%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO186+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 : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:00 EDT 2023 % Result : Theorem 17.53s 3.25s % Output : Proof 31.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GEO186+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n026.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 19:15:35 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.74/1.27 Prover 4: Preprocessing ... % 3.74/1.27 Prover 1: Preprocessing ... % 4.01/1.31 Prover 5: Preprocessing ... % 4.01/1.31 Prover 2: Preprocessing ... % 4.01/1.32 Prover 3: Preprocessing ... % 4.01/1.32 Prover 0: Preprocessing ... % 4.01/1.32 Prover 6: Preprocessing ... % 6.91/1.74 Prover 2: Proving ... % 7.15/1.76 Prover 5: Proving ... % 7.15/1.80 Prover 6: Constructing countermodel ... % 7.15/1.82 Prover 3: Constructing countermodel ... % 7.76/1.84 Prover 1: Constructing countermodel ... % 8.10/1.94 Prover 3: gave up % 8.10/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.71/2.01 Prover 7: Preprocessing ... % 8.71/2.01 Prover 6: gave up % 8.71/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.71/2.11 Prover 8: Preprocessing ... % 8.71/2.13 Prover 7: Warning: ignoring some quantifiers % 8.71/2.13 Prover 1: gave up % 8.71/2.15 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.71/2.17 Prover 7: Constructing countermodel ... % 9.95/2.18 Prover 9: Preprocessing ... % 9.95/2.19 Prover 4: Constructing countermodel ... % 10.28/2.27 Prover 0: Proving ... % 10.90/2.29 Prover 8: Warning: ignoring some quantifiers % 10.90/2.30 Prover 8: Constructing countermodel ... % 11.90/2.50 Prover 8: gave up % 11.90/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.59/2.52 Prover 9: Constructing countermodel ... % 12.59/2.55 Prover 10: Preprocessing ... % 13.24/2.59 Prover 10: Warning: ignoring some quantifiers % 13.24/2.60 Prover 10: Constructing countermodel ... % 13.24/2.64 Prover 7: gave up % 13.24/2.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.92/2.68 Prover 11: Preprocessing ... % 14.01/2.78 Prover 10: gave up % 14.01/2.80 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 14.01/2.83 Prover 12: Preprocessing ... % 16.32/3.02 Prover 12: Proving ... % 16.40/3.03 Prover 11: Constructing countermodel ... % 17.53/3.25 Prover 0: proved (2579ms) % 17.53/3.25 % 17.53/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.53/3.25 % 17.53/3.25 Prover 5: stopped % 17.53/3.25 Prover 12: stopped % 17.53/3.25 Prover 9: stopped % 17.53/3.25 Prover 2: stopped % 17.53/3.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.53/3.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.53/3.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 18.29/3.30 Prover 13: Preprocessing ... % 18.29/3.31 Prover 16: Preprocessing ... % 18.51/3.32 Prover 19: Preprocessing ... % 18.51/3.35 Prover 13: Warning: ignoring some quantifiers % 18.51/3.36 Prover 13: Constructing countermodel ... % 18.51/3.37 Prover 16: Warning: ignoring some quantifiers % 18.51/3.38 Prover 16: Constructing countermodel ... % 19.22/3.46 Prover 19: Warning: ignoring some quantifiers % 19.22/3.47 Prover 19: Constructing countermodel ... % 19.96/3.55 Prover 13: gave up % 20.48/3.64 Prover 19: gave up % 22.04/3.84 Prover 16: gave up % 29.26/5.16 Prover 4: Found proof (size 450) % 29.26/5.16 Prover 4: proved (4495ms) % 29.26/5.17 Prover 11: stopped % 29.26/5.17 % 29.26/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 29.26/5.17 % 29.37/5.22 % SZS output start Proof for theBenchmark % 29.37/5.22 Assumptions after simplification: % 29.37/5.22 --------------------------------- % 29.37/5.22 % 29.37/5.22 (a4) % 29.56/5.25 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 29.56/5.25 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.25 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 29.56/5.25 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.25 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.56/5.25 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 29.56/5.25 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 29.56/5.25 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.25 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 29.56/5.25 % 29.56/5.25 (apart3) % 29.56/5.25 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 29.56/5.25 % 29.56/5.25 (ax1) % 29.56/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_points(v0, v1) % 29.56/5.26 = v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v1) = 0) & ! [v0: $i] % 29.56/5.26 : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | % 29.56/5.26 ~ $i(v1) | ~ $i(v0) | equal_points(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] % 29.56/5.26 : ( ~ (equal_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 29.56/5.26 (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( % 29.56/5.26 ~ (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 29.56/5.26 (v2 = 0) & equal_points(v0, v1) = v2)) % 29.56/5.26 % 29.56/5.26 (ceq3) % 29.56/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 29.56/5.26 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 29.56/5.26 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 29.56/5.26 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.56/5.26 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 29.56/5.26 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.26 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 29.56/5.26 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 29.56/5.26 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.26 convergent_lines(v0, v2) = 0) % 29.56/5.26 % 29.56/5.26 (ci1) % 29.56/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 29.56/5.26 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.26 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 29.56/5.26 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.56/5.26 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 29.56/5.26 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 29.56/5.27 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 29.56/5.27 % 29.56/5.27 (ci2) % 29.56/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 29.56/5.27 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.27 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 29.56/5.27 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.56/5.27 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 29.56/5.27 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 29.56/5.27 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 29.56/5.27 % 29.56/5.27 (ci3) % 29.56/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 29.56/5.27 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.27 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 29.56/5.27 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.56/5.27 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 29.56/5.27 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 29.56/5.27 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 29.56/5.27 % 29.56/5.27 (ci4) % 29.56/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 29.56/5.27 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.27 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 29.56/5.27 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.56/5.28 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 29.56/5.28 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 29.56/5.28 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 29.56/5.28 % 29.56/5.28 (con) % 29.56/5.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 29.56/5.28 int] : ( ~ (v5 = 0) & incident_point_and_line(v0, v3) = 0 & % 29.56/5.28 incident_point_and_line(v0, v2) = 0 & equal_points(v0, v4) = v5 & % 29.56/5.28 intersection_point(v2, v3) = v4 & convergent_lines(v2, v3) = 0 & % 29.56/5.28 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 29.56/5.28 % 29.56/5.28 (con1) % 29.56/5.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 29.56/5.28 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 29.56/5.28 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 29.56/5.28 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 29.56/5.28 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 29.56/5.28 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 29.56/5.28 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 29.56/5.28 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 29.56/5.28 0))) % 29.56/5.28 % 29.56/5.28 (cotno1) % 29.56/5.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.30 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 29.56/5.30 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 29.56/5.30 any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & % 29.56/5.30 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & % 29.56/5.30 convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 % 29.56/5.30 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.56/5.30 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 29.56/5.30 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 29.56/5.30 (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & % 29.56/5.30 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = % 29.56/5.30 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: % 29.56/5.30 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.30 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 29.56/5.30 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 29.56/5.30 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 29.56/5.30 v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 % 29.56/5.30 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & % 29.56/5.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.30 (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ~ % 29.56/5.30 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 29.56/5.30 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 29.56/5.30 v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = % 29.56/5.30 v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.30 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 29.56/5.30 (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 29.56/5.30 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 29.56/5.30 : ? [v7: any] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) % 29.56/5.30 = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ % 29.56/5.30 (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! % 29.56/5.30 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | % 29.56/5.30 ~ (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.30 ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & % 29.56/5.30 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = % 29.56/5.30 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.30 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 29.56/5.30 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & % 29.56/5.30 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = % 29.56/5.30 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.30 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 29.56/5.30 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & % 29.56/5.30 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = % 29.56/5.30 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.30 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 29.56/5.30 ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & % 29.56/5.30 convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = % 29.56/5.30 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.30 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | % 29.56/5.30 ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 29.56/5.30 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = % 29.56/5.30 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.30 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 29.56/5.30 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 29.56/5.30 unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 % 29.56/5.30 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! % 29.56/5.30 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | % 29.56/5.30 ~ (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.30 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.30 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 29.56/5.30 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 % 29.56/5.30 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 29.56/5.30 % 29.56/5.30 (cu1) % 29.56/5.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 29.56/5.31 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 29.56/5.31 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 29.56/5.31 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 29.56/5.31 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 29.56/5.31 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 29.56/5.31 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 29.56/5.31 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 29.56/5.31 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 29.56/5.31 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 29.56/5.31 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 29.56/5.31 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 29.56/5.31 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.56/5.31 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 29.56/5.31 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 29.56/5.31 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 29.56/5.31 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 29.56/5.31 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 29.56/5.31 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 29.56/5.31 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 29.56/5.31 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 29.56/5.31 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 29.56/5.31 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 29.56/5.31 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 29.56/5.31 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 29.56/5.31 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 29.56/5.31 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 29.56/5.31 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 29.56/5.31 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 29.56/5.31 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 29.56/5.31 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 29.56/5.31 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 29.56/5.31 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 29.56/5.31 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 29.56/5.31 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 29.56/5.31 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 29.56/5.31 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 29.56/5.31 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 29.56/5.31 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 29.56/5.31 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 29.56/5.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 29.56/5.31 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 29.56/5.31 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 29.56/5.31 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 29.56/5.31 % 29.56/5.31 (cup1) % 29.56/5.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 29.56/5.32 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 29.56/5.32 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.32 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 & % 29.56/5.32 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 29.56/5.32 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 29.56/5.32 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 29.56/5.32 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 29.56/5.32 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = % 29.56/5.32 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 29.56/5.32 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 29.56/5.32 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 29.56/5.32 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 & % 29.56/5.32 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 29.56/5.32 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 29.56/5.32 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 29.56/5.32 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 & % 29.56/5.32 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! % 29.56/5.32 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 29.56/5.32 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 29.56/5.32 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 & % 29.56/5.32 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 29.56/5.32 % 29.56/5.32 (int1) % 29.56/5.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 29.56/5.32 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 29.56/5.32 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & % 29.56/5.32 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 29.56/5.32 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = % 29.56/5.32 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 29.56/5.32 ? [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & % 29.56/5.32 intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 % 29.56/5.32 = 0))) % 29.56/5.32 % 29.56/5.32 (oac1) % 29.56/5.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.33 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 29.56/5.33 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 29.56/5.33 any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = v6 & % 29.56/5.33 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & % 29.56/5.33 convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 % 29.56/5.33 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.56/5.33 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 29.56/5.33 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 29.56/5.33 (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & % 29.56/5.33 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = % 29.56/5.33 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: % 29.56/5.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.33 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 29.56/5.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 29.56/5.33 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 29.56/5.33 v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 % 29.56/5.33 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & % 29.56/5.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 29.56/5.33 (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ~ % 29.56/5.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 29.56/5.33 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 29.56/5.33 v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = % 29.56/5.33 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 29.56/5.33 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 29.56/5.33 (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 29.56/5.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 29.56/5.33 : ? [v7: any] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) % 29.56/5.33 = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ % 29.56/5.33 (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 29.56/5.33 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) % 29.56/5.33 | ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & % 29.56/5.33 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 29.56/5.33 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.33 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 29.56/5.33 ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & % 29.56/5.33 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 29.56/5.33 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.33 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 29.56/5.33 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & % 29.56/5.33 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 29.56/5.33 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.33 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 29.56/5.33 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 29.56/5.33 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 29.56/5.33 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.33 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 29.56/5.33 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 29.56/5.33 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 29.56/5.33 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 29.56/5.33 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 29.56/5.33 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 29.56/5.33 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 29.56/5.33 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 % 29.56/5.33 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 29.56/5.33 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | % 29.56/5.33 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.33 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 29.56/5.33 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 29.56/5.33 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 % 29.56/5.33 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.33 % 29.56/5.33 (function-axioms) % 29.56/5.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.56/5.34 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 29.56/5.34 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.56/5.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.34 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 29.56/5.34 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 29.56/5.34 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 29.56/5.34 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.56/5.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.34 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 29.56/5.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/5.34 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 29.56/5.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.34 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 29.56/5.34 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 29.56/5.34 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 29.56/5.34 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.56/5.34 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 29.56/5.34 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.56/5.34 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 29.56/5.34 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.56/5.34 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 29.56/5.34 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.56/5.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.34 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 29.56/5.34 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 29.56/5.34 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.56/5.34 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.56/5.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.34 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 29.56/5.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/5.34 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 29.56/5.34 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 29.56/5.34 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 29.56/5.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 29.56/5.34 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 29.56/5.34 % 29.56/5.34 Further assumptions not needed in the proof: % 29.56/5.34 -------------------------------------------- % 29.56/5.34 a3, a5, apart1, apart2, apart4, apart5, ax2, ax6, ceq1, ceq2, coipo1, couo1, % 29.56/5.34 cp1, cp2, occu1, ooc1, ooc2, orth1, ouo1, p1, par1 % 29.56/5.34 % 29.56/5.34 Those formulas are unsatisfiable: % 29.56/5.34 --------------------------------- % 29.56/5.34 % 29.56/5.34 Begin of proof % 29.56/5.34 | % 29.56/5.34 | ALPHA: (ci1) implies: % 29.56/5.34 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 29.56/5.34 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 29.56/5.34 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 29.56/5.34 | $i(v2))) % 29.56/5.34 | % 29.56/5.34 | ALPHA: (ci2) implies: % 29.56/5.34 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 29.56/5.34 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 29.56/5.34 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 29.56/5.34 | $i(v2))) % 29.56/5.34 | % 29.56/5.34 | ALPHA: (ci3) implies: % 29.56/5.35 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 29.56/5.35 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 29.56/5.35 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 29.56/5.35 | & $i(v2))) % 29.56/5.35 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 29.56/5.35 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.35 | (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & % 29.56/5.35 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 29.56/5.35 | % 29.56/5.35 | ALPHA: (ci4) implies: % 29.56/5.35 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 29.56/5.35 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 29.56/5.35 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 29.56/5.35 | & $i(v2))) % 29.56/5.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 29.56/5.35 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 29.56/5.35 | (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & % 29.56/5.35 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 29.56/5.35 | % 29.56/5.35 | ALPHA: (cu1) implies: % 29.56/5.35 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 29.56/5.35 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 29.56/5.35 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 29.56/5.35 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/5.35 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 29.56/5.35 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 29.56/5.35 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 29.56/5.35 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 29.56/5.35 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 29.56/5.35 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 29.56/5.35 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 29.56/5.35 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 29.56/5.35 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 29.56/5.35 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 29.56/5.35 | | v8 = 0))) % 29.56/5.35 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 29.56/5.35 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 29.56/5.35 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 29.56/5.35 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 29.56/5.35 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 29.56/5.35 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 29.56/5.35 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 29.56/5.35 | | v8 = 0))) % 29.56/5.35 | % 29.56/5.35 | ALPHA: (ceq3) implies: % 29.56/5.35 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 29.56/5.35 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) % 29.56/5.35 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, v2) = 0) % 29.56/5.35 | % 29.56/5.35 | ALPHA: (cup1) implies: % 29.56/5.36 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 29.56/5.36 | : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 29.56/5.36 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 29.56/5.36 | $i(v0) | ? [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = % 29.56/5.36 | v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 29.56/5.36 | % 29.56/5.36 | ALPHA: (oac1) implies: % 29.56/5.36 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 29.56/5.36 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) % 29.56/5.36 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 29.56/5.36 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 & % 29.56/5.36 | unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 % 29.56/5.36 | & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) % 29.56/5.36 | | (v5 = 0 & v3 = 0)))) % 29.56/5.36 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 29.56/5.36 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = % 29.56/5.36 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 29.56/5.36 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = % 29.56/5.36 | v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = % 29.56/5.36 | v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = % 29.56/5.36 | 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.36 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.36 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 29.56/5.36 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 29.56/5.36 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 29.56/5.36 | v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) % 29.56/5.36 | = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) % 29.56/5.36 | | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 29.56/5.36 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.36 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) % 29.56/5.36 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 29.56/5.36 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 29.56/5.36 | v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = % 29.56/5.36 | v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 29.56/5.36 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 29.56/5.36 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.36 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) % 29.56/5.36 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 29.56/5.36 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, v2) = % 29.56/5.36 | v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = % 29.56/5.36 | v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 29.56/5.36 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 29.56/5.37 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.37 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, % 29.56/5.37 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 29.56/5.37 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, % 29.56/5.37 | v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, % 29.56/5.37 | v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 % 29.56/5.37 | = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 29.56/5.37 | % 29.56/5.37 | ALPHA: (cotno1) implies: % 29.56/5.37 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 29.56/5.37 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 29.56/5.37 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 29.56/5.37 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 & % 29.56/5.37 | unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 % 29.56/5.37 | & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) % 29.56/5.37 | | (v5 = 0 & v4 = 0)))) % 29.56/5.37 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.37 | : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = % 29.56/5.37 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 29.56/5.37 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 29.56/5.37 | v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) % 29.56/5.37 | = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) % 29.56/5.37 | | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.37 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.37 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) % 29.56/5.37 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 29.56/5.37 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 29.56/5.37 | v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = % 29.56/5.37 | v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | % 29.56/5.37 | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.37 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 29.56/5.37 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, % 29.56/5.37 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 29.56/5.37 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, % 29.56/5.37 | v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, % 29.56/5.37 | v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 % 29.56/5.37 | = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) % 29.56/5.37 | % 29.56/5.37 | ALPHA: (con1) implies: % 29.56/5.37 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 29.56/5.37 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 29.56/5.37 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 29.56/5.37 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 29.56/5.37 | | v5 = 0))) % 29.56/5.37 | % 29.56/5.37 | ALPHA: (int1) implies: % 29.56/5.38 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 29.56/5.38 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 29.56/5.38 | [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & % 29.56/5.38 | intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = % 29.56/5.38 | 0) | v5 = 0))) % 29.56/5.38 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 29.56/5.38 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 29.56/5.38 | : ? [v5: any] : ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & % 29.56/5.38 | line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ % 29.56/5.38 | (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 29.56/5.38 | % 29.56/5.38 | ALPHA: (ax1) implies: % 29.56/5.38 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 29.56/5.38 | (equal_points(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 29.56/5.38 | distinct_points(v0, v1) = 0) % 29.56/5.38 | % 29.56/5.38 | ALPHA: (a4) implies: % 29.56/5.38 | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) % 29.56/5.38 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 29.56/5.38 | apart_point_and_line(v0, v1) = v2)) % 29.56/5.38 | % 29.56/5.38 | ALPHA: (function-axioms) implies: % 29.56/5.38 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.56/5.38 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 29.56/5.38 | (distinct_lines(v3, v2) = v0)) % 29.56/5.38 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.56/5.38 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.56/5.38 | (convergent_lines(v3, v2) = v0)) % 29.56/5.38 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.56/5.38 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 29.56/5.38 | (apart_point_and_line(v3, v2) = v0)) % 29.56/5.38 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.38 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 29.56/5.38 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.56/5.38 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 29.56/5.38 | v0)) % 29.56/5.38 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.56/5.38 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 29.56/5.38 | (unorthogonal_lines(v3, v2) = v0)) % 29.56/5.38 | % 29.56/5.38 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 29.56/5.38 | all_38_3, all_38_4, all_38_5 gives: % 29.56/5.38 | (33) ~ (all_38_0 = 0) & incident_point_and_line(all_38_5, all_38_2) = 0 & % 29.56/5.38 | incident_point_and_line(all_38_5, all_38_3) = 0 & % 29.56/5.38 | equal_points(all_38_5, all_38_1) = all_38_0 & % 29.56/5.38 | intersection_point(all_38_3, all_38_2) = all_38_1 & % 29.56/5.38 | convergent_lines(all_38_3, all_38_2) = 0 & distinct_points(all_38_5, % 29.56/5.38 | all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & % 29.56/5.38 | $i(all_38_4) & $i(all_38_5) % 29.56/5.38 | % 29.56/5.38 | ALPHA: (33) implies: % 29.56/5.38 | (34) ~ (all_38_0 = 0) % 29.56/5.38 | (35) $i(all_38_5) % 29.56/5.38 | (36) $i(all_38_4) % 29.56/5.38 | (37) $i(all_38_3) % 29.56/5.38 | (38) $i(all_38_2) % 29.56/5.38 | (39) $i(all_38_1) % 29.56/5.38 | (40) distinct_points(all_38_5, all_38_4) = 0 % 29.56/5.39 | (41) convergent_lines(all_38_3, all_38_2) = 0 % 29.56/5.39 | (42) intersection_point(all_38_3, all_38_2) = all_38_1 % 29.56/5.39 | (43) equal_points(all_38_5, all_38_1) = all_38_0 % 29.56/5.39 | (44) incident_point_and_line(all_38_5, all_38_3) = 0 % 29.56/5.39 | (45) incident_point_and_line(all_38_5, all_38_2) = 0 % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (22) with all_38_5, all_38_4, simplifying with % 29.56/5.39 | (35), (36), (40) gives: % 29.56/5.39 | (46) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 29.56/5.39 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(v2) = v3 & % 29.56/5.39 | line_connecting(all_38_5, all_38_4) = v2 & $i(v2) & ( ~ (v1 = 0) | % 29.56/5.39 | ~ (v0 = 0) | v3 = 0)) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, simplifying with (35), % 29.56/5.39 | (36), (40) gives: % 29.56/5.39 | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 29.56/5.39 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (35), % 29.56/5.39 | (36), (40) gives: % 29.56/5.39 | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 29.56/5.39 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (12) with all_38_3, all_38_2, all_38_2, 0, % 29.56/5.39 | simplifying with (37), (38), (41) gives: % 29.56/5.39 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.39 | (unorthogonal_lines(all_38_2, all_38_2) = v3 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v1 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v0 & % 29.56/5.39 | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v0 = 0) | v1 = 0 | % 29.56/5.39 | (v3 = 0 & v2 = 0))) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (18) with all_38_3, all_38_3, all_38_2, 0, % 29.56/5.39 | simplifying with (37), (38), (41) gives: % 29.56/5.39 | (50) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.39 | (unorthogonal_lines(all_38_3, all_38_2) = v3 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v2 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_3) = v1 & % 29.56/5.39 | convergent_lines(all_38_3, all_38_3) = v0 & ( ~ (v3 = 0) | v2 = 0 | % 29.56/5.39 | (v1 = 0 & v0 = 0))) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (14) with all_38_3, all_38_3, all_38_2, 0, 0, % 29.56/5.39 | simplifying with (37), (38), (41) gives: % 29.56/5.39 | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.39 | (unorthogonal_lines(all_38_3, all_38_2) = v3 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v2 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_3) = v1 & % 29.56/5.39 | convergent_lines(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 29.56/5.39 | 0) | v3 = 0 | v2 = 0)) % 29.56/5.39 | % 29.56/5.39 | GROUND_INST: instantiating (19) with all_38_3, all_38_2, all_38_2, 0, 0, % 29.56/5.39 | simplifying with (37), (38), (41) gives: % 29.56/5.39 | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.39 | (unorthogonal_lines(all_38_2, all_38_2) = v3 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v1 & % 29.56/5.39 | unorthogonal_lines(all_38_3, all_38_2) = v0 & % 29.56/5.39 | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v3 = 0) | ~ (v2 = % 29.56/5.39 | 0) | v1 = 0 | v0 = 0)) % 29.56/5.39 | % 29.56/5.40 | GROUND_INST: instantiating (23) with all_38_3, all_38_2, simplifying with % 29.56/5.40 | (37), (38), (41) gives: % 29.56/5.40 | (53) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : (point(v2) % 29.56/5.40 | = v3 & line(all_38_2) = v1 & line(all_38_3) = v0 & % 29.56/5.40 | intersection_point(all_38_3, all_38_2) = v2 & $i(v2) & ( ~ (v1 = 0) % 29.56/5.40 | | ~ (v0 = 0) | v3 = 0)) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (5) with all_38_3, all_38_2, simplifying with (37), % 29.56/5.40 | (38), (41) gives: % 29.56/5.40 | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 29.56/5.40 | intersection_point(all_38_3, all_38_2) = v0 & % 29.56/5.40 | apart_point_and_line(v0, all_38_2) = v1 & $i(v0)) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (3) with all_38_3, all_38_2, simplifying with (37), % 29.56/5.40 | (38), (41) gives: % 29.56/5.40 | (55) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 29.56/5.40 | intersection_point(all_38_3, all_38_2) = v0 & % 29.56/5.40 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (24) with all_38_3, all_38_2, all_38_1, simplifying % 29.56/5.40 | with (37), (38), (42) gives: % 29.56/5.40 | (56) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.40 | (point(all_38_1) = v3 & line(all_38_2) = v1 & line(all_38_3) = v0 & % 29.56/5.40 | convergent_lines(all_38_3, all_38_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 29.56/5.40 | 0) | ~ (v0 = 0) | v3 = 0)) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (6) with all_38_3, all_38_2, all_38_1, simplifying % 29.56/5.40 | with (37), (38), (42) gives: % 29.56/5.40 | (57) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_1, % 29.56/5.40 | all_38_2) = v1 & convergent_lines(all_38_3, all_38_2) = v0 & ( ~ % 29.56/5.40 | (v1 = 0) | ~ (v0 = 0))) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (4) with all_38_3, all_38_2, all_38_1, simplifying % 29.56/5.40 | with (37), (38), (42) gives: % 29.56/5.40 | (58) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_1, % 29.56/5.40 | all_38_3) = v1 & convergent_lines(all_38_3, all_38_2) = v0 & ( ~ % 29.56/5.40 | (v1 = 0) | ~ (v0 = 0))) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (25) with all_38_5, all_38_1, all_38_0, simplifying % 29.56/5.40 | with (35), (39), (43) gives: % 29.56/5.40 | (59) all_38_0 = 0 | distinct_points(all_38_5, all_38_1) = 0 % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (26) with all_38_5, all_38_3, simplifying with % 29.56/5.40 | (35), (37), (44) gives: % 29.56/5.40 | (60) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_3) % 29.56/5.40 | = v0) % 29.56/5.40 | % 29.56/5.40 | GROUND_INST: instantiating (26) with all_38_5, all_38_2, simplifying with % 29.56/5.40 | (35), (38), (45) gives: % 29.56/5.40 | (61) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_2) % 29.56/5.40 | = v0) % 29.56/5.40 | % 29.56/5.40 | DELTA: instantiating (61) with fresh symbol all_45_0 gives: % 29.56/5.40 | (62) ~ (all_45_0 = 0) & apart_point_and_line(all_38_5, all_38_2) = % 29.56/5.40 | all_45_0 % 29.56/5.40 | % 29.56/5.40 | ALPHA: (62) implies: % 29.56/5.40 | (63) ~ (all_45_0 = 0) % 29.56/5.40 | (64) apart_point_and_line(all_38_5, all_38_2) = all_45_0 % 29.56/5.40 | % 29.56/5.40 | DELTA: instantiating (60) with fresh symbol all_49_0 gives: % 29.56/5.40 | (65) ~ (all_49_0 = 0) & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.40 | all_49_0 % 29.56/5.40 | % 29.56/5.40 | ALPHA: (65) implies: % 29.56/5.40 | (66) ~ (all_49_0 = 0) % 29.56/5.40 | (67) apart_point_and_line(all_38_5, all_38_3) = all_49_0 % 29.56/5.40 | % 29.56/5.40 | DELTA: instantiating (54) with fresh symbols all_53_0, all_53_1 gives: % 29.56/5.41 | (68) ~ (all_53_0 = 0) & intersection_point(all_38_3, all_38_2) = all_53_1 % 29.56/5.41 | & apart_point_and_line(all_53_1, all_38_2) = all_53_0 & $i(all_53_1) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (68) implies: % 29.56/5.41 | (69) $i(all_53_1) % 29.56/5.41 | (70) apart_point_and_line(all_53_1, all_38_2) = all_53_0 % 29.56/5.41 | (71) intersection_point(all_38_3, all_38_2) = all_53_1 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (47) with fresh symbols all_55_0, all_55_1 gives: % 29.56/5.41 | (72) ~ (all_55_0 = 0) & line_connecting(all_38_5, all_38_4) = all_55_1 & % 29.56/5.41 | apart_point_and_line(all_38_4, all_55_1) = all_55_0 & $i(all_55_1) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (72) implies: % 29.56/5.41 | (73) line_connecting(all_38_5, all_38_4) = all_55_1 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (58) with fresh symbols all_57_0, all_57_1 gives: % 29.56/5.41 | (74) apart_point_and_line(all_38_1, all_38_3) = all_57_0 & % 29.56/5.41 | convergent_lines(all_38_3, all_38_2) = all_57_1 & ( ~ (all_57_0 = 0) | % 29.56/5.41 | ~ (all_57_1 = 0)) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (74) implies: % 29.56/5.41 | (75) convergent_lines(all_38_3, all_38_2) = all_57_1 % 29.56/5.41 | (76) apart_point_and_line(all_38_1, all_38_3) = all_57_0 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (57) with fresh symbols all_59_0, all_59_1 gives: % 29.56/5.41 | (77) apart_point_and_line(all_38_1, all_38_2) = all_59_0 & % 29.56/5.41 | convergent_lines(all_38_3, all_38_2) = all_59_1 & ( ~ (all_59_0 = 0) | % 29.56/5.41 | ~ (all_59_1 = 0)) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (77) implies: % 29.56/5.41 | (78) convergent_lines(all_38_3, all_38_2) = all_59_1 % 29.56/5.41 | (79) apart_point_and_line(all_38_1, all_38_2) = all_59_0 % 29.56/5.41 | (80) ~ (all_59_0 = 0) | ~ (all_59_1 = 0) % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (48) with fresh symbols all_61_0, all_61_1 gives: % 29.56/5.41 | (81) ~ (all_61_0 = 0) & line_connecting(all_38_5, all_38_4) = all_61_1 & % 29.56/5.41 | apart_point_and_line(all_38_5, all_61_1) = all_61_0 & $i(all_61_1) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (81) implies: % 29.56/5.41 | (82) ~ (all_61_0 = 0) % 29.56/5.41 | (83) $i(all_61_1) % 29.56/5.41 | (84) apart_point_and_line(all_38_5, all_61_1) = all_61_0 % 29.56/5.41 | (85) line_connecting(all_38_5, all_38_4) = all_61_1 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (55) with fresh symbols all_63_0, all_63_1 gives: % 29.56/5.41 | (86) ~ (all_63_0 = 0) & intersection_point(all_38_3, all_38_2) = all_63_1 % 29.56/5.41 | & apart_point_and_line(all_63_1, all_38_3) = all_63_0 & $i(all_63_1) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (86) implies: % 29.56/5.41 | (87) ~ (all_63_0 = 0) % 29.56/5.41 | (88) apart_point_and_line(all_63_1, all_38_3) = all_63_0 % 29.56/5.41 | (89) intersection_point(all_38_3, all_38_2) = all_63_1 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (56) with fresh symbols all_65_0, all_65_1, all_65_2, % 29.56/5.41 | all_65_3 gives: % 29.56/5.41 | (90) point(all_38_1) = all_65_0 & line(all_38_2) = all_65_2 & % 29.56/5.41 | line(all_38_3) = all_65_3 & convergent_lines(all_38_3, all_38_2) = % 29.56/5.41 | all_65_1 & ( ~ (all_65_1 = 0) | ~ (all_65_2 = 0) | ~ (all_65_3 = 0) % 29.56/5.41 | | all_65_0 = 0) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (90) implies: % 29.56/5.41 | (91) convergent_lines(all_38_3, all_38_2) = all_65_1 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (52) with fresh symbols all_67_0, all_67_1, all_67_2, % 29.56/5.41 | all_67_3 gives: % 29.56/5.41 | (92) unorthogonal_lines(all_38_2, all_38_2) = all_67_0 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_2) = all_67_2 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_2) = all_67_3 & % 29.56/5.41 | convergent_lines(all_38_2, all_38_2) = all_67_1 & ( ~ (all_67_0 = 0) | % 29.56/5.41 | ~ (all_67_1 = 0) | all_67_2 = 0 | all_67_3 = 0) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (92) implies: % 29.56/5.41 | (93) unorthogonal_lines(all_38_3, all_38_2) = all_67_3 % 29.56/5.41 | (94) unorthogonal_lines(all_38_3, all_38_2) = all_67_2 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (50) with fresh symbols all_69_0, all_69_1, all_69_2, % 29.56/5.41 | all_69_3 gives: % 29.56/5.41 | (95) unorthogonal_lines(all_38_3, all_38_2) = all_69_0 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_2) = all_69_1 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_3) = all_69_2 & % 29.56/5.41 | convergent_lines(all_38_3, all_38_3) = all_69_3 & ( ~ (all_69_0 = 0) | % 29.56/5.41 | all_69_1 = 0 | (all_69_2 = 0 & all_69_3 = 0)) % 29.56/5.41 | % 29.56/5.41 | ALPHA: (95) implies: % 29.56/5.41 | (96) convergent_lines(all_38_3, all_38_3) = all_69_3 % 29.56/5.41 | (97) unorthogonal_lines(all_38_3, all_38_3) = all_69_2 % 29.56/5.41 | (98) unorthogonal_lines(all_38_3, all_38_2) = all_69_1 % 29.56/5.41 | (99) unorthogonal_lines(all_38_3, all_38_2) = all_69_0 % 29.56/5.41 | % 29.56/5.41 | DELTA: instantiating (49) with fresh symbols all_71_0, all_71_1, all_71_2, % 29.56/5.41 | all_71_3 gives: % 29.56/5.41 | (100) unorthogonal_lines(all_38_2, all_38_2) = all_71_0 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_2) = all_71_2 & % 29.56/5.41 | unorthogonal_lines(all_38_3, all_38_2) = all_71_3 & % 29.56/5.41 | convergent_lines(all_38_2, all_38_2) = all_71_1 & ( ~ (all_71_3 = 0) % 29.56/5.41 | | all_71_2 = 0 | (all_71_0 = 0 & all_71_1 = 0)) % 29.56/5.42 | % 29.56/5.42 | ALPHA: (100) implies: % 29.56/5.42 | (101) unorthogonal_lines(all_38_3, all_38_2) = all_71_3 % 29.56/5.42 | (102) unorthogonal_lines(all_38_3, all_38_2) = all_71_2 % 29.56/5.42 | % 29.56/5.42 | DELTA: instantiating (51) with fresh symbols all_73_0, all_73_1, all_73_2, % 29.56/5.42 | all_73_3 gives: % 29.56/5.42 | (103) unorthogonal_lines(all_38_3, all_38_2) = all_73_0 & % 29.56/5.42 | unorthogonal_lines(all_38_3, all_38_2) = all_73_1 & % 29.56/5.42 | unorthogonal_lines(all_38_3, all_38_3) = all_73_2 & % 29.56/5.42 | convergent_lines(all_38_3, all_38_3) = all_73_3 & ( ~ (all_73_2 = 0) % 29.56/5.42 | | ~ (all_73_3 = 0) | all_73_0 = 0 | all_73_1 = 0) % 29.56/5.42 | % 29.56/5.42 | ALPHA: (103) implies: % 29.56/5.42 | (104) convergent_lines(all_38_3, all_38_3) = all_73_3 % 29.56/5.42 | (105) unorthogonal_lines(all_38_3, all_38_3) = all_73_2 % 29.56/5.42 | (106) unorthogonal_lines(all_38_3, all_38_2) = all_73_1 % 29.56/5.42 | (107) unorthogonal_lines(all_38_3, all_38_2) = all_73_0 % 29.56/5.42 | % 29.56/5.42 | DELTA: instantiating (46) with fresh symbols all_75_0, all_75_1, all_75_2, % 29.56/5.42 | all_75_3 gives: % 29.56/5.42 | (108) point(all_38_4) = all_75_2 & point(all_38_5) = all_75_3 & % 29.56/5.42 | line(all_75_1) = all_75_0 & line_connecting(all_38_5, all_38_4) = % 29.56/5.42 | all_75_1 & $i(all_75_1) & ( ~ (all_75_2 = 0) | ~ (all_75_3 = 0) | % 29.56/5.42 | all_75_0 = 0) % 29.56/5.42 | % 29.56/5.42 | ALPHA: (108) implies: % 29.56/5.42 | (109) line_connecting(all_38_5, all_38_4) = all_75_1 % 29.56/5.42 | % 29.56/5.42 | DELTA: instantiating (53) with fresh symbols all_77_0, all_77_1, all_77_2, % 29.56/5.42 | all_77_3 gives: % 29.56/5.42 | (110) point(all_77_1) = all_77_0 & line(all_38_2) = all_77_2 & % 29.56/5.42 | line(all_38_3) = all_77_3 & intersection_point(all_38_3, all_38_2) = % 29.56/5.42 | all_77_1 & $i(all_77_1) & ( ~ (all_77_2 = 0) | ~ (all_77_3 = 0) | % 29.56/5.42 | all_77_0 = 0) % 29.56/5.42 | % 29.56/5.42 | ALPHA: (110) implies: % 29.56/5.42 | (111) intersection_point(all_38_3, all_38_2) = all_77_1 % 29.56/5.42 | % 29.56/5.42 | BETA: splitting (59) gives: % 29.56/5.42 | % 29.56/5.42 | Case 1: % 29.56/5.42 | | % 29.56/5.42 | | (112) distinct_points(all_38_5, all_38_1) = 0 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (28) with all_69_3, all_73_3, all_38_3, all_38_3, % 29.56/5.42 | | simplifying with (96), (104) gives: % 29.56/5.42 | | (113) all_73_3 = all_69_3 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (28) with all_57_1, all_59_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (75), (78) gives: % 29.56/5.42 | | (114) all_59_1 = all_57_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (28) with 0, all_65_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (41), (91) gives: % 29.56/5.42 | | (115) all_65_1 = 0 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (28) with all_59_1, all_65_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (78), (91) gives: % 29.56/5.42 | | (116) all_65_1 = all_59_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (30) with all_61_1, all_75_1, all_38_4, all_38_5, % 29.56/5.42 | | simplifying with (85), (109) gives: % 29.56/5.42 | | (117) all_75_1 = all_61_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (30) with all_55_1, all_75_1, all_38_4, all_38_5, % 29.56/5.42 | | simplifying with (73), (109) gives: % 29.56/5.42 | | (118) all_75_1 = all_55_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (31) with all_38_1, all_77_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (42), (111) gives: % 29.56/5.42 | | (119) all_77_1 = all_38_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (31) with all_63_1, all_77_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (89), (111) gives: % 29.56/5.42 | | (120) all_77_1 = all_63_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (31) with all_53_1, all_77_1, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (71), (111) gives: % 29.56/5.42 | | (121) all_77_1 = all_53_1 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (32) with all_69_2, all_73_2, all_38_3, all_38_3, % 29.56/5.42 | | simplifying with (97), (105) gives: % 29.56/5.42 | | (122) all_73_2 = all_69_2 % 29.56/5.42 | | % 29.56/5.42 | | GROUND_INST: instantiating (32) with all_67_2, all_69_0, all_38_2, all_38_3, % 29.56/5.42 | | simplifying with (94), (99) gives: % 29.56/5.42 | | (123) all_69_0 = all_67_2 % 29.56/5.42 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_69_0, all_71_3, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (99), (101) gives: % 29.56/5.43 | | (124) all_71_3 = all_69_0 % 29.56/5.43 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_69_0, all_71_2, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (99), (102) gives: % 29.56/5.43 | | (125) all_71_2 = all_69_0 % 29.56/5.43 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_71_3, all_73_1, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (101), (106) gives: % 29.56/5.43 | | (126) all_73_1 = all_71_3 % 29.56/5.43 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_67_3, all_73_1, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (93), (106) gives: % 29.56/5.43 | | (127) all_73_1 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_71_2, all_73_0, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (102), (107) gives: % 29.56/5.43 | | (128) all_73_0 = all_71_2 % 29.56/5.43 | | % 29.56/5.43 | | GROUND_INST: instantiating (32) with all_69_1, all_73_0, all_38_2, all_38_3, % 29.56/5.43 | | simplifying with (98), (107) gives: % 29.56/5.43 | | (129) all_73_0 = all_69_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (119), (120) imply: % 29.56/5.43 | | (130) all_63_1 = all_38_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (120), (121) imply: % 29.56/5.43 | | (131) all_63_1 = all_53_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (117), (118) imply: % 29.56/5.43 | | (132) all_61_1 = all_55_1 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (132) implies: % 29.56/5.43 | | (133) all_61_1 = all_55_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (128), (129) imply: % 29.56/5.43 | | (134) all_71_2 = all_69_1 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (134) implies: % 29.56/5.43 | | (135) all_71_2 = all_69_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (126), (127) imply: % 29.56/5.43 | | (136) all_71_3 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (136) implies: % 29.56/5.43 | | (137) all_71_3 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (125), (135) imply: % 29.56/5.43 | | (138) all_69_0 = all_69_1 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (138) implies: % 29.56/5.43 | | (139) all_69_0 = all_69_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (124), (137) imply: % 29.56/5.43 | | (140) all_69_0 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (140) implies: % 29.56/5.43 | | (141) all_69_0 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (139), (141) imply: % 29.56/5.43 | | (142) all_69_1 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (123), (139) imply: % 29.56/5.43 | | (143) all_69_1 = all_67_2 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (142), (143) imply: % 29.56/5.43 | | (144) all_67_2 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (144) implies: % 29.56/5.43 | | (145) all_67_2 = all_67_3 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (115), (116) imply: % 29.56/5.43 | | (146) all_59_1 = 0 % 29.56/5.43 | | % 29.56/5.43 | | SIMP: (146) implies: % 29.56/5.43 | | (147) all_59_1 = 0 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (130), (131) imply: % 29.56/5.43 | | (148) all_53_1 = all_38_1 % 29.56/5.43 | | % 29.56/5.43 | | COMBINE_EQS: (114), (147) imply: % 29.56/5.43 | | (149) all_57_1 = 0 % 29.56/5.43 | | % 29.56/5.43 | | REDUCE: (88), (130) imply: % 29.56/5.43 | | (150) apart_point_and_line(all_38_1, all_38_3) = all_63_0 % 29.56/5.43 | | % 29.56/5.43 | | REDUCE: (70), (148) imply: % 29.56/5.43 | | (151) apart_point_and_line(all_38_1, all_38_2) = all_53_0 % 29.56/5.43 | | % 29.56/5.43 | | REDUCE: (84), (133) imply: % 29.56/5.43 | | (152) apart_point_and_line(all_38_5, all_55_1) = all_61_0 % 29.56/5.43 | | % 29.56/5.43 | | REDUCE: (83), (133) imply: % 29.56/5.43 | | (153) $i(all_55_1) % 29.56/5.43 | | % 29.56/5.43 | | BETA: splitting (80) gives: % 29.56/5.43 | | % 29.56/5.43 | | Case 1: % 29.56/5.43 | | | % 29.56/5.43 | | | (154) ~ (all_59_0 = 0) % 29.56/5.43 | | | % 29.56/5.43 | | | GROUND_INST: instantiating (29) with all_57_0, all_63_0, all_38_3, % 29.56/5.43 | | | all_38_1, simplifying with (76), (150) gives: % 29.56/5.43 | | | (155) all_63_0 = all_57_0 % 29.56/5.43 | | | % 29.56/5.43 | | | GROUND_INST: instantiating (29) with all_59_0, all_53_0, all_38_2, % 29.56/5.43 | | | all_38_1, simplifying with (79), (151) gives: % 29.56/5.43 | | | (156) all_59_0 = all_53_0 % 29.56/5.43 | | | % 29.56/5.43 | | | REDUCE: (87), (155) imply: % 29.56/5.43 | | | (157) ~ (all_57_0 = 0) % 29.56/5.43 | | | % 29.56/5.43 | | | REDUCE: (154), (156) imply: % 29.56/5.43 | | | (158) ~ (all_53_0 = 0) % 29.56/5.43 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (10) with all_38_3, all_38_2, all_38_3, % 29.56/5.44 | | | all_69_3, simplifying with (37), (38), (41), (96) gives: % 29.56/5.44 | | | (159) all_69_3 = 0 | distinct_lines(all_38_2, all_38_3) = 0 % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_38_3, % 29.56/5.44 | | | all_38_3, all_49_0, all_49_0, simplifying with (35), (37), % 29.56/5.44 | | | (39), (67), (112) gives: % 29.56/5.44 | | | (160) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 29.56/5.44 | | | (apart_point_and_line(all_38_1, all_38_3) = v2 & % 29.56/5.44 | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 29.56/5.44 | | | distinct_lines(all_38_3, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.44 | | | | v1 = 0)) % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (11) with all_38_5, all_38_3, all_38_3, % 29.56/5.44 | | | all_49_0, all_49_0, simplifying with (35), (37), (67) gives: % 29.56/5.44 | | | (161) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : % 29.56/5.44 | | | (convergent_lines(all_38_3, all_38_3) = v1 & % 29.56/5.44 | | | distinct_lines(all_38_3, all_38_3) = v0 & ( ~ (v0 = 0) | v1 = % 29.56/5.44 | | | 0)) % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_38_2, % 29.56/5.44 | | | all_38_2, all_45_0, all_45_0, simplifying with (35), (38), % 29.56/5.44 | | | (39), (64), (112) gives: % 29.56/5.44 | | | (162) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 29.56/5.44 | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 29.56/5.44 | | | apart_point_and_line(all_38_1, all_38_2) = v1 & % 29.56/5.44 | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.44 | | | | v1 = 0)) % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_4, all_38_2, % 29.56/5.44 | | | all_38_3, all_45_0, all_49_0, simplifying with (35), (36), % 29.56/5.44 | | | (37), (38), (40), (64), (67) gives: % 29.56/5.44 | | | (163) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.44 | | | [v2: any] : (apart_point_and_line(all_38_4, all_38_2) = v1 & % 29.56/5.44 | | | apart_point_and_line(all_38_4, all_38_3) = v2 & % 29.56/5.44 | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.44 | | | | v1 = 0)) % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_38_3, % 29.56/5.44 | | | all_38_2, all_49_0, all_45_0, simplifying with (35), (37), % 29.56/5.44 | | | (38), (39), (64), (67), (112) gives: % 29.56/5.44 | | | (164) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.44 | | | [v2: any] : (apart_point_and_line(all_38_1, all_38_2) = v2 & % 29.56/5.44 | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 29.56/5.44 | | | distinct_lines(all_38_3, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.44 | | | | v1 = 0)) % 29.56/5.44 | | | % 29.56/5.44 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_38_2, % 29.56/5.44 | | | all_38_3, all_45_0, all_49_0, simplifying with (35), (37), % 29.56/5.44 | | | (38), (39), (64), (67), (112) gives: % 29.56/5.45 | | | (165) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.45 | | | [v2: any] : (apart_point_and_line(all_38_1, all_38_2) = v1 & % 29.56/5.45 | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 29.56/5.45 | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.45 | | | | v1 = 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (11) with all_38_5, all_38_2, all_38_3, % 29.56/5.45 | | | all_45_0, all_49_0, simplifying with (35), (37), (38), (64), % 29.56/5.45 | | | (67) gives: % 29.56/5.45 | | | (166) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 29.56/5.45 | | | (convergent_lines(all_38_2, all_38_3) = v1 & % 29.56/5.45 | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ (v0 = 0) | v1 = % 29.56/5.45 | | | 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (9) with all_38_5, all_38_5, all_38_2, % 29.56/5.45 | | | all_38_3, all_45_0, all_49_0, simplifying with (35), (37), % 29.56/5.45 | | | (38), (64), (67) gives: % 29.56/5.45 | | | (167) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.45 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_5, % 29.56/5.45 | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.45 | | | v2 & distinct_lines(all_38_2, all_38_3) = v1 & % 29.56/5.45 | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.45 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (8) with all_38_5, all_38_5, all_38_2, % 29.56/5.45 | | | all_38_3, all_49_0, all_45_0, simplifying with (35), (37), % 29.56/5.45 | | | (38), (64), (67) gives: % 29.56/5.45 | | | (168) all_49_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.45 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_5, % 29.56/5.45 | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.45 | | | v3 & distinct_lines(all_38_2, all_38_3) = v1 & % 29.56/5.45 | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.45 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_55_1, % 29.56/5.45 | | | all_38_2, all_61_0, all_45_0, simplifying with (35), (38), % 29.56/5.45 | | | (39), (64), (112), (152), (153) gives: % 29.56/5.45 | | | (169) all_61_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.45 | | | [v2: any] : (apart_point_and_line(all_38_1, all_55_1) = v1 & % 29.56/5.45 | | | apart_point_and_line(all_38_1, all_38_2) = v2 & % 29.56/5.45 | | | distinct_lines(all_55_1, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.45 | | | | v1 = 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_38_3, % 29.56/5.45 | | | all_55_1, all_49_0, all_61_0, simplifying with (35), (37), % 29.56/5.45 | | | (39), (67), (112), (152), (153) gives: % 29.56/5.45 | | | (170) all_61_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.45 | | | [v2: any] : (apart_point_and_line(all_38_1, all_55_1) = v2 & % 29.56/5.45 | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 29.56/5.45 | | | distinct_lines(all_38_3, all_55_1) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.45 | | | | v1 = 0)) % 29.56/5.45 | | | % 29.56/5.45 | | | GROUND_INST: instantiating (7) with all_38_5, all_38_1, all_55_1, % 29.56/5.45 | | | all_38_3, all_61_0, all_49_0, simplifying with (35), (37), % 29.56/5.45 | | | (39), (67), (112), (152), (153) gives: % 29.56/5.46 | | | (171) all_61_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.46 | | | [v2: any] : (apart_point_and_line(all_38_1, all_55_1) = v1 & % 29.56/5.46 | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 29.56/5.46 | | | distinct_lines(all_55_1, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = 0 % 29.56/5.46 | | | | v1 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (9) with all_38_1, all_38_5, all_38_3, % 29.56/5.46 | | | all_38_2, all_57_0, all_45_0, simplifying with (35), (37), % 29.56/5.46 | | | (38), (39), (64), (76) gives: % 29.56/5.46 | | | (172) all_57_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.46 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.46 | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.46 | | | v3 & distinct_lines(all_38_3, all_38_2) = v1 & % 29.56/5.46 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.46 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (8) with all_38_1, all_38_5, all_38_2, % 29.56/5.46 | | | all_38_3, all_57_0, all_45_0, simplifying with (35), (37), % 29.56/5.46 | | | (38), (39), (64), (76) gives: % 29.56/5.46 | | | (173) all_57_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.46 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.46 | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.46 | | | v3 & distinct_lines(all_38_2, all_38_3) = v1 & % 29.56/5.46 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.46 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (9) with all_38_1, all_38_5, all_38_3, % 29.56/5.46 | | | all_38_3, all_57_0, all_49_0, simplifying with (35), (37), % 29.56/5.46 | | | (39), (67), (76) gives: % 29.56/5.46 | | | (174) all_57_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.46 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.46 | | | all_38_3) = v2 & apart_point_and_line(all_38_5, all_38_3) = % 29.56/5.46 | | | v3 & distinct_lines(all_38_3, all_38_3) = v1 & % 29.56/5.46 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.46 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (9) with all_38_1, all_38_1, all_38_2, % 29.56/5.46 | | | all_38_2, all_53_0, all_53_0, simplifying with (38), (39), % 29.56/5.46 | | | (151) gives: % 29.56/5.46 | | | (175) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 29.56/5.46 | | | [v3: any] : (apart_point_and_line(all_38_1, all_38_2) = v3 & % 29.56/5.46 | | | apart_point_and_line(all_38_1, all_38_2) = v2 & % 29.56/5.46 | | | distinct_lines(all_38_2, all_38_2) = v1 & % 29.56/5.46 | | | distinct_points(all_38_1, all_38_1) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.46 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (9) with all_38_1, all_38_5, all_38_2, % 29.56/5.46 | | | all_38_2, all_53_0, all_45_0, simplifying with (35), (38), % 29.56/5.46 | | | (39), (64), (151) gives: % 29.56/5.46 | | | (176) all_53_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.46 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.46 | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 29.56/5.46 | | | v3 & distinct_lines(all_38_2, all_38_2) = v1 & % 29.56/5.46 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.46 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.46 | | | % 29.56/5.46 | | | GROUND_INST: instantiating (9) with all_38_1, all_38_5, all_38_2, % 29.56/5.46 | | | all_38_3, all_53_0, all_49_0, simplifying with (35), (37), % 29.56/5.46 | | | (38), (39), (67), (151) gives: % 29.56/5.47 | | | (177) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.47 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.47 | | | all_38_3) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 29.56/5.47 | | | v3 & distinct_lines(all_38_2, all_38_3) = v1 & % 29.56/5.47 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.47 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.47 | | | % 29.56/5.47 | | | GROUND_INST: instantiating (8) with all_38_5, all_38_1, all_38_2, % 29.56/5.47 | | | all_38_3, all_49_0, all_53_0, simplifying with (35), (37), % 29.56/5.47 | | | (38), (39), (67), (151) gives: % 29.56/5.47 | | | (178) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.47 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.47 | | | all_38_3) = v3 & apart_point_and_line(all_38_5, all_38_2) = % 29.56/5.47 | | | v2 & distinct_lines(all_38_2, all_38_3) = v1 & % 29.56/5.47 | | | distinct_points(all_38_5, all_38_1) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.47 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.47 | | | % 29.56/5.47 | | | GROUND_INST: instantiating (8) with all_38_1, all_38_5, all_38_3, % 29.56/5.47 | | | all_38_2, all_53_0, all_49_0, simplifying with (35), (37), % 29.56/5.47 | | | (38), (39), (67), (151) gives: % 29.56/5.47 | | | (179) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 29.56/5.47 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_1, % 29.56/5.47 | | | all_38_3) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 29.56/5.47 | | | v3 & distinct_lines(all_38_3, all_38_2) = v1 & % 29.56/5.47 | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 29.56/5.47 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 29.56/5.47 | | | % 29.56/5.47 | | | GROUND_INST: instantiating (13) with all_38_3, all_38_2, all_38_3, % 29.56/5.47 | | | all_69_2, simplifying with (37), (38), (41), (97) gives: % 29.56/5.47 | | | (180) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 29.56/5.47 | | | (unorthogonal_lines(all_38_2, all_38_3) = v3 & % 29.56/5.47 | | | unorthogonal_lines(all_38_3, all_38_2) = v0 & % 29.56/5.47 | | | convergent_lines(all_38_2, all_38_3) = v2 & % 29.56/5.47 | | | convergent_lines(all_38_3, all_38_3) = v1 & ( ~ (v0 = 0) | (v3 % 29.56/5.47 | | | = 0 & v2 = 0) | (v1 = 0 & all_69_2 = 0))) % 29.56/5.47 | | | % 29.56/5.47 | | | GROUND_INST: instantiating (20) with all_38_3, all_38_2, all_38_3, 0, % 29.56/5.47 | | | all_69_2, simplifying with (37), (38), (41), (97) gives: % 30.68/5.47 | | | (181) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 30.68/5.47 | | | (unorthogonal_lines(all_38_2, all_38_3) = v3 & % 30.68/5.47 | | | unorthogonal_lines(all_38_3, all_38_2) = v0 & % 30.68/5.47 | | | convergent_lines(all_38_2, all_38_3) = v2 & % 30.68/5.47 | | | convergent_lines(all_38_3, all_38_3) = v1 & ( ~ (v3 = 0) | ~ % 30.68/5.47 | | | (v2 = 0) | v0 = 0 | (v1 = 0 & all_69_2 = 0))) % 30.68/5.47 | | | % 30.68/5.47 | | | GROUND_INST: instantiating (17) with all_38_3, all_38_3, all_38_2, % 30.68/5.47 | | | all_67_3, all_67_3, simplifying with (37), (38), (93) gives: % 30.68/5.48 | | | (182) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 30.68/5.48 | | | (unorthogonal_lines(all_38_3, all_38_3) = v1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = v3 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = v2 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ % 30.68/5.48 | | | (v0 = 0) | (v3 = 0 & all_67_3 = 0) | (v2 = 0 & all_67_3 = % 30.68/5.48 | | | 0))) % 30.68/5.48 | | | % 30.68/5.48 | | | GROUND_INST: instantiating (21) with all_38_3, all_38_2, all_38_3, % 30.68/5.48 | | | all_67_3, all_69_2, simplifying with (37), (38), (93), (97) % 30.68/5.48 | | | gives: % 30.68/5.48 | | | (183) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 30.68/5.48 | | | (unorthogonal_lines(all_38_2, all_38_3) = v3 & % 30.68/5.48 | | | convergent_lines(all_38_2, all_38_3) = v2 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = v0 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = v1 & ( ~ (v3 = 0) | ~ % 30.68/5.48 | | | (v2 = 0) | (v1 = 0 & all_69_2 = 0) | (v0 = 0 & all_67_3 = % 30.68/5.48 | | | 0))) % 30.68/5.48 | | | % 30.68/5.48 | | | GROUND_INST: instantiating (16) with all_38_3, all_38_3, all_38_2, 0, % 30.68/5.48 | | | all_67_3, simplifying with (37), (38), (41), (93) gives: % 30.68/5.48 | | | (184) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 30.68/5.48 | | | (unorthogonal_lines(all_38_3, all_38_2) = v2 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_3) = v1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = v3 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ % 30.68/5.48 | | | (v0 = 0) | v2 = 0 | (v3 = 0 & all_67_3 = 0))) % 30.68/5.48 | | | % 30.68/5.48 | | | GROUND_INST: instantiating (15) with all_38_3, all_38_3, all_38_2, % 30.68/5.48 | | | all_67_3, 0, simplifying with (37), (38), (41), (93) gives: % 30.68/5.48 | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 30.68/5.48 | | | (unorthogonal_lines(all_38_3, all_38_2) = v3 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_3) = v1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = v2 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ % 30.68/5.48 | | | (v0 = 0) | v3 = 0 | (v2 = 0 & all_67_3 = 0))) % 30.68/5.48 | | | % 30.68/5.48 | | | DELTA: instantiating (181) with fresh symbols all_126_0, all_126_1, % 30.68/5.48 | | | all_126_2, all_126_3 gives: % 30.68/5.48 | | | (186) unorthogonal_lines(all_38_2, all_38_3) = all_126_0 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_2) = all_126_3 & % 30.68/5.48 | | | convergent_lines(all_38_2, all_38_3) = all_126_1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = all_126_2 & ( ~ (all_126_0 % 30.68/5.48 | | | = 0) | ~ (all_126_1 = 0) | all_126_3 = 0 | (all_126_2 = 0 & % 30.68/5.48 | | | all_69_2 = 0)) % 30.68/5.48 | | | % 30.68/5.48 | | | ALPHA: (186) implies: % 30.68/5.48 | | | (187) convergent_lines(all_38_3, all_38_3) = all_126_2 % 30.68/5.48 | | | % 30.68/5.48 | | | DELTA: instantiating (180) with fresh symbols all_128_0, all_128_1, % 30.68/5.48 | | | all_128_2, all_128_3 gives: % 30.68/5.48 | | | (188) unorthogonal_lines(all_38_2, all_38_3) = all_128_0 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_2) = all_128_3 & % 30.68/5.48 | | | convergent_lines(all_38_2, all_38_3) = all_128_1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = all_128_2 & ( ~ (all_128_3 % 30.68/5.48 | | | = 0) | (all_128_0 = 0 & all_128_1 = 0) | (all_128_2 = 0 & % 30.68/5.48 | | | all_69_2 = 0)) % 30.68/5.48 | | | % 30.68/5.48 | | | ALPHA: (188) implies: % 30.68/5.48 | | | (189) convergent_lines(all_38_3, all_38_3) = all_128_2 % 30.68/5.48 | | | % 30.68/5.48 | | | DELTA: instantiating (185) with fresh symbols all_132_0, all_132_1, % 30.68/5.48 | | | all_132_2, all_132_3 gives: % 30.68/5.48 | | | (190) unorthogonal_lines(all_38_3, all_38_2) = all_132_0 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_3) = all_132_2 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = all_132_1 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = all_132_3 & ( ~ (all_132_2 % 30.68/5.48 | | | = 0) | ~ (all_132_3 = 0) | all_132_0 = 0 | (all_132_1 = 0 & % 30.68/5.48 | | | all_67_3 = 0)) % 30.68/5.48 | | | % 30.68/5.48 | | | ALPHA: (190) implies: % 30.68/5.48 | | | (191) convergent_lines(all_38_3, all_38_3) = all_132_3 % 30.68/5.48 | | | % 30.68/5.48 | | | DELTA: instantiating (184) with fresh symbols all_134_0, all_134_1, % 30.68/5.48 | | | all_134_2, all_134_3 gives: % 30.68/5.48 | | | (192) unorthogonal_lines(all_38_3, all_38_2) = all_134_1 & % 30.68/5.48 | | | unorthogonal_lines(all_38_3, all_38_3) = all_134_2 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_2) = all_134_0 & % 30.68/5.48 | | | convergent_lines(all_38_3, all_38_3) = all_134_3 & ( ~ (all_134_2 % 30.68/5.48 | | | = 0) | ~ (all_134_3 = 0) | all_134_1 = 0 | (all_134_0 = 0 & % 30.68/5.48 | | | all_67_3 = 0)) % 30.68/5.48 | | | % 30.68/5.48 | | | ALPHA: (192) implies: % 30.68/5.49 | | | (193) convergent_lines(all_38_3, all_38_3) = all_134_3 % 30.68/5.49 | | | % 30.68/5.49 | | | DELTA: instantiating (182) with fresh symbols all_136_0, all_136_1, % 30.68/5.49 | | | all_136_2, all_136_3 gives: % 30.68/5.49 | | | (194) unorthogonal_lines(all_38_3, all_38_3) = all_136_2 & % 30.68/5.49 | | | convergent_lines(all_38_3, all_38_2) = all_136_0 & % 30.68/5.49 | | | convergent_lines(all_38_3, all_38_2) = all_136_1 & % 30.68/5.49 | | | convergent_lines(all_38_3, all_38_3) = all_136_3 & ( ~ (all_136_2 % 30.68/5.49 | | | = 0) | ~ (all_136_3 = 0) | (all_136_0 = 0 & all_67_3 = 0) | % 30.68/5.49 | | | (all_136_1 = 0 & all_67_3 = 0)) % 30.68/5.49 | | | % 30.68/5.49 | | | ALPHA: (194) implies: % 30.68/5.49 | | | (195) convergent_lines(all_38_3, all_38_3) = all_136_3 % 30.68/5.49 | | | % 30.68/5.49 | | | DELTA: instantiating (183) with fresh symbols all_140_0, all_140_1, % 30.68/5.49 | | | all_140_2, all_140_3 gives: % 30.68/5.49 | | | (196) unorthogonal_lines(all_38_2, all_38_3) = all_140_0 & % 30.68/5.49 | | | convergent_lines(all_38_2, all_38_3) = all_140_1 & % 30.68/5.49 | | | convergent_lines(all_38_3, all_38_2) = all_140_3 & % 30.68/5.49 | | | convergent_lines(all_38_3, all_38_3) = all_140_2 & ( ~ (all_140_0 % 30.68/5.49 | | | = 0) | ~ (all_140_1 = 0) | (all_140_2 = 0 & all_69_2 = 0) | % 30.68/5.49 | | | (all_140_3 = 0 & all_67_3 = 0)) % 30.68/5.49 | | | % 30.68/5.49 | | | ALPHA: (196) implies: % 30.68/5.49 | | | (197) convergent_lines(all_38_3, all_38_3) = all_140_2 % 30.68/5.49 | | | % 30.68/5.49 | | | BETA: splitting (165) gives: % 30.68/5.49 | | | % 30.68/5.49 | | | Case 1: % 30.68/5.49 | | | | % 30.68/5.49 | | | | (198) all_49_0 = 0 % 30.68/5.49 | | | | % 30.68/5.49 | | | | REDUCE: (66), (198) imply: % 30.68/5.49 | | | | (199) $false % 30.68/5.49 | | | | % 30.68/5.49 | | | | CLOSE: (199) is inconsistent. % 30.68/5.49 | | | | % 30.68/5.49 | | | Case 2: % 30.68/5.49 | | | | % 30.68/5.49 | | | | (200) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.49 | | | | (apart_point_and_line(all_38_1, all_38_2) = v1 & % 30.68/5.49 | | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.49 | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = % 30.68/5.49 | | | | 0 | v1 = 0)) % 30.68/5.49 | | | | % 30.68/5.49 | | | | BETA: splitting (164) gives: % 30.68/5.49 | | | | % 30.68/5.49 | | | | Case 1: % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | (201) all_49_0 = 0 % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | REDUCE: (66), (201) imply: % 30.68/5.49 | | | | | (202) $false % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | CLOSE: (202) is inconsistent. % 30.68/5.49 | | | | | % 30.68/5.49 | | | | Case 2: % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | (203) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.49 | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.49 | | | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 30.68/5.49 | | | | | distinct_lines(all_38_3, all_38_2) = v0 & ( ~ (v0 = 0) | v2 % 30.68/5.49 | | | | | = 0 | v1 = 0)) % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | BETA: splitting (171) gives: % 30.68/5.49 | | | | | % 30.68/5.49 | | | | | Case 1: % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | (204) all_61_0 = 0 % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | REDUCE: (82), (204) imply: % 30.68/5.49 | | | | | | (205) $false % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | CLOSE: (205) is inconsistent. % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | Case 2: % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | (206) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.49 | | | | | | (apart_point_and_line(all_38_1, all_55_1) = v1 & % 30.68/5.49 | | | | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.49 | | | | | | distinct_lines(all_55_1, all_38_3) = v0 & ( ~ (v0 = 0) | % 30.68/5.49 | | | | | | v2 = 0 | v1 = 0)) % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | BETA: splitting (170) gives: % 30.68/5.49 | | | | | | % 30.68/5.49 | | | | | | Case 1: % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | (207) all_61_0 = 0 % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | REDUCE: (82), (207) imply: % 30.68/5.49 | | | | | | | (208) $false % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | CLOSE: (208) is inconsistent. % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | Case 2: % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | (209) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 30.68/5.49 | | | | | | | : (apart_point_and_line(all_38_1, all_55_1) = v2 & % 30.68/5.49 | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 30.68/5.49 | | | | | | | distinct_lines(all_38_3, all_55_1) = v0 & ( ~ (v0 = 0) % 30.68/5.49 | | | | | | | | v2 = 0 | v1 = 0)) % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | BETA: splitting (168) gives: % 30.68/5.49 | | | | | | | % 30.68/5.49 | | | | | | | Case 1: % 30.68/5.49 | | | | | | | | % 30.68/5.49 | | | | | | | | (210) all_49_0 = 0 % 30.68/5.49 | | | | | | | | % 30.68/5.49 | | | | | | | | REDUCE: (66), (210) imply: % 30.68/5.49 | | | | | | | | (211) $false % 30.68/5.49 | | | | | | | | % 30.68/5.49 | | | | | | | | CLOSE: (211) is inconsistent. % 30.68/5.49 | | | | | | | | % 30.68/5.49 | | | | | | | Case 2: % 30.68/5.49 | | | | | | | | % 30.68/5.50 | | | | | | | | (212) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 30.68/5.50 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_38_5, % 30.68/5.50 | | | | | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, % 30.68/5.50 | | | | | | | | all_38_3) = v3 & distinct_lines(all_38_2, all_38_3) % 30.68/5.50 | | | | | | | | = v1 & distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 30.68/5.50 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.50 | | | | | | | | % 30.68/5.50 | | | | | | | | BETA: splitting (167) gives: % 30.68/5.50 | | | | | | | | % 30.68/5.50 | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | (213) all_49_0 = 0 % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | REDUCE: (66), (213) imply: % 30.68/5.50 | | | | | | | | | (214) $false % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | CLOSE: (214) is inconsistent. % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | (215) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 30.68/5.50 | | | | | | | | | any] : ? [v3: any] : % 30.68/5.50 | | | | | | | | | (apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.50 | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v2 & % 30.68/5.50 | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.50 | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 % 30.68/5.50 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | BETA: splitting (166) gives: % 30.68/5.50 | | | | | | | | | % 30.68/5.50 | | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | (216) all_49_0 = 0 % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | REDUCE: (66), (216) imply: % 30.68/5.50 | | | | | | | | | | (217) $false % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | CLOSE: (217) is inconsistent. % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | (218) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 30.68/5.50 | | | | | | | | | | (convergent_lines(all_38_2, all_38_3) = v1 & % 30.68/5.50 | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ (v0 % 30.68/5.50 | | | | | | | | | | = 0) | v1 = 0)) % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | BETA: splitting (169) gives: % 30.68/5.50 | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | (219) all_61_0 = 0 % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | REDUCE: (82), (219) imply: % 30.68/5.50 | | | | | | | | | | | (220) $false % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | CLOSE: (220) is inconsistent. % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | (221) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.50 | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_1, % 30.68/5.50 | | | | | | | | | | | all_55_1) = v1 & % 30.68/5.50 | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.50 | | | | | | | | | | | distinct_lines(all_55_1, all_38_2) = v0 & ( ~ % 30.68/5.50 | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | BETA: splitting (163) gives: % 30.68/5.50 | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | (222) all_49_0 = 0 % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | REDUCE: (66), (222) imply: % 30.68/5.50 | | | | | | | | | | | | (223) $false % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | (224) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.50 | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_4, % 30.68/5.50 | | | | | | | | | | | | all_38_2) = v1 & % 30.68/5.50 | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_3) = v2 & % 30.68/5.50 | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ % 30.68/5.50 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | BETA: splitting (160) gives: % 30.68/5.50 | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | (225) all_49_0 = 0 % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | REDUCE: (66), (225) imply: % 30.68/5.50 | | | | | | | | | | | | | (226) $false % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | (227) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.50 | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.50 | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 30.68/5.50 | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_3) = v0 & ( ~ % 30.68/5.50 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_268_0, % 30.68/5.50 | | | | | | | | | | | | | all_268_1, all_268_2 gives: % 30.68/5.50 | | | | | | | | | | | | | (228) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.50 | | | | | | | | | | | | | all_268_0 & apart_point_and_line(all_38_1, % 30.68/5.50 | | | | | | | | | | | | | all_38_3) = all_268_1 & distinct_lines(all_38_3, % 30.68/5.50 | | | | | | | | | | | | | all_38_3) = all_268_2 & ( ~ (all_268_2 = 0) | % 30.68/5.50 | | | | | | | | | | | | | all_268_0 = 0 | all_268_1 = 0) % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | ALPHA: (228) implies: % 30.68/5.50 | | | | | | | | | | | | | (229) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.50 | | | | | | | | | | | | | all_268_0 % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | BETA: splitting (162) gives: % 30.68/5.50 | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | Case 1: % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | (230) all_45_0 = 0 % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | REDUCE: (63), (230) imply: % 30.68/5.50 | | | | | | | | | | | | | | (231) $false % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | Case 2: % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.50 | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.50 | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_2) = v1 & % 30.68/5.50 | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ % 30.68/5.50 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_273_0, % 30.68/5.50 | | | | | | | | | | | | | | all_273_1, all_273_2 gives: % 30.68/5.50 | | | | | | | | | | | | | | (233) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.50 | | | | | | | | | | | | | | all_273_0 & apart_point_and_line(all_38_1, % 30.68/5.50 | | | | | | | | | | | | | | all_38_2) = all_273_1 & distinct_lines(all_38_2, % 30.68/5.50 | | | | | | | | | | | | | | all_38_2) = all_273_2 & ( ~ (all_273_2 = 0) | % 30.68/5.50 | | | | | | | | | | | | | | all_273_0 = 0 | all_273_1 = 0) % 30.68/5.50 | | | | | | | | | | | | | | % 30.68/5.50 | | | | | | | | | | | | | | ALPHA: (233) implies: % 30.68/5.50 | | | | | | | | | | | | | | (234) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.50 | | | | | | | | | | | | | | all_273_1 % 30.68/5.51 | | | | | | | | | | | | | | (235) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | all_273_0 % 30.68/5.51 | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | BETA: splitting (175) gives: % 30.68/5.51 | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | Case 1: % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | (236) all_53_0 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | REDUCE: (158), (236) imply: % 30.68/5.51 | | | | | | | | | | | | | | | (237) $false % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent. % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | Case 2: % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | (238) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.51 | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 30.68/5.51 | | | | | | | | | | | | | | | all_38_2) = v3 & % 30.68/5.51 | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.51 | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 30.68/5.51 | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_1) = v0 & ( ~ % 30.68/5.51 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | DELTA: instantiating (238) with fresh symbols all_293_0, % 30.68/5.51 | | | | | | | | | | | | | | | all_293_1, all_293_2, all_293_3 gives: % 30.68/5.51 | | | | | | | | | | | | | | | (239) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | all_293_0 & apart_point_and_line(all_38_1, % 30.68/5.51 | | | | | | | | | | | | | | | all_38_2) = all_293_1 & distinct_lines(all_38_2, % 30.68/5.51 | | | | | | | | | | | | | | | all_38_2) = all_293_2 & % 30.68/5.51 | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_1) = all_293_3 & % 30.68/5.51 | | | | | | | | | | | | | | | ( ~ (all_293_2 = 0) | ~ (all_293_3 = 0) | % 30.68/5.51 | | | | | | | | | | | | | | | all_293_0 = 0 | all_293_1 = 0) % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | ALPHA: (239) implies: % 30.68/5.51 | | | | | | | | | | | | | | | (240) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | all_293_1 % 30.68/5.51 | | | | | | | | | | | | | | | (241) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | all_293_0 % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 30.68/5.51 | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | Case 1: % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | (242) all_49_0 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | REDUCE: (66), (242) imply: % 30.68/5.51 | | | | | | | | | | | | | | | | (243) $false % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent. % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | Case 2: % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | (244) ? [v0: any] : ? [v1: any] : % 30.68/5.51 | | | | | | | | | | | | | | | | (convergent_lines(all_38_3, all_38_3) = v1 & % 30.68/5.51 | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_3) = v0 & ( ~ % 30.68/5.51 | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | DELTA: instantiating (244) with fresh symbols all_303_0, % 30.68/5.51 | | | | | | | | | | | | | | | | all_303_1 gives: % 30.68/5.51 | | | | | | | | | | | | | | | | (245) convergent_lines(all_38_3, all_38_3) = all_303_0 & % 30.68/5.51 | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_3) = all_303_1 & ( % 30.68/5.51 | | | | | | | | | | | | | | | | ~ (all_303_1 = 0) | all_303_0 = 0) % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 30.68/5.51 | | | | | | | | | | | | | | | | (246) convergent_lines(all_38_3, all_38_3) = all_303_0 % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 30.68/5.51 | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | Case 1: % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | (247) all_45_0 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | REDUCE: (63), (247) imply: % 30.68/5.51 | | | | | | | | | | | | | | | | | (248) $false % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | Case 2: % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.51 | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v1 & % 30.68/5.51 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.51 | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ % 30.68/5.51 | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_342_0, % 30.68/5.51 | | | | | | | | | | | | | | | | | all_342_1, all_342_2 gives: % 30.68/5.51 | | | | | | | | | | | | | | | | | (250) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | | | all_342_1 & apart_point_and_line(all_38_1, % 30.68/5.51 | | | | | | | | | | | | | | | | | all_38_3) = all_342_0 & distinct_lines(all_38_2, % 30.68/5.51 | | | | | | | | | | | | | | | | | all_38_3) = all_342_2 & ( ~ (all_342_2 = 0) | % 30.68/5.51 | | | | | | | | | | | | | | | | | all_342_0 = 0 | all_342_1 = 0) % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 30.68/5.51 | | | | | | | | | | | | | | | | | (251) distinct_lines(all_38_2, all_38_3) = all_342_2 % 30.68/5.51 | | | | | | | | | | | | | | | | | (252) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.51 | | | | | | | | | | | | | | | | | all_342_0 % 30.68/5.51 | | | | | | | | | | | | | | | | | (253) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | | | all_342_1 % 30.68/5.51 | | | | | | | | | | | | | | | | | (254) ~ (all_342_2 = 0) | all_342_0 = 0 | all_342_1 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 30.68/5.51 | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | (255) all_45_0 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | REDUCE: (63), (255) imply: % 30.68/5.51 | | | | | | | | | | | | | | | | | | (256) $false % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | (257) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.51 | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.51 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 30.68/5.51 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v0 & ( ~ % 30.68/5.51 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | DELTA: instantiating (257) with fresh symbols all_347_0, % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_347_1, all_347_2 gives: % 30.68/5.51 | | | | | | | | | | | | | | | | | | (258) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_347_0 & apart_point_and_line(all_38_1, % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_38_3) = all_347_1 & distinct_lines(all_38_3, % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_38_2) = all_347_2 & ( ~ (all_347_2 = 0) | % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_347_0 = 0 | all_347_1 = 0) % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | ALPHA: (258) implies: % 30.68/5.51 | | | | | | | | | | | | | | | | | | (259) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_347_1 % 30.68/5.51 | | | | | | | | | | | | | | | | | | (260) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.51 | | | | | | | | | | | | | | | | | | all_347_0 % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 30.68/5.51 | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.51 | | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | | (261) all_49_0 = 0 % 30.68/5.51 | | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | | REDUCE: (66), (261) imply: % 30.68/5.51 | | | | | | | | | | | | | | | | | | | (262) $false % 30.68/5.51 | | | | | | | | | | | | | | | | | | | % 30.68/5.51 | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 30.68/5.51 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | (263) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.52 | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_55_1) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | distinct_lines(all_55_1, all_38_3) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_372_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_372_1, all_372_2 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | (264) apart_point_and_line(all_38_1, all_55_1) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_372_1 & apart_point_and_line(all_38_1, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_38_3) = all_372_0 & distinct_lines(all_55_1, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_38_3) = all_372_2 & ( ~ (all_372_2 = 0) | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_372_0 = 0 | all_372_1 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | (265) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | all_372_0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (266) all_49_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (266) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (267) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (268) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_55_1) = v2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_55_1) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_377_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_377_1, all_377_2 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (269) apart_point_and_line(all_38_1, all_55_1) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_377_0 & apart_point_and_line(all_38_1, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_38_3) = all_377_1 & distinct_lines(all_38_3, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_55_1) = all_377_2 & ( ~ (all_377_2 = 0) | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_377_0 = 0 | all_377_1 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | (270) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | all_377_1 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (271) all_45_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (271) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (272) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (272) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (273) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_5, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (273) with fresh symbols all_402_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_402_1, all_402_2, all_402_3 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (274) apart_point_and_line(all_38_5, all_38_2) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_402_1 & apart_point_and_line(all_38_5, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_402_0 & distinct_lines(all_38_2, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_402_2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_402_3 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_402_2 = 0) | ~ (all_402_3 = 0) | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | all_402_0 = 0 | all_402_1 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | (275) distinct_lines(all_38_2, all_38_3) = all_402_2 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (276) all_45_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (276) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (277) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (278) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_5, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (278) with fresh symbols all_407_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_407_1, all_407_2, all_407_3 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (279) apart_point_and_line(all_38_5, all_38_2) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_407_0 & apart_point_and_line(all_38_5, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_407_1 & distinct_lines(all_38_2, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_407_2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_407_3 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_407_2 = 0) | ~ (all_407_3 = 0) | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | all_407_0 = 0 | all_407_1 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | (280) distinct_lines(all_38_2, all_38_3) = all_407_2 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (281) all_45_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (281) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (282) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (282) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (283) ? [v0: any] : ? [v1: any] : % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (convergent_lines(all_38_2, all_38_3) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (283) with fresh symbols all_437_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | all_437_1 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (284) convergent_lines(all_38_2, all_38_3) = all_437_0 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_437_1 & ( % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_437_1 = 0) | all_437_0 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | (285) distinct_lines(all_38_2, all_38_3) = all_437_1 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (286) all_45_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (286) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (287) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (288) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_55_1) = v1 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_55_1, all_38_2) = v0 & ( ~ % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (288) with fresh symbols all_447_0, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_447_1, all_447_2 gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (289) apart_point_and_line(all_38_1, all_55_1) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_447_1 & apart_point_and_line(all_38_1, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_447_0 & distinct_lines(all_55_1, % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_447_2 & ( ~ (all_447_2 = 0) | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_447_0 = 0 | all_447_1 = 0) % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | (290) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | all_447_0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_45_0 = 0 % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (291) imply: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | (292) $false % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | (293) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_3) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (293) with fresh symbols all_457_0, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | all_457_1, all_457_2 gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | (294) apart_point_and_line(all_38_4, all_38_2) = % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | all_457_1 & apart_point_and_line(all_38_4, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_457_0 & distinct_lines(all_38_2, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_457_2 & ( ~ (all_457_2 = 0) | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | all_457_0 = 0 | all_457_1 = 0) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | (295) distinct_lines(all_38_2, all_38_3) = all_457_2 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_53_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (296) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (297) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_57_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (299) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_53_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (302) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_53_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (305) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_57_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (308) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_2) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_57_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (311) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_3) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_3) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_49_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (314) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (316) with fresh symbols all_553_0, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_1, all_553_2, all_553_3 gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_1 & apart_point_and_line(all_38_5, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_553_0 & distinct_lines(all_38_3, % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_553_2 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_553_3 & % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_553_2 = 0) | ~ (all_553_3 = 0) | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_0 = 0 | all_553_1 = 0) % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_553_1 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_45_0 = 0 % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (319) imply: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) $false % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent. % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (321) with fresh symbols all_583_0, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_583_1, all_583_2, all_583_3 gives: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_583_1 & apart_point_and_line(all_38_5, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_583_0 & distinct_lines(all_38_3, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_583_2 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_583_3 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_583_2 = 0) | ~ (all_583_3 = 0) | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_583_0 = 0 | all_583_1 = 0) % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) apart_point_and_line(all_38_1, all_38_2) = % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_583_1 % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_49_0 = 0 % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (324) imply: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) $false % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent. % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v2 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (326) with fresh symbols all_618_0, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_618_1, all_618_2, all_618_3 gives: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_618_1 & apart_point_and_line(all_38_5, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_618_0 & distinct_lines(all_38_2, % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_618_2 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_618_3 & % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_618_2 = 0) | ~ (all_618_3 = 0) | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_618_0 = 0 | all_618_1 = 0) % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) distinct_lines(all_38_2, all_38_3) = all_618_2 % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) apart_point_and_line(all_38_1, all_38_3) = % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_618_1 % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_45_0 = 0 % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (330) imply: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) $false % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 30.68/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (332) with fresh symbols all_623_0, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_623_1, all_623_2, all_623_3 gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) apart_point_and_line(all_38_1, all_38_2) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_623_1 & apart_point_and_line(all_38_5, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_623_0 & distinct_lines(all_38_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_623_2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_623_3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_623_2 = 0) | ~ (all_623_3 = 0) | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_623_0 = 0 | all_623_1 = 0) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) apart_point_and_line(all_38_1, all_38_2) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_623_1 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_45_0 = 0 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (335) imply: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (337) with fresh symbols all_628_0, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_628_1, all_628_2, all_628_3 gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) apart_point_and_line(all_38_1, all_38_2) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_628_1 & apart_point_and_line(all_38_5, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_628_0 & distinct_lines(all_38_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_628_2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_628_3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_628_2 = 0) | ~ (all_628_3 = 0) | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_628_0 = 0 | all_628_1 = 0) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) distinct_lines(all_38_2, all_38_3) = all_628_2 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) apart_point_and_line(all_38_1, all_38_2) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_628_1 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_49_0 = 0 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (341) imply: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) $false % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent. % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_3) = v3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_3) = v1 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = v0 & ( ~ % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (343) with fresh symbols all_658_0, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_658_1, all_658_2, all_658_3 gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) apart_point_and_line(all_38_1, all_38_3) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_658_1 & apart_point_and_line(all_38_5, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_658_0 & distinct_lines(all_38_3, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_658_2 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_5) = all_658_3 & % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_658_2 = 0) | ~ (all_658_3 = 0) | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_658_0 = 0 | all_658_1 = 0) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) apart_point_and_line(all_38_1, all_38_3) = % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_658_1 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_437_1, all_457_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (285), (295) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_457_2 = all_437_1 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_457_2, all_618_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (295), (328) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_618_2 = all_457_2 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_342_2, all_618_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (251), (328) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_618_2 = all_342_2 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_437_1, all_628_2, % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (285), (339) % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_628_2 = all_437_1 % 31.07/5.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_407_2, all_628_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (280), (339) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_628_2 = all_407_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_402_2, all_628_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (275), (339) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_628_2 = all_402_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_126_2, all_128_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (187), (189) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_128_2 = all_126_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_128_2, all_132_3, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (189), (191) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_132_3 = all_128_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_136_3, all_140_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (195), (197) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_140_2 = all_136_3 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_134_3, all_140_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (193), (197) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_140_2 = all_134_3 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_132_3, all_140_2, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (191), (197) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_140_2 = all_132_3 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_69_3, all_303_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (96), (246) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_303_0 = all_69_3 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_140_2, all_303_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (197), (246) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_303_0 = all_140_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_347_1, all_372_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (259), (265) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_372_0 = all_347_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_57_0, all_377_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (76), (270) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_377_1 = all_57_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_347_1, all_377_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (259), (270) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_377_1 = all_347_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_372_0, all_553_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (265), (318) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_553_1 = all_372_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_268_0, all_553_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (229), (318) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_553_1 = all_268_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_377_1, all_618_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (270), (329) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_618_1 = all_377_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_618_1, all_658_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (329), (345) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_658_1 = all_618_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_342_0, all_658_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (252), (345) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_658_1 = all_342_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_273_0, all_347_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (235), (260) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_347_0 = all_273_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_273_1, all_347_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (234), (260) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_347_0 = all_273_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_53_0, all_447_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (151), (290) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_447_0 = all_53_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_293_1, all_447_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (240), (290) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_447_0 = all_293_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_273_0, all_447_0, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (235), (290) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_447_0 = all_273_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_347_0, all_583_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (260), (323) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_583_1 = all_347_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_583_1, all_623_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (323), (334) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_623_1 = all_583_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_293_0, all_623_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (241), (334) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_623_1 = all_293_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_347_0, all_628_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (260), (340) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_628_1 = all_347_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_342_1, all_628_1, % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (253), (340) % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_628_1 = all_342_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (366) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_618_1 = all_342_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (377) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_618_1 = all_342_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (376) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_347_0 = all_342_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_347_0 = all_342_1 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (350) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_437_1 = all_407_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (381) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_437_1 = all_407_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (351) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_407_2 = all_402_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (374) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_583_1 = all_293_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (384) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_583_1 = all_293_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (378) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_377_1 = all_342_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (386) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_377_1 = all_342_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (348) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_457_2 = all_342_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (388) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_457_2 = all_342_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (385) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_347_0 = all_293_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_347_0 = all_293_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (362), (363) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_372_0 = all_268_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (392) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_372_0 = all_268_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (389) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_437_1 = all_342_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (394) implies: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_437_1 = all_342_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (371) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_293_1 = all_273_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (369), (370) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_293_1 = all_53_0 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (395) imply: % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_407_2 = all_342_2 % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (398) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_407_2 = all_342_2 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (399) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_402_2 = all_342_2 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (400) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_402_2 = all_342_2 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (387) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_347_1 = all_342_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (402) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_347_1 = all_342_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (387) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_342_0 = all_57_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (393) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_347_1 = all_268_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (405) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_347_1 = all_268_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (368), (380) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_342_1 = all_273_1 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (380) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_342_1 = all_273_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (391) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_342_1 = all_293_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (406) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_342_0 = all_268_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (410) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_342_0 = all_268_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (404), (411) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_268_0 = all_57_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (409) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_293_0 = all_273_1 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (409) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_293_0 = all_273_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (358) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_140_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (415) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_140_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (414) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_273_0 = all_273_1 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (417) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_273_0 = all_273_1 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (396), (397) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_273_0 = all_53_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (419) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_273_0 = all_53_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (418), (420) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_273_1 = all_53_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (356) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_136_3 = all_132_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (355) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_136_3 = all_134_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (416) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_136_3 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (423), (424) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_134_3 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (422), (423) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_134_3 = all_132_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (426) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_132_3 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (427) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_132_3 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (428) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_128_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (429) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_128_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (430) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_126_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (431) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_126_2 = all_69_3 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (421) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_293_0 = all_53_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (433) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_342_1 = all_53_0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_53_0 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (435) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) $false % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (436) is inconsistent. % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_1, all_38_3) = v3 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_1) = v0 & ( ~ % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_49_0 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (438) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) $false % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent. % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_1, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v3 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_1) = v0 & ( ~ % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_698_0, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_698_1, all_698_2, all_698_3 gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) apart_point_and_line(all_38_1, all_38_3) = % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_698_0 & apart_point_and_line(all_38_5, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_698_1 & distinct_lines(all_38_2, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_698_2 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_1) = all_698_3 & % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_698_2 = 0) | ~ (all_698_3 = 0) | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_698_0 = 0 | all_698_1 = 0) % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) distinct_lines(all_38_2, all_38_3) = all_698_2 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_342_2 = 0) % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) distinct_lines(all_38_2, all_38_3) = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_342_2, all_698_2, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (251), (442) % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_698_2 = all_342_2 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_698_2, all_38_3, % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (442), (444) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_698_2 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (446) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_342_2 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (447) implies: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_342_2 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (448) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) $false % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent. % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_69_3 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (450) imply: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) convergent_lines(all_38_3, all_38_3) = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_3, simplifying % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (37), (451) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) $false % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (452) is inconsistent. % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_342_0 = 0 | all_342_1 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_342_0 = 0 % 31.07/5.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (404), (454) imply: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_57_0 = 0 % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_57_0 = 0 % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (456) imply: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) $false % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (457) is inconsistent. % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_342_1 = 0 % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (434), (458) imply: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_53_0 = 0 % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (459) implies: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_53_0 = 0 % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (460) imply: % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) $false % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (461) is inconsistent. % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | | % 31.07/5.57 | | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | | % 31.07/5.57 | | | | | | | | | End of split % 31.07/5.57 | | | | | | | | | % 31.07/5.57 | | | | | | | | End of split % 31.07/5.57 | | | | | | | | % 31.07/5.57 | | | | | | | End of split % 31.07/5.57 | | | | | | | % 31.07/5.57 | | | | | | End of split % 31.07/5.57 | | | | | | % 31.07/5.57 | | | | | End of split % 31.07/5.57 | | | | | % 31.07/5.57 | | | | End of split % 31.07/5.57 | | | | % 31.07/5.57 | | | End of split % 31.07/5.57 | | | % 31.07/5.57 | | Case 2: % 31.07/5.57 | | | % 31.07/5.57 | | | (462) ~ (all_59_1 = 0) % 31.07/5.57 | | | % 31.07/5.57 | | | REDUCE: (147), (462) imply: % 31.07/5.57 | | | (463) $false % 31.07/5.57 | | | % 31.07/5.57 | | | CLOSE: (463) is inconsistent. % 31.07/5.57 | | | % 31.07/5.57 | | End of split % 31.07/5.57 | | % 31.07/5.57 | Case 2: % 31.07/5.57 | | % 31.07/5.57 | | (464) all_38_0 = 0 % 31.07/5.57 | | % 31.07/5.57 | | REDUCE: (34), (464) imply: % 31.07/5.57 | | (465) $false % 31.07/5.57 | | % 31.07/5.57 | | CLOSE: (465) is inconsistent. % 31.07/5.57 | | % 31.07/5.57 | End of split % 31.07/5.57 | % 31.07/5.57 End of proof % 31.07/5.57 % SZS output end Proof for theBenchmark % 31.07/5.57 % 31.07/5.57 4935ms %------------------------------------------------------------------------------