%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO191+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:05 EDT 2023 % Result : Theorem 36.74s 5.81s % Output : Proof 127.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO191+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n032.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Tue Aug 29 21:47:02 EDT 2023 % 0.11/0.32 % CPUTime : % 0.16/0.61 ________ _____ % 0.16/0.61 ___ __ \_________(_)________________________________ % 0.16/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.61 % 0.16/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.61 (2023-06-19) % 0.16/0.61 % 0.16/0.61 (c) Philipp Rümmer, 2009-2023 % 0.16/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.61 Amanda Stjerna. % 0.16/0.61 Free software under BSD-3-Clause. % 0.16/0.61 % 0.16/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.61 % 0.16/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.63 Running up to 7 provers in parallel. % 0.52/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.05/1.27 Prover 4: Preprocessing ... % 3.05/1.27 Prover 1: Preprocessing ... % 3.89/1.33 Prover 0: Preprocessing ... % 3.89/1.33 Prover 6: Preprocessing ... % 3.89/1.33 Prover 3: Preprocessing ... % 3.89/1.33 Prover 2: Preprocessing ... % 3.89/1.34 Prover 5: Preprocessing ... % 8.05/1.89 Prover 5: Proving ... % 8.05/1.90 Prover 2: Proving ... % 8.05/2.00 Prover 3: Constructing countermodel ... % 8.05/2.01 Prover 1: Constructing countermodel ... % 8.05/2.02 Prover 6: Constructing countermodel ... % 10.85/2.30 Prover 3: gave up % 10.85/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.77/2.43 Prover 6: gave up % 11.77/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.77/2.48 Prover 7: Preprocessing ... % 11.77/2.50 Prover 8: Preprocessing ... % 12.40/2.51 Prover 4: Constructing countermodel ... % 12.40/2.52 Prover 1: gave up % 12.40/2.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.40/2.57 Prover 9: Preprocessing ... % 12.40/2.63 Prover 7: Warning: ignoring some quantifiers % 12.40/2.66 Prover 0: Proving ... % 13.34/2.68 Prover 7: Constructing countermodel ... % 14.44/2.79 Prover 8: Warning: ignoring some quantifiers % 14.44/2.80 Prover 8: Constructing countermodel ... % 15.99/3.04 Prover 8: gave up % 15.99/3.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.75/3.09 Prover 9: Constructing countermodel ... % 17.05/3.13 Prover 10: Preprocessing ... % 17.05/3.25 Prover 10: Warning: ignoring some quantifiers % 17.05/3.30 Prover 7: gave up % 17.05/3.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.05/3.31 Prover 10: Constructing countermodel ... % 17.05/3.35 Prover 11: Preprocessing ... % 21.62/3.79 Prover 10: gave up % 21.62/3.80 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 22.30/3.85 Prover 11: Constructing countermodel ... % 22.79/3.89 Prover 12: Preprocessing ... % 24.40/4.12 Prover 12: Proving ... % 36.74/5.80 Prover 0: proved (5151ms) % 36.74/5.80 % 36.74/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.74/5.81 % 36.74/5.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 36.74/5.81 Prover 9: stopped % 36.74/5.81 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 36.74/5.81 Prover 5: stopped % 36.74/5.81 Prover 12: stopped % 36.74/5.81 Prover 2: stopped % 37.44/5.85 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 37.44/5.87 Prover 13: Preprocessing ... % 37.44/5.87 Prover 19: Preprocessing ... % 37.44/5.88 Prover 16: Preprocessing ... % 37.91/5.93 Prover 13: Warning: ignoring some quantifiers % 37.91/5.94 Prover 13: Constructing countermodel ... % 38.62/6.04 Prover 16: Warning: ignoring some quantifiers % 38.62/6.05 Prover 19: Warning: ignoring some quantifiers % 38.62/6.06 Prover 16: Constructing countermodel ... % 38.62/6.07 Prover 19: Constructing countermodel ... % 40.18/6.23 Prover 13: gave up % 40.18/6.28 Prover 19: gave up % 63.92/10.16 Prover 16: gave up % 123.60/28.05 Prover 4: stopped % 126.18/29.91 Prover 11: Found proof (size 993) % 126.18/29.91 Prover 11: proved (26613ms) % 126.18/29.91 % 126.18/29.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 126.18/29.91 % 126.18/29.94 % SZS output start Proof for theBenchmark % 126.18/29.95 Assumptions after simplification: % 126.18/29.95 --------------------------------- % 126.18/29.95 % 126.18/29.95 (apart3) % 126.36/29.98 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 126.36/29.98 % 126.36/29.98 (ceq1) % 126.36/29.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 126.36/29.98 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 126.36/29.98 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 126.36/29.98 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 126.36/29.98 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 126.36/29.98 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 126.36/29.98 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 126.36/29.98 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 126.36/29.98 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 126.36/29.98 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 126.36/29.98 % 126.36/29.98 (ceq3) % 126.36/29.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 126.36/29.99 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 126.36/29.99 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 126.36/29.99 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 126.36/29.99 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 126.36/29.99 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 126.36/29.99 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 126.36/29.99 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 126.36/29.99 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 126.36/29.99 convergent_lines(v0, v2) = 0) % 126.36/29.99 % 126.36/29.99 (ci3) % 126.36/29.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 126.36/29.99 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 126.36/29.99 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 126.36/29.99 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 126.36/29.99 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 126.36/29.99 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 126.36/29.99 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 126.36/29.99 % 126.36/29.99 (ci4) % 126.36/30.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 126.36/30.00 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 126.36/30.00 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 126.36/30.00 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 126.36/30.00 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 126.36/30.00 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 126.36/30.00 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 126.36/30.00 % 126.36/30.00 (con) % 126.36/30.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 126.36/30.00 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ( ~ (v9 = % 126.36/30.00 0) & ~ (v8 = 0) & intersection_point(v2, v3) = v7 & % 126.36/30.00 intersection_point(v0, v1) = v4 & apart_point_and_line(v7, v1) = v9 & % 126.36/30.00 apart_point_and_line(v7, v0) = v8 & convergent_lines(v2, v3) = 0 & % 126.36/30.00 convergent_lines(v0, v1) = 0 & $i(v7) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 126.36/30.00 $i(v0) & ((v6 = 0 & apart_point_and_line(v4, v3) = 0) | (v5 = 0 & % 126.36/30.00 apart_point_and_line(v4, v2) = 0))) % 126.36/30.00 % 126.36/30.00 (cu1) % 126.36/30.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 126.36/30.01 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 126.36/30.01 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 126.36/30.01 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 126.36/30.01 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 126.36/30.01 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 126.36/30.01 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 126.36/30.01 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 126.36/30.02 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 126.36/30.02 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 126.36/30.02 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 126.36/30.02 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 126.36/30.02 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 126.36/30.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 126.36/30.02 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 126.36/30.02 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 126.36/30.02 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 126.36/30.02 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 126.36/30.02 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 126.36/30.02 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 126.36/30.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 126.36/30.02 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 126.36/30.02 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 126.36/30.02 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 126.36/30.02 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 126.36/30.02 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 126.36/30.02 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 126.36/30.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 126.36/30.02 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 126.36/30.02 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 126.36/30.02 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 126.36/30.02 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 126.36/30.02 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 126.36/30.02 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 126.36/30.02 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 126.36/30.02 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 126.36/30.02 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 126.36/30.02 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 126.36/30.02 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 126.36/30.02 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 126.36/30.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 126.36/30.02 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 126.36/30.02 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 126.36/30.02 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 126.36/30.02 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 126.36/30.02 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 126.36/30.02 % 126.36/30.02 (cup1) % 126.36/30.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 126.36/30.02 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 126.36/30.02 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 126.36/30.02 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~ % 126.36/30.02 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 126.36/30.02 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 126.36/30.02 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 126.36/30.02 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 126.36/30.02 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 126.36/30.02 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 126.36/30.02 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ % 126.36/30.02 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 126.36/30.02 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( % 126.36/30.02 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] % 126.36/30.02 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = % 126.36/30.02 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 126.36/30.02 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 126.36/30.02 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] % 126.36/30.02 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 126.36/30.02 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 126.36/30.02 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 126.36/30.02 (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 126.36/30.02 % 126.36/30.02 (function-axioms) % 126.36/30.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 126.36/30.03 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 126.36/30.03 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 126.36/30.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.36/30.03 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 126.36/30.03 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 126.36/30.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 126.36/30.03 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 126.36/30.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.36/30.03 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 126.36/30.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 126.36/30.03 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 126.36/30.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.36/30.03 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 126.36/30.03 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 126.36/30.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 126.36/30.03 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 126.36/30.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 126.36/30.03 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 126.36/30.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 126.36/30.03 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 126.36/30.03 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 126.36/30.03 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 126.36/30.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.36/30.03 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 126.36/30.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 126.36/30.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 126.36/30.03 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 126.36/30.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.36/30.03 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 126.36/30.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 126.36/30.03 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 126.36/30.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 126.36/30.03 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 126.36/30.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 126.36/30.03 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 126.36/30.03 % 126.36/30.03 Further assumptions not needed in the proof: % 126.36/30.03 -------------------------------------------- % 126.36/30.03 a3, a4, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ceq2, ci1, ci2, % 126.36/30.03 coipo1, con1, cotno1, couo1, cp1, cp2, int1, oac1, occu1, ooc1, ooc2, orth1, % 126.36/30.03 ouo1, p1, par1 % 126.36/30.03 % 126.36/30.03 Those formulas are unsatisfiable: % 126.36/30.03 --------------------------------- % 126.36/30.03 % 126.36/30.03 Begin of proof % 126.36/30.03 | % 126.36/30.03 | ALPHA: (ci3) implies: % 126.36/30.04 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 126.36/30.04 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 126.36/30.04 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 126.36/30.04 | & $i(v2))) % 126.36/30.04 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 126.36/30.04 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 126.36/30.04 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 126.36/30.04 | convergent_lines(v0, v1) = v3))) % 126.36/30.04 | % 126.36/30.04 | ALPHA: (ci4) implies: % 126.36/30.04 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 126.36/30.04 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 126.36/30.04 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 126.36/30.04 | & $i(v2))) % 126.36/30.04 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 126.36/30.04 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 126.36/30.04 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 126.36/30.04 | convergent_lines(v0, v1) = v3))) % 126.36/30.04 | % 126.36/30.04 | ALPHA: (cu1) implies: % 126.36/30.04 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 126.36/30.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 126.36/30.04 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 126.36/30.04 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 126.36/30.04 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 126.36/30.04 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 126.36/30.04 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 126.36/30.04 | v1) = v6))) % 126.36/30.04 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 126.36/30.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 126.36/30.04 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 126.36/30.04 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 126.36/30.04 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 126.36/30.04 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 126.36/30.04 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 126.36/30.04 | v1) = v6))) % 126.36/30.04 | % 126.36/30.04 | ALPHA: (ceq1) implies: % 126.76/30.04 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 126.76/30.04 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 126.76/30.04 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 126.76/30.04 | distinct_points(v0, v2) = 0) % 126.76/30.04 | % 126.76/30.04 | ALPHA: (ceq3) implies: % 126.76/30.05 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 126.76/30.05 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 126.76/30.05 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 126.76/30.05 | % 126.76/30.05 | ALPHA: (cup1) implies: % 126.76/30.05 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 126.76/30.05 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 126.76/30.05 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 126.76/30.05 | $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 126.76/30.05 | convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 126.76/30.05 | v2) = v5))) % 126.76/30.05 | % 126.76/30.05 | ALPHA: (function-axioms) implies: % 126.76/30.05 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 126.76/30.05 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 126.76/30.05 | (distinct_points(v3, v2) = v0)) % 126.76/30.05 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 126.76/30.05 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 126.76/30.05 | (distinct_lines(v3, v2) = v0)) % 126.76/30.05 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 126.76/30.05 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 126.76/30.05 | (convergent_lines(v3, v2) = v0)) % 126.76/30.05 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 126.76/30.05 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 126.76/30.05 | (apart_point_and_line(v3, v2) = v0)) % 126.76/30.05 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 126.76/30.05 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 126.76/30.05 | v0)) % 126.76/30.05 | % 126.76/30.05 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 126.76/30.05 | all_38_3, all_38_4, all_38_5, all_38_6, all_38_7, all_38_8, all_38_9 % 126.76/30.05 | gives: % 126.76/30.05 | (15) ~ (all_38_0 = 0) & ~ (all_38_1 = 0) & intersection_point(all_38_7, % 126.76/30.05 | all_38_6) = all_38_2 & intersection_point(all_38_9, all_38_8) = % 126.76/30.05 | all_38_5 & apart_point_and_line(all_38_2, all_38_8) = all_38_0 & % 126.76/30.05 | apart_point_and_line(all_38_2, all_38_9) = all_38_1 & % 126.76/30.05 | convergent_lines(all_38_7, all_38_6) = 0 & convergent_lines(all_38_9, % 126.76/30.05 | all_38_8) = 0 & $i(all_38_2) & $i(all_38_5) & $i(all_38_6) & % 126.76/30.05 | $i(all_38_7) & $i(all_38_8) & $i(all_38_9) & ((all_38_3 = 0 & % 126.76/30.05 | apart_point_and_line(all_38_5, all_38_6) = 0) | (all_38_4 = 0 & % 126.76/30.05 | apart_point_and_line(all_38_5, all_38_7) = 0)) % 126.76/30.05 | % 126.76/30.05 | ALPHA: (15) implies: % 126.76/30.05 | (16) ~ (all_38_1 = 0) % 126.76/30.05 | (17) ~ (all_38_0 = 0) % 126.76/30.05 | (18) $i(all_38_9) % 126.76/30.05 | (19) $i(all_38_8) % 126.76/30.05 | (20) $i(all_38_7) % 126.76/30.05 | (21) $i(all_38_6) % 126.76/30.05 | (22) $i(all_38_2) % 126.76/30.05 | (23) convergent_lines(all_38_9, all_38_8) = 0 % 126.76/30.06 | (24) convergent_lines(all_38_7, all_38_6) = 0 % 126.76/30.06 | (25) apart_point_and_line(all_38_2, all_38_9) = all_38_1 % 126.76/30.06 | (26) apart_point_and_line(all_38_2, all_38_8) = all_38_0 % 126.76/30.06 | (27) intersection_point(all_38_9, all_38_8) = all_38_5 % 126.76/30.06 | (28) intersection_point(all_38_7, all_38_6) = all_38_2 % 126.76/30.06 | (29) (all_38_3 = 0 & apart_point_and_line(all_38_5, all_38_6) = 0) | % 126.76/30.06 | (all_38_4 = 0 & apart_point_and_line(all_38_5, all_38_7) = 0) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (3) with all_38_9, all_38_8, simplifying with (18), % 126.76/30.06 | (19), (23) gives: % 126.76/30.06 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 126.76/30.06 | intersection_point(all_38_9, all_38_8) = v0 & % 126.76/30.06 | apart_point_and_line(v0, all_38_8) = v1 & $i(v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (1) with all_38_9, all_38_8, simplifying with (18), % 126.76/30.06 | (19), (23) gives: % 126.76/30.06 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 126.76/30.06 | intersection_point(all_38_9, all_38_8) = v0 & % 126.76/30.06 | apart_point_and_line(v0, all_38_9) = v1 & $i(v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (3) with all_38_7, all_38_6, simplifying with (20), % 126.76/30.06 | (21), (24) gives: % 126.76/30.06 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 126.76/30.06 | intersection_point(all_38_7, all_38_6) = v0 & % 126.76/30.06 | apart_point_and_line(v0, all_38_6) = v1 & $i(v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (1) with all_38_7, all_38_6, simplifying with (20), % 126.76/30.06 | (21), (24) gives: % 126.76/30.06 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 126.76/30.06 | intersection_point(all_38_7, all_38_6) = v0 & % 126.76/30.06 | apart_point_and_line(v0, all_38_7) = v1 & $i(v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (9) with all_38_2, all_38_8, all_38_9, all_38_0, % 126.76/30.06 | all_38_1, simplifying with (18), (19), (22), (25), (26) gives: % 126.76/30.06 | (34) all_38_0 = 0 | all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 126.76/30.06 | convergent_lines(all_38_8, all_38_9) = 0) | ( ~ (v0 = 0) & % 126.76/30.06 | distinct_lines(all_38_8, all_38_9) = v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (4) with all_38_9, all_38_8, all_38_5, simplifying % 126.76/30.06 | with (18), (19), (27) gives: % 126.76/30.06 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 126.76/30.06 | apart_point_and_line(all_38_5, all_38_8) = v1) | ( ~ (v0 = 0) & % 126.76/30.06 | convergent_lines(all_38_9, all_38_8) = v0)) % 126.76/30.06 | % 126.76/30.06 | GROUND_INST: instantiating (2) with all_38_9, all_38_8, all_38_5, simplifying % 126.76/30.06 | with (18), (19), (27) gives: % 126.76/30.07 | (36) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 126.76/30.07 | apart_point_and_line(all_38_5, all_38_9) = v1) | ( ~ (v0 = 0) & % 126.76/30.07 | convergent_lines(all_38_9, all_38_8) = v0)) % 126.76/30.07 | % 126.76/30.07 | GROUND_INST: instantiating (4) with all_38_7, all_38_6, all_38_2, simplifying % 126.76/30.07 | with (20), (21), (28) gives: % 126.76/30.07 | (37) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 126.76/30.07 | apart_point_and_line(all_38_2, all_38_6) = v1) | ( ~ (v0 = 0) & % 126.76/30.07 | convergent_lines(all_38_7, all_38_6) = v0)) % 126.76/30.07 | % 126.76/30.07 | GROUND_INST: instantiating (2) with all_38_7, all_38_6, all_38_2, simplifying % 126.76/30.07 | with (20), (21), (28) gives: % 126.76/30.07 | (38) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 126.76/30.07 | apart_point_and_line(all_38_2, all_38_7) = v1) | ( ~ (v0 = 0) & % 126.76/30.07 | convergent_lines(all_38_7, all_38_6) = v0)) % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (33) with fresh symbols all_49_0, all_49_1 gives: % 126.76/30.07 | (39) ~ (all_49_0 = 0) & intersection_point(all_38_7, all_38_6) = all_49_1 % 126.76/30.07 | & apart_point_and_line(all_49_1, all_38_7) = all_49_0 & $i(all_49_1) % 126.76/30.07 | % 126.76/30.07 | ALPHA: (39) implies: % 126.76/30.07 | (40) $i(all_49_1) % 126.76/30.07 | (41) apart_point_and_line(all_49_1, all_38_7) = all_49_0 % 126.76/30.07 | (42) intersection_point(all_38_7, all_38_6) = all_49_1 % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (31) with fresh symbols all_51_0, all_51_1 gives: % 126.76/30.07 | (43) ~ (all_51_0 = 0) & intersection_point(all_38_9, all_38_8) = all_51_1 % 126.76/30.07 | & apart_point_and_line(all_51_1, all_38_9) = all_51_0 & $i(all_51_1) % 126.76/30.07 | % 126.76/30.07 | ALPHA: (43) implies: % 126.76/30.07 | (44) $i(all_51_1) % 126.76/30.07 | (45) apart_point_and_line(all_51_1, all_38_9) = all_51_0 % 126.76/30.07 | (46) intersection_point(all_38_9, all_38_8) = all_51_1 % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (30) with fresh symbols all_53_0, all_53_1 gives: % 126.76/30.07 | (47) ~ (all_53_0 = 0) & intersection_point(all_38_9, all_38_8) = all_53_1 % 126.76/30.07 | & apart_point_and_line(all_53_1, all_38_8) = all_53_0 & $i(all_53_1) % 126.76/30.07 | % 126.76/30.07 | ALPHA: (47) implies: % 126.76/30.07 | (48) apart_point_and_line(all_53_1, all_38_8) = all_53_0 % 126.76/30.07 | (49) intersection_point(all_38_9, all_38_8) = all_53_1 % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (32) with fresh symbols all_55_0, all_55_1 gives: % 126.76/30.07 | (50) ~ (all_55_0 = 0) & intersection_point(all_38_7, all_38_6) = all_55_1 % 126.76/30.07 | & apart_point_and_line(all_55_1, all_38_6) = all_55_0 & $i(all_55_1) % 126.76/30.07 | % 126.76/30.07 | ALPHA: (50) implies: % 126.76/30.07 | (51) apart_point_and_line(all_55_1, all_38_6) = all_55_0 % 126.76/30.07 | (52) intersection_point(all_38_7, all_38_6) = all_55_1 % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (38) with fresh symbols all_57_0, all_57_1 gives: % 126.76/30.07 | (53) ( ~ (all_57_0 = 0) & apart_point_and_line(all_38_2, all_38_7) = % 126.76/30.07 | all_57_0) | ( ~ (all_57_1 = 0) & convergent_lines(all_38_7, % 126.76/30.07 | all_38_6) = all_57_1) % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (36) with fresh symbols all_58_0, all_58_1 gives: % 126.76/30.07 | (54) ( ~ (all_58_0 = 0) & apart_point_and_line(all_38_5, all_38_9) = % 126.76/30.07 | all_58_0) | ( ~ (all_58_1 = 0) & convergent_lines(all_38_9, % 126.76/30.07 | all_38_8) = all_58_1) % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (35) with fresh symbols all_59_0, all_59_1 gives: % 126.76/30.07 | (55) ( ~ (all_59_0 = 0) & apart_point_and_line(all_38_5, all_38_8) = % 126.76/30.07 | all_59_0) | ( ~ (all_59_1 = 0) & convergent_lines(all_38_9, % 126.76/30.07 | all_38_8) = all_59_1) % 126.76/30.07 | % 126.76/30.07 | DELTA: instantiating (37) with fresh symbols all_60_0, all_60_1 gives: % 126.76/30.07 | (56) ( ~ (all_60_0 = 0) & apart_point_and_line(all_38_2, all_38_6) = % 126.76/30.07 | all_60_0) | ( ~ (all_60_1 = 0) & convergent_lines(all_38_7, % 126.76/30.07 | all_38_6) = all_60_1) % 126.76/30.07 | % 126.76/30.07 | BETA: splitting (54) gives: % 126.76/30.07 | % 126.76/30.07 | Case 1: % 126.76/30.07 | | % 126.76/30.07 | | (57) ~ (all_58_0 = 0) & apart_point_and_line(all_38_5, all_38_9) = % 126.76/30.07 | | all_58_0 % 126.76/30.07 | | % 126.76/30.07 | | ALPHA: (57) implies: % 126.76/30.07 | | (58) ~ (all_58_0 = 0) % 126.76/30.07 | | (59) apart_point_and_line(all_38_5, all_38_9) = all_58_0 % 126.76/30.07 | | % 126.76/30.07 | | BETA: splitting (34) gives: % 126.76/30.07 | | % 126.76/30.07 | | Case 1: % 126.76/30.07 | | | % 126.76/30.07 | | | (60) all_38_0 = 0 % 126.76/30.07 | | | % 126.76/30.07 | | | REDUCE: (17), (60) imply: % 126.76/30.07 | | | (61) $false % 126.76/30.08 | | | % 126.76/30.08 | | | CLOSE: (61) is inconsistent. % 126.76/30.08 | | | % 126.76/30.08 | | Case 2: % 126.76/30.08 | | | % 126.76/30.08 | | | (62) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 126.76/30.08 | | | convergent_lines(all_38_8, all_38_9) = 0) | ( ~ (v0 = 0) & % 126.76/30.08 | | | distinct_lines(all_38_8, all_38_9) = v0)) % 126.76/30.08 | | | % 126.76/30.08 | | | BETA: splitting (53) gives: % 126.76/30.08 | | | % 126.76/30.08 | | | Case 1: % 126.76/30.08 | | | | % 126.76/30.08 | | | | (63) ~ (all_57_0 = 0) & apart_point_and_line(all_38_2, all_38_7) = % 126.76/30.08 | | | | all_57_0 % 126.76/30.08 | | | | % 126.76/30.08 | | | | ALPHA: (63) implies: % 126.76/30.08 | | | | (64) ~ (all_57_0 = 0) % 126.76/30.08 | | | | (65) apart_point_and_line(all_38_2, all_38_7) = all_57_0 % 126.76/30.08 | | | | % 126.76/30.08 | | | | BETA: splitting (55) gives: % 126.76/30.08 | | | | % 126.76/30.08 | | | | Case 1: % 126.76/30.08 | | | | | % 126.76/30.08 | | | | | (66) ~ (all_59_0 = 0) & apart_point_and_line(all_38_5, all_38_8) = % 126.76/30.08 | | | | | all_59_0 % 126.76/30.08 | | | | | % 126.76/30.08 | | | | | ALPHA: (66) implies: % 126.76/30.08 | | | | | (67) ~ (all_59_0 = 0) % 126.76/30.08 | | | | | (68) apart_point_and_line(all_38_5, all_38_8) = all_59_0 % 126.76/30.08 | | | | | % 126.76/30.08 | | | | | BETA: splitting (56) gives: % 126.76/30.08 | | | | | % 126.76/30.08 | | | | | Case 1: % 126.76/30.08 | | | | | | % 126.76/30.08 | | | | | | (69) ~ (all_60_0 = 0) & apart_point_and_line(all_38_2, all_38_6) % 126.76/30.08 | | | | | | = all_60_0 % 126.76/30.08 | | | | | | % 126.76/30.08 | | | | | | ALPHA: (69) implies: % 126.76/30.08 | | | | | | (70) ~ (all_60_0 = 0) % 126.76/30.08 | | | | | | (71) apart_point_and_line(all_38_2, all_38_6) = all_60_0 % 126.76/30.08 | | | | | | % 126.76/30.08 | | | | | | BETA: splitting (62) gives: % 126.76/30.08 | | | | | | % 126.76/30.08 | | | | | | Case 1: % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | (72) all_38_1 = 0 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (16), (72) imply: % 126.76/30.08 | | | | | | | (73) $false % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | CLOSE: (73) is inconsistent. % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | Case 2: % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | (74) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 126.76/30.08 | | | | | | | convergent_lines(all_38_8, all_38_9) = 0) | ( ~ (v0 = % 126.76/30.08 | | | | | | | 0) & distinct_lines(all_38_8, all_38_9) = v0)) % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | DELTA: instantiating (74) with fresh symbols all_135_0, all_135_1 % 126.76/30.08 | | | | | | | gives: % 126.76/30.08 | | | | | | | (75) (all_135_0 = 0 & convergent_lines(all_38_8, all_38_9) = 0) % 126.76/30.08 | | | | | | | | ( ~ (all_135_1 = 0) & distinct_lines(all_38_8, all_38_9) % 126.76/30.08 | | | | | | | = all_135_1) % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | GROUND_INST: instantiating (14) with all_38_5, all_53_1, all_38_8, % 126.76/30.08 | | | | | | | all_38_9, simplifying with (27), (49) gives: % 126.76/30.08 | | | | | | | (76) all_53_1 = all_38_5 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | GROUND_INST: instantiating (14) with all_51_1, all_53_1, all_38_8, % 126.76/30.08 | | | | | | | all_38_9, simplifying with (46), (49) gives: % 126.76/30.08 | | | | | | | (77) all_53_1 = all_51_1 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | GROUND_INST: instantiating (14) with all_38_2, all_55_1, all_38_6, % 126.76/30.08 | | | | | | | all_38_7, simplifying with (28), (52) gives: % 126.76/30.08 | | | | | | | (78) all_55_1 = all_38_2 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | GROUND_INST: instantiating (14) with all_49_1, all_55_1, all_38_6, % 126.76/30.08 | | | | | | | all_38_7, simplifying with (42), (52) gives: % 126.76/30.08 | | | | | | | (79) all_55_1 = all_49_1 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | COMBINE_EQS: (78), (79) imply: % 126.76/30.08 | | | | | | | (80) all_49_1 = all_38_2 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | COMBINE_EQS: (76), (77) imply: % 126.76/30.08 | | | | | | | (81) all_51_1 = all_38_5 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | SIMP: (81) implies: % 126.76/30.08 | | | | | | | (82) all_51_1 = all_38_5 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (51), (78) imply: % 126.76/30.08 | | | | | | | (83) apart_point_and_line(all_38_2, all_38_6) = all_55_0 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (48), (76) imply: % 126.76/30.08 | | | | | | | (84) apart_point_and_line(all_38_5, all_38_8) = all_53_0 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (45), (82) imply: % 126.76/30.08 | | | | | | | (85) apart_point_and_line(all_38_5, all_38_9) = all_51_0 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (41), (80) imply: % 126.76/30.08 | | | | | | | (86) apart_point_and_line(all_38_2, all_38_7) = all_49_0 % 126.76/30.08 | | | | | | | % 126.76/30.08 | | | | | | | REDUCE: (44), (82) imply: % 126.76/30.08 | | | | | | | (87) $i(all_38_5) % 126.76/30.08 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (13) with all_58_0, all_51_0, all_38_9, % 126.96/30.09 | | | | | | | all_38_5, simplifying with (59), (85) gives: % 126.96/30.09 | | | | | | | (88) all_58_0 = all_51_0 % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (13) with all_59_0, all_53_0, all_38_8, % 126.96/30.09 | | | | | | | all_38_5, simplifying with (68), (84) gives: % 126.96/30.09 | | | | | | | (89) all_59_0 = all_53_0 % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (13) with all_57_0, all_49_0, all_38_7, % 126.96/30.09 | | | | | | | all_38_2, simplifying with (65), (86) gives: % 126.96/30.09 | | | | | | | (90) all_57_0 = all_49_0 % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (13) with all_60_0, all_55_0, all_38_6, % 126.96/30.09 | | | | | | | all_38_2, simplifying with (71), (83) gives: % 126.96/30.09 | | | | | | | (91) all_60_0 = all_55_0 % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | REDUCE: (70), (91) imply: % 126.96/30.09 | | | | | | | (92) ~ (all_55_0 = 0) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | REDUCE: (67), (89) imply: % 126.96/30.09 | | | | | | | (93) ~ (all_53_0 = 0) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | REDUCE: (58), (88) imply: % 126.96/30.09 | | | | | | | (94) ~ (all_51_0 = 0) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | REDUCE: (64), (90) imply: % 126.96/30.09 | | | | | | | (95) ~ (all_49_0 = 0) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_2, all_38_9, % 126.96/30.09 | | | | | | | all_38_8, all_51_0, all_38_0, simplifying with (18), % 126.96/30.09 | | | | | | | (19), (22), (26), (85), (87) gives: % 126.96/30.09 | | | | | | | (96) all_51_0 = 0 | all_38_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.09 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.09 | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = % 126.96/30.09 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( % 126.96/30.09 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_9, all_38_8) = v1) % 126.96/30.09 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.09 | | | | | | | v0)) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_2, all_38_8, % 126.96/30.09 | | | | | | | all_38_9, all_51_0, all_38_0, simplifying with (18), % 126.96/30.09 | | | | | | | (19), (22), (26), (85), (87) gives: % 126.96/30.09 | | | | | | | (97) all_51_0 = 0 | all_38_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.09 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.09 | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = % 126.96/30.09 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( % 126.96/30.09 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_8, all_38_9) = v1) % 126.96/30.09 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.09 | | | | | | | v0)) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_2, all_38_8, % 126.96/30.09 | | | | | | | all_38_9, all_53_0, all_38_1, simplifying with (18), % 126.96/30.09 | | | | | | | (19), (22), (25), (84), (87) gives: % 126.96/30.09 | | | | | | | (98) all_53_0 = 0 | all_38_1 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.09 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.09 | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = % 126.96/30.09 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( % 126.96/30.09 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_8, all_38_9) = v1) % 126.96/30.09 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.09 | | | | | | | v0)) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_2, all_38_9, % 126.96/30.09 | | | | | | | all_38_8, all_53_0, all_38_1, simplifying with (18), % 126.96/30.09 | | | | | | | (19), (22), (25), (84), (87) gives: % 126.96/30.09 | | | | | | | (99) all_53_0 = 0 | all_38_1 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.09 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.09 | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = % 126.96/30.09 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( % 126.96/30.09 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_9, all_38_8) = v1) % 126.96/30.09 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.09 | | | | | | | v0)) % 126.96/30.09 | | | | | | | % 126.96/30.09 | | | | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_5, all_38_8, % 126.96/30.10 | | | | | | | all_38_9, all_53_0, all_51_0, simplifying with (18), % 126.96/30.10 | | | | | | | (19), (84), (85), (87) gives: % 126.96/30.10 | | | | | | | (100) all_53_0 = 0 | all_51_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.10 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | (v2 = % 126.96/30.10 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( % 126.96/30.10 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_8, all_38_9) = v1) % 126.96/30.10 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_5) = % 126.96/30.10 | | | | | | | v0)) % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_5, all_38_8, % 126.96/30.10 | | | | | | | all_38_9, all_51_0, all_53_0, simplifying with (18), % 126.96/30.10 | | | | | | | (19), (84), (85), (87) gives: % 126.96/30.10 | | | | | | | (101) all_53_0 = 0 | all_51_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.10 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) | (v2 = % 126.96/30.10 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( % 126.96/30.10 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_8, all_38_9) = v1) % 126.96/30.10 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_5) = % 126.96/30.10 | | | | | | | v0)) % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_2, all_38_7, % 126.96/30.10 | | | | | | | all_38_9, all_51_0, all_49_0, simplifying with (18), % 126.96/30.10 | | | | | | | (20), (22), (85), (86), (87) gives: % 126.96/30.10 | | | | | | | (102) all_51_0 = 0 | all_49_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.10 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = % 126.96/30.10 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_7) = 0) | ( % 126.96/30.10 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_7, all_38_9) = v1) % 126.96/30.10 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.10 | | | | | | | v0)) % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_2, all_38_8, % 126.96/30.10 | | | | | | | all_38_6, all_53_0, all_55_0, simplifying with (19), % 126.96/30.10 | | | | | | | (21), (22), (83), (84), (87) gives: % 126.96/30.10 | | | | | | | (103) all_55_0 = 0 | all_53_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.10 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = % 126.96/30.10 | | | | | | | 0 & apart_point_and_line(all_38_5, all_38_6) = 0) | ( % 126.96/30.10 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_8, all_38_6) = v1) % 126.96/30.10 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = % 126.96/30.10 | | | | | | | v0)) % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | GROUND_INST: instantiating (6) with all_38_2, all_38_5, all_38_6, % 126.96/30.10 | | | | | | | all_38_9, all_55_0, all_51_0, simplifying with (18), % 126.96/30.10 | | | | | | | (21), (22), (83), (85), (87) gives: % 126.96/30.10 | | | | | | | (104) all_55_0 = 0 | all_51_0 = 0 | ? [v0: int] : ? [v1: int] % 126.96/30.10 | | | | | | | : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | apart_point_and_line(all_38_5, all_38_6) = 0) | (v2 = % 126.96/30.10 | | | | | | | 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | ( % 126.96/30.10 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_6, all_38_9) = v1) % 126.96/30.10 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_2, all_38_5) = % 126.96/30.10 | | | | | | | v0)) % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | BETA: splitting (29) gives: % 126.96/30.10 | | | | | | | % 126.96/30.10 | | | | | | | Case 1: % 126.96/30.10 | | | | | | | | % 126.96/30.10 | | | | | | | | (105) all_38_3 = 0 & apart_point_and_line(all_38_5, all_38_6) % 126.96/30.10 | | | | | | | | = 0 % 126.96/30.10 | | | | | | | | % 126.96/30.10 | | | | | | | | ALPHA: (105) implies: % 126.96/30.10 | | | | | | | | (106) apart_point_and_line(all_38_5, all_38_6) = 0 % 126.96/30.10 | | | | | | | | % 126.96/30.10 | | | | | | | | BETA: splitting (101) gives: % 126.96/30.10 | | | | | | | | % 126.96/30.10 | | | | | | | | Case 1: % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | (107) all_53_0 = 0 % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | REDUCE: (93), (107) imply: % 126.96/30.10 | | | | | | | | | (108) $false % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | CLOSE: (108) is inconsistent. % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | Case 2: % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | (109) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 126.96/30.10 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) | % 126.96/30.10 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, all_38_8) % 126.96/30.10 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_38_8, % 126.96/30.10 | | | | | | | | | all_38_9) = v1) | ( ~ (v0 = 0) & % 126.96/30.10 | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0)) % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | BETA: splitting (100) gives: % 126.96/30.10 | | | | | | | | | % 126.96/30.10 | | | | | | | | | Case 1: % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | (110) all_53_0 = 0 % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | REDUCE: (93), (110) imply: % 126.96/30.10 | | | | | | | | | | (111) $false % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | CLOSE: (111) is inconsistent. % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | Case 2: % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | (112) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.10 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.10 | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | % 126.96/30.10 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.10 | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.10 | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.10 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_5) % 126.96/30.10 | | | | | | | | | | = v0)) % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | BETA: splitting (98) gives: % 126.96/30.10 | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | Case 1: % 126.96/30.10 | | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | | (113) all_53_0 = 0 % 126.96/30.10 | | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | | REDUCE: (93), (113) imply: % 126.96/30.10 | | | | | | | | | | | (114) $false % 126.96/30.10 | | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | | CLOSE: (114) is inconsistent. % 126.96/30.10 | | | | | | | | | | | % 126.96/30.10 | | | | | | | | | | Case 2: % 126.96/30.10 | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | (115) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.11 | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.11 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.11 | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | BETA: splitting (99) gives: % 126.96/30.11 | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | (116) all_53_0 = 0 % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | REDUCE: (93), (116) imply: % 126.96/30.11 | | | | | | | | | | | | (117) $false % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | (118) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.11 | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.11 | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.11 | | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | BETA: splitting (97) gives: % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | (119) all_51_0 = 0 % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | REDUCE: (94), (119) imply: % 126.96/30.11 | | | | | | | | | | | | | (120) $false % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | CLOSE: (120) is inconsistent. % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | (121) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.11 | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.11 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.11 | | | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | BETA: splitting (96) gives: % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | (122) all_51_0 = 0 % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | REDUCE: (94), (122) imply: % 126.96/30.11 | | | | | | | | | | | | | | (123) $false % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | (124) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.11 | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.11 | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.11 | | | | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | BETA: splitting (102) gives: % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | (125) all_51_0 = 0 % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | REDUCE: (94), (125) imply: % 126.96/30.11 | | | | | | | | | | | | | | | (126) $false % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | (127) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.11 | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.11 | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | | | | all_38_7) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | | | | | distinct_lines(all_38_7, all_38_9) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.11 | | | | | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | (128) all_51_0 = 0 % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | REDUCE: (94), (128) imply: % 126.96/30.11 | | | | | | | | | | | | | | | | (129) $false % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | (130) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.11 | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 126.96/30.11 | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.11 | | | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.11 | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_5) % 126.96/30.11 | | | | | | | | | | | | | | | | = v0)) % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_491_0, % 126.96/30.11 | | | | | | | | | | | | | | | | all_491_1, all_491_2, all_491_3 gives: % 126.96/30.11 | | | | | | | | | | | | | | | | (131) (all_491_0 = 0 & apart_point_and_line(all_38_5, % 126.96/30.11 | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_491_1 = 0 & % 126.96/30.11 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | % 126.96/30.11 | | | | | | | | | | | | | | | | ( ~ (all_491_2 = 0) & distinct_lines(all_38_8, % 126.96/30.11 | | | | | | | | | | | | | | | | all_38_9) = all_491_2) | ( ~ (all_491_3 = 0) & % 126.96/30.11 | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_491_3) % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (13), (16), (17), (18), % 126.96/30.11 | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (75), (83), % 126.96/30.11 | | | | | | | | | | | | | | | | (84), (85), (87), (92), (93), (94), (95), (106), % 126.96/30.11 | | | | | | | | | | | | | | | | (112), (115), (118), (121), (124), (127), (131), % 126.96/30.11 | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #3. % 126.96/30.11 | | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | | % 126.96/30.11 | | | | | | | | | End of split % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | End of split % 126.96/30.11 | | | | | | | | % 126.96/30.11 | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | % 126.96/30.11 | | | | | | | | (132) all_38_4 = 0 & apart_point_and_line(all_38_5, all_38_7) % 126.96/30.11 | | | | | | | | = 0 % 126.96/30.11 | | | | | | | | % 126.96/30.11 | | | | | | | | ALPHA: (132) implies: % 126.96/30.11 | | | | | | | | (133) apart_point_and_line(all_38_5, all_38_7) = 0 % 126.96/30.11 | | | | | | | | % 126.96/30.11 | | | | | | | | BETA: splitting (101) gives: % 126.96/30.11 | | | | | | | | % 126.96/30.11 | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | (134) all_53_0 = 0 % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | REDUCE: (93), (134) imply: % 126.96/30.11 | | | | | | | | | (135) $false % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | CLOSE: (135) is inconsistent. % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | Case 2: % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | (136) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 126.96/30.11 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.11 | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) | % 126.96/30.11 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, all_38_8) % 126.96/30.11 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_38_8, % 126.96/30.11 | | | | | | | | | all_38_9) = v1) | ( ~ (v0 = 0) & % 126.96/30.11 | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0)) % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | BETA: splitting (100) gives: % 126.96/30.11 | | | | | | | | | % 126.96/30.11 | | | | | | | | | Case 1: % 126.96/30.11 | | | | | | | | | | % 126.96/30.11 | | | | | | | | | | (137) all_53_0 = 0 % 126.96/30.11 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | REDUCE: (93), (137) imply: % 126.96/30.12 | | | | | | | | | | (138) $false % 126.96/30.12 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | CLOSE: (138) is inconsistent. % 126.96/30.12 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | (139) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | % 126.96/30.12 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_5) % 126.96/30.12 | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | BETA: splitting (103) gives: % 126.96/30.12 | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | (140) all_55_0 = 0 % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | REDUCE: (92), (140) imply: % 126.96/30.12 | | | | | | | | | | | (141) $false % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | CLOSE: (141) is inconsistent. % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | (142) all_53_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.12 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | all_38_6) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | distinct_lines(all_38_8, all_38_6) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | BETA: splitting (98) gives: % 126.96/30.12 | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | (143) all_53_0 = 0 % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | REDUCE: (93), (143) imply: % 126.96/30.12 | | | | | | | | | | | | (144) $false % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | (145) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.12 | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | BETA: splitting (99) gives: % 126.96/30.12 | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | (146) all_53_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | REDUCE: (93), (146) imply: % 126.96/30.12 | | | | | | | | | | | | | (147) $false % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | (148) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.12 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | BETA: splitting (97) gives: % 126.96/30.12 | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | (149) all_51_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | REDUCE: (94), (149) imply: % 126.96/30.12 | | | | | | | | | | | | | | (150) $false % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | (151) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.12 | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | BETA: splitting (96) gives: % 126.96/30.12 | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | (152) all_51_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | REDUCE: (94), (152) imply: % 126.96/30.12 | | | | | | | | | | | | | | | (153) $false % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | (154) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.12 | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 126.96/30.12 | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | (155) all_51_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | REDUCE: (94), (155) imply: % 126.96/30.12 | | | | | | | | | | | | | | | | (156) $false % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | (157) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.12 | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | | | | | all_38_7) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | | | | distinct_lines(all_38_7, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.12 | | | | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 126.96/30.12 | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | (158) all_55_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | REDUCE: (92), (158) imply: % 126.96/30.12 | | | | | | | | | | | | | | | | | (159) $false % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | (160) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 126.96/30.12 | | | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_6) = 0) % 126.96/30.12 | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_2, % 126.96/30.12 | | | | | | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | | | | | distinct_lines(all_38_6, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_2, all_38_5) % 126.96/30.12 | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 126.96/30.12 | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | (161) all_51_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | REDUCE: (94), (161) imply: % 126.96/30.12 | | | | | | | | | | | | | | | | | | (162) $false % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | (163) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.12 | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.12 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 126.96/30.12 | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.12 | | | | | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.12 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.12 | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_5) % 126.96/30.12 | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 126.96/30.12 | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.12 | | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | | (164) all_53_0 = 0 % 126.96/30.12 | | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | | REDUCE: (93), (164) imply: % 126.96/30.12 | | | | | | | | | | | | | | | | | | | (165) $false % 126.96/30.12 | | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 126.96/30.12 | | | | | | | | | | | | | | | | | | | % 126.96/30.12 | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.12 | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | (166) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.13 | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | all_38_6) = 0) | ( ~ (v1 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_6) = v1) | ( ~ % 126.96/30.13 | | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (166) with fresh symbols all_531_0, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | all_531_1, all_531_2, all_531_3 gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | (167) (all_531_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_531_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_6) = 0) | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | ( ~ (all_531_2 = 0) & distinct_lines(all_38_8, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | all_38_6) = all_531_2) | ( ~ (all_531_3 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_531_3) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (168) all_38_1 = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (168) imply: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (169) $false % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (170) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (170) with fresh symbols all_584_0, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | all_584_1, all_584_2, all_584_3 gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | (171) (all_584_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_584_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | ( ~ (all_584_2 = 0) & distinct_lines(all_38_8, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | all_38_9) = all_584_2) | ( ~ (all_584_3 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_584_3) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (172) all_38_1 = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (172) imply: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (173) $false % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (174) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_8) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | ( ~ (v1 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_592_0, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | all_592_1, all_592_2, all_592_3 gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | (175) (all_592_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_592_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_592_2 = 0) & distinct_lines(all_38_9, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_592_2) | ( ~ (all_592_3 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_592_3) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (176) all_38_0 = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (176) imply: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (177) $false % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (178) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (178) with fresh symbols all_604_0, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | all_604_1, all_604_2, all_604_3 gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | (179) (all_604_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_604_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_604_2) | ( ~ (all_604_3 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_604_3) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (180) all_38_0 = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (180) imply: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (181) $false % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (182) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_9) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | ( ~ (v1 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_9, all_38_8) = v1) | ( ~ % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | = v0)) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbols all_608_0, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | all_608_1, all_608_2, all_608_3 gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | (183) (all_608_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_608_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_608_2 = 0) & distinct_lines(all_38_9, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_608_2) | ( ~ (all_608_3 = 0) & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_608_3) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | (184) all_51_0 = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (184) imply: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | (185) $false % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_7, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_49_0, simplifying with (20), (22), % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (133) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | (186) all_49_0 = 0 | distinct_points(all_38_5, all_38_2) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | (187) distinct_points(all_38_5, all_38_2) = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (188) (all_584_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_584_1 = 0 & % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_584_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) apart_point_and_line(all_38_2, all_38_8) = 0 % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (26), (190) are inconsistent by % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_584_1 = 0 & apart_point_and_line(all_38_5, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) apart_point_and_line(all_38_5, all_38_9) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (85), (94), (192) are inconsistent by % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (193) ( ~ (all_584_2 = 0) & distinct_lines(all_38_8, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_584_2) | ( ~ (all_584_3 = 0) & % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_584_3) % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_584_2 = 0) & distinct_lines(all_38_8, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_584_2 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) distinct_lines(all_38_8, all_38_9) = all_584_2 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) (all_604_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_604_1 = 0 & % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_604_0 = 0 & apart_point_and_line(all_38_2, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) apart_point_and_line(all_38_2, all_38_9) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (198) are inconsistent by % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_604_1 = 0 & apart_point_and_line(all_38_5, % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) apart_point_and_line(all_38_5, all_38_8) = 0 % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (84), (93), (200) are inconsistent by % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 126.96/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) ( ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_604_2) | ( ~ (all_604_3 = 0) & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_604_3) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_604_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) ~ (all_604_2 = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) distinct_lines(all_38_8, all_38_9) = all_604_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) (all_608_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_608_1 = 0 & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_608_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) apart_point_and_line(all_38_2, all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (207) are inconsistent by % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_608_1 = 0 & apart_point_and_line(all_38_5, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (84), (93), (209) are inconsistent by % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) ( ~ (all_608_2 = 0) & distinct_lines(all_38_9, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_608_2) | ( ~ (all_608_3 = 0) & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_608_3) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) ~ (all_608_2 = 0) & distinct_lines(all_38_9, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_608_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) ~ (all_608_2 = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) distinct_lines(all_38_9, all_38_8) = all_608_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_592_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_592_1 = 0 & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_592_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) apart_point_and_line(all_38_2, all_38_8) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (26), (216) are inconsistent by % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_592_1 = 0 & apart_point_and_line(all_38_5, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (85), (94), (218) are inconsistent by % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) ( ~ (all_592_2 = 0) & distinct_lines(all_38_9, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_592_2) | ( ~ (all_592_3 = 0) & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_592_3) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_592_2 = 0) & distinct_lines(all_38_9, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = all_592_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) distinct_lines(all_38_9, all_38_8) = all_592_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_592_2, all_608_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8, all_38_9, simplifying with (213), (221) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_608_2 = all_592_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_584_2, all_604_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (195), (204) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_604_2 = all_584_2 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (222) imply: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) ~ (all_592_2 = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (223) imply: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) ~ (all_584_2 = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_135_0 = 0 & convergent_lines(all_38_8, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) convergent_lines(all_38_8, all_38_9) = 0 % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_531_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_531_1 = 0 & % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_6) = 0) % 127.21/30.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (13), (16), (17), (18), % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (75), (83), % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (85), (87), (92), (93), (94), (95), (139), % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (148), (151), (154), (157), (163), (228), % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #2. % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) ( ~ (all_531_2 = 0) & distinct_lines(all_38_8, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_6) = all_531_2) | ( ~ (all_531_3 = 0) & % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_531_3) % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_8, all_38_9, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8, all_592_2, simplifying with (18), (19), % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221), (227) gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_592_2 = 0 | convergent_lines(all_38_8, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) convergent_lines(all_38_8, all_38_8) = 0 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_8, simplifying % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (19), (231) gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) $false % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_592_2 = 0 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (233) imply: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) $false % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_531_3 = 0) & distinct_points(all_38_5, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_531_3 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (187), (235) are inconsistent by sub-proof % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1. % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_135_1 = 0) & distinct_lines(all_38_8, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_135_1 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) distinct_lines(all_38_8, all_38_9) = all_135_1 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_584_2, all_135_1, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (195), (237) % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_584_2 = all_135_1 % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (225), (238) imply: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (all_135_1 = 0) % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_531_0 = 0 & apart_point_and_line(all_38_2, % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_531_1 = 0 & % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_6) = 0) % 127.21/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (13), (16), (17), (18), % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (75), (83), % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (85), (87), (92), (93), (94), (95), (139), % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (148), (151), (154), (157), (163), (240), % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #2. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) ( ~ (all_531_2 = 0) & distinct_lines(all_38_8, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_6) = all_531_2) | ( ~ (all_531_3 = 0) & % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_531_3) % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_9, all_38_8, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9, all_135_1, simplifying with (18), (19), % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (237) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_135_1 = 0 | convergent_lines(all_38_9, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (239), (242), (apart3) are inconsistent by % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) ~ (all_531_3 = 0) & distinct_points(all_38_5, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_531_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (187), (243) are inconsistent by sub-proof % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_592_3 = 0) & distinct_points(all_38_5, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_592_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_592_3 = 0) % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) distinct_points(all_38_5, all_38_2) = all_592_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_592_3, all_38_2, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (187), (246) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_592_3 = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (247) imply: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_608_3 = 0) & distinct_points(all_38_5, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_608_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_608_3 = 0) % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) distinct_points(all_38_5, all_38_2) = all_608_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_608_3, all_38_2, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (187), (251) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_608_3 = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_604_3 = 0) & distinct_points(all_38_5, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_604_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) ~ (all_604_3 = 0) % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) distinct_points(all_38_5, all_38_2) = all_604_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_604_3, all_38_2, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (187), (256) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_604_3 = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (257) imply: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) $false % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) ~ (all_584_3 = 0) & distinct_points(all_38_5, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_584_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) ~ (all_584_3 = 0) % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) distinct_points(all_38_5, all_38_2) = all_584_3 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_584_3, all_38_2, % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (187), (261) gives: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_584_3 = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (260), (262) imply: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) $false % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_49_0 = 0 % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (264) imply: % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (265) $false % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | | End of split % 127.27/30.15 | | | | | | | | | | | % 127.27/30.15 | | | | | | | | | | End of split % 127.27/30.16 | | | | | | | | | | % 127.27/30.16 | | | | | | | | | End of split % 127.27/30.16 | | | | | | | | | % 127.27/30.16 | | | | | | | | End of split % 127.27/30.16 | | | | | | | | % 127.27/30.16 | | | | | | | End of split % 127.27/30.16 | | | | | | | % 127.27/30.16 | | | | | | End of split % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | Case 2: % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | | (266) ~ (all_60_1 = 0) & convergent_lines(all_38_7, all_38_6) = % 127.27/30.16 | | | | | | all_60_1 % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | | ALPHA: (266) implies: % 127.27/30.16 | | | | | | (267) ~ (all_60_1 = 0) % 127.27/30.16 | | | | | | (268) convergent_lines(all_38_7, all_38_6) = all_60_1 % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | | GROUND_INST: instantiating (12) with 0, all_60_1, all_38_6, % 127.27/30.16 | | | | | | all_38_7, simplifying with (24), (268) gives: % 127.27/30.16 | | | | | | (269) all_60_1 = 0 % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | | REDUCE: (267), (269) imply: % 127.27/30.16 | | | | | | (270) $false % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | | CLOSE: (270) is inconsistent. % 127.27/30.16 | | | | | | % 127.27/30.16 | | | | | End of split % 127.27/30.16 | | | | | % 127.27/30.16 | | | | Case 2: % 127.27/30.16 | | | | | % 127.27/30.16 | | | | | (271) ~ (all_59_1 = 0) & convergent_lines(all_38_9, all_38_8) = % 127.27/30.16 | | | | | all_59_1 % 127.27/30.16 | | | | | % 127.27/30.16 | | | | | ALPHA: (271) implies: % 127.27/30.16 | | | | | (272) ~ (all_59_1 = 0) % 127.27/30.16 | | | | | (273) convergent_lines(all_38_9, all_38_8) = all_59_1 % 127.27/30.16 | | | | | % 127.27/30.16 | | | | | GROUND_INST: instantiating (12) with 0, all_59_1, all_38_8, all_38_9, % 127.27/30.16 | | | | | simplifying with (23), (273) gives: % 127.27/30.16 | | | | | (274) all_59_1 = 0 % 127.27/30.16 | | | | | % 127.27/30.16 | | | | | REDUCE: (272), (274) imply: % 127.27/30.16 | | | | | (275) $false % 127.27/30.16 | | | | | % 127.27/30.16 | | | | | CLOSE: (275) is inconsistent. % 127.27/30.16 | | | | | % 127.27/30.16 | | | | End of split % 127.27/30.16 | | | | % 127.27/30.16 | | | Case 2: % 127.27/30.16 | | | | % 127.27/30.16 | | | | (276) ~ (all_57_1 = 0) & convergent_lines(all_38_7, all_38_6) = % 127.27/30.16 | | | | all_57_1 % 127.27/30.16 | | | | % 127.27/30.16 | | | | ALPHA: (276) implies: % 127.27/30.16 | | | | (277) ~ (all_57_1 = 0) % 127.27/30.16 | | | | (278) convergent_lines(all_38_7, all_38_6) = all_57_1 % 127.27/30.16 | | | | % 127.27/30.16 | | | | GROUND_INST: instantiating (12) with 0, all_57_1, all_38_6, all_38_7, % 127.27/30.16 | | | | simplifying with (24), (278) gives: % 127.27/30.16 | | | | (279) all_57_1 = 0 % 127.27/30.16 | | | | % 127.27/30.16 | | | | REDUCE: (277), (279) imply: % 127.27/30.16 | | | | (280) $false % 127.27/30.16 | | | | % 127.27/30.16 | | | | CLOSE: (280) is inconsistent. % 127.27/30.16 | | | | % 127.27/30.16 | | | End of split % 127.27/30.16 | | | % 127.27/30.16 | | End of split % 127.27/30.16 | | % 127.27/30.16 | Case 2: % 127.27/30.16 | | % 127.27/30.16 | | (281) ~ (all_58_1 = 0) & convergent_lines(all_38_9, all_38_8) = all_58_1 % 127.27/30.16 | | % 127.27/30.16 | | ALPHA: (281) implies: % 127.27/30.16 | | (282) ~ (all_58_1 = 0) % 127.27/30.16 | | (283) convergent_lines(all_38_9, all_38_8) = all_58_1 % 127.27/30.16 | | % 127.27/30.16 | | GROUND_INST: instantiating (12) with 0, all_58_1, all_38_8, all_38_9, % 127.27/30.16 | | simplifying with (23), (283) gives: % 127.27/30.16 | | (284) all_58_1 = 0 % 127.27/30.16 | | % 127.27/30.16 | | REDUCE: (282), (284) imply: % 127.27/30.16 | | (285) $false % 127.27/30.16 | | % 127.27/30.16 | | CLOSE: (285) is inconsistent. % 127.27/30.16 | | % 127.27/30.16 | End of split % 127.27/30.16 | % 127.27/30.16 End of proof % 127.27/30.16 % 127.27/30.16 Sub-proof #1 shows that the following formulas are inconsistent: % 127.27/30.16 ---------------------------------------------------------------- % 127.27/30.16 (1) ~ (all_531_3 = 0) & distinct_points(all_38_5, all_38_2) = all_531_3 % 127.27/30.16 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.16 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 127.27/30.16 (distinct_points(v3, v2) = v0)) % 127.27/30.16 (3) distinct_points(all_38_5, all_38_2) = 0 % 127.27/30.16 % 127.27/30.16 Begin of proof % 127.27/30.16 | % 127.27/30.16 | ALPHA: (1) implies: % 127.27/30.16 | (4) ~ (all_531_3 = 0) % 127.27/30.16 | (5) distinct_points(all_38_5, all_38_2) = all_531_3 % 127.27/30.16 | % 127.27/30.16 | GROUND_INST: instantiating (2) with 0, all_531_3, all_38_2, all_38_5, % 127.27/30.16 | simplifying with (3), (5) gives: % 127.27/30.16 | (6) all_531_3 = 0 % 127.27/30.16 | % 127.27/30.16 | REDUCE: (4), (6) imply: % 127.27/30.16 | (7) $false % 127.27/30.16 | % 127.27/30.16 | CLOSE: (7) is inconsistent. % 127.27/30.16 | % 127.27/30.16 End of proof % 127.27/30.16 % 127.27/30.16 Sub-proof #2 shows that the following formulas are inconsistent: % 127.27/30.16 ---------------------------------------------------------------- % 127.27/30.16 (1) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.16 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.16 apart_point_and_line(all_38_5, all_38_7) = 0) | ( ~ (v1 = 0) & % 127.27/30.16 distinct_lines(all_38_7, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.16 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.16 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 127.27/30.16 (3) apart_point_and_line(all_38_2, all_38_6) = all_55_0 % 127.27/30.16 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.16 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 127.27/30.16 (distinct_points(v3, v2) = v0)) % 127.27/30.16 (5) apart_point_and_line(all_38_5, all_38_8) = all_53_0 % 127.27/30.16 (6) apart_point_and_line(all_38_5, all_38_9) = all_51_0 % 127.27/30.16 (7) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.16 : ((v3 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | (v2 = 0 & % 127.27/30.16 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.16 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.16 distinct_points(all_38_5, all_38_5) = v0)) % 127.27/30.16 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 127.27/30.16 (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 127.27/30.16 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 127.27/30.16 (9) $i(all_38_9) % 127.27/30.16 (10) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 127.27/30.16 apart_point_and_line(all_38_5, all_38_9) = 0) | (v2 = 0 & % 127.27/30.16 apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ (v1 = 0) & % 127.27/30.16 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.16 distinct_points(all_38_5, all_38_5) = v0)) % 127.27/30.16 (11) ~ (all_38_0 = 0) % 127.27/30.16 (12) ~ (all_38_1 = 0) % 127.27/30.16 (13) ~ (all_53_0 = 0) % 127.27/30.16 (14) ~ (all_55_0 = 0) % 127.27/30.17 (15) $i(all_38_8) % 127.27/30.17 (16) ~ (all_51_0 = 0) % 127.27/30.17 (17) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_9, all_38_8) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.17 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.17 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.27/30.17 (apart_point_and_line(v3, v2) = v0)) % 127.27/30.17 (19) $i(all_38_2) % 127.27/30.17 (20) (all_531_0 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | % 127.27/30.17 (all_531_1 = 0 & apart_point_and_line(all_38_5, all_38_6) = 0) % 127.27/30.17 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 127.27/30.17 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) % 127.27/30.17 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = % 127.27/30.17 0) % 127.27/30.17 (22) convergent_lines(all_38_9, all_38_8) = 0 % 127.27/30.17 (23) apart_point_and_line(all_38_2, all_38_9) = all_38_1 % 127.27/30.17 (24) ~ (all_49_0 = 0) % 127.27/30.17 (25) (all_135_0 = 0 & convergent_lines(all_38_8, all_38_9) = 0) | ( ~ % 127.27/30.17 (all_135_1 = 0) & distinct_lines(all_38_8, all_38_9) = all_135_1) % 127.27/30.17 (26) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_9, all_38_8) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.17 (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.17 ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 127.27/30.17 (distinct_lines(v3, v2) = v0)) % 127.27/30.17 (28) apart_point_and_line(all_38_2, all_38_8) = all_38_0 % 127.27/30.17 (29) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.17 (30) $i(all_38_5) % 127.27/30.17 (31) $i(all_38_6) % 127.27/30.17 (32) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.17 % 127.27/30.17 Begin of proof % 127.27/30.17 | % 127.27/30.17 | BETA: splitting (20) gives: % 127.27/30.17 | % 127.27/30.17 | Case 1: % 127.27/30.17 | | % 127.27/30.17 | | (33) all_531_0 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0 % 127.27/30.17 | | % 127.27/30.17 | | ALPHA: (33) implies: % 127.27/30.17 | | (34) apart_point_and_line(all_38_2, all_38_8) = 0 % 127.27/30.17 | | % 127.27/30.17 | | REF_CLOSE: (11), (18), (28), (34) are inconsistent by sub-proof #10. % 127.27/30.17 | | % 127.27/30.17 | Case 2: % 127.27/30.17 | | % 127.27/30.17 | | (35) all_531_1 = 0 & apart_point_and_line(all_38_5, all_38_6) = 0 % 127.27/30.17 | | % 127.27/30.17 | | ALPHA: (35) implies: % 127.27/30.17 | | (36) apart_point_and_line(all_38_5, all_38_6) = 0 % 127.27/30.17 | | % 127.27/30.17 | | DELTA: instantiating (10) with fresh symbols all_491_0, all_491_1, % 127.27/30.17 | | all_491_2, all_491_3 gives: % 127.27/30.17 | | (37) (all_491_0 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | % 127.27/30.17 | | (all_491_1 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ % 127.27/30.17 | | (all_491_2 = 0) & distinct_lines(all_38_8, all_38_9) = all_491_2) % 127.27/30.17 | | | ( ~ (all_491_3 = 0) & distinct_points(all_38_5, all_38_5) = % 127.27/30.17 | | all_491_3) % 127.27/30.17 | | % 127.27/30.17 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 127.27/30.17 | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), % 127.27/30.17 | | (26), (27), (28), (29), (30), (31), (32), (36), (37) are % 127.27/30.17 | | inconsistent by sub-proof #3. % 127.27/30.17 | | % 127.27/30.17 | End of split % 127.27/30.17 | % 127.27/30.17 End of proof % 127.27/30.17 % 127.27/30.17 Sub-proof #3 shows that the following formulas are inconsistent: % 127.27/30.17 ---------------------------------------------------------------- % 127.27/30.17 (1) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_7) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_7, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.17 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 127.27/30.17 (3) apart_point_and_line(all_38_2, all_38_6) = all_55_0 % 127.27/30.17 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.17 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 127.27/30.17 (distinct_points(v3, v2) = v0)) % 127.27/30.17 (5) apart_point_and_line(all_38_5, all_38_8) = all_53_0 % 127.27/30.17 (6) apart_point_and_line(all_38_5, all_38_9) = all_51_0 % 127.27/30.17 (7) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.17 : ((v3 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | (v2 = 0 & % 127.27/30.17 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.17 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.17 distinct_points(all_38_5, all_38_5) = v0)) % 127.27/30.17 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 127.27/30.17 (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 127.27/30.17 $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 127.27/30.17 (9) (all_491_0 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | % 127.27/30.17 (all_491_1 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ % 127.27/30.17 (all_491_2 = 0) & distinct_lines(all_38_8, all_38_9) = all_491_2) | ( ~ % 127.27/30.17 (all_491_3 = 0) & distinct_points(all_38_5, all_38_5) = all_491_3) % 127.27/30.17 (10) $i(all_38_9) % 127.27/30.17 (11) apart_point_and_line(all_38_5, all_38_6) = 0 % 127.27/30.17 (12) ~ (all_38_0 = 0) % 127.27/30.18 (13) ~ (all_38_1 = 0) % 127.27/30.18 (14) ~ (all_53_0 = 0) % 127.27/30.18 (15) ~ (all_55_0 = 0) % 127.27/30.18 (16) $i(all_38_8) % 127.27/30.18 (17) ~ (all_51_0 = 0) % 127.27/30.18 (18) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.18 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.18 apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 distinct_lines(all_38_9, all_38_8) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.18 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.27/30.18 (apart_point_and_line(v3, v2) = v0)) % 127.27/30.18 (20) $i(all_38_2) % 127.27/30.18 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 127.27/30.18 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) % 127.27/30.18 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = % 127.27/30.18 0) % 127.27/30.18 (22) convergent_lines(all_38_9, all_38_8) = 0 % 127.27/30.18 (23) apart_point_and_line(all_38_2, all_38_9) = all_38_1 % 127.27/30.18 (24) ~ (all_49_0 = 0) % 127.27/30.18 (25) (all_135_0 = 0 & convergent_lines(all_38_8, all_38_9) = 0) | ( ~ % 127.27/30.18 (all_135_1 = 0) & distinct_lines(all_38_8, all_38_9) = all_135_1) % 127.27/30.18 (26) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.18 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = 0 & % 127.27/30.18 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 distinct_lines(all_38_9, all_38_8) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.27/30.18 ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 127.27/30.18 (distinct_lines(v3, v2) = v0)) % 127.27/30.18 (28) apart_point_and_line(all_38_2, all_38_8) = all_38_0 % 127.27/30.18 (29) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.18 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 = 0 & % 127.27/30.18 apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 (30) $i(all_38_5) % 127.27/30.18 (31) $i(all_38_6) % 127.27/30.18 (32) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] % 127.27/30.18 : ((v3 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = 0 & % 127.27/30.18 apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 % 127.27/30.18 Begin of proof % 127.27/30.18 | % 127.27/30.18 | BETA: splitting (7) gives: % 127.27/30.18 | % 127.27/30.18 | Case 1: % 127.27/30.18 | | % 127.27/30.18 | | (33) all_51_0 = 0 % 127.27/30.18 | | % 127.27/30.18 | | REDUCE: (17), (33) imply: % 127.27/30.18 | | (34) $false % 127.27/30.18 | | % 127.27/30.18 | | CLOSE: (34) is inconsistent. % 127.27/30.18 | | % 127.27/30.18 | Case 2: % 127.27/30.18 | | % 127.27/30.18 | | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 127.27/30.18 | | & apart_point_and_line(all_38_5, all_38_8) = 0) | (v2 = 0 & % 127.27/30.18 | | apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 | | distinct_points(all_38_5, all_38_5) = v0)) % 127.27/30.18 | | % 127.27/30.18 | | DELTA: instantiating (35) with fresh symbols all_495_0, all_495_1, % 127.27/30.18 | | all_495_2, all_495_3 gives: % 127.27/30.18 | | (36) (all_495_0 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | % 127.27/30.18 | | (all_495_1 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ % 127.27/30.18 | | (all_495_2 = 0) & distinct_lines(all_38_8, all_38_9) = all_495_2) % 127.27/30.18 | | | ( ~ (all_495_3 = 0) & distinct_points(all_38_5, all_38_5) = % 127.27/30.18 | | all_495_3) % 127.27/30.18 | | % 127.27/30.18 | | BETA: splitting (32) gives: % 127.27/30.18 | | % 127.27/30.18 | | Case 1: % 127.27/30.18 | | | % 127.27/30.18 | | | (37) all_38_1 = 0 % 127.27/30.18 | | | % 127.27/30.18 | | | REDUCE: (13), (37) imply: % 127.27/30.18 | | | (38) $false % 127.27/30.18 | | | % 127.27/30.18 | | | CLOSE: (38) is inconsistent. % 127.27/30.18 | | | % 127.27/30.18 | | Case 2: % 127.27/30.18 | | | % 127.27/30.18 | | | (39) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = % 127.27/30.18 | | | 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = 0 & % 127.27/30.18 | | | apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 = 0) & % 127.27/30.18 | | | distinct_lines(all_38_8, all_38_9) = v1) | ( ~ (v0 = 0) & % 127.27/30.18 | | | distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 | | | % 127.27/30.18 | | | DELTA: instantiating (39) with fresh symbols all_584_0, all_584_1, % 127.27/30.18 | | | all_584_2, all_584_3 gives: % 127.27/30.18 | | | (40) (all_584_0 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | % 127.27/30.18 | | | (all_584_1 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( % 127.27/30.18 | | | ~ (all_584_2 = 0) & distinct_lines(all_38_8, all_38_9) = % 127.27/30.18 | | | all_584_2) | ( ~ (all_584_3 = 0) & distinct_points(all_38_5, % 127.27/30.18 | | | all_38_2) = all_584_3) % 127.27/30.18 | | | % 127.27/30.18 | | | BETA: splitting (26) gives: % 127.27/30.18 | | | % 127.27/30.18 | | | Case 1: % 127.27/30.18 | | | | % 127.27/30.18 | | | | (41) all_38_1 = 0 % 127.27/30.18 | | | | % 127.27/30.18 | | | | REDUCE: (13), (41) imply: % 127.27/30.18 | | | | (42) $false % 127.27/30.18 | | | | % 127.27/30.18 | | | | CLOSE: (42) is inconsistent. % 127.27/30.18 | | | | % 127.27/30.18 | | | Case 2: % 127.27/30.18 | | | | % 127.27/30.18 | | | | (43) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 % 127.27/30.18 | | | | = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | (v2 = % 127.27/30.18 | | | | 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | ( ~ (v1 % 127.27/30.18 | | | | = 0) & distinct_lines(all_38_9, all_38_8) = v1) | ( ~ (v0 % 127.27/30.18 | | | | = 0) & distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.18 | | | | % 127.27/30.18 | | | | DELTA: instantiating (43) with fresh symbols all_592_0, all_592_1, % 127.27/30.18 | | | | all_592_2, all_592_3 gives: % 127.27/30.18 | | | | (44) (all_592_0 = 0 & apart_point_and_line(all_38_2, all_38_8) = 0) | % 127.27/30.18 | | | | (all_592_1 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) | % 127.27/30.18 | | | | ( ~ (all_592_2 = 0) & distinct_lines(all_38_9, all_38_8) = % 127.27/30.18 | | | | all_592_2) | ( ~ (all_592_3 = 0) & distinct_points(all_38_5, % 127.27/30.18 | | | | all_38_2) = all_592_3) % 127.27/30.18 | | | | % 127.27/30.18 | | | | BETA: splitting (29) gives: % 127.27/30.18 | | | | % 127.27/30.18 | | | | Case 1: % 127.27/30.18 | | | | | % 127.27/30.18 | | | | | (45) all_38_0 = 0 % 127.27/30.18 | | | | | % 127.27/30.18 | | | | | REDUCE: (12), (45) imply: % 127.27/30.18 | | | | | (46) $false % 127.27/30.18 | | | | | % 127.27/30.18 | | | | | CLOSE: (46) is inconsistent. % 127.27/30.18 | | | | | % 127.27/30.18 | | | | Case 2: % 127.27/30.18 | | | | | % 127.27/30.18 | | | | | (47) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 127.27/30.18 | | | | | ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | (v2 % 127.27/30.19 | | | | | = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | ( ~ % 127.27/30.19 | | | | | (v1 = 0) & distinct_lines(all_38_8, all_38_9) = v1) | ( ~ % 127.27/30.19 | | | | | (v0 = 0) & distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.19 | | | | | % 127.27/30.19 | | | | | DELTA: instantiating (47) with fresh symbols all_604_0, all_604_1, % 127.27/30.19 | | | | | all_604_2, all_604_3 gives: % 127.27/30.19 | | | | | (48) (all_604_0 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) % 127.27/30.19 | | | | | | (all_604_1 = 0 & apart_point_and_line(all_38_5, all_38_8) = % 127.27/30.19 | | | | | 0) | ( ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 127.27/30.19 | | | | | all_38_9) = all_604_2) | ( ~ (all_604_3 = 0) & % 127.27/30.19 | | | | | distinct_points(all_38_5, all_38_2) = all_604_3) % 127.27/30.19 | | | | | % 127.27/30.19 | | | | | BETA: splitting (18) gives: % 127.27/30.19 | | | | | % 127.27/30.19 | | | | | Case 1: % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | (49) all_38_0 = 0 % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | REDUCE: (12), (49) imply: % 127.27/30.19 | | | | | | (50) $false % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | CLOSE: (50) is inconsistent. % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | Case 2: % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | (51) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 127.27/30.19 | | | | | | ((v3 = 0 & apart_point_and_line(all_38_2, all_38_9) = 0) | % 127.27/30.19 | | | | | | (v2 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | % 127.27/30.19 | | | | | | ( ~ (v1 = 0) & distinct_lines(all_38_9, all_38_8) = v1) | % 127.27/30.19 | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_2) = v0)) % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | DELTA: instantiating (51) with fresh symbols all_608_0, all_608_1, % 127.27/30.19 | | | | | | all_608_2, all_608_3 gives: % 127.27/30.19 | | | | | | (52) (all_608_0 = 0 & apart_point_and_line(all_38_2, all_38_9) = % 127.27/30.19 | | | | | | 0) | (all_608_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.19 | | | | | | all_38_8) = 0) | ( ~ (all_608_2 = 0) & % 127.27/30.19 | | | | | | distinct_lines(all_38_9, all_38_8) = all_608_2) | ( ~ % 127.27/30.19 | | | | | | (all_608_3 = 0) & distinct_points(all_38_5, all_38_2) = % 127.27/30.19 | | | | | | all_608_3) % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | BETA: splitting (1) gives: % 127.27/30.19 | | | | | | % 127.27/30.19 | | | | | | Case 1: % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | (53) all_49_0 = 0 % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | REDUCE: (24), (53) imply: % 127.27/30.19 | | | | | | | (54) $false % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | CLOSE: (54) is inconsistent. % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | Case 2: % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | GROUND_INST: instantiating (21) with all_38_5, all_38_6, all_38_2, % 127.27/30.19 | | | | | | | all_55_0, simplifying with (3), (11), (20), (30), % 127.27/30.19 | | | | | | | (31) gives: % 127.27/30.19 | | | | | | | (55) all_55_0 = 0 | distinct_points(all_38_5, all_38_2) = 0 % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | BETA: splitting (55) gives: % 127.27/30.19 | | | | | | | % 127.27/30.19 | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | % 127.27/30.19 | | | | | | | | (56) distinct_points(all_38_5, all_38_2) = 0 % 127.27/30.19 | | | | | | | | % 127.27/30.19 | | | | | | | | BETA: splitting (44) gives: % 127.27/30.19 | | | | | | | | % 127.27/30.19 | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | (57) (all_592_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | all_38_8) = 0) | (all_592_1 = 0 & % 127.27/30.19 | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | BETA: splitting (57) gives: % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | (58) all_592_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | ALPHA: (58) implies: % 127.27/30.19 | | | | | | | | | | (59) apart_point_and_line(all_38_2, all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | REF_CLOSE: (12), (19), (28), (59) are inconsistent by % 127.27/30.19 | | | | | | | | | | sub-proof #10. % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | (60) all_592_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.19 | | | | | | | | | | all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | ALPHA: (60) implies: % 127.27/30.19 | | | | | | | | | | (61) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | REF_CLOSE: (6), (17), (19), (61) are inconsistent by % 127.27/30.19 | | | | | | | | | | sub-proof #9. % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | End of split % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | (62) ( ~ (all_592_2 = 0) & distinct_lines(all_38_9, % 127.27/30.19 | | | | | | | | | all_38_8) = all_592_2) | ( ~ (all_592_3 = 0) & % 127.27/30.19 | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_592_3) % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | BETA: splitting (62) gives: % 127.27/30.19 | | | | | | | | | % 127.27/30.19 | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | (63) ~ (all_592_2 = 0) & distinct_lines(all_38_9, % 127.27/30.19 | | | | | | | | | | all_38_8) = all_592_2 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | ALPHA: (63) implies: % 127.27/30.19 | | | | | | | | | | (64) distinct_lines(all_38_9, all_38_8) = all_592_2 % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | BETA: splitting (52) gives: % 127.27/30.19 | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | (65) (all_608_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | all_38_9) = 0) | (all_608_1 = 0 & % 127.27/30.19 | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | BETA: splitting (65) gives: % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | (66) all_608_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | ALPHA: (66) implies: % 127.27/30.19 | | | | | | | | | | | | (67) apart_point_and_line(all_38_2, all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | REF_CLOSE: (13), (19), (23), (67) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | sub-proof #8. % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | (68) all_608_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.19 | | | | | | | | | | | | all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | ALPHA: (68) implies: % 127.27/30.19 | | | | | | | | | | | | (69) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | REF_CLOSE: (5), (14), (19), (69) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | sub-proof #7. % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | End of split % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | (70) ( ~ (all_608_2 = 0) & distinct_lines(all_38_9, % 127.27/30.19 | | | | | | | | | | | all_38_8) = all_608_2) | ( ~ (all_608_3 = 0) & % 127.27/30.19 | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_608_3) % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | BETA: splitting (70) gives: % 127.27/30.19 | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | (71) ~ (all_608_2 = 0) & distinct_lines(all_38_9, % 127.27/30.19 | | | | | | | | | | | | all_38_8) = all_608_2 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | ALPHA: (71) implies: % 127.27/30.19 | | | | | | | | | | | | (72) ~ (all_608_2 = 0) % 127.27/30.19 | | | | | | | | | | | | (73) distinct_lines(all_38_9, all_38_8) = all_608_2 % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | BETA: splitting (48) gives: % 127.27/30.19 | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | (74) (all_604_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | | | all_38_9) = 0) | (all_604_1 = 0 & % 127.27/30.19 | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | BETA: splitting (74) gives: % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | (75) all_604_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | ALPHA: (75) implies: % 127.27/30.19 | | | | | | | | | | | | | | (76) apart_point_and_line(all_38_2, all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (23), (76) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | | | sub-proof #8. % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | (77) all_604_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.19 | | | | | | | | | | | | | | all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | ALPHA: (77) implies: % 127.27/30.19 | | | | | | | | | | | | | | (78) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (19), (78) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | | | sub-proof #7. % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | End of split % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | (79) ( ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 127.27/30.19 | | | | | | | | | | | | | all_38_9) = all_604_2) | ( ~ (all_604_3 = 0) & % 127.27/30.19 | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_604_3) % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | BETA: splitting (79) gives: % 127.27/30.19 | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | (80) ~ (all_604_2 = 0) & distinct_lines(all_38_8, % 127.27/30.19 | | | | | | | | | | | | | | all_38_9) = all_604_2 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | ALPHA: (80) implies: % 127.27/30.19 | | | | | | | | | | | | | | (81) ~ (all_604_2 = 0) % 127.27/30.19 | | | | | | | | | | | | | | (82) distinct_lines(all_38_8, all_38_9) = all_604_2 % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | BETA: splitting (40) gives: % 127.27/30.19 | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | (83) (all_584_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | | | | | all_38_8) = 0) | (all_584_1 = 0 & % 127.27/30.19 | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 127.27/30.19 | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | BETA: splitting (83) gives: % 127.27/30.19 | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | Case 1: % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | (84) all_584_0 = 0 & apart_point_and_line(all_38_2, % 127.27/30.19 | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | ALPHA: (84) implies: % 127.27/30.19 | | | | | | | | | | | | | | | | (85) apart_point_and_line(all_38_2, all_38_8) = 0 % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (28), (85) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | | | | | sub-proof #10. % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | (86) all_584_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.19 | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | ALPHA: (86) implies: % 127.27/30.19 | | | | | | | | | | | | | | | | (87) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (87) are inconsistent by % 127.27/30.19 | | | | | | | | | | | | | | | | sub-proof #9. % 127.27/30.19 | | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | | End of split % 127.27/30.19 | | | | | | | | | | | | | | | % 127.27/30.19 | | | | | | | | | | | | | | Case 2: % 127.27/30.19 | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | (88) ( ~ (all_584_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | all_38_9) = all_584_2) | ( ~ (all_584_3 = 0) & % 127.27/30.20 | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_2) = all_584_3) % 127.27/30.20 | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 127.27/30.20 | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | (89) ~ (all_584_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | all_38_9) = all_584_2 % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | ALPHA: (89) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | (90) distinct_lines(all_38_8, all_38_9) = all_584_2 % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_592_2, all_608_2, % 127.27/30.20 | | | | | | | | | | | | | | | | all_38_8, all_38_9, simplifying with (64), (73) % 127.27/30.20 | | | | | | | | | | | | | | | | gives: % 127.27/30.20 | | | | | | | | | | | | | | | | (91) all_608_2 = all_592_2 % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_584_2, all_604_2, % 127.27/30.20 | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (82), (90) % 127.27/30.20 | | | | | | | | | | | | | | | | gives: % 127.27/30.20 | | | | | | | | | | | | | | | | (92) all_604_2 = all_584_2 % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | REDUCE: (72), (91) imply: % 127.27/30.20 | | | | | | | | | | | | | | | | (93) ~ (all_592_2 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | REDUCE: (81), (92) imply: % 127.27/30.20 | | | | | | | | | | | | | | | | (94) ~ (all_584_2 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | (95) all_135_0 = 0 & convergent_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | ALPHA: (95) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | (96) convergent_lines(all_38_8, all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | (97) (all_491_0 = 0 & apart_point_and_line(all_38_5, % 127.27/30.20 | | | | | | | | | | | | | | | | | | all_38_9) = 0) | (all_491_1 = 0 & % 127.27/30.20 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_8) = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (98) all_491_0 = 0 & apart_point_and_line(all_38_5, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | ALPHA: (98) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (99) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (99) are inconsistent by % 127.27/30.20 | | | | | | | | | | | | | | | | | | | sub-proof #9. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (100) all_491_1 = 0 & apart_point_and_line(all_38_5, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | ALPHA: (100) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (101) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (19), (101) are inconsistent by % 127.27/30.20 | | | | | | | | | | | | | | | | | | | sub-proof #7. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | (102) ( ~ (all_491_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | all_38_9) = all_491_2) | ( ~ (all_491_3 = 0) & % 127.27/30.20 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_491_3) % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (103) ~ (all_491_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_9) = all_491_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | ALPHA: (103) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (104) distinct_lines(all_38_8, all_38_9) = all_491_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_584_2, all_491_2, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (90), (104) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (105) all_584_2 = all_491_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | REDUCE: (94), (105) imply: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (106) ~ (all_491_2 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (107) (all_495_0 = 0 & apart_point_and_line(all_38_5, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_495_1 = 0 & % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (17), (19), (107) are inconsistent % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | by sub-proof #6. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (108) ( ~ (all_495_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | all_38_9) = all_495_2) | ( ~ (all_495_3 = 0) & % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_495_3) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (109) ~ (all_495_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9) = all_495_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (110) ~ (all_495_2 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (111) distinct_lines(all_38_8, all_38_9) = all_495_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_491_2, all_495_2, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (104), (111) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (112) all_495_2 = all_491_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_9, all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9, all_491_2, simplifying with (10), (16), % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (22), (104) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (113) all_491_2 = 0 | convergent_lines(all_38_9, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (106), (113) are inconsistent by % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_9, all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9, all_491_2, simplifying with (10), (16), % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (22), (104) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | (114) all_491_2 = 0 | convergent_lines(all_38_9, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (106), (114) are inconsistent by % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_8, all_38_9, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_8, all_592_2, simplifying with (10), (16), % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (64), (96) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (115) all_592_2 = 0 | convergent_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_8) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (116) convergent_lines(all_38_8, all_38_8) = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_38_8, simplifying with % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (16), (116) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (117) $false % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (118) all_592_2 = 0 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (118) imply: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | (119) $false % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 127.27/30.20 | | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | End of split % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | (120) ~ (all_135_1 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | all_38_9) = all_135_1 % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | ALPHA: (120) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | (121) ~ (all_135_1 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | (122) distinct_lines(all_38_8, all_38_9) = all_135_1 % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | (123) (all_495_0 = 0 & apart_point_and_line(all_38_5, % 127.27/30.20 | | | | | | | | | | | | | | | | | | all_38_8) = 0) | (all_495_1 = 0 & % 127.27/30.20 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_9) = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (17), (19), (123) are inconsistent % 127.27/30.20 | | | | | | | | | | | | | | | | | | by sub-proof #6. % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | (124) ( ~ (all_495_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | all_38_9) = all_495_2) | ( ~ (all_495_3 = 0) & % 127.27/30.20 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_495_3) % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | Case 1: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (125) ~ (all_495_2 = 0) & distinct_lines(all_38_8, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_9) = all_495_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (126) ~ (all_495_2 = 0) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (127) distinct_lines(all_38_8, all_38_9) = all_495_2 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.20 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_135_1, all_495_2, % 127.27/30.20 | | | | | | | | | | | | | | | | | | | all_38_9, all_38_8, simplifying with (122), (127) % 127.27/30.20 | | | | | | | | | | | | | | | | | | | gives: % 127.27/30.20 | | | | | | | | | | | | | | | | | | | (128) all_495_2 = all_135_1 % 127.27/30.20 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_9, all_38_8, % 127.27/30.21 | | | | | | | | | | | | | | | | | | | all_38_9, all_135_1, simplifying with (10), (16), % 127.27/30.21 | | | | | | | | | | | | | | | | | | | (22), (122) gives: % 127.27/30.21 | | | | | | | | | | | | | | | | | | | (129) all_135_1 = 0 | convergent_lines(all_38_9, % 127.27/30.21 | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (121), (129) are inconsistent by % 127.27/30.21 | | | | | | | | | | | | | | | | | | | sub-proof #4. % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | Case 2: % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_9, all_38_8, % 127.27/30.21 | | | | | | | | | | | | | | | | | | | all_38_9, all_135_1, simplifying with (10), (16), % 127.27/30.21 | | | | | | | | | | | | | | | | | | | (22), (122) gives: % 127.27/30.21 | | | | | | | | | | | | | | | | | | | (130) all_135_1 = 0 | convergent_lines(all_38_9, % 127.27/30.21 | | | | | | | | | | | | | | | | | | | all_38_9) = 0 % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (121), (130) are inconsistent by % 127.27/30.21 | | | | | | | | | | | | | | | | | | | sub-proof #4. % 127.27/30.21 | | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | Case 2: % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | (131) ~ (all_584_3 = 0) & distinct_points(all_38_5, % 127.27/30.21 | | | | | | | | | | | | | | | | all_38_2) = all_584_3 % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | ALPHA: (131) implies: % 127.27/30.21 | | | | | | | | | | | | | | | | (132) ~ (all_584_3 = 0) % 127.27/30.21 | | | | | | | | | | | | | | | | (133) distinct_points(all_38_5, all_38_2) = all_584_3 % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_584_3, all_38_2, % 127.27/30.21 | | | | | | | | | | | | | | | | all_38_5, simplifying with (56), (133) gives: % 127.27/30.21 | | | | | | | | | | | | | | | | (134) all_584_3 = 0 % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | REDUCE: (132), (134) imply: % 127.27/30.21 | | | | | | | | | | | | | | | | (135) $false % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 127.27/30.21 | | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | Case 2: % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | (136) ~ (all_604_3 = 0) & distinct_points(all_38_5, % 127.27/30.21 | | | | | | | | | | | | | | all_38_2) = all_604_3 % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | ALPHA: (136) implies: % 127.27/30.21 | | | | | | | | | | | | | | (137) ~ (all_604_3 = 0) % 127.27/30.21 | | | | | | | | | | | | | | (138) distinct_points(all_38_5, all_38_2) = all_604_3 % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_604_3, all_38_2, % 127.27/30.21 | | | | | | | | | | | | | | all_38_5, simplifying with (56), (138) gives: % 127.27/30.21 | | | | | | | | | | | | | | (139) all_604_3 = 0 % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | REDUCE: (137), (139) imply: % 127.27/30.21 | | | | | | | | | | | | | | (140) $false % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 127.27/30.21 | | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | End of split % 127.27/30.21 | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | Case 2: % 127.27/30.21 | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | (141) ~ (all_608_3 = 0) & distinct_points(all_38_5, % 127.27/30.21 | | | | | | | | | | | | all_38_2) = all_608_3 % 127.27/30.21 | | | | | | | | | | | | % 127.27/30.21 | | | | | | | | | | | | ALPHA: (141) implies: % 127.27/30.21 | | | | | | | | | | | | (142) ~ (all_608_3 = 0) % 127.27/30.21 | | | | | | | | | | | | (143) distinct_points(all_38_5, all_38_2) = all_608_3 % 127.27/30.21 | | | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_608_3, all_38_2, % 127.53/30.21 | | | | | | | | | | | | all_38_5, simplifying with (56), (143) gives: % 127.53/30.21 | | | | | | | | | | | | (144) all_608_3 = 0 % 127.53/30.21 | | | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | | | REDUCE: (142), (144) imply: % 127.53/30.21 | | | | | | | | | | | | (145) $false % 127.53/30.21 | | | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 127.53/30.21 | | | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | | End of split % 127.53/30.21 | | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | End of split % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | Case 2: % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | (146) ~ (all_592_3 = 0) & distinct_points(all_38_5, % 127.53/30.21 | | | | | | | | | | all_38_2) = all_592_3 % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | ALPHA: (146) implies: % 127.53/30.21 | | | | | | | | | | (147) ~ (all_592_3 = 0) % 127.53/30.21 | | | | | | | | | | (148) distinct_points(all_38_5, all_38_2) = all_592_3 % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_592_3, all_38_2, % 127.53/30.21 | | | | | | | | | | all_38_5, simplifying with (56), (148) gives: % 127.53/30.21 | | | | | | | | | | (149) all_592_3 = 0 % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | REDUCE: (147), (149) imply: % 127.53/30.21 | | | | | | | | | | (150) $false % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | | CLOSE: (150) is inconsistent. % 127.53/30.21 | | | | | | | | | | % 127.53/30.21 | | | | | | | | | End of split % 127.53/30.21 | | | | | | | | | % 127.53/30.21 | | | | | | | | End of split % 127.53/30.21 | | | | | | | | % 127.53/30.21 | | | | | | | Case 2: % 127.53/30.21 | | | | | | | | % 127.53/30.21 | | | | | | | | (151) all_55_0 = 0 % 127.53/30.21 | | | | | | | | % 127.53/30.21 | | | | | | | | REDUCE: (15), (151) imply: % 127.53/30.21 | | | | | | | | (152) $false % 127.53/30.21 | | | | | | | | % 127.53/30.21 | | | | | | | | CLOSE: (152) is inconsistent. % 127.53/30.21 | | | | | | | | % 127.53/30.21 | | | | | | | End of split % 127.53/30.21 | | | | | | | % 127.53/30.21 | | | | | | End of split % 127.53/30.21 | | | | | | % 127.53/30.21 | | | | | End of split % 127.53/30.21 | | | | | % 127.53/30.21 | | | | End of split % 127.53/30.21 | | | | % 127.53/30.21 | | | End of split % 127.53/30.21 | | | % 127.53/30.21 | | End of split % 127.53/30.21 | | % 127.53/30.21 | End of split % 127.53/30.21 | % 127.53/30.21 End of proof % 127.53/30.21 % 127.53/30.21 Sub-proof #4 shows that the following formulas are inconsistent: % 127.53/30.21 ---------------------------------------------------------------- % 127.53/30.21 (1) all_135_1 = 0 | convergent_lines(all_38_9, all_38_9) = 0 % 127.53/30.21 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 127.53/30.21 (3) $i(all_38_9) % 127.53/30.21 (4) ~ (all_135_1 = 0) % 127.53/30.21 % 127.53/30.21 Begin of proof % 127.53/30.21 | % 127.53/30.21 | BETA: splitting (1) gives: % 127.53/30.21 | % 127.53/30.21 | Case 1: % 127.53/30.21 | | % 127.53/30.21 | | (5) convergent_lines(all_38_9, all_38_9) = 0 % 127.53/30.21 | | % 127.53/30.21 | | GROUND_INST: instantiating (2) with all_38_9, simplifying with (3), (5) % 127.53/30.21 | | gives: % 127.53/30.21 | | (6) $false % 127.53/30.21 | | % 127.53/30.21 | | CLOSE: (6) is inconsistent. % 127.53/30.21 | | % 127.53/30.21 | Case 2: % 127.53/30.21 | | % 127.53/30.21 | | (7) all_135_1 = 0 % 127.53/30.21 | | % 127.53/30.21 | | REDUCE: (4), (7) imply: % 127.53/30.21 | | (8) $false % 127.53/30.21 | | % 127.53/30.21 | | CLOSE: (8) is inconsistent. % 127.53/30.21 | | % 127.53/30.21 | End of split % 127.53/30.21 | % 127.53/30.21 End of proof % 127.53/30.21 % 127.53/30.21 Sub-proof #5 shows that the following formulas are inconsistent: % 127.53/30.21 ---------------------------------------------------------------- % 127.53/30.21 (1) all_491_2 = 0 | convergent_lines(all_38_9, all_38_9) = 0 % 127.53/30.21 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 127.53/30.21 (3) $i(all_38_9) % 127.53/30.21 (4) ~ (all_491_2 = 0) % 127.53/30.21 % 127.53/30.21 Begin of proof % 127.53/30.21 | % 127.53/30.21 | BETA: splitting (1) gives: % 127.53/30.21 | % 127.53/30.21 | Case 1: % 127.53/30.21 | | % 127.53/30.21 | | (5) convergent_lines(all_38_9, all_38_9) = 0 % 127.53/30.21 | | % 127.53/30.21 | | GROUND_INST: instantiating (2) with all_38_9, simplifying with (3), (5) % 127.53/30.21 | | gives: % 127.53/30.21 | | (6) $false % 127.53/30.21 | | % 127.53/30.21 | | CLOSE: (6) is inconsistent. % 127.53/30.21 | | % 127.53/30.21 | Case 2: % 127.53/30.21 | | % 127.53/30.21 | | (7) all_491_2 = 0 % 127.53/30.21 | | % 127.53/30.21 | | REDUCE: (4), (7) imply: % 127.53/30.21 | | (8) $false % 127.53/30.21 | | % 127.53/30.21 | | CLOSE: (8) is inconsistent. % 127.53/30.21 | | % 127.53/30.21 | End of split % 127.53/30.21 | % 127.53/30.21 End of proof % 127.53/30.21 % 127.53/30.21 Sub-proof #6 shows that the following formulas are inconsistent: % 127.53/30.21 ---------------------------------------------------------------- % 127.53/30.21 (1) apart_point_and_line(all_38_5, all_38_8) = all_53_0 % 127.53/30.21 (2) apart_point_and_line(all_38_5, all_38_9) = all_51_0 % 127.53/30.21 (3) (all_495_0 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0) | % 127.53/30.21 (all_495_1 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0) % 127.53/30.21 (4) ~ (all_53_0 = 0) % 127.53/30.21 (5) ~ (all_51_0 = 0) % 127.53/30.21 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.53/30.21 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.53/30.21 (apart_point_and_line(v3, v2) = v0)) % 127.53/30.21 % 127.53/30.21 Begin of proof % 127.53/30.21 | % 127.53/30.21 | BETA: splitting (3) gives: % 127.53/30.21 | % 127.53/30.21 | Case 1: % 127.53/30.21 | | % 127.53/30.21 | | (7) all_495_0 = 0 & apart_point_and_line(all_38_5, all_38_8) = 0 % 127.53/30.21 | | % 127.53/30.21 | | ALPHA: (7) implies: % 127.53/30.21 | | (8) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.53/30.21 | | % 127.53/30.21 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #7. % 127.53/30.21 | | % 127.53/30.21 | Case 2: % 127.53/30.21 | | % 127.53/30.21 | | (9) all_495_1 = 0 & apart_point_and_line(all_38_5, all_38_9) = 0 % 127.53/30.21 | | % 127.53/30.21 | | ALPHA: (9) implies: % 127.53/30.21 | | (10) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.53/30.21 | | % 127.53/30.21 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #9. % 127.53/30.21 | | % 127.53/30.21 | End of split % 127.53/30.21 | % 127.53/30.21 End of proof % 127.53/30.21 % 127.53/30.21 Sub-proof #7 shows that the following formulas are inconsistent: % 127.53/30.21 ---------------------------------------------------------------- % 127.53/30.21 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.53/30.21 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.53/30.21 (apart_point_and_line(v3, v2) = v0)) % 127.53/30.21 (2) apart_point_and_line(all_38_5, all_38_8) = all_53_0 % 127.53/30.21 (3) apart_point_and_line(all_38_5, all_38_8) = 0 % 127.53/30.21 (4) ~ (all_53_0 = 0) % 127.53/30.21 % 127.53/30.21 Begin of proof % 127.53/30.21 | % 127.53/30.21 | GROUND_INST: instantiating (1) with all_53_0, 0, all_38_8, all_38_5, % 127.53/30.21 | simplifying with (2), (3) gives: % 127.53/30.21 | (5) all_53_0 = 0 % 127.53/30.21 | % 127.53/30.21 | REDUCE: (4), (5) imply: % 127.53/30.21 | (6) $false % 127.53/30.21 | % 127.53/30.21 | CLOSE: (6) is inconsistent. % 127.53/30.21 | % 127.53/30.21 End of proof % 127.53/30.21 % 127.53/30.21 Sub-proof #8 shows that the following formulas are inconsistent: % 127.53/30.21 ---------------------------------------------------------------- % 127.53/30.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.53/30.22 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.53/30.22 (apart_point_and_line(v3, v2) = v0)) % 127.53/30.22 (2) apart_point_and_line(all_38_2, all_38_9) = all_38_1 % 127.53/30.22 (3) apart_point_and_line(all_38_2, all_38_9) = 0 % 127.53/30.22 (4) ~ (all_38_1 = 0) % 127.53/30.22 % 127.53/30.22 Begin of proof % 127.53/30.22 | % 127.53/30.22 | GROUND_INST: instantiating (1) with all_38_1, 0, all_38_9, all_38_2, % 127.53/30.22 | simplifying with (2), (3) gives: % 127.53/30.22 | (5) all_38_1 = 0 % 127.53/30.22 | % 127.53/30.22 | REDUCE: (4), (5) imply: % 127.53/30.22 | (6) $false % 127.53/30.22 | % 127.53/30.22 | CLOSE: (6) is inconsistent. % 127.53/30.22 | % 127.53/30.22 End of proof % 127.53/30.22 % 127.53/30.22 Sub-proof #9 shows that the following formulas are inconsistent: % 127.53/30.22 ---------------------------------------------------------------- % 127.53/30.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.53/30.22 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.53/30.22 (apart_point_and_line(v3, v2) = v0)) % 127.53/30.22 (2) apart_point_and_line(all_38_5, all_38_9) = all_51_0 % 127.53/30.22 (3) apart_point_and_line(all_38_5, all_38_9) = 0 % 127.53/30.22 (4) ~ (all_51_0 = 0) % 127.53/30.22 % 127.53/30.22 Begin of proof % 127.53/30.22 | % 127.53/30.22 | GROUND_INST: instantiating (1) with all_51_0, 0, all_38_9, all_38_5, % 127.53/30.22 | simplifying with (2), (3) gives: % 127.53/30.22 | (5) all_51_0 = 0 % 127.53/30.22 | % 127.53/30.22 | REDUCE: (4), (5) imply: % 127.53/30.22 | (6) $false % 127.53/30.22 | % 127.53/30.22 | CLOSE: (6) is inconsistent. % 127.53/30.22 | % 127.53/30.22 End of proof % 127.53/30.22 % 127.53/30.22 Sub-proof #10 shows that the following formulas are inconsistent: % 127.53/30.22 ---------------------------------------------------------------- % 127.53/30.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 127.53/30.22 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 127.53/30.22 (apart_point_and_line(v3, v2) = v0)) % 127.53/30.22 (2) apart_point_and_line(all_38_2, all_38_8) = all_38_0 % 127.53/30.22 (3) apart_point_and_line(all_38_2, all_38_8) = 0 % 127.53/30.22 (4) ~ (all_38_0 = 0) % 127.53/30.22 % 127.53/30.22 Begin of proof % 127.53/30.22 | % 127.53/30.22 | GROUND_INST: instantiating (1) with all_38_0, 0, all_38_8, all_38_2, % 127.53/30.22 | simplifying with (2), (3) gives: % 127.53/30.22 | (5) all_38_0 = 0 % 127.53/30.22 | % 127.53/30.22 | REDUCE: (4), (5) imply: % 127.53/30.22 | (6) $false % 127.53/30.22 | % 127.53/30.22 | CLOSE: (6) is inconsistent. % 127.53/30.22 | % 127.53/30.22 End of proof % 127.53/30.22 % SZS output end Proof for theBenchmark % 127.53/30.22 % 127.53/30.22 29607ms %------------------------------------------------------------------------------