%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO217+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 : n003.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 23:22:27 EDT 2023 % Result : Theorem 15.20s 2.72s % Output : Proof 48.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO217+3 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 22:16:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.51/0.62 ________ _____ % 0.51/0.62 ___ __ \_________(_)________________________________ % 0.51/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.62 (2023-06-19) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2023 % 0.51/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.62 Amanda Stjerna. % 0.51/0.62 Free software under BSD-3-Clause. % 0.51/0.62 % 0.51/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.63 Running up to 7 provers in parallel. % 0.51/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.13/1.16 Prover 1: Preprocessing ... % 3.13/1.16 Prover 4: Preprocessing ... % 3.13/1.20 Prover 3: Preprocessing ... % 3.13/1.20 Prover 6: Preprocessing ... % 3.13/1.20 Prover 0: Preprocessing ... % 3.13/1.20 Prover 5: Preprocessing ... % 3.51/1.21 Prover 2: Preprocessing ... % 6.57/1.59 Prover 5: Proving ... % 6.57/1.59 Prover 2: Proving ... % 6.91/1.63 Prover 6: Constructing countermodel ... % 6.91/1.64 Prover 3: Constructing countermodel ... % 6.91/1.65 Prover 1: Constructing countermodel ... % 7.52/1.76 Prover 3: gave up % 7.52/1.77 Prover 6: gave up % 7.52/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.52/1.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.52/1.79 Prover 1: gave up % 8.11/1.83 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.11/1.84 Prover 7: Preprocessing ... % 8.11/1.86 Prover 8: Preprocessing ... % 8.11/1.88 Prover 9: Preprocessing ... % 8.91/1.91 Prover 7: Warning: ignoring some quantifiers % 9.03/1.94 Prover 4: Constructing countermodel ... % 9.03/1.95 Prover 7: Constructing countermodel ... % 9.03/2.01 Prover 0: Proving ... % 9.03/2.01 Prover 8: Warning: ignoring some quantifiers % 9.76/2.04 Prover 8: Constructing countermodel ... % 10.34/2.11 Prover 7: gave up % 10.34/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.98/2.17 Prover 10: Preprocessing ... % 11.04/2.20 Prover 8: gave up % 11.04/2.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.37/2.23 Prover 10: Warning: ignoring some quantifiers % 11.37/2.23 Prover 11: Preprocessing ... % 11.37/2.23 Prover 9: Constructing countermodel ... % 11.37/2.26 Prover 10: Constructing countermodel ... % 12.66/2.40 Prover 10: gave up % 12.66/2.40 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 12.66/2.44 Prover 12: Preprocessing ... % 13.87/2.57 Prover 11: Constructing countermodel ... % 14.06/2.61 Prover 12: Proving ... % 15.20/2.72 Prover 9: proved (893ms) % 15.20/2.72 % 15.20/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.20/2.72 % 15.20/2.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.20/2.72 Prover 0: stopped % 15.20/2.73 Prover 2: stopped % 15.20/2.73 Prover 5: stopped % 15.20/2.73 Prover 12: stopped % 15.20/2.73 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.20/2.73 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.20/2.75 Prover 13: Preprocessing ... % 15.20/2.76 Prover 16: Preprocessing ... % 15.59/2.77 Prover 19: Preprocessing ... % 15.59/2.79 Prover 16: Warning: ignoring some quantifiers % 15.59/2.79 Prover 13: Warning: ignoring some quantifiers % 15.59/2.79 Prover 16: Constructing countermodel ... % 15.59/2.79 Prover 13: Constructing countermodel ... % 16.18/2.86 Prover 19: Warning: ignoring some quantifiers % 16.36/2.89 Prover 19: Constructing countermodel ... % 16.36/2.90 Prover 13: gave up % 16.93/2.99 Prover 19: gave up % 16.93/3.03 Prover 16: gave up % 46.94/8.85 Prover 11: Found proof (size 886) % 46.94/8.85 Prover 11: proved (6645ms) % 46.94/8.85 Prover 4: stopped % 46.94/8.85 % 46.94/8.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 46.94/8.85 % 47.18/8.88 % SZS output start Proof for theBenchmark % 47.18/8.88 Assumptions after simplification: % 47.18/8.88 --------------------------------- % 47.18/8.88 % 47.18/8.89 (a3) % 47.18/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0, % 47.18/8.92 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & ! % 47.18/8.92 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, v1) % 47.18/8.92 = v2) | ~ $i(v1) | ~ $i(v0) | parallel_lines(v0, v1) = 0) & ! [v0: $i] % 47.18/8.92 : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 47.18/8.92 [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0: $i] : % 47.18/8.92 ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 47.18/8.92 [v2: int] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 47.18/8.92 % 47.18/8.92 (ax6) % 47.18/8.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 47.18/8.92 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 47.18/8.92 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 47.18/8.92 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 47.18/8.92 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 47.18/8.92 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.92 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 47.18/8.92 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 47.18/8.92 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.92 convergent_lines(v1, v2) = 0) % 47.18/8.92 % 47.18/8.92 (ceq2) % 47.18/8.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 47.18/8.93 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 47.18/8.93 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 47.18/8.93 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 47.18/8.93 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 47.18/8.93 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.93 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 47.18/8.93 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 47.18/8.93 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.93 apart_point_and_line(v0, v2) = 0) % 47.18/8.93 % 47.18/8.93 (ceq3) % 47.18/8.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 47.18/8.93 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 47.18/8.93 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 47.18/8.93 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 47.18/8.93 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 47.18/8.93 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.93 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 47.18/8.93 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 47.18/8.93 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.93 convergent_lines(v0, v2) = 0) % 47.18/8.93 % 47.18/8.93 (ci3) % 47.18/8.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 47.18/8.94 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 47.18/8.94 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 47.18/8.94 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 47.18/8.94 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 47.18/8.94 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 47.18/8.94 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 47.18/8.94 % 47.18/8.94 (ci4) % 47.18/8.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 47.18/8.94 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 47.18/8.94 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 47.18/8.94 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 47.18/8.94 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 47.18/8.94 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 47.18/8.94 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 47.18/8.94 % 47.18/8.94 (coipo1) % 47.18/8.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 47.18/8.94 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.94 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 47.18/8.94 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.18/8.94 unorthogonal_lines(v0, v1) = 0) % 47.18/8.94 % 47.18/8.94 (con) % 47.18/8.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 47.18/8.95 parallel_lines(v1, v2) = v3 & parallel_lines(v0, v2) = 0 & % 47.18/8.95 parallel_lines(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 47.18/8.95 % 47.18/8.95 (cotno1) % 47.63/8.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 47.63/8.97 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 47.63/8.97 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 47.63/8.97 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 47.63/8.97 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/8.97 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 47.63/8.97 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 47.63/8.97 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 47.63/8.97 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.97 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/8.97 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/8.97 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 47.63/8.97 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 47.63/8.97 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 47.63/8.97 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 47.63/8.97 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 47.63/8.97 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 47.63/8.97 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/8.97 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 47.63/8.97 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 47.63/8.97 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 47.63/8.97 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/8.97 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/8.97 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/8.97 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 47.63/8.97 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 47.63/8.98 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 47.63/8.98 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 47.63/8.98 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 47.63/8.98 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 47.63/8.98 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 47.63/8.98 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 47.63/8.98 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 47.63/8.98 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 47.63/8.98 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/8.98 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 47.63/8.98 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 47.63/8.98 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 47.63/8.98 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 47.63/8.98 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 47.63/8.98 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 47.63/8.98 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/8.98 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 47.63/8.98 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/8.98 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 47.63/8.98 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 47.63/8.98 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 47.63/8.98 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 47.63/8.98 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/8.98 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 47.63/8.98 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 47.63/8.98 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/8.98 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 47.63/8.98 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 47.63/8.98 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 47.63/8.98 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 47.63/8.98 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 47.63/8.98 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 47.63/8.98 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 47.63/8.98 unorthogonal_lines(v1, v2) = v7))) % 47.63/8.98 % 47.63/8.98 (couo1) % 47.63/8.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 47.63/8.98 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 47.63/8.98 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.98 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 47.63/8.98 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 47.63/8.98 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 47.63/8.98 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 47.63/8.98 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 47.63/8.98 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/8.98 unorthogonal_lines(v0, v2) = 0) % 47.63/8.98 % 47.63/8.98 (cup1) % 47.63/8.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 47.63/8.99 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 47.63/8.99 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.99 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~ % 47.63/8.99 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 47.63/8.99 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 47.63/8.99 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 47.63/8.99 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 47.63/8.99 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 47.63/8.99 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 47.63/8.99 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ % 47.63/8.99 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/8.99 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( % 47.63/8.99 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] % 47.63/8.99 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = % 47.63/8.99 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 47.63/8.99 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 47.63/8.99 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] % 47.63/8.99 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 47.63/8.99 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 47.63/8.99 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 47.63/8.99 (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 47.63/8.99 % 47.63/8.99 (oac1) % 47.63/9.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 47.63/9.01 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 47.63/9.01 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 47.63/9.01 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 47.63/9.01 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.01 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 47.63/9.01 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 47.63/9.01 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 47.63/9.01 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/9.01 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.01 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 47.63/9.01 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 47.63/9.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 47.63/9.01 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 47.63/9.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 47.63/9.01 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 47.63/9.01 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.01 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 47.63/9.01 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 47.63/9.01 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 47.63/9.01 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.01 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 47.63/9.01 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 47.63/9.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 47.63/9.01 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 47.63/9.01 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 47.63/9.01 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 47.63/9.01 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 47.63/9.01 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 47.63/9.01 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/9.01 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 47.63/9.01 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 47.63/9.01 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 47.63/9.01 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 47.63/9.01 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/9.01 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 47.63/9.01 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 47.63/9.01 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/9.01 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 47.63/9.01 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/9.01 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 47.63/9.01 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 47.63/9.01 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/9.01 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 47.63/9.01 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/9.01 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 47.63/9.01 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 47.63/9.01 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 47.63/9.01 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.63/9.01 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 47.63/9.01 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 47.63/9.01 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/9.01 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 47.63/9.01 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/9.01 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 47.63/9.01 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 47.63/9.01 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 47.63/9.01 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 47.63/9.01 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 47.63/9.01 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.01 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 47.63/9.01 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 47.63/9.01 unorthogonal_lines(v0, v1) = v4))) % 47.63/9.01 % 47.63/9.01 (occu1) % 47.63/9.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 47.63/9.01 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.01 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 47.63/9.01 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.01 unorthogonal_lines(v0, v1) = 0) % 47.63/9.01 % 47.63/9.01 (p1) % 47.63/9.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, % 47.63/9.01 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 47.63/9.01 distinct_lines(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 47.63/9.01 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, % 47.63/9.01 v1) = 0) % 47.63/9.01 % 47.63/9.01 (function-axioms) % 47.63/9.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 47.63/9.02 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 47.63/9.02 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 47.63/9.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.02 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 47.63/9.02 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 47.63/9.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 47.63/9.02 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 47.63/9.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.02 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 47.63/9.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 47.63/9.02 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 47.63/9.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.02 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 47.63/9.02 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 47.63/9.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 47.63/9.02 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/9.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 47.63/9.02 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 47.63/9.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 47.63/9.02 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 47.63/9.02 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 47.63/9.02 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 47.63/9.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.02 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 47.63/9.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 47.63/9.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 47.63/9.02 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 47.63/9.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.02 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 47.63/9.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 47.63/9.02 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 47.63/9.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 47.63/9.02 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 47.63/9.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 47.63/9.02 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 47.63/9.02 % 47.63/9.02 Further assumptions not needed in the proof: % 47.63/9.02 -------------------------------------------- % 47.63/9.02 a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ceq1, ci1, ci2, con1, % 47.63/9.02 cp1, cp2, cu1, int1, ooc1, ooc2, orth1, ouo1, par1 % 47.63/9.02 % 47.63/9.02 Those formulas are unsatisfiable: % 47.63/9.02 --------------------------------- % 47.63/9.02 % 47.63/9.02 Begin of proof % 47.63/9.02 | % 47.63/9.02 | ALPHA: (ax6) implies: % 47.63/9.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 47.63/9.02 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 47.63/9.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 47.63/9.02 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 47.63/9.02 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 47.63/9.02 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.02 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 47.63/9.02 | % 47.63/9.02 | ALPHA: (ci3) implies: % 47.63/9.02 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 47.63/9.02 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 47.63/9.02 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 47.63/9.02 | & $i(v2))) % 47.63/9.02 | % 47.63/9.02 | ALPHA: (ci4) implies: % 47.63/9.02 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 47.63/9.02 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 47.63/9.02 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 47.63/9.02 | & $i(v2))) % 47.63/9.02 | % 47.63/9.02 | ALPHA: (ceq2) implies: % 47.63/9.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 47.63/9.02 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 47.63/9.02 | (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.02 | ? [v5: int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 47.63/9.02 | % 47.63/9.02 | ALPHA: (ceq3) implies: % 47.63/9.02 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 47.63/9.02 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 47.63/9.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 47.63/9.03 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 47.63/9.03 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ % 47.63/9.03 | (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.03 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 47.63/9.03 | % 47.63/9.03 | ALPHA: (p1) implies: % 47.63/9.03 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 47.63/9.03 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 47.63/9.03 | int] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 47.63/9.03 | % 47.63/9.03 | ALPHA: (cup1) implies: % 47.63/9.03 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 47.63/9.03 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 47.63/9.03 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 47.63/9.03 | $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 47.63/9.03 | convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 47.63/9.03 | v2) = v5))) % 47.63/9.03 | % 47.63/9.03 | ALPHA: (oac1) implies: % 47.63/9.03 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 47.63/9.03 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = % 47.63/9.03 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 47.63/9.03 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.03 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 47.63/9.03 | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) % 47.63/9.03 | & convergent_lines(v0, v1) = v4))) % 47.63/9.03 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 47.63/9.03 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 47.63/9.03 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 47.63/9.03 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 47.63/9.03 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 47.63/9.03 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 47.63/9.03 | convergent_lines(v0, v1) = v4))) % 47.63/9.03 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.03 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 47.63/9.03 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.03 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.03 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.03 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.03 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 47.63/9.03 | convergent_lines(v0, v1) = v5))) % 47.63/9.03 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.03 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) % 47.63/9.03 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.03 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.03 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.03 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.03 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 47.63/9.03 | convergent_lines(v0, v1) = v5))) % 47.63/9.04 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.04 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) % 47.63/9.04 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.04 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.04 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.04 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 47.63/9.04 | convergent_lines(v0, v1) = v5))) % 47.63/9.04 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.04 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, % 47.63/9.04 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 47.63/9.04 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 47.63/9.04 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 47.63/9.04 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 47.63/9.04 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 47.63/9.04 | convergent_lines(v0, v1) = v5))) % 47.63/9.04 | % 47.63/9.04 | ALPHA: (occu1) implies: % 47.63/9.04 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 47.63/9.04 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.04 | unorthogonal_lines(v0, v1) = 0) % 47.63/9.04 | % 47.63/9.04 | ALPHA: (cotno1) implies: % 47.63/9.04 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 47.63/9.04 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) % 47.63/9.04 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 47.63/9.04 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 47.63/9.04 | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) % 47.63/9.04 | & unorthogonal_lines(v1, v2) = v7))) % 47.63/9.04 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 47.63/9.04 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 47.63/9.04 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 47.63/9.04 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 47.63/9.04 | ( ~ (v7 = 0) & unorthogonal_lines(v1, v2) = v7))) % 47.63/9.04 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.04 | : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = % 47.63/9.04 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.04 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/9.04 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/9.04 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 47.63/9.04 | convergent_lines(v1, v2) = v7))) % 47.63/9.05 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.05 | : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) % 47.63/9.05 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.05 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/9.05 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/9.05 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/9.05 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 47.63/9.05 | convergent_lines(v1, v2) = v7))) % 47.63/9.05 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.05 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) % 47.63/9.05 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 47.63/9.05 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/9.05 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/9.05 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/9.05 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 47.63/9.05 | convergent_lines(v1, v2) = v7))) % 47.63/9.05 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 47.63/9.05 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, % 47.63/9.05 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 47.63/9.05 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 47.63/9.05 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 47.63/9.05 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 47.63/9.05 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 47.63/9.05 | convergent_lines(v1, v2) = v7))) % 47.63/9.05 | % 47.63/9.05 | ALPHA: (couo1) implies: % 47.63/9.05 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 47.63/9.05 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = % 47.63/9.05 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, % 47.63/9.05 | v1) = 0) % 47.63/9.05 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 47.63/9.05 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 47.63/9.05 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 47.63/9.05 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = % 47.63/9.05 | v5)) % 47.63/9.05 | % 47.63/9.05 | ALPHA: (a3) implies: % 47.63/9.05 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ % 47.63/9.05 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 47.63/9.05 | convergent_lines(v0, v1) = v2)) % 47.63/9.05 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 47.63/9.05 | (parallel_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 47.63/9.05 | convergent_lines(v0, v1) = 0) % 47.63/9.05 | % 47.63/9.05 | ALPHA: (function-axioms) implies: % 47.63/9.05 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 47.63/9.05 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 47.63/9.05 | (convergent_lines(v3, v2) = v0)) % 47.63/9.05 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.63/9.05 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 47.63/9.05 | v0)) % 47.63/9.05 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 47.63/9.05 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 47.63/9.05 | (unorthogonal_lines(v3, v2) = v0)) % 47.63/9.05 | % 47.63/9.05 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 47.63/9.05 | all_38_3 gives: % 47.63/9.06 | (30) ~ (all_38_0 = 0) & parallel_lines(all_38_2, all_38_1) = all_38_0 & % 47.63/9.06 | parallel_lines(all_38_3, all_38_1) = 0 & parallel_lines(all_38_3, % 47.63/9.06 | all_38_2) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 47.63/9.06 | % 47.63/9.06 | ALPHA: (30) implies: % 47.63/9.06 | (31) ~ (all_38_0 = 0) % 47.63/9.06 | (32) $i(all_38_3) % 47.63/9.06 | (33) $i(all_38_2) % 47.63/9.06 | (34) $i(all_38_1) % 47.63/9.06 | (35) parallel_lines(all_38_3, all_38_2) = 0 % 47.63/9.06 | (36) parallel_lines(all_38_3, all_38_1) = 0 % 47.63/9.06 | (37) parallel_lines(all_38_2, all_38_1) = all_38_0 % 47.63/9.06 | % 47.63/9.06 | GROUND_INST: instantiating (25) with all_38_3, all_38_2, simplifying with % 47.63/9.06 | (32), (33), (35) gives: % 47.63/9.06 | (38) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_2) = % 47.63/9.06 | v0) % 47.63/9.06 | % 47.63/9.06 | GROUND_INST: instantiating (25) with all_38_3, all_38_1, simplifying with % 47.63/9.06 | (32), (34), (36) gives: % 47.63/9.06 | (39) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_1) = % 47.63/9.06 | v0) % 47.63/9.06 | % 47.63/9.06 | GROUND_INST: instantiating (26) with all_38_2, all_38_1, all_38_0, simplifying % 47.63/9.06 | with (33), (34), (37) gives: % 47.63/9.06 | (40) all_38_0 = 0 | convergent_lines(all_38_2, all_38_1) = 0 % 47.63/9.06 | % 47.63/9.06 | DELTA: instantiating (39) with fresh symbol all_45_0 gives: % 47.63/9.06 | (41) ~ (all_45_0 = 0) & convergent_lines(all_38_3, all_38_1) = all_45_0 % 47.63/9.06 | % 47.63/9.06 | ALPHA: (41) implies: % 47.63/9.06 | (42) ~ (all_45_0 = 0) % 47.63/9.06 | (43) convergent_lines(all_38_3, all_38_1) = all_45_0 % 47.63/9.06 | % 47.63/9.06 | DELTA: instantiating (38) with fresh symbol all_47_0 gives: % 47.63/9.06 | (44) ~ (all_47_0 = 0) & convergent_lines(all_38_3, all_38_2) = all_47_0 % 47.63/9.06 | % 47.63/9.06 | ALPHA: (44) implies: % 47.63/9.06 | (45) ~ (all_47_0 = 0) % 47.63/9.06 | (46) convergent_lines(all_38_3, all_38_2) = all_47_0 % 47.63/9.06 | % 47.63/9.06 | BETA: splitting (40) gives: % 47.63/9.06 | % 47.63/9.06 | Case 1: % 47.63/9.06 | | % 47.63/9.06 | | (47) convergent_lines(all_38_2, all_38_1) = 0 % 47.87/9.06 | | % 47.87/9.06 | | GROUND_INST: instantiating (2) with all_38_3, all_38_3, all_38_2, all_47_0, % 47.87/9.06 | | all_47_0, simplifying with (32), (33), (46) gives: % 47.87/9.06 | | (48) all_47_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.87/9.06 | | convergent_lines(all_38_3, all_38_3) = v0) % 47.87/9.06 | | % 47.87/9.06 | | GROUND_INST: instantiating (12) with all_38_3, all_38_3, all_38_2, all_47_0, % 47.87/9.06 | | all_47_0, simplifying with (32), (33), (46) gives: % 47.87/9.06 | | (49) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 47.87/9.06 | | & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | % 47.87/9.06 | | (v2 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = % 47.87/9.06 | | 0) | ( ~ (v1 = 0) & unorthogonal_lines(all_38_3, all_38_3) = v1) % 47.87/9.06 | | | ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_3) = v0)) % 47.87/9.06 | | % 47.87/9.06 | | GROUND_INST: instantiating (19) with all_38_3, all_38_2, all_38_2, all_47_0, % 47.87/9.06 | | all_47_0, simplifying with (32), (33), (46) gives: % 47.87/9.06 | | (50) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 47.87/9.06 | | & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | % 47.87/9.06 | | (v0 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = % 47.87/9.06 | | 0) | ( ~ (v3 = 0) & unorthogonal_lines(all_38_2, all_38_2) = v3) % 47.87/9.06 | | | ( ~ (v2 = 0) & convergent_lines(all_38_2, all_38_2) = v2)) % 47.87/9.06 | | % 47.87/9.06 | | GROUND_INST: instantiating (16) with all_38_3, all_38_2, all_47_0, % 47.87/9.06 | | simplifying with (32), (33), (46) gives: % 47.87/9.07 | | (51) all_47_0 = 0 | unorthogonal_lines(all_38_3, all_38_2) = 0 % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (8) with all_38_3, all_38_2, all_47_0, % 47.87/9.07 | | simplifying with (32), (33), (46) gives: % 47.87/9.07 | | (52) all_47_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 47.87/9.07 | | distinct_lines(all_38_3, all_38_2) = v0) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (12) with all_38_3, all_38_3, all_38_1, all_45_0, % 47.87/9.07 | | all_45_0, simplifying with (32), (34), (43) gives: % 47.87/9.07 | | (53) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 47.87/9.07 | | & all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 47.87/9.07 | | (v2 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = % 47.87/9.07 | | 0) | ( ~ (v1 = 0) & unorthogonal_lines(all_38_3, all_38_3) = v1) % 47.87/9.07 | | | ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_3) = v0)) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (19) with all_38_3, all_38_2, all_38_1, all_47_0, % 47.87/9.07 | | all_45_0, simplifying with (32), (33), (34), (43), (46) gives: % 47.87/9.07 | | (54) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 47.87/9.07 | | & all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 47.87/9.07 | | (v0 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = % 47.87/9.07 | | 0) | ( ~ (v3 = 0) & unorthogonal_lines(all_38_2, all_38_1) = v3) % 47.87/9.07 | | | ( ~ (v2 = 0) & convergent_lines(all_38_2, all_38_1) = v2)) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (16) with all_38_3, all_38_1, all_45_0, % 47.87/9.07 | | simplifying with (32), (34), (43) gives: % 47.87/9.07 | | (55) all_45_0 = 0 | unorthogonal_lines(all_38_3, all_38_1) = 0 % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (12) with all_38_2, all_38_2, all_38_1, 0, 0, % 47.87/9.07 | | simplifying with (33), (34), (47) gives: % 47.87/9.07 | | (56) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 47.87/9.07 | | & unorthogonal_lines(all_38_2, all_38_1) = 0) | (v2 = 0 & % 47.87/9.07 | | unorthogonal_lines(all_38_2, all_38_1) = 0) | ( ~ (v1 = 0) & % 47.87/9.07 | | unorthogonal_lines(all_38_2, all_38_2) = v1) | ( ~ (v0 = 0) & % 47.87/9.07 | | convergent_lines(all_38_2, all_38_2) = v0)) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (19) with all_38_2, all_38_1, all_38_1, 0, 0, % 47.87/9.07 | | simplifying with (33), (34), (47) gives: % 47.87/9.07 | | (57) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 % 47.87/9.07 | | & unorthogonal_lines(all_38_2, all_38_1) = 0) | (v0 = 0 & % 47.87/9.07 | | unorthogonal_lines(all_38_2, all_38_1) = 0) | ( ~ (v3 = 0) & % 47.87/9.07 | | unorthogonal_lines(all_38_1, all_38_1) = v3) | ( ~ (v2 = 0) & % 47.87/9.07 | | convergent_lines(all_38_1, all_38_1) = v2)) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (12) with all_38_3, all_38_2, all_38_1, all_45_0, % 47.87/9.07 | | 0, simplifying with (32), (33), (34), (43), (47) gives: % 47.87/9.07 | | (58) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 47.87/9.07 | | & unorthogonal_lines(all_38_2, all_38_1) = 0) | (v2 = 0 & % 47.87/9.07 | | all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~ % 47.87/9.07 | | (v1 = 0) & unorthogonal_lines(all_38_3, all_38_2) = v1) | ( ~ % 47.87/9.07 | | (v0 = 0) & convergent_lines(all_38_3, all_38_2) = v0)) % 47.87/9.07 | | % 47.87/9.07 | | GROUND_INST: instantiating (18) with all_38_3, all_38_2, all_38_1, all_45_0, % 47.87/9.07 | | simplifying with (32), (33), (34), (43), (47) gives: % 47.87/9.08 | | (59) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 47.87/9.08 | | & all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 47.87/9.08 | | (v1 = 0 & v0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0 & % 47.87/9.08 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 47.87/9.08 | | unorthogonal_lines(all_38_2, all_38_1) = v3)) % 47.87/9.08 | | % 47.87/9.08 | | GROUND_INST: instantiating (17) with all_38_3, all_38_2, all_38_1, all_47_0, % 47.87/9.08 | | simplifying with (32), (33), (34), (46), (47) gives: % 47.87/9.08 | | (60) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 % 47.87/9.08 | | & v1 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0 & % 47.87/9.08 | | convergent_lines(all_38_3, all_38_1) = 0) | (v0 = 0 & all_47_0 = % 47.87/9.08 | | 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ (v3 = 0) & % 47.87/9.08 | | unorthogonal_lines(all_38_2, all_38_1) = v3)) % 47.87/9.08 | | % 47.87/9.08 | | GROUND_INST: instantiating (4) with all_38_2, all_38_1, simplifying with % 47.87/9.08 | | (33), (34), (47) gives: % 47.87/9.08 | | (61) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 47.87/9.08 | | intersection_point(all_38_2, all_38_1) = v0 & % 47.87/9.08 | | apart_point_and_line(v0, all_38_1) = v1 & $i(v0)) % 47.87/9.08 | | % 47.87/9.08 | | GROUND_INST: instantiating (3) with all_38_2, all_38_1, simplifying with % 47.87/9.08 | | (33), (34), (47) gives: % 47.87/9.08 | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 47.87/9.08 | | intersection_point(all_38_2, all_38_1) = v0 & % 47.87/9.08 | | apart_point_and_line(v0, all_38_2) = v1 & $i(v0)) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (62) with fresh symbols all_58_0, all_58_1 gives: % 47.87/9.08 | | (63) ~ (all_58_0 = 0) & intersection_point(all_38_2, all_38_1) = % 47.87/9.08 | | all_58_1 & apart_point_and_line(all_58_1, all_38_2) = all_58_0 & % 47.87/9.08 | | $i(all_58_1) % 47.87/9.08 | | % 47.87/9.08 | | ALPHA: (63) implies: % 47.87/9.08 | | (64) ~ (all_58_0 = 0) % 47.87/9.08 | | (65) apart_point_and_line(all_58_1, all_38_2) = all_58_0 % 47.87/9.08 | | (66) intersection_point(all_38_2, all_38_1) = all_58_1 % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (61) with fresh symbols all_60_0, all_60_1 gives: % 47.87/9.08 | | (67) ~ (all_60_0 = 0) & intersection_point(all_38_2, all_38_1) = % 47.87/9.08 | | all_60_1 & apart_point_and_line(all_60_1, all_38_1) = all_60_0 & % 47.87/9.08 | | $i(all_60_1) % 47.87/9.08 | | % 47.87/9.08 | | ALPHA: (67) implies: % 47.87/9.08 | | (68) $i(all_60_1) % 47.87/9.08 | | (69) intersection_point(all_38_2, all_38_1) = all_60_1 % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (57) with fresh symbols all_63_0, all_63_1, all_63_2, % 47.87/9.08 | | all_63_3 gives: % 47.87/9.08 | | (70) (all_63_2 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | % 47.87/9.08 | | (all_63_3 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | ( ~ % 47.87/9.08 | | (all_63_0 = 0) & unorthogonal_lines(all_38_1, all_38_1) = % 47.87/9.08 | | all_63_0) | ( ~ (all_63_1 = 0) & convergent_lines(all_38_1, % 47.87/9.08 | | all_38_1) = all_63_1) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (56) with fresh symbols all_64_0, all_64_1, all_64_2, % 47.87/9.08 | | all_64_3 gives: % 47.87/9.08 | | (71) (all_64_0 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | % 47.87/9.08 | | (all_64_1 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | ( ~ % 47.87/9.08 | | (all_64_2 = 0) & unorthogonal_lines(all_38_2, all_38_2) = % 47.87/9.08 | | all_64_2) | ( ~ (all_64_3 = 0) & convergent_lines(all_38_2, % 47.87/9.08 | | all_38_2) = all_64_3) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (60) with fresh symbols all_67_0, all_67_1, all_67_2, % 47.87/9.08 | | all_67_3 gives: % 47.87/9.08 | | (72) (all_67_1 = 0 & all_67_2 = 0 & unorthogonal_lines(all_38_3, % 47.87/9.08 | | all_38_1) = 0 & convergent_lines(all_38_3, all_38_1) = 0) | % 47.87/9.08 | | (all_67_3 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 47.87/9.08 | | all_38_2) = 0) | ( ~ (all_67_0 = 0) & % 47.87/9.08 | | unorthogonal_lines(all_38_2, all_38_1) = all_67_0) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (59) with fresh symbols all_68_0, all_68_1, all_68_2, % 47.87/9.08 | | all_68_3 gives: % 47.87/9.08 | | (73) (all_68_1 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 47.87/9.08 | | all_38_1) = 0) | (all_68_2 = 0 & all_68_3 = 0 & % 47.87/9.08 | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 47.87/9.08 | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ (all_68_0 = 0) & % 47.87/9.08 | | unorthogonal_lines(all_38_2, all_38_1) = all_68_0) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (58) with fresh symbols all_70_0, all_70_1, all_70_2, % 47.87/9.08 | | all_70_3 gives: % 47.87/9.08 | | (74) (all_70_0 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | % 47.87/9.08 | | (all_70_1 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 47.87/9.08 | | all_38_1) = 0) | ( ~ (all_70_2 = 0) & % 47.87/9.08 | | unorthogonal_lines(all_38_3, all_38_2) = all_70_2) | ( ~ (all_70_3 % 47.87/9.08 | | = 0) & convergent_lines(all_38_3, all_38_2) = all_70_3) % 47.87/9.08 | | % 47.87/9.08 | | DELTA: instantiating (53) with fresh symbols all_73_0, all_73_1, all_73_2, % 47.87/9.08 | | all_73_3 gives: % 48.15/9.09 | | (75) (all_73_0 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | all_38_1) = 0) | (all_73_1 = 0 & all_45_0 = 0 & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~ (all_73_2 = 0) & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_3) = all_73_2) | ( ~ (all_73_3 % 48.15/9.09 | | = 0) & convergent_lines(all_38_3, all_38_3) = all_73_3) % 48.15/9.09 | | % 48.15/9.09 | | DELTA: instantiating (50) with fresh symbols all_74_0, all_74_1, all_74_2, % 48.15/9.09 | | all_74_3 gives: % 48.15/9.09 | | (76) (all_74_2 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | all_38_2) = 0) | (all_74_3 = 0 & all_47_0 = 0 & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ (all_74_0 = 0) & % 48.15/9.09 | | unorthogonal_lines(all_38_2, all_38_2) = all_74_0) | ( ~ (all_74_1 % 48.15/9.09 | | = 0) & convergent_lines(all_38_2, all_38_2) = all_74_1) % 48.15/9.09 | | % 48.15/9.09 | | DELTA: instantiating (54) with fresh symbols all_75_0, all_75_1, all_75_2, % 48.15/9.09 | | all_75_3 gives: % 48.15/9.09 | | (77) (all_75_2 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | all_38_1) = 0) | (all_75_3 = 0 & all_47_0 = 0 & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ (all_75_0 = 0) & % 48.15/9.09 | | unorthogonal_lines(all_38_2, all_38_1) = all_75_0) | ( ~ (all_75_1 % 48.15/9.09 | | = 0) & convergent_lines(all_38_2, all_38_1) = all_75_1) % 48.15/9.09 | | % 48.15/9.09 | | DELTA: instantiating (49) with fresh symbols all_76_0, all_76_1, all_76_2, % 48.15/9.09 | | all_76_3 gives: % 48.15/9.09 | | (78) (all_76_0 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | all_38_2) = 0) | (all_76_1 = 0 & all_47_0 = 0 & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ (all_76_2 = 0) & % 48.15/9.09 | | unorthogonal_lines(all_38_3, all_38_3) = all_76_2) | ( ~ (all_76_3 % 48.15/9.09 | | = 0) & convergent_lines(all_38_3, all_38_3) = all_76_3) % 48.15/9.09 | | % 48.15/9.09 | | BETA: splitting (51) gives: % 48.15/9.09 | | % 48.15/9.09 | | Case 1: % 48.15/9.09 | | | % 48.15/9.09 | | | (79) unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.15/9.09 | | | % 48.15/9.09 | | | BETA: splitting (55) gives: % 48.15/9.09 | | | % 48.15/9.09 | | | Case 1: % 48.15/9.09 | | | | % 48.15/9.09 | | | | (80) unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.15/9.09 | | | | % 48.15/9.09 | | | | BETA: splitting (72) gives: % 48.15/9.09 | | | | % 48.15/9.09 | | | | Case 1: % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | (81) all_67_1 = 0 & all_67_2 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | | | | all_38_1) = 0 & convergent_lines(all_38_3, all_38_1) = 0 % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | ALPHA: (81) implies: % 48.15/9.09 | | | | | (82) convergent_lines(all_38_3, all_38_1) = 0 % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | REF_CLOSE: (27), (42), (43), (82) are inconsistent by sub-proof #5. % 48.15/9.09 | | | | | % 48.15/9.09 | | | | Case 2: % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | (83) (all_67_3 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | | | | all_38_2) = 0) | ( ~ (all_67_0 = 0) & % 48.15/9.09 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_67_0) % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | BETA: splitting (83) gives: % 48.15/9.09 | | | | | % 48.15/9.09 | | | | | Case 1: % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | (84) all_67_3 = 0 & all_47_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | | | | | all_38_2) = 0 % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | ALPHA: (84) implies: % 48.15/9.09 | | | | | | (85) all_47_0 = 0 % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | REDUCE: (45), (85) imply: % 48.15/9.09 | | | | | | (86) $false % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | CLOSE: (86) is inconsistent. % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | Case 2: % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | (87) ~ (all_67_0 = 0) & unorthogonal_lines(all_38_2, all_38_1) = % 48.15/9.09 | | | | | | all_67_0 % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | ALPHA: (87) implies: % 48.15/9.09 | | | | | | (88) ~ (all_67_0 = 0) % 48.15/9.09 | | | | | | (89) unorthogonal_lines(all_38_2, all_38_1) = all_67_0 % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | BETA: splitting (73) gives: % 48.15/9.09 | | | | | | % 48.15/9.09 | | | | | | Case 1: % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | (90) all_68_1 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 48.15/9.09 | | | | | | | all_38_1) = 0 % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | ALPHA: (90) implies: % 48.15/9.09 | | | | | | | (91) all_45_0 = 0 % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | REDUCE: (42), (91) imply: % 48.15/9.09 | | | | | | | (92) $false % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | CLOSE: (92) is inconsistent. % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | Case 2: % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | (93) (all_68_2 = 0 & all_68_3 = 0 & % 48.15/9.09 | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 48.15/9.09 | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 48.15/9.09 | | | | | | | (all_68_0 = 0) & unorthogonal_lines(all_38_2, all_38_1) % 48.15/9.09 | | | | | | | = all_68_0) % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | BETA: splitting (93) gives: % 48.15/9.09 | | | | | | | % 48.15/9.09 | | | | | | | Case 1: % 48.15/9.09 | | | | | | | | % 48.15/9.09 | | | | | | | | (94) all_68_2 = 0 & all_68_3 = 0 & % 48.15/9.09 | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 48.15/9.09 | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 48.15/9.09 | | | | | | | | % 48.15/9.09 | | | | | | | | ALPHA: (94) implies: % 48.15/9.09 | | | | | | | | (95) convergent_lines(all_38_3, all_38_2) = 0 % 48.15/9.09 | | | | | | | | % 48.15/9.10 | | | | | | | | REF_CLOSE: (27), (45), (46), (95) are inconsistent by sub-proof % 48.15/9.10 | | | | | | | | #4. % 48.15/9.10 | | | | | | | | % 48.15/9.10 | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | % 48.15/9.10 | | | | | | | | (96) ~ (all_68_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.10 | | | | | | | | all_38_1) = all_68_0 % 48.15/9.10 | | | | | | | | % 48.15/9.10 | | | | | | | | ALPHA: (96) implies: % 48.15/9.10 | | | | | | | | (97) ~ (all_68_0 = 0) % 48.15/9.10 | | | | | | | | (98) unorthogonal_lines(all_38_2, all_38_1) = all_68_0 % 48.15/9.10 | | | | | | | | % 48.15/9.10 | | | | | | | | BETA: splitting (48) gives: % 48.15/9.10 | | | | | | | | % 48.15/9.10 | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | (99) all_47_0 = 0 % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | REDUCE: (45), (99) imply: % 48.15/9.10 | | | | | | | | | (100) $false % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | CLOSE: (100) is inconsistent. % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | (101) ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.10 | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0) % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | DELTA: instantiating (101) with fresh symbol all_101_0 gives: % 48.15/9.10 | | | | | | | | | (102) ~ (all_101_0 = 0) & convergent_lines(all_38_3, % 48.15/9.10 | | | | | | | | | all_38_3) = all_101_0 % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | ALPHA: (102) implies: % 48.15/9.10 | | | | | | | | | (103) ~ (all_101_0 = 0) % 48.15/9.10 | | | | | | | | | (104) convergent_lines(all_38_3, all_38_3) = all_101_0 % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | BETA: splitting (77) gives: % 48.15/9.10 | | | | | | | | | % 48.15/9.10 | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | (105) (all_75_2 = 0 & all_45_0 = 0 & % 48.15/9.10 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | % 48.15/9.10 | | | | | | | | | | (all_75_3 = 0 & all_47_0 = 0 & % 48.15/9.10 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | BETA: splitting (105) gives: % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | (106) all_75_2 = 0 & all_45_0 = 0 & % 48.15/9.10 | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | ALPHA: (106) implies: % 48.15/9.10 | | | | | | | | | | | (107) all_45_0 = 0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | REDUCE: (42), (107) imply: % 48.15/9.10 | | | | | | | | | | | (108) $false % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | CLOSE: (108) is inconsistent. % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | (109) all_75_3 = 0 & all_47_0 = 0 & % 48.15/9.10 | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | ALPHA: (109) implies: % 48.15/9.10 | | | | | | | | | | | (110) all_47_0 = 0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | REDUCE: (45), (110) imply: % 48.15/9.10 | | | | | | | | | | | (111) $false % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | CLOSE: (111) is inconsistent. % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | End of split % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | (112) ( ~ (all_75_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.10 | | | | | | | | | | all_38_1) = all_75_0) | ( ~ (all_75_1 = 0) & % 48.15/9.10 | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = all_75_1) % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | BETA: splitting (112) gives: % 48.15/9.10 | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | (113) ~ (all_75_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.10 | | | | | | | | | | | all_38_1) = all_75_0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | ALPHA: (113) implies: % 48.15/9.10 | | | | | | | | | | | (114) unorthogonal_lines(all_38_2, all_38_1) = all_75_0 % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | BETA: splitting (52) gives: % 48.15/9.10 | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | (115) all_47_0 = 0 % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | REDUCE: (45), (115) imply: % 48.15/9.10 | | | | | | | | | | | | (116) $false % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | (117) ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.10 | | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v0) % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | DELTA: instantiating (117) with fresh symbol all_110_0 % 48.15/9.10 | | | | | | | | | | | | gives: % 48.15/9.10 | | | | | | | | | | | | (118) ~ (all_110_0 = 0) & distinct_lines(all_38_3, % 48.15/9.10 | | | | | | | | | | | | all_38_2) = all_110_0 % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | ALPHA: (118) implies: % 48.15/9.10 | | | | | | | | | | | | (119) ~ (all_110_0 = 0) % 48.15/9.10 | | | | | | | | | | | | (120) distinct_lines(all_38_3, all_38_2) = all_110_0 % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | BETA: splitting (74) gives: % 48.15/9.10 | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | (121) (all_70_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.10 | | | | | | | | | | | | | all_38_1) = 0) | (all_70_1 = 0 & all_45_0 = 0 % 48.15/9.10 | | | | | | | | | | | | | & unorthogonal_lines(all_38_3, all_38_1) = 0) % 48.15/9.10 | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | BETA: splitting (121) gives: % 48.15/9.10 | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | Case 1: % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | (122) all_70_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.10 | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | ALPHA: (122) implies: % 48.15/9.10 | | | | | | | | | | | | | | (123) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | REF_CLOSE: (29), (88), (89), (98), (114), (123) are % 48.15/9.10 | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | (124) all_70_1 = 0 & all_45_0 = 0 & % 48.15/9.10 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | ALPHA: (124) implies: % 48.15/9.10 | | | | | | | | | | | | | | (125) all_45_0 = 0 % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | REDUCE: (42), (125) imply: % 48.15/9.10 | | | | | | | | | | | | | | (126) $false % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 48.15/9.10 | | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | | End of split % 48.15/9.10 | | | | | | | | | | | | | % 48.15/9.10 | | | | | | | | | | | | Case 2: % 48.15/9.10 | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | (127) ( ~ (all_70_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.11 | | | | | | | | | | | | | all_38_2) = all_70_2) | ( ~ (all_70_3 = 0) & % 48.15/9.11 | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = all_70_3) % 48.15/9.11 | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | BETA: splitting (127) gives: % 48.15/9.11 | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | Case 1: % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | (128) ~ (all_70_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.11 | | | | | | | | | | | | | | all_38_2) = all_70_2 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | ALPHA: (128) implies: % 48.15/9.11 | | | | | | | | | | | | | | (129) ~ (all_70_2 = 0) % 48.15/9.11 | | | | | | | | | | | | | | (130) unorthogonal_lines(all_38_3, all_38_2) = all_70_2 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_70_2, all_38_2, % 48.15/9.11 | | | | | | | | | | | | | | all_38_3, simplifying with (79), (130) gives: % 48.15/9.11 | | | | | | | | | | | | | | (131) all_70_2 = 0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | REDUCE: (129), (131) imply: % 48.15/9.11 | | | | | | | | | | | | | | (132) $false % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | Case 2: % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | (133) ~ (all_70_3 = 0) & convergent_lines(all_38_3, % 48.15/9.11 | | | | | | | | | | | | | | all_38_2) = all_70_3 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | ALPHA: (133) implies: % 48.15/9.11 | | | | | | | | | | | | | | (134) ~ (all_70_3 = 0) % 48.15/9.11 | | | | | | | | | | | | | | (135) convergent_lines(all_38_3, all_38_2) = all_70_3 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_47_0, all_70_3, % 48.15/9.11 | | | | | | | | | | | | | | all_38_2, all_38_3, simplifying with (46), (135) % 48.15/9.11 | | | | | | | | | | | | | | gives: % 48.15/9.11 | | | | | | | | | | | | | | (136) all_70_3 = all_47_0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_58_1, all_60_1, % 48.15/9.11 | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (66), (69) % 48.15/9.11 | | | | | | | | | | | | | | gives: % 48.15/9.11 | | | | | | | | | | | | | | (137) all_60_1 = all_58_1 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_68_0, all_75_0, % 48.15/9.11 | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (98), (114) % 48.15/9.11 | | | | | | | | | | | | | | gives: % 48.15/9.11 | | | | | | | | | | | | | | (138) all_75_0 = all_68_0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_67_0, all_75_0, % 48.15/9.11 | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (89), (114) % 48.15/9.11 | | | | | | | | | | | | | | gives: % 48.15/9.11 | | | | | | | | | | | | | | (139) all_75_0 = all_67_0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | COMBINE_EQS: (138), (139) imply: % 48.15/9.11 | | | | | | | | | | | | | | (140) all_68_0 = all_67_0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | SIMP: (140) implies: % 48.15/9.11 | | | | | | | | | | | | | | (141) all_68_0 = all_67_0 % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | REDUCE: (68), (137) imply: % 48.15/9.11 | | | | | | | | | | | | | | (142) $i(all_58_1) % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_38_3, all_38_1, % 48.15/9.11 | | | | | | | | | | | | | | all_38_3, all_45_0, all_101_0, simplifying with % 48.15/9.11 | | | | | | | | | | | | | | (32), (34), (43), (104) gives: % 48.15/9.11 | | | | | | | | | | | | | | (143) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.11 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & all_101_0 = 0 & % 48.15/9.11 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.11 | | | | | | | | | | | | | | (v0 = 0 & all_45_0 = 0 & % 48.15/9.11 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | % 48.15/9.11 | | | | | | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_1, % 48.15/9.11 | | | | | | | | | | | | | | all_38_3) = v3) | ( ~ (v2 = 0) & % 48.15/9.11 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = v2)) % 48.15/9.11 | | | | | | | | | | | | | | % 48.15/9.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_38_3, all_38_3, % 48.15/9.11 | | | | | | | | | | | | | | all_38_3, all_101_0, all_101_0, simplifying with % 48.15/9.11 | | | | | | | | | | | | | | (32), (104) gives: % 48.15/9.12 | | | | | | | | | | | | | | (144) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_101_0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.12 | | | | | | | | | | | | | | (v2 = 0 & all_101_0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.12 | | | | | | | | | | | | | | ( ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_38_3, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3, all_101_0, all_101_0, simplifying with % 48.15/9.12 | | | | | | | | | | | | | | (32), (104) gives: % 48.15/9.12 | | | | | | | | | | | | | | (145) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & all_101_0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.12 | | | | | | | | | | | | | | (v0 = 0 & all_101_0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.12 | | | | | | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v3) | ( ~ (v2 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v2)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_38_3, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_101_0, simplifying with (32), (104) gives: % 48.15/9.12 | | | | | | | | | | | | | | (146) all_101_0 = 0 | unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = 0 % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_1, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, all_110_0, all_58_0, simplifying with % 48.15/9.12 | | | | | | | | | | | | | | (32), (33), (65), (120), (142) gives: % 48.15/9.12 | | | | | | | | | | | | | | (147) all_110_0 = 0 | all_58_0 = 0 | ? [v0: int] : ( ~ % 48.15/9.12 | | | | | | | | | | | | | | (v0 = 0) & apart_point_and_line(all_58_1, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v0) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_38_3, all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, 0, 0, simplifying with (32), (33), (79) % 48.15/9.12 | | | | | | | | | | | | | | gives: % 48.15/9.12 | | | | | | | | | | | | | | (148) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & convergent_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = 0) | (v0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = v3) | ( ~ (v2 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = v2)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_38_3, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, 0, 0, simplifying with (32), (33), (79) % 48.15/9.12 | | | | | | | | | | | | | | gives: % 48.15/9.12 | | | | | | | | | | | | | | (149) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = 0) | (v2 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_38_3, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, all_47_0, 0, simplifying with (32), % 48.15/9.12 | | | | | | | | | | | | | | (33), (46), (79) gives: % 48.15/9.12 | | | | | | | | | | | | | | (150) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = 0) | (v2 = 0 & all_47_0 = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_38_3, all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, 0, all_47_0, simplifying with (32), % 48.15/9.12 | | | | | | | | | | | | | | (33), (46), (79) gives: % 48.15/9.12 | | | | | | | | | | | | | | (151) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_47_0 = 0) | (v2 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_38_3, all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, all_47_0, 0, simplifying with (32), % 48.15/9.12 | | | | | | | | | | | | | | (33), (46), (79) gives: % 48.15/9.12 | | | | | | | | | | | | | | (152) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & convergent_lines(all_38_3, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = 0) | (v0 = 0 & all_47_0 = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = v3) | ( ~ (v2 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = v2)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_38_3, all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2, 0, all_47_0, simplifying with (32), % 48.15/9.12 | | | | | | | | | | | | | | (33), (46), (79) gives: % 48.15/9.12 | | | | | | | | | | | | | | (153) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.12 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & all_47_0 = 0) | (v0 = 0 & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( % 48.15/9.12 | | | | | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.12 | | | | | | | | | | | | | | all_38_2) = v3) | ( ~ (v2 = 0) & % 48.15/9.12 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = v2)) % 48.15/9.12 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_38_3, all_38_1, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, 0, simplifying with (32), (34), (80) % 48.15/9.13 | | | | | | | | | | | | | | gives: % 48.15/9.13 | | | | | | | | | | | | | | (154) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (v1 = 0 & convergent_lines(all_38_3, all_38_1) = % 48.15/9.13 | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & convergent_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_38_3, all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, 0, 0, simplifying with (32), (34), (80) % 48.15/9.13 | | | | | | | | | | | | | | gives: % 48.15/9.13 | | | | | | | | | | | | | | (155) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1) = 0) | (v2 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) | ( % 48.15/9.13 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_38_3, all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_45_0, 0, simplifying with (32), % 48.15/9.13 | | | | | | | | | | | | | | (34), (43), (80) gives: % 48.15/9.13 | | | | | | | | | | | | | | (156) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1) = 0) | (v2 = 0 & all_45_0 = 0) | ( % 48.15/9.13 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_38_3, all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, 0, all_45_0, simplifying with (32), % 48.15/9.13 | | | | | | | | | | | | | | (34), (43), (80) gives: % 48.15/9.13 | | | | | | | | | | | | | | (157) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_45_0 = 0) | (v2 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) | ( % 48.15/9.13 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.13 | | | | | | | | | | | | | | all_38_3) = v1) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_38_3, all_38_1, % 48.15/9.13 | | | | | | | | | | | | | | all_38_3, 0, all_101_0, simplifying with (32), % 48.15/9.13 | | | | | | | | | | | | | | (34), (80), (104) gives: % 48.15/9.13 | | | | | | | | | | | | | | (158) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & all_101_0 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (v0 = 0 & convergent_lines(all_38_3, all_38_1) = % 48.15/9.13 | | | | | | | | | | | | | | 0) | ( ~ (v3 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_3) = v3) | % 48.15/9.13 | | | | | | | | | | | | | | ( ~ (v2 = 0) & convergent_lines(all_38_1, % 48.15/9.13 | | | | | | | | | | | | | | all_38_3) = v2)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_38_3, all_38_1, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_45_0, simplifying with (32), (34), % 48.15/9.13 | | | | | | | | | | | | | | (43), (80) gives: % 48.15/9.13 | | | | | | | | | | | | | | (159) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (v1 = 0 & all_45_0 = 0) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_38_2, all_38_1, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_67_0, all_67_0, simplifying with % 48.15/9.13 | | | | | | | | | | | | | | (33), (34), (89) gives: % 48.15/9.13 | | | | | | | | | | | | | | (160) all_67_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = v0) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_38_2, all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_67_0, all_67_0, simplifying with % 48.15/9.13 | | | | | | | | | | | | | | (33), (34), (89) gives: % 48.15/9.13 | | | | | | | | | | | | | | (161) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_67_0 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (v2 = 0 & all_67_0 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | ( % 48.15/9.13 | | | | | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_2) = v1) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_38_2, all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_67_0, simplifying with (33), (34), % 48.15/9.13 | | | | | | | | | | | | | | (47), (89) gives: % 48.15/9.13 | | | | | | | | | | | | | | (162) all_67_0 = 0 | unorthogonal_lines(all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_2) = 0 % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_38_2, all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, 0, all_67_0, simplifying with (33), % 48.15/9.13 | | | | | | | | | | | | | | (34), (47), (89) gives: % 48.15/9.13 | | | | | | | | | | | | | | (163) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_67_0 = 0) | (v2 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | ( ~ (v1 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_2) = v1) | ( ~ (v0 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_38_2, all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_1, all_67_0, 0, simplifying with (33), % 48.15/9.13 | | | | | | | | | | | | | | (34), (47), (89) gives: % 48.15/9.13 | | | | | | | | | | | | | | (164) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.15/9.13 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (v2 = 0 & all_67_0 = 0) | ( ~ (v1 = 0) & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = v1) | % 48.15/9.13 | | | | | | | | | | | | | | ( ~ (v0 = 0) & convergent_lines(all_38_2, % 48.15/9.13 | | | | | | | | | | | | | | all_38_2) = v0)) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_129_0, % 48.15/9.13 | | | | | | | | | | | | | | all_129_1, all_129_2, all_129_3 gives: % 48.15/9.13 | | | | | | | | | | | | | | (165) (all_129_0 = 0 & all_129_1 = 0 & % 48.15/9.13 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.15/9.13 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | % 48.15/9.13 | | | | | | | | | | | | | | (all_129_2 = 0 & all_45_0 = 0) | ( ~ (all_129_3 = % 48.15/9.13 | | | | | | | | | | | | | | 0) & convergent_lines(all_38_3, all_38_1) = % 48.15/9.13 | | | | | | | | | | | | | | all_129_3) % 48.15/9.13 | | | | | | | | | | | | | | % 48.15/9.13 | | | | | | | | | | | | | | DELTA: instantiating (157) with fresh symbols all_131_0, % 48.15/9.13 | | | | | | | | | | | | | | all_131_1, all_131_2, all_131_3 gives: % 48.15/9.13 | | | | | | | | | | | | | | (166) (all_131_0 = 0 & all_45_0 = 0) | (all_131_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_131_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_131_2) | ( ~ (all_131_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_131_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (155) with fresh symbols all_133_0, % 48.15/9.14 | | | | | | | | | | | | | | all_133_1, all_133_2, all_133_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (167) (all_133_0 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_1) = 0) | (all_133_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_133_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_133_2) | ( ~ (all_133_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_133_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_135_0, % 48.15/9.14 | | | | | | | | | | | | | | all_135_1, all_135_2, all_135_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (168) (all_135_0 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_1) = 0) | (all_135_1 = 0 & all_45_0 = % 48.15/9.14 | | | | | | | | | | | | | | 0) | ( ~ (all_135_2 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_135_2) | ( ~ (all_135_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_135_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_138_0, % 48.15/9.14 | | | | | | | | | | | | | | all_138_1, all_138_2, all_138_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (169) (all_138_2 = 0 & all_47_0 = 0) | (all_138_3 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_138_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = all_138_0) | ( ~ (all_138_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_138_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_139_0, % 48.15/9.14 | | | | | | | | | | | | | | all_139_1, all_139_2, all_139_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (170) (all_139_2 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = 0) | (all_139_3 = 0 & all_47_0 = % 48.15/9.14 | | | | | | | | | | | | | | 0) | ( ~ (all_139_0 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_139_0) | ( ~ (all_139_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_139_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (164) with fresh symbols all_142_0, % 48.15/9.14 | | | | | | | | | | | | | | all_142_1, all_142_2, all_142_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (171) (all_142_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | all_38_1) = 0) | (all_142_1 = 0 & all_67_0 = % 48.15/9.14 | | | | | | | | | | | | | | 0) | ( ~ (all_142_2 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_142_2) | ( ~ (all_142_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_142_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_143_0, % 48.15/9.14 | | | | | | | | | | | | | | all_143_1, all_143_2, all_143_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (172) (all_143_0 = 0 & all_67_0 = 0) | (all_143_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0) | ( % 48.15/9.14 | | | | | | | | | | | | | | ~ (all_143_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = all_143_2) | ( ~ (all_143_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_143_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (151) with fresh symbols all_144_0, % 48.15/9.14 | | | | | | | | | | | | | | all_144_1, all_144_2, all_144_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (173) (all_144_0 = 0 & all_47_0 = 0) | (all_144_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_144_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_144_2) | ( ~ (all_144_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_144_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_145_0, % 48.15/9.14 | | | | | | | | | | | | | | all_145_1, all_145_2, all_145_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (174) (all_145_0 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = 0) | (all_145_1 = 0 & all_47_0 = % 48.15/9.14 | | | | | | | | | | | | | | 0) | ( ~ (all_145_2 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_145_2) | ( ~ (all_145_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_145_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (149) with fresh symbols all_147_0, % 48.15/9.14 | | | | | | | | | | | | | | all_147_1, all_147_2, all_147_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (175) (all_147_0 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = 0) | (all_147_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_147_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_147_2) | ( ~ (all_147_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_147_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_150_0, % 48.15/9.14 | | | | | | | | | | | | | | all_150_1, all_150_2, all_150_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (176) (all_150_0 = 0 & all_150_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_150_2 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_1) = 0) | ( ~ (all_150_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = % 48.15/9.14 | | | | | | | | | | | | | | all_150_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (148) with fresh symbols all_153_0, % 48.15/9.14 | | | | | | | | | | | | | | all_153_1, all_153_2, all_153_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (177) (all_153_2 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = 0) | (all_153_3 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_153_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = all_153_0) | ( ~ (all_153_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_153_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (158) with fresh symbols all_156_0, % 48.15/9.14 | | | | | | | | | | | | | | all_156_1, all_156_2, all_156_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (178) (all_156_2 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_156_3 = 0 & convergent_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_1) = 0) | ( ~ (all_156_0 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_156_0) | ( ~ (all_156_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_156_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_165_0, % 48.15/9.14 | | | | | | | | | | | | | | all_165_1, all_165_2, all_165_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (179) (all_165_0 = 0 & all_67_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_165_1 = 0 & all_67_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~ % 48.15/9.14 | | | | | | | | | | | | | | (all_165_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | all_38_2) = all_165_2) | ( ~ (all_165_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | all_165_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (145) with fresh symbols all_166_0, % 48.15/9.14 | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (180) (all_166_2 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_166_3 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | ( % 48.15/9.14 | | | | | | | | | | | | | | ~ (all_166_0 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_166_0) | ( ~ (all_166_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_166_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_168_0, % 48.15/9.14 | | | | | | | | | | | | | | all_168_1, all_168_2, all_168_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (181) (all_168_0 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_168_1 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | ( % 48.15/9.14 | | | | | | | | | | | | | | ~ (all_168_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_168_2) | ( ~ (all_168_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_168_3) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | DELTA: instantiating (143) with fresh symbols all_169_0, % 48.15/9.14 | | | | | | | | | | | | | | all_169_1, all_169_2, all_169_3 gives: % 48.15/9.14 | | | | | | | | | | | | | | (182) (all_169_2 = 0 & all_101_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.15/9.14 | | | | | | | | | | | | | | (all_169_3 = 0 & all_45_0 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | ( % 48.15/9.14 | | | | | | | | | | | | | | ~ (all_169_0 = 0) & unorthogonal_lines(all_38_1, % 48.15/9.14 | | | | | | | | | | | | | | all_38_3) = all_169_0) | ( ~ (all_169_1 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = % 48.15/9.14 | | | | | | | | | | | | | | all_169_1) % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | BETA: splitting (162) gives: % 48.15/9.14 | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | (183) unorthogonal_lines(all_38_2, all_38_2) = 0 % 48.15/9.14 | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 48.15/9.14 | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | (184) all_110_0 = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | REDUCE: (119), (184) imply: % 48.15/9.14 | | | | | | | | | | | | | | | | (185) $false % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | Case 2: % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | (186) all_58_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | | | apart_point_and_line(all_58_1, all_38_3) = v0) % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 48.15/9.14 | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | (187) (all_143_0 = 0 & all_67_0 = 0) | (all_143_1 = 0 & % 48.15/9.14 | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0) % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | (188) all_143_0 = 0 & all_67_0 = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (189) all_67_0 = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | REDUCE: (88), (189) imply: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (190) $false % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent. % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | (191) all_143_1 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (192) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (88), (89), (98), (114), (192) are % 48.15/9.14 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | End of split % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | Case 2: % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | (193) ( ~ (all_143_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | | | | all_38_2) = all_143_2) | ( ~ (all_143_3 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.14 | | | | | | | | | | | | | | | | | all_143_3) % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 48.15/9.14 | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | (194) ~ (all_143_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | | | | | all_38_2) = all_143_2 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (195) ~ (all_143_2 = 0) % 48.15/9.14 | | | | | | | | | | | | | | | | | | (196) unorthogonal_lines(all_38_2, all_38_2) = all_143_2 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_143_2, all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (196) gives: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (197) all_143_2 = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | REDUCE: (195), (197) imply: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (198) $false % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | (199) ~ (all_143_3 = 0) & convergent_lines(all_38_2, % 48.15/9.14 | | | | | | | | | | | | | | | | | | all_38_2) = all_143_3 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 48.15/9.14 | | | | | | | | | | | | | | | | | | (200) convergent_lines(all_38_2, all_38_2) = all_143_3 % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 48.15/9.14 | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | | (201) all_67_0 = 0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | | REDUCE: (88), (201) imply: % 48.15/9.14 | | | | | | | | | | | | | | | | | | | (202) $false % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | | (203) ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.14 | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = v0) % 48.15/9.14 | | | | | | | | | | | | | | | | | | | % 48.15/9.14 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (203) with fresh symbol all_237_0 % 48.15/9.14 | | | | | | | | | | | | | | | | | | | gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | (204) ~ (all_237_0 = 0) & convergent_lines(all_38_1, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | all_38_1) = all_237_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | (205) ~ (all_237_0 = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | (206) convergent_lines(all_38_1, all_38_1) = all_237_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | (207) (all_139_2 = 0 & convergent_lines(all_38_3, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_139_3 = 0 & all_47_0 = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (208) all_139_2 = 0 & convergent_lines(all_38_3, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (209) convergent_lines(all_38_3, all_38_2) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (209) are inconsistent by % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (210) all_139_3 = 0 & all_47_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (211) all_47_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (211) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (212) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | (213) ( ~ (all_139_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | all_38_2) = all_139_0) | ( ~ (all_139_1 = 0) & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | all_139_1) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (214) ~ (all_139_0 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_139_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_139_0 = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (216) unorthogonal_lines(all_38_2, all_38_2) = all_139_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_139_0, all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (216) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (217) all_139_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (217) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (218) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_139_1 = 0) & convergent_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_139_1 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | (220) convergent_lines(all_38_2, all_38_2) = all_139_1 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | (221) (all_64_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_64_1 = 0 & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (222) all_64_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (223) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (88), (89), (98), (114), (223) are % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (224) all_64_1 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (225) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (88), (89), (98), (114), (225) are % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | (226) ( ~ (all_64_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_64_2) | ( ~ (all_64_3 = 0) & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = all_64_3) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_64_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_64_2 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_64_2 = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (229) unorthogonal_lines(all_38_2, all_38_2) = all_64_2 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_64_2, all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (229) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (230) all_64_2 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (228), (230) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (231) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_64_3 = 0) & convergent_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_64_3 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | (233) convergent_lines(all_38_2, all_38_2) = all_64_3 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (234) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (235) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (236) ? [v0: int] : ( ~ (v0 = 0) & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_58_1, all_38_3) = v0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (236) with fresh symbol all_268_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_268_0 = 0) & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_58_1, all_38_3) = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | all_268_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_268_0 = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | (239) apart_point_and_line(all_58_1, all_38_3) = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | all_268_0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_129_0 = 0 & all_129_1 = 0 & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | (241) convergent_lines(all_38_1, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | (242) unorthogonal_lines(all_38_1, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (29), (70), (88), (89), (98), (114), (206), % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242) are inconsistent by sub-proof #2. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_129_2 = 0 & all_45_0 = 0) | ( ~ (all_129_3 = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | 0) & convergent_lines(all_38_3, all_38_1) = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | all_129_3) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_129_2 = 0 & all_45_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_45_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (245) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_129_3 = 0) & convergent_lines(all_38_3, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_129_3 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_129_3 = 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) convergent_lines(all_38_3, all_38_1) = all_129_3 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) (all_142_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_142_1 = 0 & all_67_0 = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_142_0 = 0 & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (88), (89), (98), (114), (252) are % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_142_1 = 0 & all_67_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_67_0 = 0 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (254) imply: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) $false % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (255) is inconsistent. % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ( ~ (all_142_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_142_2) | ( ~ (all_142_3 = 0) & % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_142_3) % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_142_2 = 0) & unorthogonal_lines(all_38_2, % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_142_2 % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies: % 48.15/9.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) ~ (all_142_2 = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) unorthogonal_lines(all_38_2, all_38_2) = all_142_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_142_2, all_38_2, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (259) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_142_2 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (260) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) ~ (all_142_3 = 0) & convergent_lines(all_38_2, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_142_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) convergent_lines(all_38_2, all_38_2) = all_142_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_73_0 = 0 & all_45_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_73_1 = 0 & all_45_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_73_0 = 0 & all_45_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_45_0 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (267) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_73_1 = 0 & all_45_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_45_0 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (270) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) ( ~ (all_73_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_73_2) | ( ~ (all_73_3 = 0) & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = all_73_3) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_73_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_73_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) ~ (all_73_2 = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) unorthogonal_lines(all_38_3, all_38_3) = all_73_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_73_2, all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (275) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_73_2 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (276) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) ~ (all_73_3 = 0) & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_73_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) convergent_lines(all_38_3, all_38_3) = all_73_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_76_0 = 0 & all_47_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_76_1 = 0 & all_47_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_76_0 = 0 & all_47_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_47_0 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (282) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_76_1 = 0 & all_47_0 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_47_0 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (285) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ( ~ (all_76_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_2) | ( ~ (all_76_3 = 0) & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = all_76_3) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_76_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_76_2 = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) unorthogonal_lines(all_38_3, all_38_3) = all_76_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_76_2, all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (290) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_76_2 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (289), (291) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) ~ (all_76_3 = 0) & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) ~ (all_76_3 = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) convergent_lines(all_38_3, all_38_3) = all_76_3 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_133_0 = 0 & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_133_1 = 0 & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_133_0 = 0 & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) convergent_lines(all_38_3, all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (298) are inconsistent by % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_133_1 = 0 & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) convergent_lines(all_38_3, all_38_1) = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (300) are inconsistent by % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) ( ~ (all_133_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_133_2) | ( ~ (all_133_3 = 0) & % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_133_2 = 0) & unorthogonal_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_133_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_133_2 = 0) % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) unorthogonal_lines(all_38_3, all_38_3) = all_133_2 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_133_2, all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (304) gives: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_133_2 = 0 % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (305) imply: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) $false % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent. % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) ~ (all_133_3 = 0) & convergent_lines(all_38_3, % 48.15/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_133_3 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) convergent_lines(all_38_3, all_38_3) = all_133_3 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_74_2 = 0 & all_47_0 = 0 & % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_74_3 = 0 & all_47_0 = 0 & % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_74_2 = 0 & all_47_0 = 0 & % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_47_0 = 0 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (311) imply: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) $false % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_74_3 = 0 & all_47_0 = 0 & % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_47_0 = 0 % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (314) imply: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) $false % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) ( ~ (all_74_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_74_0) | ( ~ (all_74_1 = 0) & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = all_74_1) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_74_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_74_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_74_0 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) unorthogonal_lines(all_38_2, all_38_2) = all_74_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_74_0, all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (319) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_74_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (318), (320) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) ~ (all_74_1 = 0) & convergent_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_74_1 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_74_1 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) convergent_lines(all_38_2, all_38_2) = all_74_1 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) (all_131_0 = 0 & all_45_0 = 0) | (all_131_1 = 0 & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_131_0 = 0 & all_45_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_45_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (327) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (328) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_131_1 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) convergent_lines(all_38_3, all_38_1) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (330) are inconsistent by % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ( ~ (all_131_2 = 0) & unorthogonal_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_131_2) | ( ~ (all_131_3 = 0) & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_131_3) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) ~ (all_131_2 = 0) & unorthogonal_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_131_2 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_131_2 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) unorthogonal_lines(all_38_3, all_38_3) = all_131_2 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_131_2, all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (334) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_131_2 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (335) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_131_3 = 0) & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_131_3 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) convergent_lines(all_38_3, all_38_3) = all_131_3 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) (all_138_2 = 0 & all_47_0 = 0) | (all_138_3 = 0 & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_138_2 = 0 & all_47_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_47_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (341) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_138_3 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (343) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) convergent_lines(all_38_3, all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (344) are inconsistent by % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ( ~ (all_138_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_138_0) | ( ~ (all_138_1 = 0) & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_138_1) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_138_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_138_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) ~ (all_138_0 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) unorthogonal_lines(all_38_2, all_38_2) = all_138_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_138_0, all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (348) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_138_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (349) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_138_1 = 0) & convergent_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_138_1 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) convergent_lines(all_38_2, all_38_2) = all_138_1 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) (all_145_0 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_145_1 = 0 & all_47_0 = % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_145_0 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) convergent_lines(all_38_3, all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (355) are inconsistent by % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_145_1 = 0 & all_47_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_47_0 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (357) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) ( ~ (all_145_2 = 0) & unorthogonal_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_145_2) | ( ~ (all_145_3 = 0) & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_145_3) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (359) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_145_2 = 0) & unorthogonal_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_145_2 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_145_2 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) unorthogonal_lines(all_38_3, all_38_3) = all_145_2 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_145_2, all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (362) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_145_2 = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (363) imply: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) $false % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (364) is inconsistent. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_145_3 = 0) & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_145_3 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) convergent_lines(all_38_3, all_38_3) = all_145_3 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) (all_153_2 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_153_3 = 0 & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_153_2 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) convergent_lines(all_38_3, all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (369) are inconsistent by % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_153_3 = 0 & convergent_lines(all_38_3, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) convergent_lines(all_38_3, all_38_2) = 0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (371) are inconsistent by % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) ( ~ (all_153_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_153_0) | ( ~ (all_153_1 = 0) & % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_153_1) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_153_0 = 0) & unorthogonal_lines(all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_153_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies: % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_153_0 = 0) % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) unorthogonal_lines(all_38_2, all_38_2) = all_153_0 % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_153_0, all_38_2, % 48.53/9.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (375) gives: % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_153_0 = 0 % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (376) imply: % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 48.53/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_153_1 = 0) & convergent_lines(all_38_2, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_153_1 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) convergent_lines(all_38_2, all_38_2) = all_153_1 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) (all_135_0 = 0 & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_135_1 = 0 & all_45_0 = % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_135_0 = 0 & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (381) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) convergent_lines(all_38_3, all_38_1) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (382) are inconsistent by % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_135_1 = 0 & all_45_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_45_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (384) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ( ~ (all_135_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_135_2) | ( ~ (all_135_3 = 0) & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_135_3) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_135_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_135_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (387) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) ~ (all_135_2 = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) unorthogonal_lines(all_38_3, all_38_3) = all_135_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_135_2, all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (389) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_135_2 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (390) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (391) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_135_3 = 0) & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_135_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (392) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) convergent_lines(all_38_3, all_38_3) = all_135_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) (all_144_0 = 0 & all_47_0 = 0) | (all_144_1 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_144_0 = 0 & all_47_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_47_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (396) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (397) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_144_1 = 0 & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (398) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) convergent_lines(all_38_3, all_38_2) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (399) are inconsistent by % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ( ~ (all_144_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_144_2) | ( ~ (all_144_3 = 0) & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_144_3) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) ~ (all_144_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_144_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (401) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_144_2 = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) unorthogonal_lines(all_38_3, all_38_3) = all_144_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_144_2, all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (403) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_144_2 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (402), (404) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ~ (all_144_3 = 0) & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_144_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (406) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) convergent_lines(all_38_3, all_38_3) = all_144_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) (all_166_2 = 0 & all_101_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_166_3 = 0 & all_101_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_166_2 = 0 & all_101_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (409) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_101_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (410) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_166_3 = 0 & all_101_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_101_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (413) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) ( ~ (all_166_0 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_166_0) | ( ~ (all_166_1 = 0) & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_166_1) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) ~ (all_166_0 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_166_0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) ~ (all_166_0 = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) unorthogonal_lines(all_38_3, all_38_3) = all_166_0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_166_0, all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (418) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_166_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (419) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) ~ (all_166_1 = 0) & convergent_lines(all_38_3, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_166_1 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (421) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) convergent_lines(all_38_3, all_38_3) = all_166_1 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) (all_165_0 = 0 & all_67_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_165_1 = 0 & all_67_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_165_0 = 0 & all_67_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_67_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (425) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (426) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_165_1 = 0 & all_67_0 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_67_0 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (428) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) ( ~ (all_165_2 = 0) & unorthogonal_lines(all_38_2, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_165_2) | ( ~ (all_165_3 = 0) & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_165_3) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_165_2 = 0) & unorthogonal_lines(all_38_2, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_165_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (all_165_2 = 0) % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) unorthogonal_lines(all_38_2, all_38_2) = all_165_2 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_165_2, all_38_2, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (183), (433) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_165_2 = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (432), (434) imply: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) $false % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (435) is inconsistent. % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) ~ (all_165_3 = 0) & convergent_lines(all_38_2, % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_165_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) convergent_lines(all_38_2, all_38_2) = all_165_3 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_150_0 = 0 & all_150_1 = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 & % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0 % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) convergent_lines(all_38_1, all_38_1) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) unorthogonal_lines(all_38_1, all_38_1) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (29), (70), (88), (89), (98), (114), (206), % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (440) are inconsistent by sub-proof #2. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) (all_150_2 = 0 & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | ( ~ (all_150_3 = 0) & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_1) = % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_150_3) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_150_2 = 0 & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) convergent_lines(all_38_3, all_38_1) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (443) are inconsistent by % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_150_3 = 0) & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_150_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (444) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) convergent_lines(all_38_3, all_38_1) = all_150_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) (all_168_0 = 0 & all_101_0 = 0 & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_168_1 = 0 & all_101_0 = 0 & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_168_0 = 0 & all_101_0 = 0 & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_101_0 = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (448) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) $false % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_168_1 = 0 & all_101_0 = 0 & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_101_0 = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (451) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) $false % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (452) is inconsistent. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) ( ~ (all_168_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_168_2) | ( ~ (all_168_3 = 0) & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_3) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) ~ (all_168_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_168_2 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) ~ (all_168_2 = 0) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) unorthogonal_lines(all_38_3, all_38_3) = all_168_2 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_168_2, all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (456) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_168_2 = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (455), (457) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) $false % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (458) is inconsistent. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) ~ (all_168_3 = 0) & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_168_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) convergent_lines(all_38_3, all_38_3) = all_168_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) (all_147_0 = 0 & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_147_1 = 0 & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_147_0 = 0 & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) convergent_lines(all_38_3, all_38_2) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (463) are inconsistent by % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_147_1 = 0 & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) convergent_lines(all_38_3, all_38_2) = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (45), (46), (465) are inconsistent by % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) ( ~ (all_147_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_147_2) | ( ~ (all_147_3 = 0) & % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_147_3) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) ~ (all_147_2 = 0) & unorthogonal_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_147_2 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (467) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) ~ (all_147_2 = 0) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) unorthogonal_lines(all_38_3, all_38_3) = all_147_2 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_147_2, all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (264), (469) gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_147_2 = 0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (468), (470) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) $false % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (471) is inconsistent. % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_147_3 = 0) & convergent_lines(all_38_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_147_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (472) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) convergent_lines(all_38_3, all_38_3) = all_147_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_101_0, all_131_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (104), (338) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_131_3 = all_101_0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_73_3, all_131_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (279), (338) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_131_3 = all_73_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_101_0, all_135_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (104), (393) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_135_3 = all_101_0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_135_3, all_145_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (366), (393) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_145_3 = all_135_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_133_3, all_145_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (308), (366) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_145_3 = all_133_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_145_3, all_166_1, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (366), (422) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_166_1 = all_145_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_144_3, all_166_1, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (407), (422) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_166_1 = all_144_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_147_3, all_168_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (460), (473) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_168_3 = all_147_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_135_3, all_168_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (393), (460) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_168_3 = all_135_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_76_3, all_168_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (295), (460) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_168_3 = all_76_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_45_0, all_150_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (43), (445) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_150_3 = all_45_0 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_129_3, all_150_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (249), (445) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_150_3 = all_129_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_64_3, all_139_1, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (220), (233) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_139_1 = all_64_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_139_1, all_142_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (220), (263) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_142_3 = all_139_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_74_1, all_142_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (263), (324) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_142_3 = all_74_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_153_1, all_165_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (379), (437) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_165_3 = all_153_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_143_3, all_165_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (200), (437) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_165_3 = all_143_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_139_1, all_165_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (220), (437) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_165_3 = all_139_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_138_1, all_165_3, % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_2, simplifying with (352), (437) % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_165_3 = all_138_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (481), (482) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_147_3 = all_135_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (481), (483) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_147_3 = all_76_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (480) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_145_3 = all_144_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (495) implies: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_145_3 = all_144_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (489), (491) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_153_1 = all_139_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (489), (492) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_153_1 = all_138_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (489), (490) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_153_1 = all_143_3 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (498), (499) imply: % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_143_3 = all_138_1 % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (499) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_143_3 = all_139_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (484), (485) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_129_3 = all_45_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (493), (494) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_135_3 = all_76_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (503) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_135_3 = all_76_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (496) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_144_3 = all_135_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (496) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_144_3 = all_133_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (505), (506) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_135_3 = all_133_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (507) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_135_3 = all_133_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (500), (501) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_139_1 = all_138_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (509) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_139_1 = all_138_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (487), (488) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_139_1 = all_74_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_139_1 = all_74_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (486), (510) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_138_1 = all_64_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (510), (512) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_138_1 = all_74_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (514) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_74_1 = all_64_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (504), (508) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_133_3 = all_76_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (508) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_133_3 = all_101_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (516), (517) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_101_0 = all_76_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (518) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_101_0 = all_76_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (475) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_101_0 = all_73_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (520) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_101_0 = all_73_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (519), (521) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_76_3 = all_73_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (522) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_76_3 = all_73_3 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (294), (523) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) ~ (all_73_3 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (323), (515) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) ~ (all_64_3 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_38_2, all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_64_3, simplifying with (33), (34), % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (233) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_64_3 = 0 | convergent_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_38_2, all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_110_0, all_64_3, simplifying with % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (120), (233) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_110_0 = 0 | all_64_3 = 0 | ? [v0: int] : ( ~ % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_38_2, all_38_3) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_38_1, all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_237_0, all_45_0, simplifying with % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (34), (43), (206) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_237_0 = 0 | all_45_0 = 0 | ? [v0: int] : ( ~ % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_38_1, all_38_3) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_58_1, all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_58_0, all_268_0, simplifying with % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (65), (142), (239) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_268_0 = 0 | all_58_0 = 0 | ? [v0: int] : ? % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: int] : ((v1 = 0 & convergent_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (v0 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v0)) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_38_3, all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_45_0, 0, simplifying with (32), % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (43), (264) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & convergent_lines(all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | (v0 = 0 & all_45_0 = 0 & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v3) | ( ~ (v2 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = v2)) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (530) with fresh symbols all_444_0, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_444_1, all_444_2, all_444_3 gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) (all_444_2 = 0 & convergent_lines(all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | (all_444_3 = 0 & all_45_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & unorthogonal_lines(all_38_3, all_38_1) = 0) | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_444_0 = 0) & unorthogonal_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_444_0) | ( ~ (all_444_1 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_444_1) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) convergent_lines(all_38_1, all_38_2) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_237_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (533) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (534) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_110_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (536) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (537) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_64_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_45_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (539) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (540) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) ? [v0: int] : ( ~ (v0 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (541) with fresh symbol all_502_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_502_0 = 0) & convergent_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_502_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) ~ (all_502_0 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) convergent_lines(all_38_1, all_38_3) = all_502_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_64_3 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (545) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (546) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) ? [v0: int] : ( ~ (v0 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = v0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (547) with fresh symbol all_511_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) ~ (all_511_0 = 0) & convergent_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_511_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) ~ (all_511_0 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) convergent_lines(all_38_2, all_38_3) = all_511_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_268_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (238), (551) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (552) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_58_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & convergent_lines(all_38_2, all_38_3) = % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & distinct_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v0)) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_58_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (554) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (555) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0) | ( % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0) & distinct_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = v0)) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (556) with fresh symbols all_698_0, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_698_1 gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) (all_698_0 = 0 & convergent_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (all_698_1 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_698_1) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_698_0 = 0 & convergent_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) convergent_lines(all_38_2, all_38_3) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_511_0, all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (550), (559) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_511_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (560) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (561) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) ~ (all_698_1 = 0) & distinct_lines(all_38_2, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_698_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) ~ (all_698_1 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) distinct_lines(all_38_2, all_38_3) = all_698_1 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) (all_156_2 = 0 & all_101_0 = 0 & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_156_3 = 0 & convergent_lines(all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_156_2 = 0 & all_101_0 = 0 & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_101_0 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (521), (567) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_73_3 = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (524), (568) imply: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) $false % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (569) is inconsistent. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_156_3 = 0 & convergent_lines(all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) convergent_lines(all_38_3, all_38_1) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (43), (571) are inconsistent by % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) ( ~ (all_156_0 = 0) & unorthogonal_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_156_0) | ( ~ (all_156_1 = 0) & % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) ~ (all_156_0 = 0) & unorthogonal_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_156_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (573) implies: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) ~ (all_156_0 = 0) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) unorthogonal_lines(all_38_1, all_38_3) = all_156_0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_38_1, all_38_3, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_502_0, simplifying with (32), (34), (544) % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_502_0 = 0 | unorthogonal_lines(all_38_1, % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) unorthogonal_lines(all_38_1, all_38_3) = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_156_0, all_38_3, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (575), (577) gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_156_0 = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (578) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) $false % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (579) is inconsistent. % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_502_0 = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (543), (580) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) $false % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (581) is inconsistent. % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) ~ (all_156_1 = 0) & convergent_lines(all_38_1, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_156_1 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (582) implies: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) convergent_lines(all_38_1, all_38_3) = all_156_1 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_502_0, all_156_1, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (544), (583) % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_502_0 = all_156_1 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (543), (584) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) ~ (all_156_1 = 0) % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) (all_169_2 = 0 & all_101_0 = 0 & % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_169_3 = 0 & all_45_0 = 0 & % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_169_2 = 0 & all_101_0 = 0 & % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_101_0 = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (521), (588) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_73_3 = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (524), (589) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) $false % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (590) is inconsistent. % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_169_3 = 0 & all_45_0 = 0 & % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (591) implies: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_45_0 = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (592) imply: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) $false % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (593) is inconsistent. % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) ( ~ (all_169_0 = 0) & unorthogonal_lines(all_38_1, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_169_0) | ( ~ (all_169_1 = 0) & % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) = % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (594) gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_38_1, all_38_3, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, simplifying with (32), (34), (583) % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_156_1 = 0 | unorthogonal_lines(all_38_1, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (29), (32), (33), (34), (42), (43), % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (279), (521), (524), (531), (532), (544), % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563), (564), (585), (595) are inconsistent by % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) ~ (all_169_1 = 0) & convergent_lines(all_38_1, % 48.58/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_169_1 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (all_169_1 = 0) % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) convergent_lines(all_38_1, all_38_3) = all_169_1 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_156_1, all_169_1, % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_1, simplifying with (583), (598) % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_169_1 = all_156_1 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_38_1, all_38_3, % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, simplifying with (32), (34), (583) % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_156_1 = 0 | unorthogonal_lines(all_38_1, % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (29), (32), (33), (34), (42), (43), % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (279), (521), (524), (531), (532), (544), % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563), (564), (585), (600) are inconsistent by % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_64_3 = 0 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (601) imply: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) $false % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (602) is inconsistent. % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) all_101_0 = 0 % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (603) imply: % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) $false % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (604) is inconsistent. % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | Case 2: % 48.75/9.21 | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | (605) all_67_0 = 0 % 48.75/9.21 | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | REDUCE: (88), (605) imply: % 48.75/9.21 | | | | | | | | | | | | | | | (606) $false % 48.75/9.21 | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | | CLOSE: (606) is inconsistent. % 48.75/9.21 | | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | Case 2: % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | (607) ~ (all_75_1 = 0) & convergent_lines(all_38_2, % 48.75/9.21 | | | | | | | | | | | all_38_1) = all_75_1 % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | ALPHA: (607) implies: % 48.75/9.21 | | | | | | | | | | | (608) ~ (all_75_1 = 0) % 48.75/9.21 | | | | | | | | | | | (609) convergent_lines(all_38_2, all_38_1) = all_75_1 % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_75_1, all_38_1, % 48.75/9.21 | | | | | | | | | | | all_38_2, simplifying with (47), (609) gives: % 48.75/9.21 | | | | | | | | | | | (610) all_75_1 = 0 % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | REDUCE: (608), (610) imply: % 48.75/9.21 | | | | | | | | | | | (611) $false % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | | CLOSE: (611) is inconsistent. % 48.75/9.21 | | | | | | | | | | | % 48.75/9.21 | | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | | % 48.75/9.21 | | | | | | | | | End of split % 48.75/9.21 | | | | | | | | | % 48.75/9.21 | | | | | | | | End of split % 48.75/9.21 | | | | | | | | % 48.75/9.21 | | | | | | | End of split % 48.75/9.21 | | | | | | | % 48.75/9.21 | | | | | | End of split % 48.75/9.21 | | | | | | % 48.75/9.21 | | | | | End of split % 48.75/9.21 | | | | | % 48.75/9.21 | | | | End of split % 48.75/9.21 | | | | % 48.75/9.21 | | | Case 2: % 48.75/9.21 | | | | % 48.75/9.21 | | | | (612) all_45_0 = 0 % 48.75/9.21 | | | | % 48.75/9.21 | | | | REDUCE: (42), (612) imply: % 48.75/9.21 | | | | (613) $false % 48.75/9.21 | | | | % 48.75/9.21 | | | | CLOSE: (613) is inconsistent. % 48.75/9.21 | | | | % 48.75/9.21 | | | End of split % 48.75/9.21 | | | % 48.75/9.21 | | Case 2: % 48.75/9.21 | | | % 48.75/9.21 | | | (614) all_47_0 = 0 % 48.75/9.21 | | | % 48.75/9.21 | | | REDUCE: (45), (614) imply: % 48.75/9.21 | | | (615) $false % 48.75/9.21 | | | % 48.75/9.21 | | | CLOSE: (615) is inconsistent. % 48.75/9.21 | | | % 48.75/9.21 | | End of split % 48.75/9.21 | | % 48.75/9.21 | Case 2: % 48.75/9.21 | | % 48.75/9.21 | | (616) all_38_0 = 0 % 48.75/9.21 | | % 48.75/9.21 | | REDUCE: (31), (616) imply: % 48.75/9.21 | | (617) $false % 48.75/9.21 | | % 48.75/9.21 | | CLOSE: (617) is inconsistent. % 48.75/9.21 | | % 48.75/9.21 | End of split % 48.75/9.21 | % 48.75/9.21 End of proof % 48.75/9.22 % 48.75/9.22 Sub-proof #1 shows that the following formulas are inconsistent: % 48.75/9.22 ---------------------------------------------------------------- % 48.75/9.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.75/9.22 (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 48.75/9.22 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 48.75/9.22 (2) $i(all_38_2) % 48.75/9.22 (3) convergent_lines(all_38_1, all_38_2) = 0 % 48.75/9.22 (4) convergent_lines(all_38_3, all_38_3) = all_73_3 % 48.75/9.22 (5) distinct_lines(all_38_2, all_38_3) = all_698_1 % 48.75/9.22 (6) (all_156_2 = 0 & all_101_0 = 0 & unorthogonal_lines(all_38_3, all_38_3) = % 48.75/9.22 0) | (all_156_3 = 0 & convergent_lines(all_38_3, all_38_1) = 0) | ( ~ % 48.75/9.22 (all_156_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = all_156_0) | % 48.75/9.22 ( ~ (all_156_1 = 0) & convergent_lines(all_38_1, all_38_3) = all_156_1) % 48.75/9.22 (7) convergent_lines(all_38_1, all_38_3) = all_502_0 % 48.75/9.22 (8) ~ (all_698_1 = 0) % 48.75/9.22 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.22 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 48.75/9.22 (unorthogonal_lines(v3, v2) = v0)) % 48.75/9.22 (10) all_101_0 = all_73_3 % 48.75/9.22 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.22 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.75/9.22 (convergent_lines(v3, v2) = v0)) % 48.75/9.22 (12) ~ (all_45_0 = 0) % 48.75/9.22 (13) ~ (all_73_3 = 0) % 48.75/9.22 (14) $i(all_38_1) % 48.75/9.22 (15) convergent_lines(all_38_3, all_38_1) = all_45_0 % 48.75/9.22 (16) all_156_1 = 0 | unorthogonal_lines(all_38_1, all_38_3) = 0 % 48.75/9.22 (17) (all_444_2 = 0 & convergent_lines(all_38_3, all_38_3) = 0) | (all_444_3 % 48.75/9.22 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~ % 48.75/9.22 (all_444_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = all_444_0) % 48.75/9.22 | ( ~ (all_444_1 = 0) & convergent_lines(all_38_1, all_38_3) = % 48.75/9.22 all_444_1) % 48.75/9.22 (18) ~ (all_156_1 = 0) % 48.75/9.22 (19) $i(all_38_3) % 48.75/9.22 % 48.75/9.22 Begin of proof % 48.75/9.22 | % 48.75/9.22 | GROUND_INST: instantiating (1) with all_38_1, all_38_2, all_38_3, all_698_1, % 48.75/9.22 | simplifying with (2), (3), (5), (14), (19) gives: % 48.75/9.22 | (20) all_698_1 = 0 | convergent_lines(all_38_1, all_38_3) = 0 % 48.75/9.22 | % 48.75/9.22 | BETA: splitting (16) gives: % 48.75/9.22 | % 48.75/9.22 | Case 1: % 48.75/9.22 | | % 48.75/9.22 | | (21) unorthogonal_lines(all_38_1, all_38_3) = 0 % 48.75/9.22 | | % 48.75/9.22 | | BETA: splitting (17) gives: % 48.75/9.22 | | % 48.75/9.22 | | Case 1: % 48.75/9.22 | | | % 48.75/9.22 | | | (22) (all_444_2 = 0 & convergent_lines(all_38_3, all_38_3) = 0) | % 48.75/9.22 | | | (all_444_3 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 48.75/9.22 | | | all_38_1) = 0) % 48.75/9.22 | | | % 48.75/9.22 | | | BETA: splitting (22) gives: % 48.75/9.22 | | | % 48.75/9.22 | | | Case 1: % 48.75/9.22 | | | | % 48.75/9.22 | | | | (23) all_444_2 = 0 & convergent_lines(all_38_3, all_38_3) = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | ALPHA: (23) implies: % 48.75/9.22 | | | | (24) convergent_lines(all_38_3, all_38_3) = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | GROUND_INST: instantiating (11) with all_73_3, 0, all_38_3, all_38_3, % 48.75/9.22 | | | | simplifying with (4), (24) gives: % 48.75/9.22 | | | | (25) all_73_3 = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | REDUCE: (13), (25) imply: % 48.75/9.22 | | | | (26) $false % 48.75/9.22 | | | | % 48.75/9.22 | | | | CLOSE: (26) is inconsistent. % 48.75/9.22 | | | | % 48.75/9.22 | | | Case 2: % 48.75/9.22 | | | | % 48.75/9.22 | | | | (27) all_444_3 = 0 & all_45_0 = 0 & unorthogonal_lines(all_38_3, % 48.75/9.22 | | | | all_38_1) = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | ALPHA: (27) implies: % 48.75/9.22 | | | | (28) all_45_0 = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | REDUCE: (12), (28) imply: % 48.75/9.22 | | | | (29) $false % 48.75/9.22 | | | | % 48.75/9.22 | | | | CLOSE: (29) is inconsistent. % 48.75/9.22 | | | | % 48.75/9.22 | | | End of split % 48.75/9.22 | | | % 48.75/9.22 | | Case 2: % 48.75/9.22 | | | % 48.75/9.22 | | | (30) ( ~ (all_444_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = % 48.75/9.22 | | | all_444_0) | ( ~ (all_444_1 = 0) & convergent_lines(all_38_1, % 48.75/9.22 | | | all_38_3) = all_444_1) % 48.75/9.22 | | | % 48.75/9.22 | | | BETA: splitting (30) gives: % 48.75/9.22 | | | % 48.75/9.22 | | | Case 1: % 48.75/9.22 | | | | % 48.75/9.22 | | | | (31) ~ (all_444_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = % 48.75/9.22 | | | | all_444_0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | ALPHA: (31) implies: % 48.75/9.22 | | | | (32) ~ (all_444_0 = 0) % 48.75/9.22 | | | | (33) unorthogonal_lines(all_38_1, all_38_3) = all_444_0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | GROUND_INST: instantiating (9) with 0, all_444_0, all_38_3, all_38_1, % 48.75/9.22 | | | | simplifying with (21), (33) gives: % 48.75/9.22 | | | | (34) all_444_0 = 0 % 48.75/9.22 | | | | % 48.75/9.22 | | | | REDUCE: (32), (34) imply: % 48.75/9.22 | | | | (35) $false % 48.75/9.22 | | | | % 48.75/9.22 | | | | CLOSE: (35) is inconsistent. % 48.75/9.22 | | | | % 48.75/9.22 | | | Case 2: % 48.75/9.22 | | | | % 48.75/9.22 | | | | (36) ~ (all_444_1 = 0) & convergent_lines(all_38_1, all_38_3) = % 48.75/9.22 | | | | all_444_1 % 48.75/9.22 | | | | % 48.75/9.22 | | | | ALPHA: (36) implies: % 48.75/9.22 | | | | (37) convergent_lines(all_38_1, all_38_3) = all_444_1 % 48.75/9.22 | | | | % 48.75/9.22 | | | | BETA: splitting (20) gives: % 48.75/9.22 | | | | % 48.75/9.22 | | | | Case 1: % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | (38) convergent_lines(all_38_1, all_38_3) = 0 % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | BETA: splitting (6) gives: % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | Case 1: % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | (39) (all_156_2 = 0 & all_101_0 = 0 & % 48.75/9.22 | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0) | (all_156_3 = % 48.75/9.22 | | | | | | 0 & convergent_lines(all_38_3, all_38_1) = 0) % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | BETA: splitting (39) gives: % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | Case 1: % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | (40) all_156_2 = 0 & all_101_0 = 0 & % 48.75/9.22 | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | ALPHA: (40) implies: % 48.75/9.22 | | | | | | | (41) all_101_0 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | COMBINE_EQS: (10), (41) imply: % 48.75/9.22 | | | | | | | (42) all_73_3 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | SIMP: (42) implies: % 48.75/9.22 | | | | | | | (43) all_73_3 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | REDUCE: (13), (43) imply: % 48.75/9.22 | | | | | | | (44) $false % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | CLOSE: (44) is inconsistent. % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | Case 2: % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | (45) all_156_3 = 0 & convergent_lines(all_38_3, all_38_1) = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | ALPHA: (45) implies: % 48.75/9.22 | | | | | | | (46) convergent_lines(all_38_3, all_38_1) = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | REF_CLOSE: (11), (12), (15), (46) are inconsistent by sub-proof % 48.75/9.22 | | | | | | | #5. % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | End of split % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | Case 2: % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | (47) ( ~ (all_156_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) % 48.75/9.22 | | | | | | = all_156_0) | ( ~ (all_156_1 = 0) & % 48.75/9.22 | | | | | | convergent_lines(all_38_1, all_38_3) = all_156_1) % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | BETA: splitting (47) gives: % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | | Case 1: % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | (48) ~ (all_156_0 = 0) & unorthogonal_lines(all_38_1, % 48.75/9.22 | | | | | | | all_38_3) = all_156_0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | ALPHA: (48) implies: % 48.75/9.22 | | | | | | | (49) ~ (all_156_0 = 0) % 48.75/9.22 | | | | | | | (50) unorthogonal_lines(all_38_1, all_38_3) = all_156_0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | GROUND_INST: instantiating (9) with 0, all_156_0, all_38_3, % 48.75/9.22 | | | | | | | all_38_1, simplifying with (21), (50) gives: % 48.75/9.22 | | | | | | | (51) all_156_0 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | REDUCE: (49), (51) imply: % 48.75/9.22 | | | | | | | (52) $false % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | CLOSE: (52) is inconsistent. % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | Case 2: % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | (53) ~ (all_156_1 = 0) & convergent_lines(all_38_1, all_38_3) % 48.75/9.22 | | | | | | | = all_156_1 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | ALPHA: (53) implies: % 48.75/9.22 | | | | | | | (54) convergent_lines(all_38_1, all_38_3) = all_156_1 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_444_1, % 48.75/9.22 | | | | | | | all_38_3, all_38_1, simplifying with (37), (54) % 48.75/9.22 | | | | | | | gives: % 48.75/9.22 | | | | | | | (55) all_444_1 = all_156_1 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | GROUND_INST: instantiating (11) with all_444_1, all_502_0, % 48.75/9.22 | | | | | | | all_38_3, all_38_1, simplifying with (7), (37) gives: % 48.75/9.22 | | | | | | | (56) all_502_0 = all_444_1 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | GROUND_INST: instantiating (11) with 0, all_502_0, all_38_3, % 48.75/9.22 | | | | | | | all_38_1, simplifying with (7), (38) gives: % 48.75/9.22 | | | | | | | (57) all_502_0 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | COMBINE_EQS: (56), (57) imply: % 48.75/9.22 | | | | | | | (58) all_444_1 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | SIMP: (58) implies: % 48.75/9.22 | | | | | | | (59) all_444_1 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | COMBINE_EQS: (55), (59) imply: % 48.75/9.22 | | | | | | | (60) all_156_1 = 0 % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | REDUCE: (18), (60) imply: % 48.75/9.22 | | | | | | | (61) $false % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | | CLOSE: (61) is inconsistent. % 48.75/9.22 | | | | | | | % 48.75/9.22 | | | | | | End of split % 48.75/9.22 | | | | | | % 48.75/9.22 | | | | | End of split % 48.75/9.22 | | | | | % 48.75/9.22 | | | | Case 2: % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | (62) all_698_1 = 0 % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | REDUCE: (8), (62) imply: % 48.75/9.22 | | | | | (63) $false % 48.75/9.22 | | | | | % 48.75/9.22 | | | | | CLOSE: (63) is inconsistent. % 48.75/9.22 | | | | | % 48.75/9.22 | | | | End of split % 48.75/9.22 | | | | % 48.75/9.22 | | | End of split % 48.75/9.22 | | | % 48.75/9.22 | | End of split % 48.75/9.22 | | % 48.75/9.22 | Case 2: % 48.75/9.22 | | % 48.75/9.22 | | (64) all_156_1 = 0 % 48.75/9.22 | | % 48.75/9.22 | | REDUCE: (18), (64) imply: % 48.75/9.22 | | (65) $false % 48.75/9.22 | | % 48.75/9.22 | | CLOSE: (65) is inconsistent. % 48.75/9.22 | | % 48.75/9.22 | End of split % 48.75/9.22 | % 48.75/9.22 End of proof % 48.75/9.22 % 48.75/9.22 Sub-proof #2 shows that the following formulas are inconsistent: % 48.75/9.22 ---------------------------------------------------------------- % 48.75/9.22 (1) convergent_lines(all_38_1, all_38_1) = 0 % 48.75/9.22 (2) unorthogonal_lines(all_38_1, all_38_1) = 0 % 48.75/9.22 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.22 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 48.75/9.22 (unorthogonal_lines(v3, v2) = v0)) % 48.75/9.22 (4) (all_63_2 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | (all_63_3 = % 48.75/9.22 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | ( ~ (all_63_0 = 0) & % 48.75/9.22 unorthogonal_lines(all_38_1, all_38_1) = all_63_0) | ( ~ (all_63_1 = 0) % 48.75/9.22 & convergent_lines(all_38_1, all_38_1) = all_63_1) % 48.75/9.22 (5) unorthogonal_lines(all_38_2, all_38_1) = all_68_0 % 48.75/9.22 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.22 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.75/9.22 (convergent_lines(v3, v2) = v0)) % 48.75/9.22 (7) convergent_lines(all_38_1, all_38_1) = all_237_0 % 48.75/9.22 (8) unorthogonal_lines(all_38_2, all_38_1) = all_67_0 % 48.75/9.22 (9) unorthogonal_lines(all_38_2, all_38_1) = all_75_0 % 48.75/9.22 (10) ~ (all_67_0 = 0) % 48.75/9.22 % 48.75/9.22 Begin of proof % 48.75/9.22 | % 48.75/9.22 | BETA: splitting (4) gives: % 48.75/9.22 | % 48.75/9.22 | Case 1: % 48.75/9.22 | | % 48.75/9.22 | | (11) (all_63_2 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) | % 48.75/9.22 | | (all_63_3 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0) % 48.75/9.22 | | % 48.75/9.22 | | BETA: splitting (11) gives: % 48.75/9.22 | | % 48.75/9.22 | | Case 1: % 48.75/9.22 | | | % 48.75/9.22 | | | (12) all_63_2 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.75/9.22 | | | % 48.75/9.22 | | | ALPHA: (12) implies: % 48.75/9.22 | | | (13) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.75/9.22 | | | % 48.75/9.23 | | | REF_CLOSE: (3), (5), (8), (9), (10), (13) are inconsistent by sub-proof % 48.75/9.23 | | | #3. % 48.75/9.23 | | | % 48.75/9.23 | | Case 2: % 48.75/9.23 | | | % 48.75/9.23 | | | (14) all_63_3 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | ALPHA: (14) implies: % 48.75/9.23 | | | (15) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | REF_CLOSE: (3), (5), (8), (9), (10), (15) are inconsistent by sub-proof % 48.75/9.23 | | | #3. % 48.75/9.23 | | | % 48.75/9.23 | | End of split % 48.75/9.23 | | % 48.75/9.23 | Case 2: % 48.75/9.23 | | % 48.75/9.23 | | (16) ( ~ (all_63_0 = 0) & unorthogonal_lines(all_38_1, all_38_1) = % 48.75/9.23 | | all_63_0) | ( ~ (all_63_1 = 0) & convergent_lines(all_38_1, % 48.75/9.23 | | all_38_1) = all_63_1) % 48.75/9.23 | | % 48.75/9.23 | | BETA: splitting (16) gives: % 48.75/9.23 | | % 48.75/9.23 | | Case 1: % 48.75/9.23 | | | % 48.75/9.23 | | | (17) ~ (all_63_0 = 0) & unorthogonal_lines(all_38_1, all_38_1) = % 48.75/9.23 | | | all_63_0 % 48.75/9.23 | | | % 48.75/9.23 | | | ALPHA: (17) implies: % 48.75/9.23 | | | (18) ~ (all_63_0 = 0) % 48.75/9.23 | | | (19) unorthogonal_lines(all_38_1, all_38_1) = all_63_0 % 48.75/9.23 | | | % 48.75/9.23 | | | GROUND_INST: instantiating (3) with 0, all_63_0, all_38_1, all_38_1, % 48.75/9.23 | | | simplifying with (2), (19) gives: % 48.75/9.23 | | | (20) all_63_0 = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | REDUCE: (18), (20) imply: % 48.75/9.23 | | | (21) $false % 48.75/9.23 | | | % 48.75/9.23 | | | CLOSE: (21) is inconsistent. % 48.75/9.23 | | | % 48.75/9.23 | | Case 2: % 48.75/9.23 | | | % 48.75/9.23 | | | (22) ~ (all_63_1 = 0) & convergent_lines(all_38_1, all_38_1) = % 48.75/9.23 | | | all_63_1 % 48.75/9.23 | | | % 48.75/9.23 | | | ALPHA: (22) implies: % 48.75/9.23 | | | (23) ~ (all_63_1 = 0) % 48.75/9.23 | | | (24) convergent_lines(all_38_1, all_38_1) = all_63_1 % 48.75/9.23 | | | % 48.75/9.23 | | | GROUND_INST: instantiating (6) with all_63_1, all_237_0, all_38_1, % 48.75/9.23 | | | all_38_1, simplifying with (7), (24) gives: % 48.75/9.23 | | | (25) all_237_0 = all_63_1 % 48.75/9.23 | | | % 48.75/9.23 | | | GROUND_INST: instantiating (6) with 0, all_237_0, all_38_1, all_38_1, % 48.75/9.23 | | | simplifying with (1), (7) gives: % 48.75/9.23 | | | (26) all_237_0 = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | COMBINE_EQS: (25), (26) imply: % 48.75/9.23 | | | (27) all_63_1 = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | SIMP: (27) implies: % 48.75/9.23 | | | (28) all_63_1 = 0 % 48.75/9.23 | | | % 48.75/9.23 | | | REDUCE: (23), (28) imply: % 48.75/9.23 | | | (29) $false % 48.75/9.23 | | | % 48.75/9.23 | | | CLOSE: (29) is inconsistent. % 48.75/9.23 | | | % 48.75/9.23 | | End of split % 48.75/9.23 | | % 48.75/9.23 | End of split % 48.75/9.23 | % 48.75/9.23 End of proof % 48.75/9.23 % 48.75/9.23 Sub-proof #3 shows that the following formulas are inconsistent: % 48.75/9.23 ---------------------------------------------------------------- % 48.75/9.23 (1) unorthogonal_lines(all_38_2, all_38_1) = 0 % 48.75/9.23 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.23 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 48.75/9.23 (unorthogonal_lines(v3, v2) = v0)) % 48.75/9.23 (3) unorthogonal_lines(all_38_2, all_38_1) = all_68_0 % 48.75/9.23 (4) unorthogonal_lines(all_38_2, all_38_1) = all_67_0 % 48.75/9.23 (5) unorthogonal_lines(all_38_2, all_38_1) = all_75_0 % 48.75/9.23 (6) ~ (all_67_0 = 0) % 48.75/9.23 % 48.75/9.23 Begin of proof % 48.75/9.23 | % 48.75/9.23 | GROUND_INST: instantiating (2) with all_67_0, all_68_0, all_38_1, all_38_2, % 48.75/9.23 | simplifying with (3), (4) gives: % 48.75/9.23 | (7) all_68_0 = all_67_0 % 48.75/9.23 | % 48.75/9.23 | GROUND_INST: instantiating (2) with all_68_0, all_75_0, all_38_1, all_38_2, % 48.75/9.23 | simplifying with (3), (5) gives: % 48.75/9.23 | (8) all_75_0 = all_68_0 % 48.75/9.23 | % 48.75/9.23 | GROUND_INST: instantiating (2) with 0, all_75_0, all_38_1, all_38_2, % 48.75/9.23 | simplifying with (1), (5) gives: % 48.75/9.23 | (9) all_75_0 = 0 % 48.75/9.23 | % 48.75/9.23 | COMBINE_EQS: (8), (9) imply: % 48.75/9.23 | (10) all_68_0 = 0 % 48.75/9.23 | % 48.75/9.23 | SIMP: (10) implies: % 48.75/9.23 | (11) all_68_0 = 0 % 48.75/9.23 | % 48.75/9.23 | COMBINE_EQS: (7), (11) imply: % 48.75/9.23 | (12) all_67_0 = 0 % 48.75/9.23 | % 48.75/9.23 | SIMP: (12) implies: % 48.75/9.23 | (13) all_67_0 = 0 % 48.75/9.23 | % 48.75/9.23 | REDUCE: (6), (13) imply: % 48.75/9.23 | (14) $false % 48.75/9.23 | % 48.75/9.23 | CLOSE: (14) is inconsistent. % 48.75/9.23 | % 48.75/9.23 End of proof % 48.75/9.23 % 48.75/9.23 Sub-proof #4 shows that the following formulas are inconsistent: % 48.75/9.23 ---------------------------------------------------------------- % 48.75/9.23 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.75/9.23 (convergent_lines(v3, v2) = v0)) % 48.75/9.23 (2) convergent_lines(all_38_3, all_38_2) = all_47_0 % 48.75/9.23 (3) convergent_lines(all_38_3, all_38_2) = 0 % 48.75/9.23 (4) ~ (all_47_0 = 0) % 48.75/9.23 % 48.75/9.23 Begin of proof % 48.75/9.23 | % 48.75/9.23 | GROUND_INST: instantiating (1) with all_47_0, 0, all_38_2, all_38_3, % 48.75/9.23 | simplifying with (2), (3) gives: % 48.75/9.23 | (5) all_47_0 = 0 % 48.75/9.23 | % 48.75/9.23 | REDUCE: (4), (5) imply: % 48.75/9.23 | (6) $false % 48.75/9.23 | % 48.75/9.23 | CLOSE: (6) is inconsistent. % 48.75/9.23 | % 48.75/9.23 End of proof % 48.75/9.23 % 48.75/9.23 Sub-proof #5 shows that the following formulas are inconsistent: % 48.75/9.23 ---------------------------------------------------------------- % 48.75/9.23 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.75/9.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.75/9.23 (convergent_lines(v3, v2) = v0)) % 48.75/9.23 (2) convergent_lines(all_38_3, all_38_1) = all_45_0 % 48.75/9.23 (3) convergent_lines(all_38_3, all_38_1) = 0 % 48.75/9.23 (4) ~ (all_45_0 = 0) % 48.75/9.23 % 48.75/9.23 Begin of proof % 48.75/9.23 | % 48.75/9.23 | GROUND_INST: instantiating (1) with all_45_0, 0, all_38_1, all_38_3, % 48.75/9.23 | simplifying with (2), (3) gives: % 48.75/9.23 | (5) all_45_0 = 0 % 48.75/9.23 | % 48.75/9.23 | REDUCE: (4), (5) imply: % 48.75/9.23 | (6) $false % 48.75/9.23 | % 48.75/9.23 | CLOSE: (6) is inconsistent. % 48.75/9.23 | % 48.75/9.23 End of proof % 48.75/9.23 % SZS output end Proof for theBenchmark % 48.75/9.23 % 48.75/9.23 8610ms %------------------------------------------------------------------------------