%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO181+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:21:56 EDT 2023 % Result : Theorem 12.13s 2.34s % Output : Proof 16.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO181+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 22:56:53 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.37/1.04 Prover 1: Preprocessing ... % 2.37/1.04 Prover 4: Preprocessing ... % 2.37/1.07 Prover 5: Preprocessing ... % 2.37/1.07 Prover 6: Preprocessing ... % 2.37/1.07 Prover 3: Preprocessing ... % 2.37/1.07 Prover 2: Preprocessing ... % 2.37/1.07 Prover 0: Preprocessing ... % 4.58/1.29 Prover 2: Proving ... % 4.58/1.30 Prover 5: Proving ... % 4.58/1.30 Prover 6: Constructing countermodel ... % 4.58/1.30 Prover 3: Constructing countermodel ... % 4.58/1.31 Prover 1: Constructing countermodel ... % 4.58/1.41 Prover 3: gave up % 4.58/1.42 Prover 4: Constructing countermodel ... % 4.58/1.42 Prover 1: gave up % 4.58/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.58/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.58/1.44 Prover 6: gave up % 4.58/1.44 Prover 0: Proving ... % 4.58/1.44 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.75/1.46 Prover 8: Preprocessing ... % 5.90/1.49 Prover 9: Preprocessing ... % 5.90/1.50 Prover 7: Preprocessing ... % 6.17/1.53 Prover 7: Warning: ignoring some quantifiers % 6.28/1.53 Prover 7: Constructing countermodel ... % 6.28/1.56 Prover 8: Warning: ignoring some quantifiers % 6.28/1.57 Prover 8: Constructing countermodel ... % 6.88/1.62 Prover 8: gave up % 6.88/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.88/1.65 Prover 7: gave up % 6.88/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.88/1.65 Prover 10: Preprocessing ... % 6.88/1.65 Prover 9: Constructing countermodel ... % 6.88/1.67 Prover 10: Warning: ignoring some quantifiers % 7.36/1.68 Prover 10: Constructing countermodel ... % 7.36/1.68 Prover 11: Preprocessing ... % 7.36/1.70 Prover 10: gave up % 7.36/1.72 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 7.36/1.73 Prover 12: Preprocessing ... % 8.43/1.82 Prover 11: Constructing countermodel ... % 8.57/1.85 Prover 12: Proving ... % 12.13/2.34 Prover 9: proved (895ms) % 12.13/2.34 % 12.13/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.13/2.34 % 12.13/2.34 Prover 0: stopped % 12.13/2.34 Prover 2: stopped % 12.13/2.34 Prover 5: stopped % 12.13/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.13/2.35 Prover 12: stopped % 12.13/2.35 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.13/2.35 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.13/2.36 Prover 16: Preprocessing ... % 12.13/2.36 Prover 13: Preprocessing ... % 12.13/2.36 Prover 19: Preprocessing ... % 12.13/2.38 Prover 16: Warning: ignoring some quantifiers % 12.13/2.38 Prover 16: Constructing countermodel ... % 12.62/2.39 Prover 13: Warning: ignoring some quantifiers % 12.62/2.40 Prover 19: Warning: ignoring some quantifiers % 12.62/2.40 Prover 13: Constructing countermodel ... % 12.62/2.41 Prover 19: Constructing countermodel ... % 12.62/2.44 Prover 19: gave up % 13.24/2.47 Prover 13: gave up % 13.36/2.48 Prover 16: gave up % 15.96/2.95 Prover 4: Found proof (size 255) % 15.96/2.95 Prover 4: proved (2307ms) % 15.96/2.95 Prover 11: stopped % 15.96/2.95 % 15.96/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.96/2.95 % 16.21/2.99 % SZS output start Proof for theBenchmark % 16.21/2.99 Assumptions after simplification: % 16.21/2.99 --------------------------------- % 16.21/2.99 % 16.21/2.99 (apart1) % 16.21/3.04 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 16.21/3.04 % 16.21/3.04 (apart4) % 16.48/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.48/3.05 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 16.48/3.05 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 16.48/3.05 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.48/3.05 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 16.48/3.05 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.48/3.05 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.48/3.05 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 16.48/3.05 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.48/3.05 distinct_points(v1, v2) = 0) % 16.48/3.05 % 16.48/3.05 (ceq1) % 16.48/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.48/3.06 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 16.48/3.06 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 16.48/3.06 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 16.48/3.06 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.48/3.06 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 16.48/3.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 16.48/3.06 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.48/3.06 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 16.48/3.06 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 16.48/3.06 % 16.48/3.06 (ceq2) % 16.48/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.48/3.06 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 16.48/3.06 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 16.48/3.06 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 16.48/3.06 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 16.48/3.06 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.48/3.06 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.48/3.06 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 16.48/3.06 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.48/3.06 apart_point_and_line(v0, v2) = 0) % 16.48/3.06 % 16.56/3.06 (ci1) % 16.56/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.56/3.06 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.56/3.06 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 16.56/3.06 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.56/3.06 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 16.56/3.06 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 16.56/3.06 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 16.56/3.06 % 16.56/3.06 (ci2) % 16.56/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.56/3.07 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.56/3.07 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 16.56/3.07 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.56/3.07 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 16.56/3.07 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 16.56/3.07 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 16.56/3.07 % 16.56/3.07 (con) % 16.56/3.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.56/3.07 int] : ( ~ (v5 = 0) & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) % 16.56/3.07 = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v1, v4) = v5 % 16.56/3.07 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.56/3.07 % 16.56/3.07 (cu1) % 16.56/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.56/3.08 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.56/3.08 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.56/3.08 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 16.56/3.08 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 16.56/3.08 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 16.56/3.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 16.56/3.08 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 16.56/3.08 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 16.56/3.08 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 16.56/3.08 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 16.56/3.08 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 16.56/3.08 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.56/3.08 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 16.56/3.08 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 16.56/3.08 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 16.56/3.08 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 16.56/3.08 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 16.56/3.08 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 16.56/3.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 16.56/3.08 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 16.56/3.08 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.56/3.08 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 16.56/3.08 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 16.56/3.08 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 16.56/3.08 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 16.56/3.08 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 16.56/3.08 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 16.56/3.08 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.56/3.08 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 16.56/3.08 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 16.56/3.08 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 16.56/3.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.56/3.08 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 16.56/3.08 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.56/3.08 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 16.56/3.08 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 16.56/3.08 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 16.56/3.08 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.56/3.08 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 16.56/3.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 16.56/3.08 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 16.56/3.08 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 16.56/3.08 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 16.56/3.08 % 16.56/3.08 (function-axioms) % 16.56/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.56/3.08 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.56/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.56/3.08 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.56/3.08 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.56/3.08 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.56/3.08 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.56/3.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.56/3.08 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.56/3.08 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.56/3.08 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.56/3.08 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.56/3.08 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.56/3.08 (distinct_points(v3, v2) = v0)) % 16.56/3.08 % 16.56/3.08 Further assumptions not needed in the proof: % 16.56/3.08 -------------------------------------------- % 16.56/3.08 apart2, apart3, apart5, ax6, ceq3, ci3, ci4 % 16.56/3.08 % 16.56/3.08 Those formulas are unsatisfiable: % 16.56/3.08 --------------------------------- % 16.56/3.08 % 16.56/3.08 Begin of proof % 16.56/3.08 | % 16.56/3.08 | ALPHA: (apart4) implies: % 16.56/3.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.56/3.08 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 16.56/3.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 16.56/3.08 | % 16.56/3.08 | ALPHA: (ci1) implies: % 16.56/3.08 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.56/3.08 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.56/3.08 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.56/3.08 | $i(v2))) % 16.56/3.08 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.56/3.08 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.56/3.08 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 16.56/3.08 | ~ (v4 = 0) | ~ (v3 = 0)))) % 16.56/3.08 | % 16.56/3.08 | ALPHA: (ci2) implies: % 16.56/3.08 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.56/3.08 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.56/3.08 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.56/3.08 | $i(v2))) % 16.56/3.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.56/3.09 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.56/3.09 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 16.56/3.09 | ~ (v4 = 0) | ~ (v3 = 0)))) % 16.56/3.09 | % 16.56/3.09 | ALPHA: (cu1) implies: % 16.56/3.09 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.56/3.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 16.56/3.09 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 16.56/3.09 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.56/3.09 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 16.56/3.09 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 16.56/3.09 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 16.56/3.09 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.56/3.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 16.56/3.09 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.56/3.09 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 16.56/3.09 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 16.56/3.09 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 16.56/3.09 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 16.56/3.09 | | v8 = 0))) % 16.56/3.09 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.56/3.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.56/3.09 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.56/3.09 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 16.56/3.09 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 16.56/3.09 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 16.56/3.09 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 16.56/3.09 | | v8 = 0))) % 16.56/3.09 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.56/3.09 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.56/3.09 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 16.56/3.09 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.56/3.09 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 16.56/3.09 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 16.56/3.09 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 16.56/3.09 | % 16.56/3.09 | ALPHA: (ceq1) implies: % 16.56/3.09 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.56/3.09 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 16.56/3.09 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.56/3.09 | distinct_points(v0, v2) = 0) % 16.56/3.09 | % 16.56/3.09 | ALPHA: (ceq2) implies: % 16.56/3.09 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.56/3.09 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 16.56/3.09 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.56/3.09 | distinct_lines(v1, v2) = 0) % 16.56/3.09 | % 16.56/3.09 | ALPHA: (function-axioms) implies: % 16.56/3.09 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.56/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.56/3.09 | (distinct_points(v3, v2) = v0)) % 16.56/3.09 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.56/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 16.56/3.09 | (distinct_lines(v3, v2) = v0)) % 16.56/3.09 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.56/3.09 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.56/3.09 | (apart_point_and_line(v3, v2) = v0)) % 16.56/3.09 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.56/3.09 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 16.56/3.09 | % 16.56/3.09 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 16.56/3.09 | all_17_3, all_17_4, all_17_5 gives: % 16.56/3.10 | (16) ~ (all_17_0 = 0) & line_connecting(all_17_5, all_17_3) = all_17_1 & % 16.56/3.10 | line_connecting(all_17_5, all_17_4) = all_17_2 & % 16.56/3.10 | apart_point_and_line(all_17_3, all_17_2) = 0 & % 16.56/3.10 | apart_point_and_line(all_17_4, all_17_1) = all_17_0 & % 16.56/3.10 | distinct_points(all_17_5, all_17_4) = 0 & $i(all_17_1) & $i(all_17_2) % 16.56/3.10 | & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) % 16.56/3.10 | % 16.56/3.10 | ALPHA: (16) implies: % 16.56/3.10 | (17) ~ (all_17_0 = 0) % 16.56/3.10 | (18) $i(all_17_5) % 16.56/3.10 | (19) $i(all_17_4) % 16.56/3.10 | (20) $i(all_17_3) % 16.56/3.10 | (21) $i(all_17_1) % 16.56/3.10 | (22) distinct_points(all_17_5, all_17_4) = 0 % 16.56/3.10 | (23) apart_point_and_line(all_17_4, all_17_1) = all_17_0 % 16.56/3.10 | (24) apart_point_and_line(all_17_3, all_17_2) = 0 % 16.56/3.10 | (25) line_connecting(all_17_5, all_17_4) = all_17_2 % 16.56/3.10 | (26) line_connecting(all_17_5, all_17_3) = all_17_1 % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (18), % 16.56/3.10 | (19), (22) gives: % 16.56/3.10 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 16.56/3.10 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (18), % 16.56/3.10 | (19), (22) gives: % 16.56/3.10 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 16.56/3.10 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (9) with all_17_5, all_17_4, all_17_1, all_17_1, % 16.56/3.10 | all_17_0, all_17_0, simplifying with (18), (19), (21), (22), (23) % 16.56/3.10 | gives: % 16.56/3.10 | (29) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.56/3.10 | (apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.56/3.10 | apart_point_and_line(all_17_5, all_17_1) = v1 & % 16.56/3.10 | distinct_lines(all_17_1, all_17_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 16.56/3.10 | = 0)) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_17_1, all_17_1, % 16.56/3.10 | all_17_0, all_17_0, simplifying with (19), (21), (23) gives: % 16.56/3.10 | (30) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 16.56/3.10 | any] : (apart_point_and_line(all_17_4, all_17_1) = v3 & % 16.56/3.10 | apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.56/3.10 | distinct_lines(all_17_1, all_17_1) = v1 & distinct_points(all_17_4, % 16.56/3.10 | all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying % 16.56/3.10 | with (18), (19), (25) gives: % 16.56/3.10 | (31) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4, % 16.56/3.10 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.56/3.10 | (v1 = 0) | ~ (v0 = 0))) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying % 16.56/3.10 | with (18), (19), (25) gives: % 16.56/3.10 | (32) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5, % 16.56/3.10 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.56/3.10 | (v1 = 0) | ~ (v0 = 0))) % 16.56/3.10 | % 16.56/3.10 | GROUND_INST: instantiating (5) with all_17_5, all_17_3, all_17_1, simplifying % 16.56/3.10 | with (18), (20), (26) gives: % 16.56/3.11 | (33) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_3, % 16.56/3.11 | all_17_1) = v1 & distinct_points(all_17_5, all_17_3) = v0 & ( ~ % 16.56/3.11 | (v1 = 0) | ~ (v0 = 0))) % 16.56/3.11 | % 16.56/3.11 | GROUND_INST: instantiating (3) with all_17_5, all_17_3, all_17_1, simplifying % 16.56/3.11 | with (18), (20), (26) gives: % 16.56/3.11 | (34) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5, % 16.56/3.11 | all_17_1) = v1 & distinct_points(all_17_5, all_17_3) = v0 & ( ~ % 16.56/3.11 | (v1 = 0) | ~ (v0 = 0))) % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (34) with fresh symbols all_24_0, all_24_1 gives: % 16.56/3.11 | (35) apart_point_and_line(all_17_5, all_17_1) = all_24_0 & % 16.56/3.11 | distinct_points(all_17_5, all_17_3) = all_24_1 & ( ~ (all_24_0 = 0) | % 16.56/3.11 | ~ (all_24_1 = 0)) % 16.56/3.11 | % 16.56/3.11 | ALPHA: (35) implies: % 16.56/3.11 | (36) distinct_points(all_17_5, all_17_3) = all_24_1 % 16.56/3.11 | (37) apart_point_and_line(all_17_5, all_17_1) = all_24_0 % 16.56/3.11 | (38) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (33) with fresh symbols all_26_0, all_26_1 gives: % 16.56/3.11 | (39) apart_point_and_line(all_17_3, all_17_1) = all_26_0 & % 16.56/3.11 | distinct_points(all_17_5, all_17_3) = all_26_1 & ( ~ (all_26_0 = 0) | % 16.56/3.11 | ~ (all_26_1 = 0)) % 16.56/3.11 | % 16.56/3.11 | ALPHA: (39) implies: % 16.56/3.11 | (40) distinct_points(all_17_5, all_17_3) = all_26_1 % 16.56/3.11 | (41) apart_point_and_line(all_17_3, all_17_1) = all_26_0 % 16.56/3.11 | (42) ~ (all_26_0 = 0) | ~ (all_26_1 = 0) % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (28) with fresh symbols all_28_0, all_28_1 gives: % 16.56/3.11 | (43) ~ (all_28_0 = 0) & line_connecting(all_17_5, all_17_4) = all_28_1 & % 16.56/3.11 | apart_point_and_line(all_17_5, all_28_1) = all_28_0 & $i(all_28_1) % 16.56/3.11 | % 16.56/3.11 | ALPHA: (43) implies: % 16.56/3.11 | (44) $i(all_28_1) % 16.56/3.11 | (45) apart_point_and_line(all_17_5, all_28_1) = all_28_0 % 16.56/3.11 | (46) line_connecting(all_17_5, all_17_4) = all_28_1 % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (27) with fresh symbols all_30_0, all_30_1 gives: % 16.56/3.11 | (47) ~ (all_30_0 = 0) & line_connecting(all_17_5, all_17_4) = all_30_1 & % 16.56/3.11 | apart_point_and_line(all_17_4, all_30_1) = all_30_0 & $i(all_30_1) % 16.56/3.11 | % 16.56/3.11 | ALPHA: (47) implies: % 16.56/3.11 | (48) apart_point_and_line(all_17_4, all_30_1) = all_30_0 % 16.56/3.11 | (49) line_connecting(all_17_5, all_17_4) = all_30_1 % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1 gives: % 16.56/3.11 | (50) apart_point_and_line(all_17_5, all_17_2) = all_32_0 & % 16.56/3.11 | distinct_points(all_17_5, all_17_4) = all_32_1 & ( ~ (all_32_0 = 0) | % 16.56/3.11 | ~ (all_32_1 = 0)) % 16.56/3.11 | % 16.56/3.11 | ALPHA: (50) implies: % 16.56/3.11 | (51) distinct_points(all_17_5, all_17_4) = all_32_1 % 16.56/3.11 | (52) apart_point_and_line(all_17_5, all_17_2) = all_32_0 % 16.56/3.11 | (53) ~ (all_32_0 = 0) | ~ (all_32_1 = 0) % 16.56/3.11 | % 16.56/3.11 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives: % 16.56/3.11 | (54) apart_point_and_line(all_17_4, all_17_2) = all_34_0 & % 16.56/3.11 | distinct_points(all_17_5, all_17_4) = all_34_1 & ( ~ (all_34_0 = 0) | % 16.80/3.11 | ~ (all_34_1 = 0)) % 16.80/3.11 | % 16.80/3.11 | ALPHA: (54) implies: % 16.80/3.11 | (55) distinct_points(all_17_5, all_17_4) = all_34_1 % 16.80/3.11 | (56) apart_point_and_line(all_17_4, all_17_2) = all_34_0 % 16.80/3.11 | (57) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 16.80/3.11 | % 16.80/3.11 | BETA: splitting (29) gives: % 16.80/3.11 | % 16.80/3.11 | Case 1: % 16.80/3.11 | | % 16.80/3.11 | | (58) all_17_0 = 0 % 16.80/3.11 | | % 16.80/3.11 | | REDUCE: (17), (58) imply: % 16.80/3.11 | | (59) $false % 16.80/3.11 | | % 16.80/3.11 | | CLOSE: (59) is inconsistent. % 16.80/3.11 | | % 16.80/3.11 | Case 2: % 16.80/3.11 | | % 16.80/3.12 | | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.80/3.12 | | (apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.80/3.12 | | apart_point_and_line(all_17_5, all_17_1) = v1 & % 16.80/3.12 | | distinct_lines(all_17_1, all_17_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 16.80/3.12 | | v1 = 0)) % 16.80/3.12 | | % 16.80/3.12 | | DELTA: instantiating (60) with fresh symbols all_40_0, all_40_1, all_40_2 % 16.80/3.12 | | gives: % 16.80/3.12 | | (61) apart_point_and_line(all_17_5, all_17_1) = all_40_0 & % 16.80/3.12 | | apart_point_and_line(all_17_5, all_17_1) = all_40_1 & % 16.80/3.12 | | distinct_lines(all_17_1, all_17_1) = all_40_2 & ( ~ (all_40_2 = 0) | % 16.80/3.12 | | all_40_0 = 0 | all_40_1 = 0) % 16.80/3.12 | | % 16.80/3.12 | | ALPHA: (61) implies: % 16.80/3.12 | | (62) apart_point_and_line(all_17_5, all_17_1) = all_40_1 % 16.80/3.12 | | (63) apart_point_and_line(all_17_5, all_17_1) = all_40_0 % 16.80/3.12 | | % 16.80/3.12 | | BETA: splitting (30) gives: % 16.80/3.12 | | % 16.80/3.12 | | Case 1: % 16.80/3.12 | | | % 16.80/3.12 | | | (64) all_17_0 = 0 % 16.80/3.12 | | | % 16.80/3.12 | | | REDUCE: (17), (64) imply: % 16.80/3.12 | | | (65) $false % 16.80/3.12 | | | % 16.80/3.12 | | | CLOSE: (65) is inconsistent. % 16.80/3.12 | | | % 16.80/3.12 | | Case 2: % 16.80/3.12 | | | % 16.80/3.12 | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.80/3.12 | | | (apart_point_and_line(all_17_4, all_17_1) = v3 & % 16.80/3.12 | | | apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.12 | | | distinct_lines(all_17_1, all_17_1) = v1 & % 16.80/3.12 | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ (v0 % 16.80/3.12 | | | = 0) | v3 = 0 | v2 = 0)) % 16.80/3.12 | | | % 16.80/3.12 | | | DELTA: instantiating (66) with fresh symbols all_45_0, all_45_1, all_45_2, % 16.80/3.12 | | | all_45_3 gives: % 16.80/3.12 | | | (67) apart_point_and_line(all_17_4, all_17_1) = all_45_0 & % 16.80/3.12 | | | apart_point_and_line(all_17_4, all_17_1) = all_45_1 & % 16.80/3.12 | | | distinct_lines(all_17_1, all_17_1) = all_45_2 & % 16.80/3.12 | | | distinct_points(all_17_4, all_17_4) = all_45_3 & ( ~ (all_45_2 = % 16.80/3.12 | | | 0) | ~ (all_45_3 = 0) | all_45_0 = 0 | all_45_1 = 0) % 16.80/3.12 | | | % 16.80/3.12 | | | ALPHA: (67) implies: % 16.80/3.12 | | | (68) apart_point_and_line(all_17_4, all_17_1) = all_45_1 % 16.80/3.12 | | | (69) apart_point_and_line(all_17_4, all_17_1) = all_45_0 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (12) with 0, all_34_1, all_17_4, all_17_5, % 16.80/3.12 | | | simplifying with (22), (55) gives: % 16.80/3.12 | | | (70) all_34_1 = 0 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (12) with all_32_1, all_34_1, all_17_4, % 16.80/3.12 | | | all_17_5, simplifying with (51), (55) gives: % 16.80/3.12 | | | (71) all_34_1 = all_32_1 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (12) with all_24_1, all_26_1, all_17_3, % 16.80/3.12 | | | all_17_5, simplifying with (36), (40) gives: % 16.80/3.12 | | | (72) all_26_1 = all_24_1 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (14) with all_40_1, all_40_0, all_17_1, % 16.80/3.12 | | | all_17_5, simplifying with (62), (63) gives: % 16.80/3.12 | | | (73) all_40_0 = all_40_1 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (14) with all_24_0, all_40_0, all_17_1, % 16.80/3.12 | | | all_17_5, simplifying with (37), (63) gives: % 16.80/3.12 | | | (74) all_40_0 = all_24_0 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (14) with all_17_0, all_45_0, all_17_1, % 16.80/3.12 | | | all_17_4, simplifying with (23), (69) gives: % 16.80/3.12 | | | (75) all_45_0 = all_17_0 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (14) with all_45_1, all_45_0, all_17_1, % 16.80/3.12 | | | all_17_4, simplifying with (68), (69) gives: % 16.80/3.12 | | | (76) all_45_0 = all_45_1 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (15) with all_17_2, all_30_1, all_17_4, % 16.80/3.12 | | | all_17_5, simplifying with (25), (49) gives: % 16.80/3.12 | | | (77) all_30_1 = all_17_2 % 16.80/3.12 | | | % 16.80/3.12 | | | GROUND_INST: instantiating (15) with all_28_1, all_30_1, all_17_4, % 16.80/3.12 | | | all_17_5, simplifying with (46), (49) gives: % 16.80/3.12 | | | (78) all_30_1 = all_28_1 % 16.80/3.12 | | | % 16.80/3.12 | | | COMBINE_EQS: (75), (76) imply: % 16.80/3.12 | | | (79) all_45_1 = all_17_0 % 16.80/3.12 | | | % 16.80/3.12 | | | COMBINE_EQS: (73), (74) imply: % 16.80/3.12 | | | (80) all_40_1 = all_24_0 % 16.80/3.12 | | | % 16.80/3.12 | | | SIMP: (80) implies: % 16.80/3.12 | | | (81) all_40_1 = all_24_0 % 16.80/3.12 | | | % 16.80/3.12 | | | COMBINE_EQS: (70), (71) imply: % 16.80/3.12 | | | (82) all_32_1 = 0 % 16.80/3.12 | | | % 16.80/3.12 | | | COMBINE_EQS: (77), (78) imply: % 16.80/3.12 | | | (83) all_28_1 = all_17_2 % 16.80/3.12 | | | % 16.80/3.12 | | | SIMP: (83) implies: % 16.80/3.12 | | | (84) all_28_1 = all_17_2 % 16.80/3.12 | | | % 16.80/3.12 | | | REDUCE: (48), (77) imply: % 16.80/3.12 | | | (85) apart_point_and_line(all_17_4, all_17_2) = all_30_0 % 16.80/3.12 | | | % 16.80/3.12 | | | REDUCE: (45), (84) imply: % 16.80/3.12 | | | (86) apart_point_and_line(all_17_5, all_17_2) = all_28_0 % 16.80/3.12 | | | % 16.80/3.12 | | | REDUCE: (44), (84) imply: % 16.80/3.12 | | | (87) $i(all_17_2) % 16.80/3.12 | | | % 16.80/3.12 | | | BETA: splitting (57) gives: % 16.80/3.12 | | | % 16.80/3.12 | | | Case 1: % 16.80/3.12 | | | | % 16.80/3.12 | | | | (88) ~ (all_34_0 = 0) % 16.80/3.12 | | | | % 16.80/3.12 | | | | BETA: splitting (53) gives: % 16.80/3.12 | | | | % 16.80/3.12 | | | | Case 1: % 16.80/3.12 | | | | | % 16.80/3.12 | | | | | (89) ~ (all_32_0 = 0) % 16.80/3.12 | | | | | % 16.80/3.12 | | | | | GROUND_INST: instantiating (14) with all_32_0, all_28_0, all_17_2, % 16.80/3.12 | | | | | all_17_5, simplifying with (52), (86) gives: % 16.80/3.12 | | | | | (90) all_32_0 = all_28_0 % 16.80/3.12 | | | | | % 16.80/3.12 | | | | | GROUND_INST: instantiating (14) with all_34_0, all_30_0, all_17_2, % 16.80/3.12 | | | | | all_17_4, simplifying with (56), (85) gives: % 16.80/3.12 | | | | | (91) all_34_0 = all_30_0 % 16.80/3.12 | | | | | % 16.80/3.12 | | | | | REDUCE: (88), (91) imply: % 16.80/3.12 | | | | | (92) ~ (all_30_0 = 0) % 16.80/3.12 | | | | | % 16.80/3.12 | | | | | REDUCE: (89), (90) imply: % 16.80/3.12 | | | | | (93) ~ (all_28_0 = 0) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (10) with all_17_3, all_17_2, all_17_5, % 16.80/3.13 | | | | | all_28_0, simplifying with (18), (20), (24), (86), (87) % 16.80/3.13 | | | | | gives: % 16.80/3.13 | | | | | (94) all_28_0 = 0 | distinct_points(all_17_3, all_17_5) = 0 % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (8) with all_17_5, all_17_4, all_17_2, % 16.80/3.13 | | | | | all_17_1, all_28_0, all_17_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (23), (86), (87) gives: % 16.80/3.13 | | | | | (95) all_28_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.13 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_2) = v3 & apart_point_and_line(all_17_5, all_17_1) % 16.80/3.13 | | | | | = v2 & distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 16.80/3.13 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (7) with all_17_5, all_17_4, all_17_1, % 16.80/3.13 | | | | | all_17_2, all_28_0, all_17_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (23), (86), (87) gives: % 16.80/3.13 | | | | | (96) all_28_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.13 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_2) = v3 & apart_point_and_line(all_17_5, all_17_1) % 16.80/3.13 | | | | | = v2 & distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 16.80/3.13 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (8) with all_17_5, all_17_5, all_17_2, % 16.80/3.13 | | | | | all_17_2, all_28_0, all_28_0, simplifying with (18), % 16.80/3.13 | | | | | (86), (87) gives: % 16.80/3.13 | | | | | (97) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.13 | | | | | [v3: any] : (apart_point_and_line(all_17_5, all_17_2) = v3 & % 16.80/3.13 | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.13 | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v1 = 0) | ~ % 16.80/3.13 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_5, all_17_1, % 16.80/3.13 | | | | | all_17_1, all_17_0, all_24_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (23), (37) gives: % 16.80/3.13 | | | | | (98) all_24_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.13 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_1) = v2 & apart_point_and_line(all_17_5, all_17_1) % 16.80/3.13 | | | | | = v3 & distinct_lines(all_17_1, all_17_1) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 = 0) | ~ % 16.80/3.13 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (6) with all_17_5, all_17_4, all_17_2, % 16.80/3.13 | | | | | all_17_1, all_28_0, all_24_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (22), (37), (86), (87) gives: % 16.80/3.13 | | | | | (99) all_28_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.13 | | | | | [v2: any] : (apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.13 | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 16.80/3.13 | | | | | distinct_lines(all_17_2, all_17_1) = v0 & ( ~ (v0 = 0) | v2 % 16.80/3.13 | | | | | = 0 | v1 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (8) with all_17_5, all_17_4, all_17_1, % 16.80/3.13 | | | | | all_17_2, all_24_0, all_30_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (37), (85), (87) gives: % 16.80/3.13 | | | | | (100) all_30_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.80/3.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_1) = v3 & apart_point_and_line(all_17_5, all_17_2) % 16.80/3.13 | | | | | = v2 & distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ (v1 = 0) | % 16.80/3.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_5, all_17_2, % 16.80/3.13 | | | | | all_17_1, all_30_0, all_24_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (37), (85), (87) gives: % 16.80/3.13 | | | | | (101) all_30_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.80/3.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_1) = v2 & apart_point_and_line(all_17_5, all_17_2) % 16.80/3.13 | | | | | = v3 & distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 = 0) | % 16.80/3.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (7) with all_17_5, all_17_4, all_17_2, % 16.80/3.13 | | | | | all_17_1, all_24_0, all_30_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (37), (85), (87) gives: % 16.80/3.13 | | | | | (102) all_30_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.80/3.13 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.13 | | | | | all_17_1) = v3 & apart_point_and_line(all_17_5, all_17_2) % 16.80/3.13 | | | | | = v2 & distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.13 | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ (v1 = 0) | % 16.80/3.13 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.13 | | | | | % 16.80/3.13 | | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_5, all_17_1, % 16.80/3.13 | | | | | all_17_2, all_30_0, all_24_0, simplifying with (18), % 16.80/3.13 | | | | | (19), (21), (37), (85), (87) gives: % 16.80/3.14 | | | | | (103) all_30_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.80/3.14 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.14 | | | | | all_17_1) = v2 & apart_point_and_line(all_17_5, all_17_2) % 16.80/3.14 | | | | | = v3 & distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.14 | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 = 0) | % 16.80/3.14 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | % 16.80/3.14 | | | | | GROUND_INST: instantiating (11) with all_17_3, all_17_2, all_17_1, % 16.80/3.14 | | | | | all_26_0, simplifying with (20), (21), (24), (41), (87) % 16.80/3.14 | | | | | gives: % 16.80/3.14 | | | | | (104) all_26_0 = 0 | distinct_lines(all_17_2, all_17_1) = 0 % 16.80/3.14 | | | | | % 16.80/3.14 | | | | | BETA: splitting (38) gives: % 16.80/3.14 | | | | | % 16.80/3.14 | | | | | Case 1: % 16.80/3.14 | | | | | | % 16.80/3.14 | | | | | | (105) ~ (all_24_0 = 0) % 16.80/3.14 | | | | | | % 16.80/3.14 | | | | | | BETA: splitting (94) gives: % 16.80/3.14 | | | | | | % 16.80/3.14 | | | | | | Case 1: % 16.80/3.14 | | | | | | | % 16.80/3.14 | | | | | | | (106) distinct_points(all_17_3, all_17_5) = 0 % 16.80/3.14 | | | | | | | % 16.80/3.14 | | | | | | | BETA: splitting (97) gives: % 16.80/3.14 | | | | | | | % 16.80/3.14 | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | (107) all_28_0 = 0 % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | REDUCE: (93), (107) imply: % 16.80/3.14 | | | | | | | | (108) $false % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | CLOSE: (108) is inconsistent. % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | (109) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 16.80/3.14 | | | | | | | | any] : (apart_point_and_line(all_17_5, all_17_2) = v3 % 16.80/3.14 | | | | | | | | & apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.14 | | | | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 16.80/3.14 | | | | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v1 = % 16.80/3.14 | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | DELTA: instantiating (109) with fresh symbols all_86_0, % 16.80/3.14 | | | | | | | | all_86_1, all_86_2, all_86_3 gives: % 16.80/3.14 | | | | | | | | (110) apart_point_and_line(all_17_5, all_17_2) = all_86_0 & % 16.80/3.14 | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = all_86_1 & % 16.80/3.14 | | | | | | | | distinct_lines(all_17_2, all_17_2) = all_86_2 & % 16.80/3.14 | | | | | | | | distinct_points(all_17_5, all_17_5) = all_86_3 & ( ~ % 16.80/3.14 | | | | | | | | (all_86_2 = 0) | ~ (all_86_3 = 0) | all_86_0 = 0 | % 16.80/3.14 | | | | | | | | all_86_1 = 0) % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | ALPHA: (110) implies: % 16.80/3.14 | | | | | | | | (111) apart_point_and_line(all_17_5, all_17_2) = all_86_1 % 16.80/3.14 | | | | | | | | (112) apart_point_and_line(all_17_5, all_17_2) = all_86_0 % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | BETA: splitting (96) gives: % 16.80/3.14 | | | | | | | | % 16.80/3.14 | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | (113) all_28_0 = 0 % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | REDUCE: (93), (113) imply: % 16.80/3.14 | | | | | | | | | (114) $false % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | CLOSE: (114) is inconsistent. % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | (115) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 16.80/3.14 | | | | | | | | | any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | (apart_point_and_line(all_17_4, all_17_2) = v3 & % 16.80/3.14 | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.14 | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ (v1 % 16.80/3.14 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | BETA: splitting (95) gives: % 16.80/3.14 | | | | | | | | | % 16.80/3.14 | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | (116) all_28_0 = 0 % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | REDUCE: (93), (116) imply: % 16.80/3.14 | | | | | | | | | | (117) $false % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | CLOSE: (117) is inconsistent. % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | (118) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_2) = v3 & % 16.80/3.14 | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.14 | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | BETA: splitting (100) gives: % 16.80/3.14 | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | (119) all_30_0 = 0 % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | REDUCE: (92), (119) imply: % 16.80/3.14 | | | | | | | | | | | (120) $false % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | CLOSE: (120) is inconsistent. % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | (121) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v3 & % 16.80/3.14 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.14 | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.14 | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | BETA: splitting (98) gives: % 16.80/3.14 | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | (122) all_24_0 = 0 % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | REDUCE: (105), (122) imply: % 16.80/3.14 | | | | | | | | | | | | (123) $false % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | (124) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v3 & % 16.80/3.14 | | | | | | | | | | | | distinct_lines(all_17_1, all_17_1) = v1 & % 16.80/3.14 | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | BETA: splitting (102) gives: % 16.80/3.14 | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | (125) all_30_0 = 0 % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | REDUCE: (92), (125) imply: % 16.80/3.14 | | | | | | | | | | | | | (126) $false % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | (127) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v3 & % 16.80/3.14 | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.14 | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.14 | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | BETA: splitting (103) gives: % 16.80/3.14 | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | (128) all_30_0 = 0 % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | REDUCE: (92), (128) imply: % 16.80/3.14 | | | | | | | | | | | | | | (129) $false % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | (130) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 16.80/3.14 | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.14 | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | BETA: splitting (101) gives: % 16.80/3.14 | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | (131) all_30_0 = 0 % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | REDUCE: (92), (131) imply: % 16.80/3.14 | | | | | | | | | | | | | | | (132) $false % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | (133) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.14 | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 16.80/3.14 | | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 16.80/3.14 | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.14 | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 16.80/3.14 | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | (134) all_17_0 = 0 % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | REDUCE: (17), (134) imply: % 16.80/3.14 | | | | | | | | | | | | | | | | (135) $false % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | (136) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.14 | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.14 | | | | | | | | | | | | | | | | all_17_1) = v2 & % 16.80/3.14 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v3 & % 16.80/3.14 | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_1) = v1 & % 16.80/3.14 | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.14 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | DELTA: instantiating (136) with fresh symbols all_125_0, % 16.80/3.14 | | | | | | | | | | | | | | | | all_125_1, all_125_2, all_125_3 gives: % 16.80/3.14 | | | | | | | | | | | | | | | | (137) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.14 | | | | | | | | | | | | | | | | all_125_1 & apart_point_and_line(all_17_5, % 16.80/3.14 | | | | | | | | | | | | | | | | all_17_1) = all_125_0 & distinct_lines(all_17_1, % 16.80/3.14 | | | | | | | | | | | | | | | | all_17_1) = all_125_2 & % 16.80/3.14 | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = all_125_3 & % 16.80/3.14 | | | | | | | | | | | | | | | | ( ~ (all_125_2 = 0) | ~ (all_125_3 = 0) | % 16.80/3.14 | | | | | | | | | | | | | | | | all_125_0 = 0 | all_125_1 = 0) % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | ALPHA: (137) implies: % 16.80/3.14 | | | | | | | | | | | | | | | | (138) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.14 | | | | | | | | | | | | | | | | all_125_1 % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | BETA: splitting (127) gives: % 16.80/3.14 | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | Case 1: % 16.80/3.14 | | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | | (139) all_24_0 = 0 % 16.80/3.14 | | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | | REDUCE: (105), (139) imply: % 16.80/3.14 | | | | | | | | | | | | | | | | | (140) $false % 16.80/3.14 | | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 16.80/3.14 | | | | | | | | | | | | | | | | | % 16.80/3.14 | | | | | | | | | | | | | | | | Case 2: % 16.80/3.14 | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | (141) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.15 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.15 | | | | | | | | | | | | | | | | | all_17_1) = v3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.15 | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.15 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.15 | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | DELTA: instantiating (141) with fresh symbols all_130_0, % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_1, all_130_2, all_130_3 gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | (142) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_0 & apart_point_and_line(all_17_5, % 16.80/3.15 | | | | | | | | | | | | | | | | | all_17_2) = all_130_1 & distinct_lines(all_17_2, % 16.80/3.15 | | | | | | | | | | | | | | | | | all_17_1) = all_130_2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_130_3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | ( ~ (all_130_2 = 0) | ~ (all_130_3 = 0) | % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_0 = 0 | all_130_1 = 0) % 16.80/3.15 | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | ALPHA: (142) implies: % 16.80/3.15 | | | | | | | | | | | | | | | | | (143) distinct_points(all_17_5, all_17_4) = all_130_3 % 16.80/3.15 | | | | | | | | | | | | | | | | | (144) distinct_lines(all_17_2, all_17_1) = all_130_2 % 16.80/3.15 | | | | | | | | | | | | | | | | | (145) apart_point_and_line(all_17_5, all_17_2) = % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_1 % 16.80/3.15 | | | | | | | | | | | | | | | | | (146) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_0 % 16.80/3.15 | | | | | | | | | | | | | | | | | (147) ~ (all_130_2 = 0) | ~ (all_130_3 = 0) | % 16.80/3.15 | | | | | | | | | | | | | | | | | all_130_0 = 0 | all_130_1 = 0 % 16.80/3.15 | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | (148) all_24_0 = 0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | REDUCE: (105), (148) imply: % 16.80/3.15 | | | | | | | | | | | | | | | | | | (149) $false % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | (150) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.15 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_17_1) = v2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.15 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_135_0, % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_135_1, all_135_2, all_135_3 gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | (151) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_135_1 & apart_point_and_line(all_17_5, % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_17_2) = all_135_0 & distinct_lines(all_17_2, % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_17_1) = all_135_2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = all_135_3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | ( ~ (all_135_2 = 0) | ~ (all_135_3 = 0) | % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_135_0 = 0 | all_135_1 = 0) % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 16.80/3.15 | | | | | | | | | | | | | | | | | | (152) distinct_lines(all_17_2, all_17_1) = all_135_2 % 16.80/3.15 | | | | | | | | | | | | | | | | | | (153) apart_point_and_line(all_17_5, all_17_2) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_135_0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | (154) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | all_135_1 % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (155) all_17_0 = 0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | REDUCE: (17), (155) imply: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (156) $false % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (157) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.15 | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_17_2) = v3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (157) with fresh symbols all_162_0, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_162_1, all_162_2, all_162_3 gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (158) apart_point_and_line(all_17_4, all_17_2) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_162_0 & apart_point_and_line(all_17_5, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_17_1) = all_162_1 & distinct_lines(all_17_1, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_17_2) = all_162_2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_162_3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | ( ~ (all_162_2 = 0) | ~ (all_162_3 = 0) | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | all_162_0 = 0 | all_162_1 = 0) % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | (159) distinct_points(all_17_5, all_17_4) = all_162_3 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (160) all_24_0 = 0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (160) imply: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (161) $false % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (162) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_17_1) = v3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_167_0, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_167_1, all_167_2, all_167_3 gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (163) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_167_0 & apart_point_and_line(all_17_5, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_17_2) = all_167_1 & distinct_lines(all_17_1, % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_17_2) = all_167_2 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_167_3 & % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | ( ~ (all_167_2 = 0) | ~ (all_167_3 = 0) | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_167_0 = 0 | all_167_1 = 0) % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (164) distinct_points(all_17_5, all_17_4) = all_167_3 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (165) apart_point_and_line(all_17_5, all_17_2) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_167_1 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | (166) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | all_167_0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | (167) all_24_0 = 0 % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (167) imply: % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | (168) $false % 16.80/3.15 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (169) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1) = v2 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_172_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_172_1, all_172_2, all_172_3 gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (170) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_172_1 & apart_point_and_line(all_17_5, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_172_0 & distinct_lines(all_17_1, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_172_2 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_5) = all_172_3 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_172_2 = 0) | ~ (all_172_3 = 0) | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_172_0 = 0 | all_172_1 = 0) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (171) apart_point_and_line(all_17_5, all_17_2) = % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_172_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (172) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_172_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_130_3, all_162_3, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_5, simplifying with (143), (159) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (173) all_162_3 = all_130_3 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_167_3, all_17_4, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_5, simplifying with (22), (164) gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (174) all_167_3 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_162_3, all_167_3, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_4, all_17_5, simplifying with (159), (164) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (175) all_167_3 = all_162_3 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_130_2, all_135_2, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_2, simplifying with (144), (152) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (176) all_135_2 = all_130_2 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_86_0, all_130_1, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (112), (145) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (177) all_130_1 = all_86_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_28_0, all_135_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (86), (153) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (178) all_135_0 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_86_0, all_135_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (112), (153) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (179) all_135_0 = all_86_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_167_1, all_172_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (165), (171) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (180) all_172_0 = all_167_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_130_1, all_172_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (145), (171) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (181) all_172_0 = all_130_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_86_1, all_172_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (111), (171) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (182) all_172_0 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_17_0, all_135_1, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (23), (154) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (183) all_135_1 = all_17_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_135_1, all_167_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (154), (166) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (184) all_167_0 = all_135_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_125_1, all_167_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (138), (166) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (185) all_167_0 = all_125_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_135_1, all_172_1, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (154), (172) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (186) all_172_1 = all_135_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_130_0, all_172_1, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (146), (172) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (187) all_172_1 = all_130_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (182) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (188) all_167_1 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (181) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (189) all_167_1 = all_130_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (187) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (190) all_135_1 = all_130_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (191) all_135_1 = all_130_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (185) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (192) all_135_1 = all_125_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (192) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (193) all_135_1 = all_125_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (189) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (194) all_130_1 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (194) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (195) all_130_1 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (175) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (196) all_162_3 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (197) all_162_3 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (197) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (198) all_130_3 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (199) all_130_3 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (179) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (200) all_86_0 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (201) all_86_0 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (191) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (202) all_130_0 = all_17_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (193) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (203) all_130_0 = all_125_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (203) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (204) all_125_1 = all_17_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (195) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (205) all_86_0 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (206) all_86_0 = all_86_1 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (206) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (207) all_86_1 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (208) all_86_1 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (208) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | (209) all_130_1 = all_28_0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | (210) all_28_0 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (210) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | (211) $false % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | (212) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_17_4, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | all_17_1) = v2 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v0 & ( ~ % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (213) all_24_0 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (213) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (214) $false % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (215) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v0 & ( ~ % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (215) with fresh symbols all_190_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | all_190_1, all_190_2 gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (216) apart_point_and_line(all_17_4, all_17_1) = % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | all_190_0 & apart_point_and_line(all_17_4, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_190_1 & distinct_lines(all_17_2, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | all_17_1) = all_190_2 & ( ~ (all_190_2 = 0) | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | all_190_0 = 0 | all_190_1 = 0) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | (217) distinct_lines(all_17_2, all_17_1) = all_190_2 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | (218) all_17_0 = 0 % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (218) imply: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | (219) $false % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | (220) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = v3 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (220) with fresh symbols all_212_0, % 16.80/3.16 | | | | | | | | | | | | | | | | | | | | | | | | all_212_1, all_212_2, all_212_3 gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | (221) apart_point_and_line(all_17_4, all_17_2) = % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | all_212_0 & apart_point_and_line(all_17_5, % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | all_17_1) = all_212_1 & distinct_lines(all_17_2, % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | all_17_1) = all_212_2 & % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_212_3 & % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_212_2 = 0) | ~ (all_212_3 = 0) | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | all_212_0 = 0 | all_212_1 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | (222) distinct_lines(all_17_2, all_17_1) = all_212_2 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | (223) ~ (all_130_2 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (224) distinct_lines(all_17_2, all_17_1) = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_130_2, all_190_2, % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_2, simplifying with (144), (217) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_190_2 = all_130_2 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_190_2, all_212_2, % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_1, all_17_2, simplifying with (217), (222) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_212_2 = all_190_2 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_212_2, all_17_1, % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | all_17_2, simplifying with (222), (224) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_212_2 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (227) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_190_2 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_190_2 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (229) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_130_2 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_130_2 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (231) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) $false % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_26_0 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_26_0 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (234) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) $false % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_26_1 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (236) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_24_1 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (20), (36), (106), (237), (apart1) are % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_130_3 = 0) | all_130_0 = 0 | all_130_1 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (all_130_3 = 0) % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (239) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (240) $false % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_130_0 = 0 | all_130_1 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_130_0 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (242) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_17_0 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (243) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) $false % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_130_1 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (245) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_28_0 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (246) implies: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_28_0 = 0 % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (247) imply: % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | | % 16.80/3.17 | | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | | % 16.80/3.17 | | | | | | | | | End of split % 16.80/3.17 | | | | | | | | | % 16.80/3.17 | | | | | | | | End of split % 16.80/3.17 | | | | | | | | % 16.80/3.17 | | | | | | | End of split % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | Case 2: % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | (249) all_28_0 = 0 % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | REDUCE: (93), (249) imply: % 16.80/3.17 | | | | | | | (250) $false % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | CLOSE: (250) is inconsistent. % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | End of split % 16.80/3.17 | | | | | | % 16.80/3.17 | | | | | Case 2: % 16.80/3.17 | | | | | | % 16.80/3.17 | | | | | | (251) ~ (all_24_1 = 0) % 16.80/3.17 | | | | | | % 16.80/3.17 | | | | | | BETA: splitting (94) gives: % 16.80/3.17 | | | | | | % 16.80/3.17 | | | | | | Case 1: % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | (252) distinct_points(all_17_3, all_17_5) = 0 % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | REF_CLOSE: (1), (18), (20), (36), (251), (252), (apart1) are % 16.80/3.17 | | | | | | | inconsistent by sub-proof #1. % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | Case 2: % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | (253) all_28_0 = 0 % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | REDUCE: (93), (253) imply: % 16.80/3.17 | | | | | | | (254) $false % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | | CLOSE: (254) is inconsistent. % 16.80/3.17 | | | | | | | % 16.80/3.17 | | | | | | End of split % 16.80/3.17 | | | | | | % 16.80/3.17 | | | | | End of split % 16.80/3.17 | | | | | % 16.80/3.17 | | | | Case 2: % 16.80/3.17 | | | | | % 16.80/3.17 | | | | | (255) ~ (all_32_1 = 0) % 16.80/3.17 | | | | | % 16.80/3.17 | | | | | REDUCE: (82), (255) imply: % 16.80/3.17 | | | | | (256) $false % 16.80/3.17 | | | | | % 16.80/3.17 | | | | | CLOSE: (256) is inconsistent. % 16.80/3.17 | | | | | % 16.80/3.17 | | | | End of split % 16.80/3.17 | | | | % 16.80/3.17 | | | Case 2: % 16.80/3.17 | | | | % 16.80/3.17 | | | | (257) ~ (all_34_1 = 0) % 16.80/3.17 | | | | % 16.80/3.17 | | | | REDUCE: (70), (257) imply: % 16.80/3.17 | | | | (258) $false % 16.80/3.17 | | | | % 16.80/3.17 | | | | CLOSE: (258) is inconsistent. % 16.80/3.17 | | | | % 16.80/3.17 | | | End of split % 16.80/3.17 | | | % 16.80/3.17 | | End of split % 16.80/3.17 | | % 16.80/3.17 | End of split % 16.80/3.17 | % 16.80/3.17 End of proof % 16.80/3.17 % 16.80/3.17 Sub-proof #1 shows that the following formulas are inconsistent: % 16.80/3.17 ---------------------------------------------------------------- % 16.80/3.17 (1) ~ (all_24_1 = 0) % 16.80/3.17 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 16.80/3.17 (3) distinct_points(all_17_5, all_17_3) = all_24_1 % 16.80/3.17 (4) $i(all_17_5) % 16.80/3.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.80/3.17 (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.80/3.17 $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 16.80/3.17 (6) distinct_points(all_17_3, all_17_5) = 0 % 16.80/3.17 (7) $i(all_17_3) % 16.80/3.17 % 16.80/3.17 Begin of proof % 16.80/3.17 | % 16.80/3.17 | GROUND_INST: instantiating (5) with all_17_3, all_17_5, all_17_3, all_24_1, % 16.80/3.17 | simplifying with (3), (4), (6), (7) gives: % 16.80/3.17 | (8) all_24_1 = 0 | distinct_points(all_17_3, all_17_3) = 0 % 16.80/3.17 | % 16.80/3.17 | BETA: splitting (8) gives: % 16.80/3.17 | % 16.80/3.17 | Case 1: % 16.80/3.17 | | % 16.80/3.17 | | (9) distinct_points(all_17_3, all_17_3) = 0 % 16.80/3.17 | | % 16.80/3.17 | | GROUND_INST: instantiating (2) with all_17_3, simplifying with (7), (9) % 16.80/3.17 | | gives: % 16.80/3.17 | | (10) $false % 16.80/3.17 | | % 16.80/3.17 | | CLOSE: (10) is inconsistent. % 16.80/3.17 | | % 16.80/3.17 | Case 2: % 16.80/3.17 | | % 16.80/3.17 | | (11) all_24_1 = 0 % 16.80/3.17 | | % 16.80/3.17 | | REDUCE: (1), (11) imply: % 16.80/3.17 | | (12) $false % 16.80/3.17 | | % 16.80/3.17 | | CLOSE: (12) is inconsistent. % 16.80/3.17 | | % 16.80/3.17 | End of split % 16.80/3.17 | % 16.80/3.17 End of proof % 16.80/3.17 % SZS output end Proof for theBenchmark % 16.80/3.17 % 16.80/3.17 2557ms %------------------------------------------------------------------------------