/4.80 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 26.37/4.80 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 26.37/4.80 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 26.37/4.80 % 26.37/4.80 (function-axioms) % 26.37/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.37/4.80 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 26.37/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.37/4.80 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 26.37/4.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.37/4.80 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 26.37/4.80 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.37/4.80 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.37/4.80 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 26.37/4.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.37/4.80 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 26.37/4.80 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 26.37/4.80 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.37/4.80 (distinct_points(v3, v2) = v0)) % 26.37/4.80 % 26.37/4.80 Further assumptions not needed in the proof: % 26.37/4.80 -------------------------------------------- % 26.37/4.80 apart2, apart3, apart5, ax6, ceq1, ceq3, ci3, ci4 % 26.37/4.80 % 26.37/4.80 Those formulas are unsatisfiable: % 26.37/4.80 --------------------------------- % 26.37/4.80 % 26.37/4.80 Begin of proof % 26.37/4.80 | % 26.37/4.80 | ALPHA: (apart4) implies: % 26.37/4.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.37/4.80 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 26.37/4.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 26.37/4.80 | % 26.37/4.80 | ALPHA: (ci1) implies: % 26.37/4.80 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.37/4.81 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.37/4.81 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 26.37/4.81 | $i(v2))) % 26.37/4.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.37/4.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.37/4.81 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.37/4.81 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.37/4.81 | % 26.37/4.81 | ALPHA: (ci2) implies: % 26.37/4.81 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.37/4.81 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.37/4.81 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 26.37/4.81 | $i(v2))) % 26.37/4.81 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.37/4.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.37/4.81 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.37/4.81 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.37/4.81 | % 26.37/4.81 | ALPHA: (cu1) implies: % 26.37/4.81 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.37/4.81 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 26.37/4.81 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 26.37/4.81 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.37/4.81 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 26.37/4.81 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 26.37/4.81 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.37/4.81 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.37/4.81 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 26.37/4.81 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.37/4.81 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.37/4.81 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 26.37/4.81 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 26.37/4.81 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.37/4.81 | | v8 = 0))) % 26.37/4.81 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.37/4.81 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.37/4.81 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.37/4.81 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.37/4.81 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.37/4.81 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.37/4.81 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.37/4.81 | | v8 = 0))) % 26.37/4.82 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.37/4.82 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.37/4.82 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 26.37/4.82 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.37/4.82 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 26.37/4.82 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 26.37/4.82 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.37/4.82 | % 26.37/4.82 | ALPHA: (ceq2) implies: % 26.37/4.82 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.37/4.82 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 26.37/4.82 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.37/4.82 | distinct_lines(v1, v2) = 0) % 26.37/4.82 | % 26.37/4.82 | ALPHA: (function-axioms) implies: % 26.37/4.82 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.37/4.82 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.37/4.82 | (distinct_points(v3, v2) = v0)) % 26.37/4.82 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.37/4.82 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 26.37/4.82 | (distinct_lines(v3, v2) = v0)) % 26.37/4.82 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.37/4.82 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 26.37/4.82 | (apart_point_and_line(v3, v2) = v0)) % 26.37/4.82 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.37/4.82 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 26.37/4.82 | % 26.37/4.82 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 26.37/4.82 | all_17_3, all_17_4, all_17_5 gives: % 26.37/4.82 | (15) ~ (all_17_1 = 0) & line_connecting(all_17_3, all_17_4) = all_17_0 & % 26.37/4.82 | line_connecting(all_17_5, all_17_4) = all_17_2 & % 26.37/4.82 | apart_point_and_line(all_17_3, all_17_2) = all_17_1 & % 26.37/4.82 | apart_point_and_line(all_17_5, all_17_0) = 0 & % 26.37/4.82 | distinct_points(all_17_4, all_17_3) = 0 & distinct_points(all_17_5, % 26.37/4.82 | all_17_3) = 0 & distinct_points(all_17_5, all_17_4) = 0 & % 26.37/4.82 | $i(all_17_0) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & % 26.37/4.82 | $i(all_17_5) % 26.37/4.82 | % 26.37/4.82 | ALPHA: (15) implies: % 26.37/4.82 | (16) ~ (all_17_1 = 0) % 26.37/4.82 | (17) $i(all_17_5) % 26.37/4.82 | (18) $i(all_17_4) % 26.37/4.82 | (19) $i(all_17_3) % 26.37/4.82 | (20) $i(all_17_2) % 26.37/4.82 | (21) $i(all_17_0) % 26.37/4.82 | (22) distinct_points(all_17_5, all_17_4) = 0 % 26.37/4.82 | (23) distinct_points(all_17_5, all_17_3) = 0 % 26.37/4.82 | (24) distinct_points(all_17_4, all_17_3) = 0 % 26.37/4.82 | (25) apart_point_and_line(all_17_5, all_17_0) = 0 % 26.37/4.82 | (26) apart_point_and_line(all_17_3, all_17_2) = all_17_1 % 26.37/4.82 | (27) line_connecting(all_17_5, all_17_4) = all_17_2 % 26.37/4.82 | (28) line_connecting(all_17_3, all_17_4) = all_17_0 % 26.37/4.82 | % 26.37/4.82 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (17), % 26.37/4.82 | (18), (22) gives: % 26.37/4.82 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 26.37/4.82 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 26.37/4.82 | % 26.37/4.83 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (17), % 26.37/4.83 | (18), (22) gives: % 26.37/4.83 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 26.37/4.83 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (4) with all_17_5, all_17_3, simplifying with (17), % 26.37/4.83 | (19), (23) gives: % 26.37/4.83 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 26.37/4.83 | all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (2) with all_17_5, all_17_3, simplifying with (17), % 26.37/4.83 | (19), (23) gives: % 26.37/4.83 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 26.37/4.83 | all_17_3) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (4) with all_17_4, all_17_3, simplifying with (18), % 26.37/4.83 | (19), (24) gives: % 26.37/4.83 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4, % 26.37/4.83 | all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (2) with all_17_4, all_17_3, simplifying with (18), % 26.37/4.83 | (19), (24) gives: % 26.37/4.83 | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4, % 26.37/4.83 | all_17_3) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (9) with all_17_4, all_17_3, all_17_2, all_17_2, % 26.37/4.83 | all_17_1, all_17_1, simplifying with (18), (19), (20), (24), (26) % 26.37/4.83 | gives: % 26.37/4.83 | (35) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.37/4.83 | (apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.37/4.83 | apart_point_and_line(all_17_4, all_17_2) = v1 & % 26.37/4.83 | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 26.37/4.83 | = 0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (9) with all_17_5, all_17_3, all_17_2, all_17_2, % 26.37/4.83 | all_17_1, all_17_1, simplifying with (17), (19), (20), (23), (26) % 26.37/4.83 | gives: % 26.37/4.83 | (36) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.37/4.83 | (apart_point_and_line(all_17_5, all_17_2) = v2 & % 26.37/4.83 | apart_point_and_line(all_17_5, all_17_2) = v1 & % 26.37/4.83 | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 26.37/4.83 | = 0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (8) with all_17_3, all_17_3, all_17_2, all_17_2, % 26.37/4.83 | all_17_1, all_17_1, simplifying with (19), (20), (26) gives: % 26.37/4.83 | (37) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 26.37/4.83 | any] : (apart_point_and_line(all_17_3, all_17_2) = v3 & % 26.37/4.83 | apart_point_and_line(all_17_3, all_17_2) = v2 & % 26.37/4.83 | distinct_lines(all_17_2, all_17_2) = v1 & distinct_points(all_17_3, % 26.37/4.83 | all_17_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying % 26.37/4.83 | with (17), (18), (27) gives: % 26.37/4.83 | (38) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4, % 26.37/4.83 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 26.37/4.83 | (v1 = 0) | ~ (v0 = 0))) % 26.37/4.83 | % 26.37/4.83 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying % 26.37/4.84 | with (17), (18), (27) gives: % 26.37/4.84 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5, % 26.37/4.84 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 26.37/4.84 | (v1 = 0) | ~ (v0 = 0))) % 26.37/4.84 | % 26.37/4.84 | GROUND_INST: instantiating (5) with all_17_3, all_17_4, all_17_0, simplifying % 26.37/4.84 | with (18), (19), (28) gives: % 26.37/4.84 | (40) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4, % 26.37/4.84 | all_17_0) = v1 & distinct_points(all_17_3, all_17_4) = v0 & ( ~ % 26.37/4.84 | (v1 = 0) | ~ (v0 = 0))) % 26.37/4.84 | % 26.37/4.84 | GROUND_INST: instantiating (3) with all_17_3, all_17_4, all_17_0, simplifying % 26.37/4.84 | with (18), (19), (28) gives: % 26.37/4.84 | (41) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_3, % 26.37/4.84 | all_17_0) = v1 & distinct_points(all_17_3, all_17_4) = v0 & ( ~ % 26.37/4.84 | (v1 = 0) | ~ (v0 = 0))) % 26.37/4.84 | % 26.37/4.84 | DELTA: instantiating (41) with fresh symbols all_24_0, all_24_1 gives: % 26.62/4.84 | (42) apart_point_and_line(all_17_3, all_17_0) = all_24_0 & % 26.62/4.84 | distinct_points(all_17_3, all_17_4) = all_24_1 & ( ~ (all_24_0 = 0) | % 26.62/4.84 | ~ (all_24_1 = 0)) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (42) implies: % 26.62/4.84 | (43) distinct_points(all_17_3, all_17_4) = all_24_1 % 26.62/4.84 | (44) apart_point_and_line(all_17_3, all_17_0) = all_24_0 % 26.62/4.84 | (45) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (34) with fresh symbols all_26_0, all_26_1 gives: % 26.62/4.84 | (46) ~ (all_26_0 = 0) & line_connecting(all_17_4, all_17_3) = all_26_1 & % 26.62/4.84 | apart_point_and_line(all_17_4, all_26_1) = all_26_0 & $i(all_26_1) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (46) implies: % 26.62/4.84 | (47) ~ (all_26_0 = 0) % 26.62/4.84 | (48) apart_point_and_line(all_17_4, all_26_1) = all_26_0 % 26.62/4.84 | (49) line_connecting(all_17_4, all_17_3) = all_26_1 % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (40) with fresh symbols all_28_0, all_28_1 gives: % 26.62/4.84 | (50) apart_point_and_line(all_17_4, all_17_0) = all_28_0 & % 26.62/4.84 | distinct_points(all_17_3, all_17_4) = all_28_1 & ( ~ (all_28_0 = 0) | % 26.62/4.84 | ~ (all_28_1 = 0)) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (50) implies: % 26.62/4.84 | (51) distinct_points(all_17_3, all_17_4) = all_28_1 % 26.62/4.84 | (52) apart_point_and_line(all_17_4, all_17_0) = all_28_0 % 26.62/4.84 | (53) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (39) with fresh symbols all_30_0, all_30_1 gives: % 26.62/4.84 | (54) apart_point_and_line(all_17_5, all_17_2) = all_30_0 & % 26.62/4.84 | distinct_points(all_17_5, all_17_4) = all_30_1 & ( ~ (all_30_0 = 0) | % 26.62/4.84 | ~ (all_30_1 = 0)) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (54) implies: % 26.62/4.84 | (55) apart_point_and_line(all_17_5, all_17_2) = all_30_0 % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (33) with fresh symbols all_32_0, all_32_1 gives: % 26.62/4.84 | (56) ~ (all_32_0 = 0) & line_connecting(all_17_4, all_17_3) = all_32_1 & % 26.62/4.84 | apart_point_and_line(all_17_3, all_32_1) = all_32_0 & $i(all_32_1) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (56) implies: % 26.62/4.84 | (57) ~ (all_32_0 = 0) % 26.62/4.84 | (58) $i(all_32_1) % 26.62/4.84 | (59) apart_point_and_line(all_17_3, all_32_1) = all_32_0 % 26.62/4.84 | (60) line_connecting(all_17_4, all_17_3) = all_32_1 % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1 gives: % 26.62/4.84 | (61) ~ (all_34_0 = 0) & line_connecting(all_17_5, all_17_3) = all_34_1 & % 26.62/4.84 | apart_point_and_line(all_17_5, all_34_1) = all_34_0 & $i(all_34_1) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (61) implies: % 26.62/4.84 | (62) line_connecting(all_17_5, all_17_3) = all_34_1 % 26.62/4.84 | % 26.62/4.84 | DELTA: instantiating (30) with fresh symbols all_36_0, all_36_1 gives: % 26.62/4.84 | (63) ~ (all_36_0 = 0) & line_connecting(all_17_5, all_17_4) = all_36_1 & % 26.62/4.84 | apart_point_and_line(all_17_5, all_36_1) = all_36_0 & $i(all_36_1) % 26.62/4.84 | % 26.62/4.84 | ALPHA: (63) implies: % 26.62/4.84 | (64) ~ (all_36_0 = 0) % 26.62/4.84 | (65) $i(all_36_1) % 26.62/4.84 | (66) apart_point_and_line(all_17_5, all_36_1) = all_36_0 % 26.62/4.85 | (67) line_connecting(all_17_5, all_17_4) = all_36_1 % 26.62/4.85 | % 26.62/4.85 | DELTA: instantiating (38) with fresh symbols all_38_0, all_38_1 gives: % 26.62/4.85 | (68) apart_point_and_line(all_17_4, all_17_2) = all_38_0 & % 26.62/4.85 | distinct_points(all_17_5, all_17_4) = all_38_1 & ( ~ (all_38_0 = 0) | % 26.62/4.85 | ~ (all_38_1 = 0)) % 26.62/4.85 | % 26.62/4.85 | ALPHA: (68) implies: % 26.62/4.85 | (69) apart_point_and_line(all_17_4, all_17_2) = all_38_0 % 26.62/4.85 | % 26.62/4.85 | DELTA: instantiating (29) with fresh symbols all_40_0, all_40_1 gives: % 26.62/4.85 | (70) ~ (all_40_0 = 0) & line_connecting(all_17_5, all_17_4) = all_40_1 & % 26.62/4.85 | apart_point_and_line(all_17_4, all_40_1) = all_40_0 & $i(all_40_1) % 26.62/4.85 | % 26.62/4.85 | ALPHA: (70) implies: % 26.62/4.85 | (71) ~ (all_40_0 = 0) % 26.62/4.85 | (72) apart_point_and_line(all_17_4, all_40_1) = all_40_0 % 26.62/4.85 | (73) line_connecting(all_17_5, all_17_4) = all_40_1 % 26.62/4.85 | % 26.62/4.85 | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives: % 26.62/4.85 | (74) ~ (all_42_0 = 0) & line_connecting(all_17_5, all_17_3) = all_42_1 & % 26.62/4.85 | apart_point_and_line(all_17_3, all_42_1) = all_42_0 & $i(all_42_1) % 26.62/4.85 | % 26.62/4.85 | ALPHA: (74) implies: % 26.62/4.85 | (75) ~ (all_42_0 = 0) % 26.62/4.85 | (76) $i(all_42_1) % 26.62/4.85 | (77) apart_point_and_line(all_17_3, all_42_1) = all_42_0 % 26.62/4.85 | (78) line_connecting(all_17_5, all_17_3) = all_42_1 % 26.62/4.85 | % 26.62/4.85 | BETA: splitting (36) gives: % 26.62/4.85 | % 26.62/4.85 | Case 1: % 26.62/4.85 | | % 26.62/4.85 | | (79) all_17_1 = 0 % 26.62/4.85 | | % 26.62/4.85 | | REDUCE: (16), (79) imply: % 26.62/4.85 | | (80) $false % 26.62/4.85 | | % 26.62/4.85 | | CLOSE: (80) is inconsistent. % 26.62/4.85 | | % 26.62/4.85 | Case 2: % 26.62/4.85 | | % 26.62/4.85 | | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.85 | | (apart_point_and_line(all_17_5, all_17_2) = v2 & % 26.62/4.85 | | apart_point_and_line(all_17_5, all_17_2) = v1 & % 26.62/4.85 | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 26.62/4.85 | | v1 = 0)) % 26.62/4.85 | | % 26.62/4.85 | | DELTA: instantiating (81) with fresh symbols all_48_0, all_48_1, all_48_2 % 26.62/4.85 | | gives: % 26.62/4.85 | | (82) apart_point_and_line(all_17_5, all_17_2) = all_48_0 & % 26.62/4.85 | | apart_point_and_line(all_17_5, all_17_2) = all_48_1 & % 26.62/4.85 | | distinct_lines(all_17_2, all_17_2) = all_48_2 & ( ~ (all_48_2 = 0) | % 26.62/4.85 | | all_48_0 = 0 | all_48_1 = 0) % 26.62/4.85 | | % 26.62/4.85 | | ALPHA: (82) implies: % 26.62/4.85 | | (83) apart_point_and_line(all_17_5, all_17_2) = all_48_1 % 26.62/4.85 | | (84) apart_point_and_line(all_17_5, all_17_2) = all_48_0 % 26.62/4.85 | | % 26.62/4.85 | | BETA: splitting (35) gives: % 26.62/4.85 | | % 26.62/4.85 | | Case 1: % 26.62/4.85 | | | % 26.62/4.85 | | | (85) all_17_1 = 0 % 26.62/4.86 | | | % 26.62/4.86 | | | REDUCE: (16), (85) imply: % 26.62/4.86 | | | (86) $false % 26.62/4.86 | | | % 26.62/4.86 | | | CLOSE: (86) is inconsistent. % 26.62/4.86 | | | % 26.62/4.86 | | Case 2: % 26.62/4.86 | | | % 26.62/4.86 | | | (87) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.86 | | | (apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.62/4.86 | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 26.62/4.86 | | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 26.62/4.86 | | | | v1 = 0)) % 26.62/4.86 | | | % 26.62/4.86 | | | DELTA: instantiating (87) with fresh symbols all_53_0, all_53_1, all_53_2 % 26.62/4.86 | | | gives: % 26.62/4.86 | | | (88) apart_point_and_line(all_17_4, all_17_2) = all_53_0 & % 26.62/4.86 | | | apart_point_and_line(all_17_4, all_17_2) = all_53_1 & % 26.62/4.86 | | | distinct_lines(all_17_2, all_17_2) = all_53_2 & ( ~ (all_53_2 = 0) % 26.62/4.86 | | | | all_53_0 = 0 | all_53_1 = 0) % 26.62/4.86 | | | % 26.62/4.86 | | | ALPHA: (88) implies: % 26.62/4.86 | | | (89) apart_point_and_line(all_17_4, all_17_2) = all_53_1 % 26.62/4.86 | | | (90) apart_point_and_line(all_17_4, all_17_2) = all_53_0 % 26.62/4.86 | | | % 26.62/4.86 | | | BETA: splitting (37) gives: % 26.62/4.86 | | | % 26.62/4.86 | | | Case 1: % 26.62/4.86 | | | | % 26.62/4.86 | | | | (91) all_17_1 = 0 % 26.62/4.86 | | | | % 26.62/4.86 | | | | REDUCE: (16), (91) imply: % 26.62/4.86 | | | | (92) $false % 26.62/4.86 | | | | % 26.62/4.86 | | | | CLOSE: (92) is inconsistent. % 26.62/4.86 | | | | % 26.62/4.86 | | | Case 2: % 26.62/4.86 | | | | % 26.62/4.86 | | | | (93) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.62/4.86 | | | | (apart_point_and_line(all_17_3, all_17_2) = v3 & % 26.62/4.86 | | | | apart_point_and_line(all_17_3, all_17_2) = v2 & % 26.62/4.86 | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 26.62/4.86 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.86 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.86 | | | | % 26.62/4.86 | | | | DELTA: instantiating (93) with fresh symbols all_58_0, all_58_1, % 26.62/4.86 | | | | all_58_2, all_58_3 gives: % 26.62/4.86 | | | | (94) apart_point_and_line(all_17_3, all_17_2) = all_58_0 & % 26.62/4.86 | | | | apart_point_and_line(all_17_3, all_17_2) = all_58_1 & % 26.62/4.86 | | | | distinct_lines(all_17_2, all_17_2) = all_58_2 & % 26.62/4.86 | | | | distinct_points(all_17_3, all_17_3) = all_58_3 & ( ~ (all_58_2 = % 26.62/4.86 | | | | 0) | ~ (all_58_3 = 0) | all_58_0 = 0 | all_58_1 = 0) % 26.62/4.86 | | | | % 26.62/4.86 | | | | ALPHA: (94) implies: % 26.62/4.86 | | | | (95) apart_point_and_line(all_17_3, all_17_2) = all_58_1 % 26.62/4.86 | | | | (96) apart_point_and_line(all_17_3, all_17_2) = all_58_0 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (11) with all_24_1, all_28_1, all_17_4, % 26.62/4.86 | | | | all_17_3, simplifying with (43), (51) gives: % 26.62/4.86 | | | | (97) all_28_1 = all_24_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_48_1, all_48_0, all_17_2, % 26.62/4.86 | | | | all_17_5, simplifying with (83), (84) gives: % 26.62/4.86 | | | | (98) all_48_0 = all_48_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_30_0, all_48_0, all_17_2, % 26.62/4.86 | | | | all_17_5, simplifying with (55), (84) gives: % 26.62/4.86 | | | | (99) all_48_0 = all_30_0 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_53_1, all_53_0, all_17_2, % 26.62/4.86 | | | | all_17_4, simplifying with (89), (90) gives: % 26.62/4.86 | | | | (100) all_53_0 = all_53_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_38_0, all_53_0, all_17_2, % 26.62/4.86 | | | | all_17_4, simplifying with (69), (90) gives: % 26.62/4.86 | | | | (101) all_53_0 = all_38_0 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_17_1, all_58_0, all_17_2, % 26.62/4.86 | | | | all_17_3, simplifying with (26), (96) gives: % 26.62/4.86 | | | | (102) all_58_0 = all_17_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (13) with all_58_1, all_58_0, all_17_2, % 26.62/4.86 | | | | all_17_3, simplifying with (95), (96) gives: % 26.62/4.86 | | | | (103) all_58_0 = all_58_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (14) with all_17_2, all_40_1, all_17_4, % 26.62/4.86 | | | | all_17_5, simplifying with (27), (73) gives: % 26.62/4.86 | | | | (104) all_40_1 = all_17_2 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (14) with all_36_1, all_40_1, all_17_4, % 26.62/4.86 | | | | all_17_5, simplifying with (67), (73) gives: % 26.62/4.86 | | | | (105) all_40_1 = all_36_1 % 26.62/4.86 | | | | % 26.62/4.86 | | | | GROUND_INST: instantiating (14) with all_34_1, all_42_1, all_17_3, % 26.62/4.86 | | | | all_17_5, simplifying with (62), (78) gives: % 26.62/4.87 | | | | (106) all_42_1 = all_34_1 % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (14) with all_26_1, all_32_1, all_17_3, % 26.62/4.87 | | | | all_17_4, simplifying with (49), (60) gives: % 26.62/4.87 | | | | (107) all_32_1 = all_26_1 % 26.62/4.87 | | | | % 26.62/4.87 | | | | COMBINE_EQS: (102), (103) imply: % 26.62/4.87 | | | | (108) all_58_1 = all_17_1 % 26.62/4.87 | | | | % 26.62/4.87 | | | | COMBINE_EQS: (100), (101) imply: % 26.62/4.87 | | | | (109) all_53_1 = all_38_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | COMBINE_EQS: (98), (99) imply: % 26.62/4.87 | | | | (110) all_48_1 = all_30_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | COMBINE_EQS: (104), (105) imply: % 26.62/4.87 | | | | (111) all_36_1 = all_17_2 % 26.62/4.87 | | | | % 26.62/4.87 | | | | SIMP: (111) implies: % 26.62/4.87 | | | | (112) all_36_1 = all_17_2 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (77), (106) imply: % 26.62/4.87 | | | | (113) apart_point_and_line(all_17_3, all_34_1) = all_42_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (59), (107) imply: % 26.62/4.87 | | | | (114) apart_point_and_line(all_17_3, all_26_1) = all_32_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (72), (104) imply: % 26.62/4.87 | | | | (115) apart_point_and_line(all_17_4, all_17_2) = all_40_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (66), (112) imply: % 26.62/4.87 | | | | (116) apart_point_and_line(all_17_5, all_17_2) = all_36_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (76), (106) imply: % 26.62/4.87 | | | | (117) $i(all_34_1) % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (58), (107) imply: % 26.62/4.87 | | | | (118) $i(all_26_1) % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (13) with all_30_0, all_36_0, all_17_2, % 26.62/4.87 | | | | all_17_5, simplifying with (55), (116) gives: % 26.62/4.87 | | | | (119) all_36_0 = all_30_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (13) with all_38_0, all_40_0, all_17_2, % 26.62/4.87 | | | | all_17_4, simplifying with (69), (115) gives: % 26.62/4.87 | | | | (120) all_40_0 = all_38_0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (71), (120) imply: % 26.62/4.87 | | | | (121) ~ (all_38_0 = 0) % 26.62/4.87 | | | | % 26.62/4.87 | | | | REDUCE: (64), (119) imply: % 26.62/4.87 | | | | (122) ~ (all_30_0 = 0) % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (1) with all_17_4, all_17_3, all_17_4, % 26.62/4.87 | | | | all_24_1, simplifying with (18), (19), (24), (43) gives: % 26.62/4.87 | | | | (123) all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (10) with all_17_5, all_17_0, all_17_2, % 26.62/4.87 | | | | all_30_0, simplifying with (17), (20), (21), (25), (55) % 26.62/4.87 | | | | gives: % 26.62/4.87 | | | | (124) all_30_0 = 0 | distinct_lines(all_17_0, all_17_2) = 0 % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_5, all_17_2, % 26.62/4.87 | | | | all_17_2, all_38_0, all_30_0, simplifying with (17), (18), % 26.62/4.87 | | | | (20), (55), (69) gives: % 26.62/4.87 | | | | (125) all_38_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.87 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 26.62/4.87 | | | | all_17_2) = v2 & apart_point_and_line(all_17_5, all_17_2) = % 26.62/4.87 | | | | v3 & distinct_lines(all_17_2, all_17_2) = v1 & % 26.62/4.87 | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.87 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (8) with all_17_3, all_17_4, all_17_2, % 26.62/4.87 | | | | all_17_0, all_17_1, all_28_0, simplifying with (18), (19), % 26.62/4.87 | | | | (20), (21), (26), (52) gives: % 26.62/4.87 | | | | (126) all_28_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.87 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.87 | | | | all_17_0) = v2 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.87 | | | | v3 & distinct_lines(all_17_2, all_17_0) = v1 & % 26.62/4.87 | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.87 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.87 | | | | % 26.62/4.87 | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_0, % 26.62/4.87 | | | | all_17_2, all_28_0, all_17_1, simplifying with (18), (19), % 26.62/4.87 | | | | (20), (21), (26), (52) gives: % 26.62/4.88 | | | | (127) all_28_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.88 | | | | all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v2 & distinct_lines(all_17_0, all_17_2) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_3, all_17_2, % 26.62/4.88 | | | | all_17_0, all_28_0, all_17_1, simplifying with (18), (19), % 26.62/4.88 | | | | (20), (21), (26), (52) gives: % 26.62/4.88 | | | | (128) all_28_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.88 | | | | all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v2 & distinct_lines(all_17_2, all_17_0) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (6) with all_17_4, all_17_3, all_17_0, % 26.62/4.88 | | | | all_17_0, all_28_0, all_28_0, simplifying with (18), (19), % 26.62/4.88 | | | | (21), (24), (52) gives: % 26.62/4.88 | | | | (129) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.88 | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.88 | | | | apart_point_and_line(all_17_3, all_17_0) = v1 & % 26.62/4.88 | | | | distinct_lines(all_17_0, all_17_0) = v0 & ( ~ (v0 = 0) | v2 = % 26.62/4.88 | | | | 0 | v1 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (6) with all_17_4, all_17_3, all_17_2, % 26.62/4.88 | | | | all_17_0, all_38_0, all_28_0, simplifying with (18), (19), % 26.62/4.88 | | | | (20), (21), (24), (52), (69) gives: % 26.62/4.88 | | | | (130) all_38_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : (apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.88 | | | | apart_point_and_line(all_17_3, all_17_2) = v1 & % 26.62/4.88 | | | | distinct_lines(all_17_2, all_17_0) = v0 & ( ~ (v0 = 0) | v2 = % 26.62/4.88 | | | | 0 | v1 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_17_2, % 26.62/4.88 | | | | all_17_0, all_38_0, all_28_0, simplifying with (18), (20), % 26.62/4.88 | | | | (21), (52), (69) gives: % 26.62/4.88 | | | | (131) all_38_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 26.62/4.88 | | | | all_17_0) = v2 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v3 & distinct_lines(all_17_2, all_17_0) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_4, all_17_2, % 26.62/4.88 | | | | all_17_0, all_28_0, all_38_0, simplifying with (18), (20), % 26.62/4.88 | | | | (21), (52), (69) gives: % 26.62/4.88 | | | | (132) all_38_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 26.62/4.88 | | | | all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v2 & distinct_lines(all_17_2, all_17_0) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_26_1, % 26.62/4.88 | | | | all_17_2, all_26_0, all_38_0, simplifying with (18), (20), % 26.62/4.88 | | | | (48), (69), (118) gives: % 26.62/4.88 | | | | (133) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 26.62/4.88 | | | | all_26_1) = v3 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v2 & distinct_lines(all_26_1, all_17_2) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_4, all_26_1, % 26.62/4.88 | | | | all_17_2, all_38_0, all_26_0, simplifying with (18), (20), % 26.62/4.88 | | | | (48), (69), (118) gives: % 26.62/4.88 | | | | (134) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.88 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 26.62/4.88 | | | | all_26_1) = v2 & apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.88 | | | | v3 & distinct_lines(all_26_1, all_17_2) = v1 & % 26.62/4.88 | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.88 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.88 | | | | % 26.62/4.88 | | | | GROUND_INST: instantiating (8) with all_17_3, all_17_3, all_17_0, % 26.62/4.88 | | | | all_26_1, all_24_0, all_32_0, simplifying with (19), (21), % 26.62/4.88 | | | | (44), (114), (118) gives: % 26.62/4.89 | | | | (135) all_32_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_26_1) = v2 & apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.89 | | | | v3 & distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_26_1, % 26.62/4.89 | | | | all_17_0, all_24_0, all_32_0, simplifying with (19), (21), % 26.62/4.89 | | | | (44), (114), (118) gives: % 26.62/4.89 | | | | (136) all_32_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_26_1) = v2 & apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.89 | | | | v3 & distinct_lines(all_26_1, all_17_0) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_17_0, % 26.62/4.89 | | | | all_26_1, all_32_0, all_24_0, simplifying with (19), (21), % 26.62/4.89 | | | | (44), (114), (118) gives: % 26.62/4.89 | | | | (137) all_32_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_26_1) = v3 & apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.89 | | | | v2 & distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_2, % 26.62/4.89 | | | | all_26_1, all_38_0, all_32_0, simplifying with (18), (19), % 26.62/4.89 | | | | (20), (69), (114), (118) gives: % 26.62/4.89 | | | | (138) all_38_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_17_2) = v3 & apart_point_and_line(all_17_4, all_26_1) = % 26.62/4.89 | | | | v2 & distinct_lines(all_17_2, all_26_1) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (9) with all_17_4, all_17_3, all_17_2, % 26.62/4.89 | | | | all_34_1, all_17_1, all_42_0, simplifying with (18), (19), % 26.62/4.89 | | | | (20), (24), (26), (113), (117) gives: % 26.62/4.89 | | | | (139) all_42_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : (apart_point_and_line(all_17_4, all_34_1) = v2 & % 26.62/4.89 | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 26.62/4.89 | | | | distinct_lines(all_17_2, all_34_1) = v0 & ( ~ (v0 = 0) | v2 = % 26.62/4.89 | | | | 0 | v1 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_34_1, % 26.62/4.89 | | | | all_17_0, all_24_0, all_42_0, simplifying with (19), (21), % 26.62/4.89 | | | | (44), (113), (117) gives: % 26.62/4.89 | | | | (140) all_42_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_34_1) = v2 & apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.89 | | | | v3 & distinct_lines(all_34_1, all_17_0) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_3, all_34_1, % 26.62/4.89 | | | | all_26_1, all_26_0, all_42_0, simplifying with (18), (19), % 26.62/4.89 | | | | (48), (113), (117), (118) gives: % 26.62/4.89 | | | | (141) all_42_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.89 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | all_26_1) = v3 & apart_point_and_line(all_17_4, all_34_1) = % 26.62/4.89 | | | | v2 & distinct_lines(all_34_1, all_26_1) = v1 & % 26.62/4.89 | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.89 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | % 26.62/4.89 | | | | BETA: splitting (45) gives: % 26.62/4.89 | | | | % 26.62/4.89 | | | | Case 1: % 26.62/4.89 | | | | | % 26.62/4.89 | | | | | (142) ~ (all_24_0 = 0) % 26.62/4.89 | | | | | % 26.62/4.89 | | | | | BETA: splitting (124) gives: % 26.62/4.89 | | | | | % 26.62/4.89 | | | | | Case 1: % 26.62/4.89 | | | | | | % 26.62/4.89 | | | | | | (143) distinct_lines(all_17_0, all_17_2) = 0 % 26.62/4.89 | | | | | | % 26.62/4.89 | | | | | | BETA: splitting (127) gives: % 26.62/4.89 | | | | | | % 26.62/4.89 | | | | | | Case 1: % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | | (144) all_28_0 = 0 % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.62/4.89 | | | | | | | (134), (144), (apart1) are inconsistent by sub-proof % 26.62/4.89 | | | | | | | #1. % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | Case 2: % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | | (145) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 26.62/4.89 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.89 | | | | | | | all_17_0) = v3 & apart_point_and_line(all_17_4, % 26.62/4.89 | | | | | | | all_17_2) = v2 & distinct_lines(all_17_0, all_17_2) = % 26.62/4.89 | | | | | | | v1 & distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 % 26.62/4.89 | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | | BETA: splitting (138) gives: % 26.62/4.89 | | | | | | | % 26.62/4.89 | | | | | | | Case 1: % 26.62/4.89 | | | | | | | | % 26.62/4.89 | | | | | | | | (146) all_38_0 = 0 % 26.62/4.89 | | | | | | | | % 26.62/4.89 | | | | | | | | REDUCE: (121), (146) imply: % 26.62/4.90 | | | | | | | | (147) $false % 26.62/4.90 | | | | | | | | % 26.62/4.90 | | | | | | | | CLOSE: (147) is inconsistent. % 26.62/4.90 | | | | | | | | % 26.62/4.90 | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | % 26.62/4.90 | | | | | | | | (148) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 26.62/4.90 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.90 | | | | | | | | all_17_2) = v3 & apart_point_and_line(all_17_4, % 26.62/4.90 | | | | | | | | all_26_1) = v2 & distinct_lines(all_17_2, all_26_1) % 26.62/4.90 | | | | | | | | = v1 & distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | % 26.62/4.90 | | | | | | | | BETA: splitting (125) gives: % 26.62/4.90 | | | | | | | | % 26.62/4.90 | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | (149) all_38_0 = 0 % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | REDUCE: (121), (149) imply: % 26.62/4.90 | | | | | | | | | (150) $false % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | CLOSE: (150) is inconsistent. % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | (151) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 26.62/4.90 | | | | | | | | | any] : ? [v3: any] : % 26.62/4.90 | | | | | | | | | (apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.62/4.90 | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 26.62/4.90 | | | | | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 26.62/4.90 | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 % 26.62/4.90 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | BETA: splitting (137) gives: % 26.62/4.90 | | | | | | | | | % 26.62/4.90 | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | (152) all_32_0 = 0 % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | REDUCE: (57), (152) imply: % 26.62/4.90 | | | | | | | | | | (153) $false % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | CLOSE: (153) is inconsistent. % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | (154) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.90 | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.90 | | | | | | | | | | (apart_point_and_line(all_17_3, all_26_1) = v3 & % 26.62/4.90 | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.90 | | | | | | | | | | distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.90 | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | BETA: splitting (140) gives: % 26.62/4.90 | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | (155) all_42_0 = 0 % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | REDUCE: (75), (155) imply: % 26.62/4.90 | | | | | | | | | | | (156) $false % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | CLOSE: (156) is inconsistent. % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | (157) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.90 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.90 | | | | | | | | | | | (apart_point_and_line(all_17_3, all_34_1) = v2 & % 26.62/4.90 | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.90 | | | | | | | | | | | distinct_lines(all_34_1, all_17_0) = v1 & % 26.62/4.90 | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | BETA: splitting (135) gives: % 26.62/4.90 | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | (158) all_32_0 = 0 % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | REDUCE: (57), (158) imply: % 26.62/4.90 | | | | | | | | | | | | (159) $false % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | (160) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.90 | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.90 | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_26_1) = v2 & % 26.62/4.90 | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.90 | | | | | | | | | | | | distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.90 | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | BETA: splitting (136) gives: % 26.62/4.90 | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | (161) all_32_0 = 0 % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | REDUCE: (57), (161) imply: % 26.62/4.90 | | | | | | | | | | | | | (162) $false % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | (163) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.90 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.90 | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_26_1) = v2 & % 26.62/4.90 | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.90 | | | | | | | | | | | | | distinct_lines(all_26_1, all_17_0) = v1 & % 26.62/4.90 | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | BETA: splitting (139) gives: % 26.62/4.90 | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | (164) all_42_0 = 0 % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | REDUCE: (75), (164) imply: % 26.62/4.90 | | | | | | | | | | | | | | (165) $false % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | (166) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.90 | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_17_4, % 26.62/4.90 | | | | | | | | | | | | | | all_34_1) = v2 & % 26.62/4.90 | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 26.62/4.90 | | | | | | | | | | | | | | distinct_lines(all_17_2, all_34_1) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | BETA: splitting (145) gives: % 26.62/4.90 | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | Case 1: % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | (167) all_17_1 = 0 % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | REDUCE: (16), (167) imply: % 26.62/4.90 | | | | | | | | | | | | | | | (168) $false % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | Case 2: % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | (169) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.62/4.90 | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.90 | | | | | | | | | | | | | | | all_17_0) = v3 & % 26.62/4.90 | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.62/4.90 | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 & % 26.62/4.90 | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.62/4.90 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_263_0, % 26.62/4.90 | | | | | | | | | | | | | | | all_263_1, all_263_2, all_263_3 gives: % 26.62/4.90 | | | | | | | | | | | | | | | (170) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.90 | | | | | | | | | | | | | | | all_263_0 & apart_point_and_line(all_17_4, % 26.62/4.90 | | | | | | | | | | | | | | | all_17_2) = all_263_1 & distinct_lines(all_17_0, % 26.62/4.90 | | | | | | | | | | | | | | | all_17_2) = all_263_2 & % 26.62/4.90 | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = all_263_3 & % 26.62/4.90 | | | | | | | | | | | | | | | ( ~ (all_263_2 = 0) | ~ (all_263_3 = 0) | % 26.62/4.90 | | | | | | | | | | | | | | | all_263_0 = 0 | all_263_1 = 0) % 26.62/4.90 | | | | | | | | | | | | | | | % 26.62/4.90 | | | | | | | | | | | | | | | ALPHA: (170) implies: % 26.62/4.90 | | | | | | | | | | | | | | | (171) distinct_points(all_17_4, all_17_3) = all_263_3 % 26.62/4.90 | | | | | | | | | | | | | | | (172) distinct_lines(all_17_0, all_17_2) = all_263_2 % 26.62/4.90 | | | | | | | | | | | | | | | (173) apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.90 | | | | | | | | | | | | | | | all_263_1 % 26.62/4.91 | | | | | | | | | | | | | | | (174) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | all_263_0 % 26.62/4.91 | | | | | | | | | | | | | | | (175) ~ (all_263_2 = 0) | ~ (all_263_3 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | all_263_0 = 0 | all_263_1 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 26.62/4.91 | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | (176) all_28_0 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.62/4.91 | | | | | | | | | | | | | | | | (134), (176), (apart1) are inconsistent by % 26.62/4.91 | | | | | | | | | | | | | | | | sub-proof #1. % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | (177) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.91 | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.91 | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.62/4.91 | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 26.62/4.91 | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | (178) all_24_0 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | REDUCE: (142), (178) imply: % 26.62/4.91 | | | | | | | | | | | | | | | | | (179) $false % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | (180) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.62/4.91 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | all_34_1) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | distinct_lines(all_34_1, all_17_0) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbols all_319_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | all_319_1, all_319_2, all_319_3 gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | (181) apart_point_and_line(all_17_3, all_34_1) = % 26.62/4.91 | | | | | | | | | | | | | | | | | all_319_1 & apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | all_17_0) = all_319_0 & distinct_lines(all_34_1, % 26.62/4.91 | | | | | | | | | | | | | | | | | all_17_0) = all_319_2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_319_3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | ( ~ (all_319_2 = 0) | ~ (all_319_3 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | | | all_319_0 = 0 | all_319_1 = 0) % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | ALPHA: (181) implies: % 26.62/4.91 | | | | | | | | | | | | | | | | | (182) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | | | all_319_0 % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | (183) all_24_0 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | REDUCE: (142), (183) imply: % 26.62/4.91 | | | | | | | | | | | | | | | | | | (184) $false % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.62/4.91 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_26_1) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | distinct_lines(all_26_1, all_17_0) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_324_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_324_1, all_324_2, all_324_3 gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | (186) apart_point_and_line(all_17_3, all_26_1) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_324_1 & apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_17_0) = all_324_0 & distinct_lines(all_26_1, % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_17_0) = all_324_2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_324_3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | ( ~ (all_324_2 = 0) | ~ (all_324_3 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_324_0 = 0 | all_324_1 = 0) % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | ALPHA: (186) implies: % 26.62/4.91 | | | | | | | | | | | | | | | | | | (187) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | all_324_0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (188) all_17_1 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (188) imply: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (189) $false % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_34_1) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_34_1) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_334_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_334_1, all_334_2 gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (191) apart_point_and_line(all_17_4, all_34_1) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_334_0 & apart_point_and_line(all_17_4, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_17_2) = all_334_1 & distinct_lines(all_17_2, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_34_1) = all_334_2 & ( ~ (all_334_2 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_334_0 = 0 | all_334_1 = 0) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | (192) apart_point_and_line(all_17_4, all_17_2) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | all_334_1 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (193) all_28_0 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (134), (193), (apart1) are inconsistent by % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (194) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_0) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (194) with fresh symbols all_355_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_355_1, all_355_2 gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (195) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_355_0 & apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_17_0) = all_355_1 & distinct_lines(all_17_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_17_0) = all_355_2 & ( ~ (all_355_2 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_355_0 = 0 | all_355_1 = 0) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (196) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_355_1 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | (197) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | all_355_0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | (198) all_24_0 = 0 % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (198) imply: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | (199) $false % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent. % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | (200) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_26_1) = v3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (200) with fresh symbols all_368_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_368_1, all_368_2, all_368_3 gives: % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | (201) apart_point_and_line(all_17_3, all_26_1) = % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_368_0 & apart_point_and_line(all_17_3, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_368_1 & distinct_lines(all_17_0, % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_26_1) = all_368_2 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_368_3 & % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_368_2 = 0) | ~ (all_368_3 = 0) | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | all_368_0 = 0 | all_368_1 = 0) % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.91 | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | (202) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | all_368_1 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (203) all_24_0 = 0 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (203) imply: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (204) $false % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent. % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (205) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_26_1) = v2 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_26_1) = v1 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_373_0, % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_373_1, all_373_2, all_373_3 gives: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (206) apart_point_and_line(all_17_3, all_26_1) = % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_373_1 & apart_point_and_line(all_17_3, % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_373_0 & distinct_lines(all_17_0, % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_26_1) = all_373_2 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_373_3 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_373_2 = 0) | ~ (all_373_3 = 0) | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_373_0 = 0 | all_373_1 = 0) % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | (207) apart_point_and_line(all_17_3, all_17_0) = % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | all_373_0 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | (208) all_38_0 = 0 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (208) imply: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | (209) $false % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | (210) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_17_3, % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = v2 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_2) = v1 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v0 & ( ~ % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | (211) all_42_0 = 0 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (211) imply: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | (212) $false % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | (213) all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_26_1) = v3 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_34_1) = v2 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_34_1, all_26_1) = v1 & % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_28_0 = 0 % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | (134), (214), (apart1) are inconsistent by % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.62/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_38_0 = 0 % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (216) imply: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) $false % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_0) = v3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_38_0 = 0 % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (219) imply: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) $false % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_0) = v2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_32_0 = 0 % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (222) imply: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) $false % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = v3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_26_1) = v2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_26_1) = v1 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (224) with fresh symbols all_418_0, % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_418_1, all_418_2, all_418_3 gives: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) apart_point_and_line(all_17_3, all_17_2) = % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_418_0 & apart_point_and_line(all_17_4, % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_1) = all_418_1 & distinct_lines(all_17_2, % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_1) = all_418_2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = all_418_3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_418_2 = 0) | ~ (all_418_3 = 0) | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_418_0 = 0 | all_418_1 = 0) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) distinct_points(all_17_4, all_17_3) = all_418_3 % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_30_0 = 0 % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (227) imply: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) $false % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = v2 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_478_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_1, all_478_2, all_478_3 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) apart_point_and_line(all_17_4, all_17_2) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_1 & apart_point_and_line(all_17_5, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_478_0 & distinct_lines(all_17_2, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_478_2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = all_478_3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_478_2 = 0) | ~ (all_478_3 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_0 = 0 | all_478_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) apart_point_and_line(all_17_4, all_17_2) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_1 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_17_1 = 0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (232) imply: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) $false % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = v2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_498_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1, all_498_2, all_498_3 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1 & apart_point_and_line(all_17_4, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_498_0 & distinct_lines(all_17_2, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_498_2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_4) = all_498_3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_498_2 = 0) | ~ (all_498_3 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_0 = 0 | all_498_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) apart_point_and_line(all_17_4, all_17_2) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_28_0 = 0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (238), (apart1) are inconsistent by % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_2) = v1 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v0 & ( ~ % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (239) with fresh symbols all_523_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_523_1, all_523_2 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_523_0 & apart_point_and_line(all_17_3, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_523_1 & distinct_lines(all_17_2, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_523_2 & ( ~ (all_523_2 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_523_0 = 0 | all_523_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_523_0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_26_0 = 0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (242) imply: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) $false % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent. % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_1) = v3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_34_1) = v2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_34_1, all_26_1) = v1 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (244) with fresh symbols all_533_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_533_1, all_533_2, all_533_3 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) apart_point_and_line(all_17_3, all_26_1) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_533_0 & apart_point_and_line(all_17_4, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_1) = all_533_1 & distinct_lines(all_34_1, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_1) = all_533_2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = all_533_3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_533_2 = 0) | ~ (all_533_3 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_533_0 = 0 | all_533_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) distinct_points(all_17_4, all_17_3) = all_533_3 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_17_1 = 0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (247) imply: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = v3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_543_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_543_1, all_543_2, all_543_3 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_543_0 & apart_point_and_line(all_17_4, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_543_1 & distinct_lines(all_17_2, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_543_2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = all_543_3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_543_2 = 0) | ~ (all_543_3 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_543_0 = 0 | all_543_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) distinct_points(all_17_4, all_17_3) = all_543_3 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) apart_point_and_line(all_17_3, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_543_0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_28_0 = 0 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (253), (apart1) are inconsistent by % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = v3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_553_0, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_1, all_553_2, all_553_3 gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) apart_point_and_line(all_17_4, all_17_0) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_0 & apart_point_and_line(all_17_4, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_553_1 & distinct_lines(all_17_2, % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_553_2 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = all_553_3 & % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_553_2 = 0) | ~ (all_553_3 = 0) | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_0 = 0 | all_553_1 = 0) % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) apart_point_and_line(all_17_4, all_17_2) = % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_1 % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_28_0 = 0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133), % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (257), (apart1) are inconsistent by % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = v2 & % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_0) = v1 & % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_558_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_558_1, all_558_2, all_558_3 gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) apart_point_and_line(all_17_4, all_17_0) = % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_558_1 & apart_point_and_line(all_17_4, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_558_0 & distinct_lines(all_17_2, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0) = all_558_2 & % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = all_558_3 & % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_558_2 = 0) | ~ (all_558_3 = 0) | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_558_0 = 0 | all_558_1 = 0) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) apart_point_and_line(all_17_4, all_17_2) = % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_558_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_418_3, all_17_3, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_4, simplifying with (24), (226) gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_418_3 = 0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_418_3, all_533_3, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_3, all_17_4, simplifying with (226), (246) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_533_3 = all_418_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_533_3, all_543_3, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_3, all_17_4, simplifying with (246), (251) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_543_3 = all_533_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_263_3, all_543_3, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_3, all_17_4, simplifying with (171), (251) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_543_3 = all_263_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_263_2, all_17_2, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, simplifying with (143), (172) gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_263_2 = 0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_263_1, all_478_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (173), (231) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_478_1 = all_263_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_38_0, all_553_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (69), (256) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_553_1 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_498_0, all_553_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (236), (256) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_553_1 = all_498_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_498_0, all_558_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (236), (260) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_558_0 = all_498_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_478_1, all_558_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (231), (260) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_558_0 = all_478_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_334_1, all_558_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (192), (260) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_558_0 = all_334_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_355_1, all_355_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (196), (197) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_355_0 = all_355_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_263_0, all_355_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (174), (197) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_355_0 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_355_1, all_368_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (196), (202) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_368_1 = all_355_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_24_0, all_498_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (44), (237) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_498_1 = all_24_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_368_1, all_498_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (202), (237) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_498_1 = all_368_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_319_0, all_498_1, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (182), (237) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_498_1 = all_319_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_368_1, all_523_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (202), (241) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_523_0 = all_368_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_324_0, all_523_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (187), (241) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_523_0 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_523_0, all_543_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (241), (252) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_543_0 = all_523_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_373_0, all_543_0, % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (207), (252) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_543_0 = all_373_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_478_1 = all_334_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_478_1 = all_334_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (271) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_498_0 = all_334_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_498_0 = all_334_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (268) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_498_0 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_498_0 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_523_0 = all_373_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_523_0 = all_373_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (264) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_533_3 = all_263_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (290) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_533_3 = all_263_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (291) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_418_3 = all_263_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_418_3 = all_263_3 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (289) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_373_0 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (289) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_373_0 = all_368_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (287) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_334_1 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_334_1 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (277) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_319_0 = all_24_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (277) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_368_1 = all_319_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (299) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_368_1 = all_319_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (283) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_334_1 = all_263_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_334_1 = all_263_1 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (293) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_263_3 = 0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (295) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_368_1 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (304) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_368_1 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (305) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_355_1 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_355_1 = all_324_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (305) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_324_0 = all_319_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_355_1 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_355_1 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (310) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_324_0 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_324_0 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (302) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_263_1 = all_38_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (312) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_319_0 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_319_0 = all_263_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (315) imply: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_263_0 = all_24_0 % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_263_2 = 0) % 26.86/4.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (265), (317) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) $false % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_263_3 = 0) | all_263_0 = 0 | all_263_1 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_263_3 = 0) % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (320) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) $false % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_263_0 = 0 | all_263_1 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_263_0 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (323) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_24_0 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (324) implies: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_24_0 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (325) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) $false % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (326) is inconsistent. % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_263_1 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (327) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_38_0 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (328) implies: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_38_0 = 0 % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (329) imply: % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) $false % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent. % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | | % 26.86/4.95 | | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | | % 26.86/4.95 | | | | | | | | | End of split % 26.86/4.95 | | | | | | | | | % 26.86/4.95 | | | | | | | | End of split % 26.86/4.95 | | | | | | | | % 26.86/4.95 | | | | | | | End of split % 26.86/4.95 | | | | | | | % 26.86/4.95 | | | | | | End of split % 26.86/4.95 | | | | | | % 26.86/4.95 | | | | | Case 2: % 26.86/4.95 | | | | | | % 26.86/4.95 | | | | | | (331) all_30_0 = 0 % 26.86/4.95 | | | | | | % 26.86/4.95 | | | | | | REDUCE: (122), (331) imply: % 26.86/4.95 | | | | | | (332) $false % 26.86/4.95 | | | | | | % 26.86/4.95 | | | | | | CLOSE: (332) is inconsistent. % 26.86/4.95 | | | | | | % 26.86/4.95 | | | | | End of split % 26.86/4.95 | | | | | % 26.86/4.95 | | | | Case 2: % 26.86/4.95 | | | | | % 26.86/4.95 | | | | | (333) ~ (all_24_1 = 0) % 26.86/4.95 | | | | | % 26.86/4.95 | | | | | REF_CLOSE: (11), (18), (47), (121), (123), (133), (134), (333), % 26.86/4.95 | | | | | (apart1) are inconsistent by sub-proof #2. % 26.86/4.95 | | | | | % 26.86/4.95 | | | | End of split % 26.86/4.95 | | | | % 26.86/4.95 | | | End of split % 26.86/4.95 | | | % 26.86/4.95 | | End of split % 26.86/4.95 | | % 26.86/4.95 | End of split % 26.86/4.95 | % 26.86/4.95 End of proof % 26.86/4.95 % 26.86/4.95 Sub-proof #1 shows that the following formulas are inconsistent: % 26.86/4.95 ---------------------------------------------------------------- % 26.86/4.95 (1) ~ (all_38_0 = 0) % 26.86/4.95 (2) all_28_0 = 0 % 26.86/4.95 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.86/4.95 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.86/4.95 (distinct_points(v3, v2) = v0)) % 26.86/4.95 (4) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 26.86/4.95 : ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 & % 26.86/4.95 apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.95 distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4, % 26.86/4.95 all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.95 (5) all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0 % 26.86/4.95 (6) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 26.86/4.95 : ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 & % 26.86/4.95 apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.95 distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4, % 26.86/4.95 all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.95 (7) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 26.86/4.95 (8) $i(all_17_4) % 26.86/4.95 (9) ~ (all_26_0 = 0) % 26.86/4.95 (10) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 26.86/4.95 (11) all_28_1 = all_24_1 % 26.86/4.95 % 26.86/4.95 Begin of proof % 26.86/4.95 | % 26.86/4.95 | BETA: splitting (7) gives: % 26.86/4.95 | % 26.86/4.95 | Case 1: % 26.86/4.95 | | % 26.86/4.95 | | (12) ~ (all_28_0 = 0) % 26.86/4.95 | | % 26.86/4.95 | | REDUCE: (2), (12) imply: % 26.86/4.95 | | (13) $false % 26.86/4.95 | | % 26.86/4.95 | | CLOSE: (13) is inconsistent. % 26.86/4.95 | | % 26.86/4.95 | Case 2: % 26.86/4.95 | | % 26.86/4.95 | | (14) ~ (all_28_1 = 0) % 26.86/4.95 | | % 26.86/4.95 | | REDUCE: (11), (14) imply: % 26.86/4.95 | | (15) ~ (all_24_1 = 0) % 26.86/4.95 | | % 26.86/4.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (15) are inconsistent by % 26.86/4.95 | | sub-proof #2. % 26.86/4.95 | | % 26.86/4.95 | End of split % 26.86/4.95 | % 26.86/4.95 End of proof % 26.86/4.95 % 26.86/4.95 Sub-proof #2 shows that the following formulas are inconsistent: % 26.86/4.95 ---------------------------------------------------------------- % 26.86/4.95 (1) ~ (all_38_0 = 0) % 26.86/4.95 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.86/4.95 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.86/4.95 (distinct_points(v3, v2) = v0)) % 26.86/4.95 (3) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 26.86/4.95 : ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 & % 26.86/4.95 apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.95 distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4, % 26.86/4.95 all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.95 (4) all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0 % 26.86/4.95 (5) all_38_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 26.86/4.95 : ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 & % 26.86/4.95 apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.95 distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4, % 26.86/4.95 all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.95 (6) $i(all_17_4) % 26.86/4.96 (7) ~ (all_26_0 = 0) % 26.86/4.96 (8) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 26.86/4.96 (9) ~ (all_24_1 = 0) % 26.86/4.96 % 26.86/4.96 Begin of proof % 26.86/4.96 | % 26.86/4.96 | BETA: splitting (4) gives: % 26.86/4.96 | % 26.86/4.96 | Case 1: % 26.86/4.96 | | % 26.86/4.96 | | (10) distinct_points(all_17_4, all_17_4) = 0 % 26.86/4.96 | | % 26.86/4.96 | | BETA: splitting (3) gives: % 26.86/4.96 | | % 26.86/4.96 | | Case 1: % 26.86/4.96 | | | % 26.86/4.96 | | | (11) all_38_0 = 0 % 26.86/4.96 | | | % 26.86/4.96 | | | REDUCE: (1), (11) imply: % 26.86/4.96 | | | (12) $false % 26.86/4.96 | | | % 26.86/4.96 | | | CLOSE: (12) is inconsistent. % 26.86/4.96 | | | % 26.86/4.96 | | Case 2: % 26.86/4.96 | | | % 26.86/4.96 | | | (13) all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.96 | | | [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 & % 26.86/4.96 | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.96 | | | distinct_lines(all_26_1, all_17_2) = v1 & % 26.86/4.96 | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.86/4.96 | | | = 0) | v3 = 0 | v2 = 0)) % 26.86/4.96 | | | % 26.86/4.96 | | | BETA: splitting (5) gives: % 26.86/4.96 | | | % 26.86/4.96 | | | Case 1: % 26.86/4.96 | | | | % 26.86/4.96 | | | | (14) all_38_0 = 0 % 26.86/4.96 | | | | % 26.86/4.96 | | | | REDUCE: (1), (14) imply: % 26.86/4.96 | | | | (15) $false % 26.86/4.96 | | | | % 26.86/4.96 | | | | CLOSE: (15) is inconsistent. % 26.86/4.96 | | | | % 26.86/4.96 | | | Case 2: % 26.86/4.96 | | | | % 26.86/4.96 | | | | (16) all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.86/4.96 | | | | [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 & % 26.86/4.96 | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.96 | | | | distinct_lines(all_26_1, all_17_2) = v1 & % 26.86/4.96 | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.86/4.96 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.96 | | | | % 26.86/4.96 | | | | BETA: splitting (13) gives: % 26.86/4.96 | | | | % 26.86/4.96 | | | | Case 1: % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | (17) all_26_0 = 0 % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | REDUCE: (7), (17) imply: % 26.86/4.96 | | | | | (18) $false % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | CLOSE: (18) is inconsistent. % 26.86/4.96 | | | | | % 26.86/4.96 | | | | Case 2: % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.86/4.96 | | | | | (apart_point_and_line(all_17_4, all_26_1) = v3 & % 26.86/4.96 | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 26.86/4.96 | | | | | distinct_lines(all_26_1, all_17_2) = v1 & % 26.86/4.96 | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 26.86/4.96 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | DELTA: instantiating (19) with fresh symbols all_839_0, all_839_1, % 26.86/4.96 | | | | | all_839_2, all_839_3 gives: % 26.86/4.96 | | | | | (20) apart_point_and_line(all_17_4, all_26_1) = all_839_0 & % 26.86/4.96 | | | | | apart_point_and_line(all_17_4, all_17_2) = all_839_1 & % 26.86/4.96 | | | | | distinct_lines(all_26_1, all_17_2) = all_839_2 & % 26.86/4.96 | | | | | distinct_points(all_17_4, all_17_4) = all_839_3 & ( ~ % 26.86/4.96 | | | | | (all_839_2 = 0) | ~ (all_839_3 = 0) | all_839_0 = 0 | % 26.86/4.96 | | | | | all_839_1 = 0) % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | ALPHA: (20) implies: % 26.86/4.96 | | | | | (21) distinct_points(all_17_4, all_17_4) = all_839_3 % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | BETA: splitting (16) gives: % 26.86/4.96 | | | | | % 26.86/4.96 | | | | | Case 1: % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | (22) all_26_0 = 0 % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | REDUCE: (7), (22) imply: % 26.86/4.96 | | | | | | (23) $false % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | CLOSE: (23) is inconsistent. % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | Case 2: % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.86/4.96 | | | | | | (apart_point_and_line(all_17_4, all_26_1) = v2 & % 26.86/4.96 | | | | | | apart_point_and_line(all_17_4, all_17_2) = v3 & % 26.86/4.96 | | | | | | distinct_lines(all_26_1, all_17_2) = v1 & % 26.86/4.96 | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | % 26.86/4.96 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | DELTA: instantiating (24) with fresh symbols all_861_0, all_861_1, % 26.86/4.96 | | | | | | all_861_2, all_861_3 gives: % 26.86/4.96 | | | | | | (25) apart_point_and_line(all_17_4, all_26_1) = all_861_1 & % 26.86/4.96 | | | | | | apart_point_and_line(all_17_4, all_17_2) = all_861_0 & % 26.86/4.96 | | | | | | distinct_lines(all_26_1, all_17_2) = all_861_2 & % 26.86/4.96 | | | | | | distinct_points(all_17_4, all_17_4) = all_861_3 & ( ~ % 26.86/4.96 | | | | | | (all_861_2 = 0) | ~ (all_861_3 = 0) | all_861_0 = 0 | % 26.86/4.96 | | | | | | all_861_1 = 0) % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | ALPHA: (25) implies: % 26.86/4.96 | | | | | | (26) distinct_points(all_17_4, all_17_4) = all_861_3 % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | GROUND_INST: instantiating (2) with 0, all_861_3, all_17_4, % 26.86/4.96 | | | | | | all_17_4, simplifying with (10), (26) gives: % 26.86/4.96 | | | | | | (27) all_861_3 = 0 % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | GROUND_INST: instantiating (2) with all_839_3, all_861_3, all_17_4, % 26.86/4.96 | | | | | | all_17_4, simplifying with (21), (26) gives: % 26.86/4.96 | | | | | | (28) all_861_3 = all_839_3 % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | COMBINE_EQS: (27), (28) imply: % 26.86/4.96 | | | | | | (29) all_839_3 = 0 % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | GROUND_INST: instantiating (8) with all_17_4, simplifying with (6), % 26.86/4.96 | | | | | | (10) gives: % 26.86/4.96 | | | | | | (30) $false % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | | CLOSE: (30) is inconsistent. % 26.86/4.96 | | | | | | % 26.86/4.96 | | | | | End of split % 26.86/4.96 | | | | | % 26.86/4.96 | | | | End of split % 26.86/4.96 | | | | % 26.86/4.96 | | | End of split % 26.86/4.96 | | | % 26.86/4.96 | | End of split % 26.86/4.96 | | % 26.86/4.96 | Case 2: % 26.86/4.96 | | % 26.86/4.96 | | (31) all_24_1 = 0 % 26.86/4.96 | | % 26.86/4.96 | | REDUCE: (9), (31) imply: % 26.86/4.96 | | (32) $false % 26.86/4.96 | | % 26.86/4.96 | | CLOSE: (32) is inconsistent. % 26.86/4.96 | | % 26.86/4.96 | End of split % 26.86/4.96 | % 26.86/4.96 End of proof % 26.86/4.96 % SZS output end Proof for theBenchmark % 26.86/4.96 % 26.86/4.96 4367ms %------------------------------------------------------------------------------