%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO181+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 23:21:56 EDT 2023 % Result : Theorem 17.96s 3.14s % Output : Proof 27.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO181+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 23:58:42 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.58/1.09 Prover 1: Preprocessing ... % 2.58/1.10 Prover 4: Preprocessing ... % 3.27/1.13 Prover 5: Preprocessing ... % 3.27/1.13 Prover 2: Preprocessing ... % 3.27/1.13 Prover 3: Preprocessing ... % 3.27/1.13 Prover 6: Preprocessing ... % 3.27/1.13 Prover 0: Preprocessing ... % 5.86/1.54 Prover 5: Proving ... % 5.86/1.56 Prover 2: Proving ... % 6.41/1.66 Prover 3: Constructing countermodel ... % 6.41/1.66 Prover 6: Constructing countermodel ... % 7.24/1.69 Prover 1: Constructing countermodel ... % 7.48/1.80 Prover 6: gave up % 7.48/1.81 Prover 3: gave up % 7.48/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.48/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.48/1.87 Prover 8: Preprocessing ... % 8.42/1.88 Prover 7: Preprocessing ... % 8.42/1.93 Prover 4: Constructing countermodel ... % 8.42/1.95 Prover 1: gave up % 8.42/1.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.12/1.95 Prover 0: Proving ... % 9.12/1.96 Prover 7: Warning: ignoring some quantifiers % 9.12/1.97 Prover 9: Preprocessing ... % 9.12/1.99 Prover 7: Constructing countermodel ... % 9.12/2.02 Prover 8: Warning: ignoring some quantifiers % 9.12/2.03 Prover 8: Constructing countermodel ... % 11.11/2.25 Prover 9: Constructing countermodel ... % 11.48/2.28 Prover 8: gave up % 11.48/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.18/2.36 Prover 10: Preprocessing ... % 12.56/2.44 Prover 10: Warning: ignoring some quantifiers % 12.96/2.45 Prover 10: Constructing countermodel ... % 12.96/2.45 Prover 7: gave up % 12.96/2.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.96/2.50 Prover 11: Preprocessing ... % 13.98/2.60 Prover 10: gave up % 13.98/2.60 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 14.43/2.65 Prover 12: Preprocessing ... % 15.32/2.79 Prover 11: Constructing countermodel ... % 15.32/2.80 Prover 12: Proving ... % 17.96/3.14 Prover 9: proved (1190ms) % 17.96/3.14 % 17.96/3.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.96/3.14 % 17.96/3.14 Prover 12: stopped % 17.96/3.14 Prover 5: stopped % 17.96/3.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.96/3.14 Prover 2: stopped % 17.96/3.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.96/3.14 Prover 0: stopped % 17.96/3.14 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.96/3.17 Prover 16: Preprocessing ... % 17.96/3.18 Prover 19: Preprocessing ... % 17.96/3.19 Prover 13: Preprocessing ... % 17.96/3.20 Prover 16: Warning: ignoring some quantifiers % 17.96/3.20 Prover 16: Constructing countermodel ... % 18.79/3.23 Prover 13: Warning: ignoring some quantifiers % 19.09/3.27 Prover 13: Constructing countermodel ... % 19.09/3.31 Prover 19: Warning: ignoring some quantifiers % 19.73/3.36 Prover 19: Constructing countermodel ... % 20.55/3.49 Prover 19: gave up % 20.99/3.53 Prover 13: gave up % 24.34/4.08 Prover 16: gave up % 25.62/4.30 Prover 4: Found proof (size 407) % 25.62/4.30 Prover 4: proved (3661ms) % 25.62/4.30 Prover 11: stopped % 25.62/4.30 % 25.62/4.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.62/4.30 % 25.62/4.40 % SZS output start Proof for theBenchmark % 25.62/4.41 Assumptions after simplification: % 25.62/4.41 --------------------------------- % 25.62/4.41 % 25.62/4.41 (apart1) % 26.24/4.44 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 26.24/4.44 % 26.24/4.44 (apart4) % 26.24/4.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.24/4.44 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 26.24/4.44 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 26.24/4.44 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.24/4.44 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 26.24/4.44 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.44 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.24/4.44 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 26.24/4.44 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.24/4.44 distinct_points(v1, v2) = 0) % 26.24/4.44 % 26.24/4.44 (ceq1) % 26.44/4.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.44/4.45 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 26.44/4.45 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 26.44/4.45 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 26.44/4.45 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.44/4.45 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 26.44/4.45 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 26.44/4.45 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.44/4.45 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 26.44/4.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 26.44/4.45 % 26.44/4.45 (ceq2) % 26.44/4.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.44/4.45 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 26.44/4.45 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 26.44/4.45 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 26.44/4.45 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 26.44/4.45 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.44/4.45 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.44/4.45 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 26.44/4.45 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.44/4.45 apart_point_and_line(v0, v2) = 0) % 26.44/4.45 % 26.44/4.45 (ci1) % 26.44/4.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.44/4.45 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.44/4.45 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 26.44/4.45 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.44/4.45 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 26.44/4.45 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 26.44/4.45 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 26.44/4.45 % 26.44/4.45 (ci2) % 26.44/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.44/4.46 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.44/4.46 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 26.44/4.46 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.44/4.46 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 26.44/4.46 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 26.44/4.46 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 26.44/4.46 % 26.44/4.46 (con) % 26.44/4.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 26.44/4.46 int] : ( ~ (v5 = 0) & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) % 26.44/4.46 = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v1, v4) = v5 % 26.44/4.46 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.44/4.46 % 26.44/4.46 (con1) % 26.44/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.44/4.46 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 26.44/4.46 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 26.44/4.46 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 26.44/4.46 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 26.44/4.46 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 26.44/4.46 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 26.44/4.46 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 26.44/4.46 0))) % 26.44/4.46 % 26.44/4.46 (cu1) % 26.44/4.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 26.44/4.47 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 26.44/4.47 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.44/4.47 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.44/4.47 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 26.44/4.47 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.44/4.47 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.44/4.47 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 26.44/4.47 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 26.44/4.47 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 26.44/4.47 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 26.44/4.47 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 26.44/4.47 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.44/4.47 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.44/4.47 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.44/4.47 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 26.44/4.47 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.44/4.47 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.44/4.47 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 26.44/4.47 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.44/4.47 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 26.44/4.47 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.44/4.47 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 26.44/4.47 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 26.44/4.47 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 26.44/4.47 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 26.44/4.47 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.44/4.47 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.44/4.47 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.44/4.47 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.44/4.47 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 26.44/4.47 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 26.44/4.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 26.44/4.47 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 26.44/4.47 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.44/4.47 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.44/4.47 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 26.44/4.47 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.44/4.47 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.44/4.47 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 26.44/4.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 26.44/4.47 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 26.44/4.47 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 26.44/4.47 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 26.44/4.47 % 26.44/4.47 (cup1) % 26.44/4.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 26.44/4.48 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 26.44/4.48 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.44/4.48 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 & % 26.44/4.48 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 26.44/4.48 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 26.44/4.48 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 26.44/4.48 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 26.44/4.48 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = % 26.44/4.48 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.44/4.48 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 26.44/4.48 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 26.44/4.48 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 & % 26.44/4.48 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 26.44/4.48 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 26.44/4.48 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 26.44/4.48 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 & % 26.44/4.48 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! % 26.44/4.48 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 26.44/4.48 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 26.44/4.48 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 & % 26.44/4.48 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 26.44/4.48 % 26.44/4.48 (function-axioms) % 26.44/4.48 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.44/4.48 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 26.44/4.48 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.44/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.48 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 26.44/4.48 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.44/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 26.44/4.48 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.44/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.48 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 26.44/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.44/4.48 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 26.44/4.48 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.48 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 26.44/4.48 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 26.44/4.48 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 26.44/4.48 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.44/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 26.44/4.48 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.44/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 26.44/4.48 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.44/4.48 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 26.44/4.48 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.44/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.48 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 26.44/4.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.44/4.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 26.44/4.48 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.44/4.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.48 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 26.44/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.44/4.48 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 26.44/4.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.44/4.48 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 26.44/4.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.44/4.48 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 26.44/4.48 % 26.44/4.48 Further assumptions not needed in the proof: % 26.44/4.48 -------------------------------------------- % 26.44/4.48 a3, a4, a5, apart2, apart3, apart5, ax1, ax2, ax6, ceq3, ci3, ci4, coipo1, % 26.44/4.48 cotno1, couo1, cp1, cp2, int1, oac1, occu1, ooc1, ooc2, orth1, ouo1, p1, par1 % 26.44/4.48 % 26.44/4.48 Those formulas are unsatisfiable: % 26.44/4.48 --------------------------------- % 26.44/4.48 % 26.44/4.48 Begin of proof % 26.44/4.49 | % 26.44/4.49 | ALPHA: (apart4) implies: % 26.44/4.49 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.44/4.49 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 26.44/4.49 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 26.44/4.49 | % 26.44/4.49 | ALPHA: (ci1) implies: % 26.44/4.49 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.44/4.49 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.44/4.49 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 26.44/4.49 | $i(v2))) % 26.44/4.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.44/4.49 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.44/4.49 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.44/4.49 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.44/4.49 | % 26.44/4.49 | ALPHA: (ci2) implies: % 26.44/4.49 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.44/4.49 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.44/4.49 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 26.44/4.49 | $i(v2))) % 26.44/4.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.44/4.49 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.44/4.49 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.44/4.49 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.44/4.49 | % 26.44/4.49 | ALPHA: (cu1) implies: % 26.44/4.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.44/4.49 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 26.44/4.49 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 26.44/4.49 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.44/4.49 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 26.44/4.49 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 26.44/4.49 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.44/4.50 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.44/4.50 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 26.44/4.50 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.44/4.50 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.44/4.50 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 26.44/4.50 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 26.44/4.50 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.44/4.50 | | v8 = 0))) % 26.44/4.50 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.44/4.50 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.44/4.50 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.44/4.50 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.44/4.50 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.44/4.50 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.44/4.50 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.44/4.50 | | v8 = 0))) % 26.44/4.50 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.44/4.50 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.44/4.50 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 26.44/4.50 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.44/4.50 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 26.44/4.50 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 26.44/4.50 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.44/4.50 | % 26.44/4.50 | ALPHA: (ceq1) implies: % 26.44/4.50 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.44/4.50 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 26.44/4.50 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.44/4.50 | distinct_points(v0, v2) = 0) % 26.44/4.50 | % 26.44/4.50 | ALPHA: (ceq2) implies: % 26.44/4.50 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.44/4.50 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = % 26.44/4.50 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, % 26.44/4.50 | v2) = 0) % 26.44/4.50 | % 26.44/4.50 | ALPHA: (cup1) implies: % 26.44/4.50 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 26.44/4.50 | : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 26.44/4.50 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.44/4.50 | $i(v0) | ? [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = % 26.44/4.50 | v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 26.44/4.50 | % 26.44/4.50 | ALPHA: (con1) implies: % 26.44/4.50 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.44/4.50 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 26.44/4.50 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 26.44/4.50 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 26.44/4.50 | | v5 = 0))) % 26.44/4.51 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.44/4.51 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 26.44/4.51 | [v5: any] : ? [v6: any] : (point(v1) = v4 & point(v0) = v3 & % 26.44/4.51 | line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ % 26.44/4.51 | (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 26.44/4.51 | % 26.44/4.51 | ALPHA: (function-axioms) implies: % 26.44/4.51 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.44/4.51 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.44/4.51 | (distinct_points(v3, v2) = v0)) % 26.44/4.51 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.44/4.51 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 26.44/4.51 | (distinct_lines(v3, v2) = v0)) % 26.44/4.51 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.44/4.51 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 26.44/4.51 | (apart_point_and_line(v3, v2) = v0)) % 26.44/4.51 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.44/4.51 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 26.44/4.51 | % 26.44/4.51 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 26.44/4.51 | all_38_3, all_38_4, all_38_5 gives: % 26.44/4.51 | (19) ~ (all_38_0 = 0) & line_connecting(all_38_5, all_38_3) = all_38_1 & % 26.44/4.51 | line_connecting(all_38_5, all_38_4) = all_38_2 & % 26.44/4.51 | apart_point_and_line(all_38_3, all_38_2) = 0 & % 26.44/4.51 | apart_point_and_line(all_38_4, all_38_1) = all_38_0 & % 26.44/4.51 | distinct_points(all_38_5, all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) % 26.44/4.51 | & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) % 26.44/4.51 | % 26.44/4.51 | ALPHA: (19) implies: % 26.44/4.51 | (20) ~ (all_38_0 = 0) % 26.44/4.51 | (21) $i(all_38_5) % 26.44/4.51 | (22) $i(all_38_4) % 26.44/4.51 | (23) $i(all_38_3) % 26.44/4.51 | (24) $i(all_38_1) % 26.44/4.51 | (25) distinct_points(all_38_5, all_38_4) = 0 % 26.44/4.51 | (26) apart_point_and_line(all_38_4, all_38_1) = all_38_0 % 26.44/4.51 | (27) apart_point_and_line(all_38_3, all_38_2) = 0 % 26.44/4.51 | (28) line_connecting(all_38_5, all_38_4) = all_38_2 % 26.44/4.51 | (29) line_connecting(all_38_5, all_38_3) = all_38_1 % 26.44/4.51 | % 26.44/4.51 | GROUND_INST: instantiating (13) with all_38_5, all_38_4, simplifying with % 26.44/4.51 | (21), (22), (25) gives: % 26.44/4.51 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 26.44/4.51 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(v2) = v3 & % 26.44/4.51 | line_connecting(all_38_5, all_38_4) = v2 & $i(v2) & ( ~ (v1 = 0) | % 26.44/4.51 | ~ (v0 = 0) | v3 = 0)) % 26.44/4.51 | % 26.44/4.51 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, simplifying with (21), % 26.44/4.51 | (22), (25) gives: % 26.44/4.51 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 26.44/4.51 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 26.44/4.51 | % 26.44/4.52 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, simplifying with (21), % 26.44/4.52 | (22), (25) gives: % 26.44/4.52 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 26.44/4.52 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 26.44/4.52 | % 26.44/4.52 | GROUND_INST: instantiating (9) with all_38_5, all_38_4, all_38_1, all_38_1, % 26.44/4.52 | all_38_0, all_38_0, simplifying with (21), (22), (24), (25), (26) % 26.44/4.52 | gives: % 26.44/4.52 | (33) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.44/4.52 | (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.44/4.52 | apart_point_and_line(all_38_5, all_38_1) = v1 & % 26.44/4.52 | distinct_lines(all_38_1, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 26.44/4.52 | = 0)) % 26.44/4.52 | % 26.44/4.52 | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_1, all_38_1, % 26.44/4.52 | all_38_0, all_38_0, simplifying with (22), (24), (26) gives: % 26.44/4.52 | (34) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 26.44/4.52 | any] : (apart_point_and_line(all_38_4, all_38_1) = v3 & % 26.44/4.52 | apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.44/4.52 | distinct_lines(all_38_1, all_38_1) = v1 & distinct_points(all_38_4, % 26.44/4.52 | all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.44/4.52 | % 26.81/4.52 | GROUND_INST: instantiating (14) with all_38_5, all_38_4, all_38_2, simplifying % 26.81/4.52 | with (21), (22), (28) gives: % 26.81/4.52 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.81/4.52 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_2) = v3 & % 26.81/4.52 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 26.81/4.52 | 0) | ~ (v0 = 0) | v3 = 0)) % 26.81/4.52 | % 26.81/4.52 | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_2, simplifying % 26.81/4.52 | with (21), (22), (28) gives: % 26.81/4.52 | (36) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 26.81/4.52 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.81/4.52 | (v1 = 0) | ~ (v0 = 0))) % 26.81/4.52 | % 26.81/4.52 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, all_38_2, simplifying % 26.81/4.52 | with (21), (22), (28) gives: % 26.81/4.52 | (37) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5, % 26.81/4.52 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.81/4.52 | (v1 = 0) | ~ (v0 = 0))) % 26.81/4.52 | % 26.81/4.52 | GROUND_INST: instantiating (14) with all_38_5, all_38_3, all_38_1, simplifying % 26.81/4.52 | with (21), (23), (29) gives: % 26.81/4.53 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.81/4.53 | (point(all_38_3) = v1 & point(all_38_5) = v0 & line(all_38_1) = v3 & % 26.81/4.53 | distinct_points(all_38_5, all_38_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 26.81/4.53 | 0) | ~ (v0 = 0) | v3 = 0)) % 26.81/4.53 | % 26.81/4.53 | GROUND_INST: instantiating (5) with all_38_5, all_38_3, all_38_1, simplifying % 26.81/4.53 | with (21), (23), (29) gives: % 26.81/4.53 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 26.81/4.53 | all_38_1) = v1 & distinct_points(all_38_5, all_38_3) = v0 & ( ~ % 26.81/4.53 | (v1 = 0) | ~ (v0 = 0))) % 26.81/4.53 | % 26.81/4.53 | GROUND_INST: instantiating (3) with all_38_5, all_38_3, all_38_1, simplifying % 26.81/4.53 | with (21), (23), (29) gives: % 26.81/4.53 | (40) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5, % 26.81/4.53 | all_38_1) = v1 & distinct_points(all_38_5, all_38_3) = v0 & ( ~ % 26.81/4.53 | (v1 = 0) | ~ (v0 = 0))) % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (32) with fresh symbols all_49_0, all_49_1 gives: % 26.81/4.53 | (41) ~ (all_49_0 = 0) & line_connecting(all_38_5, all_38_4) = all_49_1 & % 26.81/4.53 | apart_point_and_line(all_38_5, all_49_1) = all_49_0 & $i(all_49_1) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (41) implies: % 26.81/4.53 | (42) $i(all_49_1) % 26.81/4.53 | (43) apart_point_and_line(all_38_5, all_49_1) = all_49_0 % 26.81/4.53 | (44) line_connecting(all_38_5, all_38_4) = all_49_1 % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (37) with fresh symbols all_51_0, all_51_1 gives: % 26.81/4.53 | (45) apart_point_and_line(all_38_5, all_38_2) = all_51_0 & % 26.81/4.53 | distinct_points(all_38_5, all_38_4) = all_51_1 & ( ~ (all_51_0 = 0) | % 26.81/4.53 | ~ (all_51_1 = 0)) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (45) implies: % 26.81/4.53 | (46) distinct_points(all_38_5, all_38_4) = all_51_1 % 26.81/4.53 | (47) apart_point_and_line(all_38_5, all_38_2) = all_51_0 % 26.81/4.53 | (48) ~ (all_51_0 = 0) | ~ (all_51_1 = 0) % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (36) with fresh symbols all_53_0, all_53_1 gives: % 26.81/4.53 | (49) apart_point_and_line(all_38_4, all_38_2) = all_53_0 & % 26.81/4.53 | distinct_points(all_38_5, all_38_4) = all_53_1 & ( ~ (all_53_0 = 0) | % 26.81/4.53 | ~ (all_53_1 = 0)) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (49) implies: % 26.81/4.53 | (50) distinct_points(all_38_5, all_38_4) = all_53_1 % 26.81/4.53 | (51) apart_point_and_line(all_38_4, all_38_2) = all_53_0 % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (40) with fresh symbols all_55_0, all_55_1 gives: % 26.81/4.53 | (52) apart_point_and_line(all_38_5, all_38_1) = all_55_0 & % 26.81/4.53 | distinct_points(all_38_5, all_38_3) = all_55_1 & ( ~ (all_55_0 = 0) | % 26.81/4.53 | ~ (all_55_1 = 0)) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (52) implies: % 26.81/4.53 | (53) distinct_points(all_38_5, all_38_3) = all_55_1 % 26.81/4.53 | (54) apart_point_and_line(all_38_5, all_38_1) = all_55_0 % 26.81/4.53 | (55) ~ (all_55_0 = 0) | ~ (all_55_1 = 0) % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (39) with fresh symbols all_57_0, all_57_1 gives: % 26.81/4.53 | (56) apart_point_and_line(all_38_3, all_38_1) = all_57_0 & % 26.81/4.53 | distinct_points(all_38_5, all_38_3) = all_57_1 & ( ~ (all_57_0 = 0) | % 26.81/4.53 | ~ (all_57_1 = 0)) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (56) implies: % 26.81/4.53 | (57) distinct_points(all_38_5, all_38_3) = all_57_1 % 26.81/4.53 | (58) apart_point_and_line(all_38_3, all_38_1) = all_57_0 % 26.81/4.53 | (59) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (31) with fresh symbols all_59_0, all_59_1 gives: % 26.81/4.53 | (60) ~ (all_59_0 = 0) & line_connecting(all_38_5, all_38_4) = all_59_1 & % 26.81/4.53 | apart_point_and_line(all_38_4, all_59_1) = all_59_0 & $i(all_59_1) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (60) implies: % 26.81/4.53 | (61) ~ (all_59_0 = 0) % 26.81/4.53 | (62) apart_point_and_line(all_38_4, all_59_1) = all_59_0 % 26.81/4.53 | (63) line_connecting(all_38_5, all_38_4) = all_59_1 % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (35) with fresh symbols all_61_0, all_61_1, all_61_2, % 26.81/4.53 | all_61_3 gives: % 26.81/4.53 | (64) point(all_38_4) = all_61_2 & point(all_38_5) = all_61_3 & % 26.81/4.53 | line(all_38_2) = all_61_0 & distinct_points(all_38_5, all_38_4) = % 26.81/4.53 | all_61_1 & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | ~ (all_61_3 = 0) % 26.81/4.53 | | all_61_0 = 0) % 26.81/4.53 | % 26.81/4.53 | ALPHA: (64) implies: % 26.81/4.53 | (65) distinct_points(all_38_5, all_38_4) = all_61_1 % 26.81/4.53 | % 26.81/4.53 | DELTA: instantiating (38) with fresh symbols all_63_0, all_63_1, all_63_2, % 26.81/4.53 | all_63_3 gives: % 26.81/4.54 | (66) point(all_38_3) = all_63_2 & point(all_38_5) = all_63_3 & % 26.81/4.54 | line(all_38_1) = all_63_0 & distinct_points(all_38_5, all_38_3) = % 26.81/4.54 | all_63_1 & ( ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | ~ (all_63_3 = 0) % 26.81/4.54 | | all_63_0 = 0) % 26.81/4.54 | % 26.81/4.54 | ALPHA: (66) implies: % 26.81/4.54 | (67) distinct_points(all_38_5, all_38_3) = all_63_1 % 26.81/4.54 | % 26.81/4.54 | DELTA: instantiating (30) with fresh symbols all_65_0, all_65_1, all_65_2, % 26.81/4.54 | all_65_3 gives: % 26.81/4.54 | (68) point(all_38_4) = all_65_2 & point(all_38_5) = all_65_3 & % 26.81/4.54 | line(all_65_1) = all_65_0 & line_connecting(all_38_5, all_38_4) = % 26.81/4.54 | all_65_1 & $i(all_65_1) & ( ~ (all_65_2 = 0) | ~ (all_65_3 = 0) | % 26.81/4.54 | all_65_0 = 0) % 26.81/4.54 | % 26.81/4.54 | ALPHA: (68) implies: % 26.81/4.54 | (69) line_connecting(all_38_5, all_38_4) = all_65_1 % 26.81/4.54 | % 26.81/4.54 | BETA: splitting (33) gives: % 26.81/4.54 | % 26.81/4.54 | Case 1: % 26.81/4.54 | | % 26.81/4.54 | | (70) all_38_0 = 0 % 26.81/4.54 | | % 26.81/4.54 | | REDUCE: (20), (70) imply: % 26.81/4.54 | | (71) $false % 26.81/4.54 | | % 26.81/4.54 | | CLOSE: (71) is inconsistent. % 26.81/4.54 | | % 26.81/4.54 | Case 2: % 26.81/4.54 | | % 26.81/4.54 | | (72) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.81/4.54 | | (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.81/4.54 | | apart_point_and_line(all_38_5, all_38_1) = v1 & % 26.81/4.54 | | distinct_lines(all_38_1, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 26.81/4.54 | | v1 = 0)) % 26.81/4.54 | | % 26.81/4.54 | | DELTA: instantiating (72) with fresh symbols all_75_0, all_75_1, all_75_2 % 26.81/4.54 | | gives: % 26.81/4.54 | | (73) apart_point_and_line(all_38_5, all_38_1) = all_75_0 & % 26.81/4.54 | | apart_point_and_line(all_38_5, all_38_1) = all_75_1 & % 26.81/4.54 | | distinct_lines(all_38_1, all_38_1) = all_75_2 & ( ~ (all_75_2 = 0) | % 26.81/4.54 | | all_75_0 = 0 | all_75_1 = 0) % 26.81/4.54 | | % 26.81/4.54 | | ALPHA: (73) implies: % 26.81/4.54 | | (74) apart_point_and_line(all_38_5, all_38_1) = all_75_1 % 26.81/4.54 | | (75) apart_point_and_line(all_38_5, all_38_1) = all_75_0 % 26.81/4.54 | | % 26.81/4.54 | | BETA: splitting (34) gives: % 26.81/4.54 | | % 26.81/4.54 | | Case 1: % 26.81/4.54 | | | % 26.81/4.54 | | | (76) all_38_0 = 0 % 26.81/4.54 | | | % 26.81/4.54 | | | REDUCE: (20), (76) imply: % 26.81/4.54 | | | (77) $false % 26.81/4.54 | | | % 26.81/4.54 | | | CLOSE: (77) is inconsistent. % 26.81/4.54 | | | % 26.81/4.54 | | Case 2: % 26.81/4.54 | | | % 26.81/4.54 | | | (78) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.81/4.54 | | | (apart_point_and_line(all_38_4, all_38_1) = v3 & % 26.81/4.54 | | | apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.81/4.54 | | | distinct_lines(all_38_1, all_38_1) = v1 & % 26.81/4.54 | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.81/4.54 | | | = 0) | v3 = 0 | v2 = 0)) % 26.81/4.54 | | | % 26.81/4.54 | | | DELTA: instantiating (78) with fresh symbols all_85_0, all_85_1, all_85_2, % 26.81/4.54 | | | all_85_3 gives: % 26.81/4.54 | | | (79) apart_point_and_line(all_38_4, all_38_1) = all_85_0 & % 26.81/4.54 | | | apart_point_and_line(all_38_4, all_38_1) = all_85_1 & % 26.81/4.54 | | | distinct_lines(all_38_1, all_38_1) = all_85_2 & % 26.81/4.54 | | | distinct_points(all_38_4, all_38_4) = all_85_3 & ( ~ (all_85_2 = % 26.81/4.54 | | | 0) | ~ (all_85_3 = 0) | all_85_0 = 0 | all_85_1 = 0) % 26.81/4.54 | | | % 26.81/4.54 | | | ALPHA: (79) implies: % 26.81/4.54 | | | (80) apart_point_and_line(all_38_4, all_38_1) = all_85_1 % 26.81/4.54 | | | (81) apart_point_and_line(all_38_4, all_38_1) = all_85_0 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (15) with 0, all_53_1, all_38_4, all_38_5, % 26.81/4.54 | | | simplifying with (25), (50) gives: % 26.81/4.54 | | | (82) all_53_1 = 0 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (15) with all_53_1, all_61_1, all_38_4, % 26.81/4.54 | | | all_38_5, simplifying with (50), (65) gives: % 26.81/4.54 | | | (83) all_61_1 = all_53_1 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (15) with all_51_1, all_61_1, all_38_4, % 26.81/4.54 | | | all_38_5, simplifying with (46), (65) gives: % 26.81/4.54 | | | (84) all_61_1 = all_51_1 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (15) with all_57_1, all_63_1, all_38_3, % 26.81/4.54 | | | all_38_5, simplifying with (57), (67) gives: % 26.81/4.54 | | | (85) all_63_1 = all_57_1 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (15) with all_55_1, all_63_1, all_38_3, % 26.81/4.54 | | | all_38_5, simplifying with (53), (67) gives: % 26.81/4.54 | | | (86) all_63_1 = all_55_1 % 26.81/4.54 | | | % 26.81/4.54 | | | GROUND_INST: instantiating (17) with all_75_1, all_75_0, all_38_1, % 26.81/4.54 | | | all_38_5, simplifying with (74), (75) gives: % 26.81/4.54 | | | (87) all_75_0 = all_75_1 % 26.81/4.54 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (17) with all_55_0, all_75_0, all_38_1, % 26.81/4.55 | | | all_38_5, simplifying with (54), (75) gives: % 26.81/4.55 | | | (88) all_75_0 = all_55_0 % 26.81/4.55 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (17) with all_38_0, all_85_0, all_38_1, % 26.81/4.55 | | | all_38_4, simplifying with (26), (81) gives: % 26.81/4.55 | | | (89) all_85_0 = all_38_0 % 26.81/4.55 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (17) with all_85_1, all_85_0, all_38_1, % 26.81/4.55 | | | all_38_4, simplifying with (80), (81) gives: % 26.81/4.55 | | | (90) all_85_0 = all_85_1 % 26.81/4.55 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (18) with all_49_1, all_59_1, all_38_4, % 26.81/4.55 | | | all_38_5, simplifying with (44), (63) gives: % 26.81/4.55 | | | (91) all_59_1 = all_49_1 % 26.81/4.55 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (18) with all_38_2, all_65_1, all_38_4, % 26.81/4.55 | | | all_38_5, simplifying with (28), (69) gives: % 26.81/4.55 | | | (92) all_65_1 = all_38_2 % 26.81/4.55 | | | % 26.81/4.55 | | | GROUND_INST: instantiating (18) with all_59_1, all_65_1, all_38_4, % 26.81/4.55 | | | all_38_5, simplifying with (63), (69) gives: % 26.81/4.55 | | | (93) all_65_1 = all_59_1 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (89), (90) imply: % 26.81/4.55 | | | (94) all_85_1 = all_38_0 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (87), (88) imply: % 26.81/4.55 | | | (95) all_75_1 = all_55_0 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (92), (93) imply: % 26.81/4.55 | | | (96) all_59_1 = all_38_2 % 26.81/4.55 | | | % 26.81/4.55 | | | SIMP: (96) implies: % 26.81/4.55 | | | (97) all_59_1 = all_38_2 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (85), (86) imply: % 26.81/4.55 | | | (98) all_57_1 = all_55_1 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (83), (84) imply: % 26.81/4.55 | | | (99) all_53_1 = all_51_1 % 26.81/4.55 | | | % 26.81/4.55 | | | SIMP: (99) implies: % 26.81/4.55 | | | (100) all_53_1 = all_51_1 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (91), (97) imply: % 26.81/4.55 | | | (101) all_49_1 = all_38_2 % 26.81/4.55 | | | % 26.81/4.55 | | | SIMP: (101) implies: % 26.81/4.55 | | | (102) all_49_1 = all_38_2 % 26.81/4.55 | | | % 26.81/4.55 | | | COMBINE_EQS: (82), (100) imply: % 26.81/4.55 | | | (103) all_51_1 = 0 % 26.81/4.55 | | | % 26.81/4.55 | | | REDUCE: (62), (97) imply: % 26.81/4.55 | | | (104) apart_point_and_line(all_38_4, all_38_2) = all_59_0 % 26.81/4.55 | | | % 26.81/4.55 | | | REDUCE: (43), (102) imply: % 26.81/4.55 | | | (105) apart_point_and_line(all_38_5, all_38_2) = all_49_0 % 26.81/4.55 | | | % 26.81/4.55 | | | REDUCE: (42), (102) imply: % 26.81/4.55 | | | (106) $i(all_38_2) % 26.81/4.55 | | | % 26.81/4.55 | | | BETA: splitting (48) gives: % 26.81/4.55 | | | % 26.81/4.55 | | | Case 1: % 26.81/4.55 | | | | % 26.81/4.55 | | | | (107) ~ (all_51_0 = 0) % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (17) with all_51_0, all_49_0, all_38_2, % 26.81/4.55 | | | | all_38_5, simplifying with (47), (105) gives: % 26.81/4.55 | | | | (108) all_51_0 = all_49_0 % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (17) with all_53_0, all_59_0, all_38_2, % 26.81/4.55 | | | | all_38_4, simplifying with (51), (104) gives: % 26.81/4.55 | | | | (109) all_59_0 = all_53_0 % 26.81/4.55 | | | | % 26.81/4.55 | | | | REDUCE: (61), (109) imply: % 26.81/4.55 | | | | (110) ~ (all_53_0 = 0) % 26.81/4.55 | | | | % 26.81/4.55 | | | | REDUCE: (107), (108) imply: % 26.81/4.55 | | | | (111) ~ (all_49_0 = 0) % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (10) with all_38_3, all_38_2, all_38_5, % 26.81/4.55 | | | | all_49_0, simplifying with (21), (23), (27), (105), (106) % 26.81/4.55 | | | | gives: % 26.81/4.55 | | | | (112) all_49_0 = 0 | distinct_points(all_38_3, all_38_5) = 0 % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_5, all_38_1, % 26.81/4.55 | | | | all_38_2, all_38_0, all_49_0, simplifying with (21), (22), % 26.81/4.55 | | | | (24), (26), (105), (106) gives: % 26.81/4.55 | | | | (113) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.55 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_1) = % 26.81/4.55 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 & % 26.81/4.55 | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_4, all_38_2, % 26.81/4.55 | | | | all_38_1, all_49_0, all_38_0, simplifying with (21), (22), % 26.81/4.55 | | | | (24), (26), (105), (106) gives: % 26.81/4.55 | | | | (114) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.55 | | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_1) = % 26.81/4.55 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.81/4.55 | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.55 | | | | % 26.81/4.55 | | | | GROUND_INST: instantiating (7) with all_38_4, all_38_5, all_38_2, % 26.81/4.55 | | | | all_38_1, all_38_0, all_49_0, simplifying with (21), (22), % 26.81/4.55 | | | | (24), (26), (105), (106) gives: % 26.81/4.56 | | | | (115) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.56 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_1) = % 26.81/4.56 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_4, all_38_1, % 26.81/4.56 | | | | all_38_2, all_49_0, all_38_0, simplifying with (21), (22), % 26.81/4.56 | | | | (24), (26), (105), (106) gives: % 26.81/4.56 | | | | (116) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.56 | | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_1) = % 26.81/4.56 | | | | v2 & distinct_lines(all_38_1, all_38_2) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_4, all_38_2, % 26.81/4.56 | | | | all_38_2, all_49_0, all_49_0, simplifying with (21), (22), % 26.81/4.56 | | | | (25), (105), (106) gives: % 26.81/4.56 | | | | (117) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.81/4.56 | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 & % 26.81/4.56 | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 26.81/4.56 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 26.81/4.56 | | | | 0 | v1 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_5, all_38_2, % 26.81/4.56 | | | | all_38_2, all_49_0, all_49_0, simplifying with (21), (105), % 26.81/4.56 | | | | (106) gives: % 26.81/4.56 | | | | (118) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.81/4.56 | | | | [v3: any] : (apart_point_and_line(all_38_5, all_38_2) = v3 & % 26.81/4.56 | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.81/4.56 | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (9) with all_38_5, all_38_4, all_38_1, % 26.81/4.56 | | | | all_38_2, all_38_0, all_53_0, simplifying with (21), (22), % 26.81/4.56 | | | | (24), (25), (26), (51), (106) gives: % 26.81/4.56 | | | | (119) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_38_1) = v1 & % 26.81/4.56 | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.81/4.56 | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 26.81/4.56 | | | | 0 | v1 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (9) with all_38_5, all_38_4, all_38_2, % 26.81/4.56 | | | | all_38_1, all_53_0, all_38_0, simplifying with (21), (22), % 26.81/4.56 | | | | (24), (25), (26), (51), (106) gives: % 26.81/4.56 | | | | (120) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.81/4.56 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 26.81/4.56 | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = % 26.81/4.56 | | | | 0 | v1 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (12) with all_38_4, all_38_2, all_38_1, % 26.81/4.56 | | | | all_53_0, all_38_0, simplifying with (22), (24), (26), % 26.81/4.56 | | | | (51), (106) gives: % 26.81/4.56 | | | | (121) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : % 26.81/4.56 | | | | (convergent_lines(all_38_2, all_38_1) = v1 & % 26.81/4.56 | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ (v0 = 0) | v1 = % 26.81/4.56 | | | | 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_1, % 26.81/4.56 | | | | all_38_2, all_38_0, all_53_0, simplifying with (22), (24), % 26.81/4.56 | | | | (26), (51), (106) gives: % 26.81/4.56 | | | | (122) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.56 | | | | all_38_1) = v3 & apart_point_and_line(all_38_4, all_38_2) = % 26.81/4.56 | | | | v2 & distinct_lines(all_38_1, all_38_2) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_2, % 26.81/4.56 | | | | all_38_1, all_53_0, all_38_0, simplifying with (22), (24), % 26.81/4.56 | | | | (26), (51), (106) gives: % 26.81/4.56 | | | | (123) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.56 | | | | all_38_1) = v2 & apart_point_and_line(all_38_4, all_38_2) = % 26.81/4.56 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (7) with all_38_4, all_38_4, all_38_2, % 26.81/4.56 | | | | all_38_1, all_38_0, all_53_0, simplifying with (22), (24), % 26.81/4.56 | | | | (26), (51), (106) gives: % 26.81/4.56 | | | | (124) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.56 | | | | all_38_1) = v3 & apart_point_and_line(all_38_4, all_38_2) = % 26.81/4.56 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.81/4.56 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.56 | | | | % 26.81/4.56 | | | | GROUND_INST: instantiating (7) with all_38_4, all_38_4, all_38_1, % 26.81/4.56 | | | | all_38_2, all_53_0, all_38_0, simplifying with (22), (24), % 26.81/4.56 | | | | (26), (51), (106) gives: % 26.81/4.57 | | | | (125) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.57 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.57 | | | | all_38_1) = v2 & apart_point_and_line(all_38_4, all_38_2) = % 26.81/4.57 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 & % 26.81/4.57 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.57 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | GROUND_INST: instantiating (9) with all_38_5, all_38_4, all_38_2, % 26.81/4.57 | | | | all_38_2, all_53_0, all_53_0, simplifying with (21), (22), % 26.81/4.57 | | | | (25), (51), (106) gives: % 26.81/4.57 | | | | (126) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.81/4.57 | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.81/4.57 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 26.81/4.57 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 26.81/4.57 | | | | 0 | v1 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_2, % 26.81/4.57 | | | | all_38_2, all_53_0, all_53_0, simplifying with (22), (51), % 26.81/4.57 | | | | (106) gives: % 26.81/4.57 | | | | (127) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.81/4.57 | | | | [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v3 & % 26.81/4.57 | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 26.81/4.57 | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 26.81/4.57 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.57 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_5, all_38_2, % 26.81/4.57 | | | | all_38_2, all_53_0, all_49_0, simplifying with (21), (22), % 26.81/4.57 | | | | (51), (105), (106) gives: % 26.81/4.57 | | | | (128) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.57 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.81/4.57 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 26.81/4.57 | | | | v3 & distinct_lines(all_38_2, all_38_2) = v1 & % 26.81/4.57 | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.57 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_3, all_38_1, % 26.81/4.57 | | | | all_38_1, all_38_0, all_57_0, simplifying with (22), (23), % 26.81/4.57 | | | | (24), (26), (58) gives: % 26.81/4.57 | | | | (129) all_57_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.81/4.57 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 26.81/4.57 | | | | all_38_1) = v3 & apart_point_and_line(all_38_4, all_38_1) = % 26.81/4.57 | | | | v2 & distinct_lines(all_38_1, all_38_1) = v1 & % 26.81/4.57 | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.57 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | GROUND_INST: instantiating (8) with all_38_3, all_38_3, all_38_1, % 26.81/4.57 | | | | all_38_1, all_57_0, all_57_0, simplifying with (23), (24), % 26.81/4.57 | | | | (58) gives: % 26.81/4.57 | | | | (130) all_57_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.81/4.57 | | | | [v3: any] : (apart_point_and_line(all_38_3, all_38_1) = v3 & % 26.81/4.57 | | | | apart_point_and_line(all_38_3, all_38_1) = v2 & % 26.81/4.57 | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 26.81/4.57 | | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ % 26.81/4.57 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.81/4.57 | | | | % 26.81/4.57 | | | | BETA: splitting (128) gives: % 26.81/4.57 | | | | % 26.81/4.57 | | | | Case 1: % 26.81/4.57 | | | | | % 27.05/4.57 | | | | | (131) all_53_0 = 0 % 27.05/4.57 | | | | | % 27.05/4.57 | | | | | REDUCE: (110), (131) imply: % 27.05/4.57 | | | | | (132) $false % 27.05/4.57 | | | | | % 27.05/4.57 | | | | | CLOSE: (132) is inconsistent. % 27.05/4.57 | | | | | % 27.05/4.57 | | | | Case 2: % 27.05/4.57 | | | | | % 27.05/4.57 | | | | | (133) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.05/4.57 | | | | | ? [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v2 % 27.05/4.57 | | | | | & apart_point_and_line(all_38_5, all_38_2) = v3 & % 27.05/4.57 | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 27.05/4.57 | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | % 27.05/4.57 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.57 | | | | | % 27.05/4.57 | | | | | BETA: splitting (112) gives: % 27.05/4.57 | | | | | % 27.05/4.57 | | | | | Case 1: % 27.05/4.57 | | | | | | % 27.05/4.57 | | | | | | (134) distinct_points(all_38_3, all_38_5) = 0 % 27.05/4.57 | | | | | | % 27.05/4.57 | | | | | | BETA: splitting (117) gives: % 27.05/4.57 | | | | | | % 27.05/4.57 | | | | | | Case 1: % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | (135) all_49_0 = 0 % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | REDUCE: (111), (135) imply: % 27.05/4.57 | | | | | | | (136) $false % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | CLOSE: (136) is inconsistent. % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | Case 2: % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.05/4.57 | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.57 | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 27.05/4.57 | | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) % 27.05/4.57 | | | | | | | | v2 = 0 | v1 = 0)) % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | DELTA: instantiating (137) with fresh symbols all_135_0, % 27.05/4.57 | | | | | | | all_135_1, all_135_2 gives: % 27.05/4.57 | | | | | | | (138) apart_point_and_line(all_38_4, all_38_2) = all_135_0 & % 27.05/4.57 | | | | | | | apart_point_and_line(all_38_4, all_38_2) = all_135_1 & % 27.05/4.57 | | | | | | | distinct_lines(all_38_2, all_38_2) = all_135_2 & ( ~ % 27.05/4.57 | | | | | | | (all_135_2 = 0) | all_135_0 = 0 | all_135_1 = 0) % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | ALPHA: (138) implies: % 27.05/4.57 | | | | | | | (139) apart_point_and_line(all_38_4, all_38_2) = all_135_1 % 27.05/4.57 | | | | | | | (140) apart_point_and_line(all_38_4, all_38_2) = all_135_0 % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | BETA: splitting (126) gives: % 27.05/4.57 | | | | | | | % 27.05/4.57 | | | | | | | Case 1: % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | (141) all_53_0 = 0 % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | REDUCE: (110), (141) imply: % 27.05/4.57 | | | | | | | | (142) $false % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | CLOSE: (142) is inconsistent. % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | Case 2: % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | (143) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.05/4.57 | | | | | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 & % 27.05/4.57 | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 27.05/4.57 | | | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = % 27.05/4.57 | | | | | | | | 0) | v2 = 0 | v1 = 0)) % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | DELTA: instantiating (143) with fresh symbols all_140_0, % 27.05/4.57 | | | | | | | | all_140_1, all_140_2 gives: % 27.05/4.57 | | | | | | | | (144) apart_point_and_line(all_38_5, all_38_2) = all_140_0 & % 27.05/4.57 | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = all_140_1 & % 27.05/4.57 | | | | | | | | distinct_lines(all_38_2, all_38_2) = all_140_2 & ( ~ % 27.05/4.57 | | | | | | | | (all_140_2 = 0) | all_140_0 = 0 | all_140_1 = 0) % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | ALPHA: (144) implies: % 27.05/4.57 | | | | | | | | (145) apart_point_and_line(all_38_5, all_38_2) = all_140_1 % 27.05/4.57 | | | | | | | | (146) apart_point_and_line(all_38_5, all_38_2) = all_140_0 % 27.05/4.57 | | | | | | | | (147) ~ (all_140_2 = 0) | all_140_0 = 0 | all_140_1 = 0 % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | BETA: splitting (118) gives: % 27.05/4.57 | | | | | | | | % 27.05/4.57 | | | | | | | | Case 1: % 27.05/4.57 | | | | | | | | | % 27.05/4.57 | | | | | | | | | (148) all_49_0 = 0 % 27.05/4.57 | | | | | | | | | % 27.05/4.57 | | | | | | | | | REDUCE: (111), (148) imply: % 27.05/4.57 | | | | | | | | | (149) $false % 27.05/4.57 | | | | | | | | | % 27.05/4.57 | | | | | | | | | CLOSE: (149) is inconsistent. % 27.05/4.57 | | | | | | | | | % 27.05/4.57 | | | | | | | | Case 2: % 27.05/4.57 | | | | | | | | | % 27.05/4.58 | | | | | | | | | (150) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 27.05/4.58 | | | | | | | | | any] : (apart_point_and_line(all_38_5, all_38_2) = % 27.05/4.58 | | | | | | | | | v3 & apart_point_and_line(all_38_5, all_38_2) = v2 % 27.05/4.58 | | | | | | | | | & distinct_lines(all_38_2, all_38_2) = v1 & % 27.05/4.58 | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 % 27.05/4.58 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | % 27.05/4.58 | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_150_0, % 27.05/4.58 | | | | | | | | | all_150_1, all_150_2, all_150_3 gives: % 27.05/4.58 | | | | | | | | | (151) apart_point_and_line(all_38_5, all_38_2) = all_150_0 % 27.05/4.58 | | | | | | | | | & apart_point_and_line(all_38_5, all_38_2) = % 27.05/4.58 | | | | | | | | | all_150_1 & distinct_lines(all_38_2, all_38_2) = % 27.05/4.58 | | | | | | | | | all_150_2 & distinct_points(all_38_5, all_38_5) = % 27.05/4.58 | | | | | | | | | all_150_3 & ( ~ (all_150_2 = 0) | ~ (all_150_3 = 0) % 27.05/4.58 | | | | | | | | | | all_150_0 = 0 | all_150_1 = 0) % 27.05/4.58 | | | | | | | | | % 27.05/4.58 | | | | | | | | | ALPHA: (151) implies: % 27.05/4.58 | | | | | | | | | (152) apart_point_and_line(all_38_5, all_38_2) = all_150_1 % 27.05/4.58 | | | | | | | | | (153) apart_point_and_line(all_38_5, all_38_2) = all_150_0 % 27.05/4.58 | | | | | | | | | % 27.05/4.58 | | | | | | | | | BETA: splitting (127) gives: % 27.05/4.58 | | | | | | | | | % 27.05/4.58 | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | (154) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | REDUCE: (110), (154) imply: % 27.05/4.58 | | | | | | | | | | (155) $false % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | CLOSE: (155) is inconsistent. % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | (156) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.58 | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.58 | | | | | | | | | | all_38_2) = v3 & apart_point_and_line(all_38_4, % 27.05/4.58 | | | | | | | | | | all_38_2) = v2 & distinct_lines(all_38_2, % 27.05/4.58 | | | | | | | | | | all_38_2) = v1 & distinct_points(all_38_4, % 27.05/4.58 | | | | | | | | | | all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 27.05/4.58 | | | | | | | | | | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_155_0, % 27.05/4.58 | | | | | | | | | | all_155_1, all_155_2, all_155_3 gives: % 27.05/4.58 | | | | | | | | | | (157) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.58 | | | | | | | | | | all_155_0 & apart_point_and_line(all_38_4, % 27.05/4.58 | | | | | | | | | | all_38_2) = all_155_1 & distinct_lines(all_38_2, % 27.05/4.58 | | | | | | | | | | all_38_2) = all_155_2 & distinct_points(all_38_4, % 27.05/4.58 | | | | | | | | | | all_38_4) = all_155_3 & ( ~ (all_155_2 = 0) | ~ % 27.05/4.58 | | | | | | | | | | (all_155_3 = 0) | all_155_0 = 0 | all_155_1 = 0) % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | ALPHA: (157) implies: % 27.05/4.58 | | | | | | | | | | (158) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.58 | | | | | | | | | | all_155_1 % 27.05/4.58 | | | | | | | | | | (159) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.58 | | | | | | | | | | all_155_0 % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | BETA: splitting (125) gives: % 27.05/4.58 | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | (160) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | REDUCE: (110), (160) imply: % 27.05/4.58 | | | | | | | | | | | (161) $false % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | CLOSE: (161) is inconsistent. % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | (162) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.58 | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 27.05/4.58 | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.58 | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.58 | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | BETA: splitting (116) gives: % 27.05/4.58 | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | (163) all_49_0 = 0 % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | REDUCE: (111), (163) imply: % 27.05/4.58 | | | | | | | | | | | | (164) $false % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | (165) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.58 | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.58 | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 27.05/4.58 | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.58 | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | BETA: splitting (114) gives: % 27.05/4.58 | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | (166) all_49_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | REDUCE: (111), (166) imply: % 27.05/4.58 | | | | | | | | | | | | | (167) $false % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | (168) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.58 | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.58 | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 27.05/4.58 | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.58 | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | BETA: splitting (123) gives: % 27.05/4.58 | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | (169) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | REDUCE: (110), (169) imply: % 27.05/4.58 | | | | | | | | | | | | | | (170) $false % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | (171) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.58 | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 27.05/4.58 | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.58 | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.58 | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 27.05/4.58 | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | (172) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | REDUCE: (110), (172) imply: % 27.05/4.58 | | | | | | | | | | | | | | | (173) $false % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | (174) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.58 | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v3 & % 27.05/4.58 | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.58 | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.58 | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 27.05/4.58 | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | (175) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | REDUCE: (110), (175) imply: % 27.05/4.58 | | | | | | | | | | | | | | | | (176) $false % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | (177) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_5, % 27.05/4.58 | | | | | | | | | | | | | | | | all_38_1) = v2 & % 27.05/4.58 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 27.05/4.58 | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 27.05/4.58 | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | (178) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | REDUCE: (110), (178) imply: % 27.05/4.58 | | | | | | | | | | | | | | | | | (179) $false % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | (180) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.58 | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_5, % 27.05/4.58 | | | | | | | | | | | | | | | | | all_38_1) = v1 & % 27.05/4.58 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 27.05/4.58 | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 27.05/4.58 | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 27.05/4.58 | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.58 | | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | | (181) all_53_0 = 0 % 27.05/4.58 | | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | | REDUCE: (110), (181) imply: % 27.05/4.58 | | | | | | | | | | | | | | | | | | (182) $false % 27.05/4.58 | | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 27.05/4.58 | | | | | | | | | | | | | | | | | | % 27.05/4.58 | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.58 | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | (183) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.59 | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | (184) all_49_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | REDUCE: (111), (184) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | (185) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | (186) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.59 | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | (187) all_49_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (187) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | (188) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | (189) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | (190) all_53_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (190) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | (191) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | (192) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | (convergent_lines(all_38_2, all_38_1) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (193) all_49_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (193) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (194) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (195) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (195) with fresh symbols all_204_0, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_204_1, all_204_2, all_204_3 gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (196) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_204_1 & apart_point_and_line(all_38_5, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_204_0 & distinct_lines(all_38_2, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_204_2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = all_204_3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_204_2 = 0) | ~ (all_204_3 = 0) | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_204_0 = 0 | all_204_1 = 0) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (197) apart_point_and_line(all_38_5, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_204_0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | (198) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | all_204_1 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (199) all_38_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (199) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (200) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (201) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (201) with fresh symbols all_210_0, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_210_1, all_210_2, all_210_3 gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (202) apart_point_and_line(all_38_4, all_38_1) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_210_1 & apart_point_and_line(all_38_4, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_210_0 & distinct_lines(all_38_1, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_210_2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_210_3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_210_2 = 0) | ~ (all_210_3 = 0) | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_210_0 = 0 | all_210_1 = 0) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | (203) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_210_0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (204) all_38_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (204) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (205) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (206) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_215_0, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_215_1, all_215_2, all_215_3 gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (207) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_215_0 & apart_point_and_line(all_38_5, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_215_1 & distinct_lines(all_38_1, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_215_2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = all_215_3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_215_2 = 0) | ~ (all_215_3 = 0) | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_215_0 = 0 | all_215_1 = 0) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (208) distinct_points(all_38_5, all_38_4) = all_215_3 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (209) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_215_1 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (210) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_215_0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_38_0 = 0 % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (211) imply: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | (212) $false % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | (213) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (213) with fresh symbols all_220_0, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_1, all_220_2, all_220_3 gives: % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | (214) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_0 & apart_point_and_line(all_38_5, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_220_1 & distinct_lines(all_38_2, % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_220_2 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = all_220_3 & % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_220_2 = 0) | ~ (all_220_3 = 0) | % 27.05/4.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_0 = 0 | all_220_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (215) distinct_points(all_38_5, all_38_4) = all_220_3 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (216) distinct_lines(all_38_2, all_38_1) = all_220_2 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (217) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_1 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (218) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_220_2 = 0) | ~ (all_220_3 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_220_0 = 0 | all_220_1 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (220) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (222) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (222) with fresh symbols all_225_0, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_225_1, all_225_2, all_225_3 gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (223) apart_point_and_line(all_38_4, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_225_1 & apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_225_0 & distinct_lines(all_38_2, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_225_2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_225_3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_225_2 = 0) | ~ (all_225_3 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_225_0 = 0 | all_225_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (224) distinct_lines(all_38_2, all_38_1) = all_225_2 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (225) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_225_0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (226) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (228) with fresh symbols all_230_0, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_230_1, all_230_2, all_230_3 gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) apart_point_and_line(all_38_4, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_230_0 & apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_230_1 & distinct_lines(all_38_2, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_230_2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_230_3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_230_2 = 0) | ~ (all_230_3 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_230_0 = 0 | all_230_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) distinct_lines(all_38_2, all_38_1) = all_230_2 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_230_1 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (232) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_235_0, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_235_1, all_235_2 gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_235_0 & apart_point_and_line(all_38_5, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_235_1 & distinct_lines(all_38_2, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_235_2 & ( ~ (all_235_2 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_235_0 = 0 | all_235_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) distinct_lines(all_38_2, all_38_1) = all_235_2 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) apart_point_and_line(all_38_5, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_235_1 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_235_0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (239) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (241) with fresh symbols all_240_0, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1, all_240_2 gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1 & apart_point_and_line(all_38_5, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_240_0 & distinct_lines(all_38_1, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_240_2 & ( ~ (all_240_2 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_0 = 0 | all_240_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) apart_point_and_line(all_38_5, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (245) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_245_0, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_245_1, all_245_2, all_245_3 gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) apart_point_and_line(all_38_4, all_38_1) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_245_0 & apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_245_1 & distinct_lines(all_38_1, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_245_2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_245_3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_245_2 = 0) | ~ (all_245_3 = 0) | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_245_0 = 0 | all_245_1 = 0) % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_245_1 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_38_0 = 0 % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (250) imply: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) $false % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 27.05/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (252) with fresh symbols all_250_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_1, all_250_2, all_250_3 gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_1 & apart_point_and_line(all_38_5, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_250_0 & distinct_lines(all_38_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_250_2 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = all_250_3 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_250_2 = 0) | ~ (all_250_3 = 0) | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_0 = 0 | all_250_1 = 0) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_38_0 = 0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (256) imply: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) $false % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent. % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_260_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_260_1, all_260_2, all_260_3 gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_260_1 & apart_point_and_line(all_38_5, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_260_0 & distinct_lines(all_38_2, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_260_2 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = all_260_3 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_260_2 = 0) | ~ (all_260_3 = 0) | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_260_0 = 0 | all_260_1 = 0) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) distinct_lines(all_38_2, all_38_1) = all_260_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) apart_point_and_line(all_38_5, all_38_1) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_260_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) apart_point_and_line(all_38_4, all_38_2) = % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_260_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_38_0 = 0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (263) imply: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) $false % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) ? [v0: any] : ? [v1: any] : % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (convergent_lines(all_38_2, all_38_1) = v1 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_265_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_265_1 gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) convergent_lines(all_38_2, all_38_1) = all_265_0 & % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = all_265_1 & ( % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_265_1 = 0) | all_265_0 = 0) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) distinct_lines(all_38_2, all_38_1) = all_265_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_220_3, all_38_4, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (25), (215) gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_220_3 = 0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_215_3, all_220_3, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_4, all_38_5, simplifying with (208), (215) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_220_3 = all_215_3 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_230_2, all_235_2, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (230), (236) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_235_2 = all_230_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_230_2, all_260_2, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (230), (260) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_260_2 = all_230_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_220_2, all_260_2, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (216), (260) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_260_2 = all_220_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_235_2, all_265_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (236), (267) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_265_1 = all_235_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_225_2, all_265_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (224), (267) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_265_1 = all_225_2 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_150_1, all_150_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (152), (153) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_150_0 = all_150_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_49_0, all_204_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (105), (197) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_204_0 = all_49_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_150_1, all_204_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (152), (197) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_204_0 = all_150_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_150_0, all_235_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (153), (237) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_235_1 = all_150_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_140_0, all_235_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (146), (237) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_235_1 = all_140_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_150_0, all_240_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (153), (243) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_240_0 = all_150_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_140_1, all_240_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (145), (243) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_240_0 = all_140_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_215_1, all_240_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (209), (244) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_240_1 = all_215_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_240_1, all_250_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (244), (254) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_250_0 = all_240_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_235_0, all_250_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (238), (254) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_250_0 = all_235_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_55_0, all_260_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (54), (261) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_260_0 = all_55_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_240_1, all_260_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (244), (261) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_260_0 = all_240_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_220_1, all_260_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (217), (261) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_260_0 = all_220_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_53_0, all_135_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (51), (140) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_135_0 = all_53_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_135_0, all_155_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (140), (158) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_155_1 = all_135_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_155_1, all_155_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (158), (159) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_155_0 = all_155_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_155_0, all_204_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (159), (198) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_204_1 = all_155_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_204_1, all_210_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (198), (203) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_210_0 = all_204_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_210_0, all_215_0, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (203), (210) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_215_0 = all_210_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_225_0, all_230_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (225), (231) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_230_1 = all_225_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_225_0, all_245_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (225), (249) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_245_1 = all_225_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_220_0, all_245_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (218), (249) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_245_1 = all_220_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_215_0, all_245_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (210), (249) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_245_1 = all_215_0 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_230_1, all_250_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (231), (255) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_250_1 = all_230_1 % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_250_1, all_260_1, % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (255), (262) % 27.05/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_260_1 = all_250_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_135_1, all_260_1, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (139), (262) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_260_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_235_2 = all_225_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_235_2 = all_225_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (287) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_240_1 = all_220_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (303) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_240_1 = all_220_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (287) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_220_1 = all_55_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (300) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_250_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_250_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (272) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_230_2 = all_220_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_230_2 = all_220_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (284) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_240_1 = all_235_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (310) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_240_1 = all_235_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (307) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_230_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_230_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (296) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_225_0 = all_220_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_225_0 = all_220_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (297) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_220_0 = all_215_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_150_0 = all_140_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (317) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_150_0 = all_140_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (311) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_235_0 = all_220_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (311) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_235_0 = all_215_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (319), (320) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_220_1 = all_215_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_220_1 = all_215_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (279) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_150_0 = all_140_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_150_0 = all_140_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (302) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_230_2 = all_225_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_230_2 = all_225_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (313) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_225_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (327) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_225_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (326) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_225_2 = all_220_2 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (328) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_220_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_220_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (331) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_215_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_215_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (322) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_215_1 = all_55_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (269) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_215_3 = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (293), (333) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_210_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_210_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (337) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_204_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_204_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (277) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_150_1 = all_49_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (340) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_150_1 = all_49_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (339) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_155_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (342) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_155_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (343) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_155_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_155_1 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (345) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_135_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (346) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_135_0 = all_135_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (324) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_150_1 = all_140_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_150_1 = all_140_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (324) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_140_0 = all_140_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (349) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_140_0 = all_49_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (351) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_140_0 = all_49_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (352) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_140_1 = all_49_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (347) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_135_1 = all_53_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (354) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_220_0 = all_53_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_5, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_55_1, simplifying with (21), (23), % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (134) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_55_1 = 0 | distinct_points(all_38_3, all_38_3) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_38_3, all_38_2, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_220_2, simplifying with (23), (24), % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (106), (216) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_220_2 = 0 | apart_point_and_line(all_38_3, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_55_0 = 0) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) ~ (all_220_2 = 0) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (357) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) apart_point_and_line(all_38_3, all_38_1) = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_57_0 = 0) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_57_0 = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (362) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) $false % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (363) is inconsistent. % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_3, all_38_1) = v2 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (364) with fresh symbols all_417_0, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_417_1, all_417_2, all_417_3 gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) apart_point_and_line(all_38_3, all_38_1) = % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_417_0 & apart_point_and_line(all_38_3, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_417_1 & distinct_lines(all_38_1, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_417_2 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_3) = all_417_3 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_417_2 = 0) | ~ (all_417_3 = 0) | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_417_0 = 0 | all_417_1 = 0) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) apart_point_and_line(all_38_3, all_38_1) = % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_417_1 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) apart_point_and_line(all_38_3, all_38_1) = % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_417_0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_57_0 = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (368) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) $false % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent. % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_1) = v3 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_38_0 = 0 % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (371) imply: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) $false % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (373) with fresh symbols all_441_0, % 27.05/4.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_441_1, all_441_2, all_441_3 gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) apart_point_and_line(all_38_3, all_38_1) = % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_441_0 & apart_point_and_line(all_38_4, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_441_1 & distinct_lines(all_38_1, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_441_2 & % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = all_441_3 & % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_441_2 = 0) | ~ (all_441_3 = 0) | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_441_0 = 0 | all_441_1 = 0) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) apart_point_and_line(all_38_3, all_38_1) = % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_441_0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_57_0, all_441_0, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (58), (375) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_441_0 = all_57_0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_417_0, all_441_0, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (367), (375) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_441_0 = all_417_0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_417_1, all_441_0, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (366), (375) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_441_0 = all_417_1 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_441_0, all_38_1, % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (360), (375) gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_441_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (376), (377) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_417_0 = all_57_0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (377), (378) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_417_0 = all_417_1 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (377), (379) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_417_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (382) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_417_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (381) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_417_1 = all_57_0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (384) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_57_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (385) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_57_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (386) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (387) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) ~ (all_57_1 = 0) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (388) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) ~ (all_55_1 = 0) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (356), (389), (apart1) are inconsistent by % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_220_2 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (390) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (391) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_220_3 = 0) | all_220_0 = 0 | all_220_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_220_3 = 0) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (393) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (394) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_220_0 = 0 | all_220_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_220_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (355), (396) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_53_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_53_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (398) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_220_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (400) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_55_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_55_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (402) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_55_1 = 0) % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (356), (404), (apart1) are inconsistent by % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_140_0 = 0 | all_140_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (405) gives: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_140_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (406) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_49_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (407) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_49_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (408) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (409) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_140_1 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (410) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_49_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (411) implies: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_49_0 = 0 % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (412) imply: % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) $false % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent. % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | | % 27.05/4.63 | | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | | % 27.05/4.63 | | | | | | | | | End of split % 27.05/4.63 | | | | | | | | | % 27.05/4.63 | | | | | | | | End of split % 27.05/4.63 | | | | | | | | % 27.05/4.63 | | | | | | | End of split % 27.05/4.63 | | | | | | | % 27.05/4.63 | | | | | | End of split % 27.05/4.63 | | | | | | % 27.05/4.63 | | | | | Case 2: % 27.05/4.63 | | | | | | % 27.05/4.63 | | | | | | (414) all_49_0 = 0 % 27.05/4.63 | | | | | | % 27.05/4.63 | | | | | | REDUCE: (111), (414) imply: % 27.05/4.63 | | | | | | (415) $false % 27.05/4.63 | | | | | | % 27.05/4.63 | | | | | | CLOSE: (415) is inconsistent. % 27.05/4.63 | | | | | | % 27.05/4.63 | | | | | End of split % 27.05/4.63 | | | | | % 27.05/4.63 | | | | End of split % 27.05/4.63 | | | | % 27.05/4.63 | | | Case 2: % 27.05/4.63 | | | | % 27.05/4.63 | | | | (416) ~ (all_51_1 = 0) % 27.05/4.63 | | | | % 27.05/4.63 | | | | REDUCE: (103), (416) imply: % 27.05/4.63 | | | | (417) $false % 27.05/4.63 | | | | % 27.05/4.63 | | | | CLOSE: (417) is inconsistent. % 27.05/4.63 | | | | % 27.05/4.63 | | | End of split % 27.05/4.63 | | | % 27.05/4.63 | | End of split % 27.05/4.63 | | % 27.05/4.63 | End of split % 27.05/4.63 | % 27.05/4.63 End of proof % 27.05/4.63 % 27.05/4.63 Sub-proof #1 shows that the following formulas are inconsistent: % 27.05/4.63 ---------------------------------------------------------------- % 27.05/4.63 (1) all_55_1 = 0 | distinct_points(all_38_3, all_38_3) = 0 % 27.05/4.63 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 27.05/4.63 (3) $i(all_38_3) % 27.05/4.63 (4) ~ (all_55_1 = 0) % 27.05/4.63 % 27.05/4.63 Begin of proof % 27.05/4.63 | % 27.05/4.63 | BETA: splitting (1) gives: % 27.05/4.63 | % 27.05/4.63 | Case 1: % 27.05/4.63 | | % 27.05/4.63 | | (5) distinct_points(all_38_3, all_38_3) = 0 % 27.05/4.63 | | % 27.05/4.63 | | GROUND_INST: instantiating (2) with all_38_3, simplifying with (3), (5) % 27.05/4.63 | | gives: % 27.05/4.63 | | (6) $false % 27.05/4.63 | | % 27.05/4.63 | | CLOSE: (6) is inconsistent. % 27.05/4.63 | | % 27.05/4.63 | Case 2: % 27.05/4.63 | | % 27.05/4.63 | | (7) all_55_1 = 0 % 27.05/4.63 | | % 27.05/4.63 | | REDUCE: (4), (7) imply: % 27.05/4.63 | | (8) $false % 27.05/4.63 | | % 27.05/4.63 | | CLOSE: (8) is inconsistent. % 27.05/4.63 | | % 27.05/4.63 | End of split % 27.05/4.63 | % 27.05/4.63 End of proof % 27.05/4.63 % SZS output end Proof for theBenchmark % 27.05/4.64 % 27.05/4.64 4025ms %------------------------------------------------------------------------------