%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO187+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:00 EDT 2023 % Result : Theorem 10.34s 2.11s % Output : Proof 17.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO187+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 19:52:54 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.74/1.08 Prover 4: Preprocessing ... % 2.74/1.09 Prover 1: Preprocessing ... % 2.93/1.12 Prover 2: Preprocessing ... % 2.93/1.12 Prover 5: Preprocessing ... % 2.93/1.12 Prover 3: Preprocessing ... % 2.93/1.12 Prover 6: Preprocessing ... % 2.93/1.12 Prover 0: Preprocessing ... % 4.04/1.36 Prover 2: Proving ... % 4.04/1.36 Prover 6: Constructing countermodel ... % 4.04/1.36 Prover 5: Proving ... % 4.04/1.36 Prover 1: Constructing countermodel ... % 4.78/1.37 Prover 3: Constructing countermodel ... % 5.57/1.48 Prover 4: Constructing countermodel ... % 5.57/1.50 Prover 3: gave up % 5.57/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.57/1.51 Prover 6: gave up % 5.57/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.57/1.51 Prover 0: Proving ... % 5.57/1.52 Prover 1: gave up % 6.02/1.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.02/1.54 Prover 7: Preprocessing ... % 6.02/1.56 Prover 9: Preprocessing ... % 6.23/1.56 Prover 8: Preprocessing ... % 6.23/1.59 Prover 7: Warning: ignoring some quantifiers % 6.23/1.60 Prover 7: Constructing countermodel ... % 6.23/1.62 Prover 8: Warning: ignoring some quantifiers % 6.74/1.63 Prover 8: Constructing countermodel ... % 7.05/1.69 Prover 8: gave up % 7.05/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.05/1.72 Prover 9: Constructing countermodel ... % 7.58/1.74 Prover 10: Preprocessing ... % 7.83/1.78 Prover 10: Warning: ignoring some quantifiers % 7.83/1.79 Prover 10: Constructing countermodel ... % 7.83/1.80 Prover 7: gave up % 7.83/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.83/1.83 Prover 10: gave up % 8.28/1.84 Prover 11: Preprocessing ... % 8.28/1.84 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.28/1.87 Prover 12: Preprocessing ... % 8.71/1.97 Prover 12: Proving ... % 9.39/2.02 Prover 11: Constructing countermodel ... % 10.34/2.11 Prover 0: proved (1470ms) % 10.34/2.11 % 10.34/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.34/2.11 % 10.34/2.11 Prover 9: stopped % 10.34/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.34/2.11 Prover 2: stopped % 10.34/2.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.34/2.12 Prover 5: stopped % 10.34/2.12 Prover 12: stopped % 10.34/2.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.34/2.13 Prover 16: Preprocessing ... % 10.34/2.14 Prover 13: Preprocessing ... % 10.34/2.14 Prover 19: Preprocessing ... % 10.34/2.15 Prover 16: Warning: ignoring some quantifiers % 10.34/2.16 Prover 16: Constructing countermodel ... % 10.82/2.17 Prover 13: Warning: ignoring some quantifiers % 10.82/2.17 Prover 13: Constructing countermodel ... % 10.82/2.20 Prover 19: Warning: ignoring some quantifiers % 10.82/2.21 Prover 19: Constructing countermodel ... % 10.82/2.25 Prover 19: gave up % 11.74/2.29 Prover 13: gave up % 11.74/2.32 Prover 16: gave up % 16.19/3.15 Prover 11: Found proof (size 325) % 16.19/3.15 Prover 11: proved (1345ms) % 16.19/3.15 Prover 4: stopped % 16.19/3.15 % 16.19/3.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.19/3.15 % 16.19/3.17 % SZS output start Proof for theBenchmark % 16.19/3.18 Assumptions after simplification: % 16.19/3.18 --------------------------------- % 16.19/3.18 % 16.19/3.18 (ceq2) % 16.19/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.19/3.20 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 16.19/3.20 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 16.19/3.20 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 16.19/3.20 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 16.19/3.20 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.19/3.20 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.19/3.20 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 16.19/3.20 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.19/3.20 apart_point_and_line(v0, v2) = 0) % 16.19/3.20 % 16.19/3.20 (ci1) % 16.19/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.19/3.21 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.19/3.21 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.19/3.21 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.19/3.21 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.19/3.21 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.19/3.21 $i(v2))) % 16.19/3.21 % 16.19/3.21 (ci2) % 16.19/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.19/3.21 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.19/3.21 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.19/3.21 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.19/3.21 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.19/3.21 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.19/3.21 $i(v2))) % 16.19/3.21 % 16.19/3.21 (con) % 16.19/3.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.19/3.21 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ( ~ (v6 = % 16.19/3.21 0) & ~ (v5 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) % 16.19/3.21 = v7 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 % 16.19/3.21 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & $i(v7) & % 16.19/3.21 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 & % 16.19/3.21 apart_point_and_line(v3, v7) = 0) | (v8 = 0 & apart_point_and_line(v2, % 16.19/3.21 v7) = 0))) % 16.19/3.21 % 16.19/3.21 (cu1) % 16.19/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.19/3.22 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.19/3.22 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.19/3.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.19/3.22 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 16.19/3.23 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 16.19/3.23 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.19/3.23 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 16.19/3.23 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 16.19/3.23 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 16.19/3.23 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.19/3.23 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 16.19/3.23 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.19/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.19/3.23 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.19/3.23 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.19/3.23 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.19/3.23 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.19/3.23 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.19/3.23 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.19/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.19/3.23 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.19/3.23 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.19/3.23 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.19/3.23 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 16.19/3.23 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.19/3.23 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.19/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.19/3.23 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.19/3.23 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 16.19/3.23 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.19/3.23 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.19/3.23 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 16.19/3.23 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.19/3.23 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 16.19/3.23 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 16.19/3.23 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.19/3.23 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.19/3.23 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 16.19/3.23 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 16.19/3.23 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 16.19/3.23 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.19/3.23 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 16.19/3.23 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 16.19/3.23 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 16.19/3.23 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 16.19/3.23 % 16.19/3.23 (function-axioms) % 16.19/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.19/3.23 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.19/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.19/3.23 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.19/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.19/3.23 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.19/3.23 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.19/3.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.19/3.23 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.19/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.19/3.23 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.19/3.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.19/3.23 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.19/3.23 (distinct_points(v3, v2) = v0)) % 16.19/3.23 % 16.19/3.23 Further assumptions not needed in the proof: % 16.19/3.23 -------------------------------------------- % 16.19/3.23 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq3, ci3, ci4 % 16.19/3.23 % 16.19/3.23 Those formulas are unsatisfiable: % 16.19/3.23 --------------------------------- % 16.19/3.23 % 16.19/3.23 Begin of proof % 16.19/3.23 | % 16.19/3.23 | ALPHA: (ci1) implies: % 16.19/3.23 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.19/3.23 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.19/3.23 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.19/3.23 | $i(v2))) % 16.19/3.23 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.19/3.23 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 16.19/3.23 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & % 16.19/3.23 | distinct_points(v0, v1) = v3))) % 16.19/3.23 | % 16.19/3.23 | ALPHA: (ci2) implies: % 16.19/3.23 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.19/3.23 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.19/3.23 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.19/3.23 | $i(v2))) % 16.19/3.23 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.19/3.24 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 16.19/3.24 | (v4 = 0) & apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & % 16.19/3.24 | distinct_points(v0, v1) = v3))) % 16.19/3.24 | % 16.19/3.24 | ALPHA: (cu1) implies: % 16.19/3.24 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.19/3.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 16.19/3.24 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 16.19/3.24 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.19/3.24 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.19/3.24 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.19/3.24 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 16.19/3.24 | distinct_lines(v2, v3) = v6))) % 16.19/3.24 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.19/3.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 16.19/3.24 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.19/3.24 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 16.19/3.24 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 16.19/3.24 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 16.19/3.24 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 16.19/3.24 | v1) = v6))) % 16.19/3.24 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.19/3.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.19/3.24 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.19/3.24 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 16.19/3.24 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.19/3.24 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 16.19/3.24 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 16.19/3.24 | v1) = v6))) % 16.19/3.24 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.19/3.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.19/3.24 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 16.19/3.24 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.19/3.24 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.19/3.24 | apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 16.19/3.24 | apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & % 16.19/3.24 | distinct_lines(v2, v3) = v6))) % 16.19/3.24 | % 16.19/3.24 | ALPHA: (ceq2) implies: % 16.19/3.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.19/3.24 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) % 16.19/3.24 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = % 16.19/3.24 | 0) % 16.19/3.24 | % 16.19/3.24 | ALPHA: (function-axioms) implies: % 16.19/3.24 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.19/3.24 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.19/3.24 | (distinct_points(v3, v2) = v0)) % 16.19/3.24 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.19/3.24 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 16.19/3.24 | (distinct_lines(v3, v2) = v0)) % 16.19/3.24 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.19/3.24 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.19/3.24 | (apart_point_and_line(v3, v2) = v0)) % 16.19/3.24 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.19/3.24 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 16.19/3.24 | % 16.19/3.24 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 16.19/3.24 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8, all_17_9 % 16.19/3.24 | gives: % 16.19/3.25 | (14) ~ (all_17_3 = 0) & ~ (all_17_4 = 0) & line_connecting(all_17_7, % 16.19/3.25 | all_17_6) = all_17_5 & line_connecting(all_17_9, all_17_8) = % 16.19/3.25 | all_17_2 & apart_point_and_line(all_17_8, all_17_5) = all_17_3 & % 16.19/3.25 | apart_point_and_line(all_17_9, all_17_5) = all_17_4 & % 16.19/3.25 | distinct_points(all_17_7, all_17_6) = 0 & distinct_points(all_17_9, % 16.19/3.25 | all_17_8) = 0 & $i(all_17_2) & $i(all_17_5) & $i(all_17_6) & % 16.19/3.25 | $i(all_17_7) & $i(all_17_8) & $i(all_17_9) & ((all_17_0 = 0 & % 16.19/3.25 | apart_point_and_line(all_17_6, all_17_2) = 0) | (all_17_1 = 0 & % 16.19/3.25 | apart_point_and_line(all_17_7, all_17_2) = 0)) % 16.19/3.25 | % 16.19/3.25 | ALPHA: (14) implies: % 16.19/3.25 | (15) ~ (all_17_4 = 0) % 16.19/3.25 | (16) ~ (all_17_3 = 0) % 16.19/3.25 | (17) $i(all_17_9) % 16.19/3.25 | (18) $i(all_17_8) % 16.19/3.25 | (19) $i(all_17_7) % 16.19/3.25 | (20) $i(all_17_6) % 16.19/3.25 | (21) distinct_points(all_17_9, all_17_8) = 0 % 16.19/3.25 | (22) distinct_points(all_17_7, all_17_6) = 0 % 16.19/3.25 | (23) apart_point_and_line(all_17_9, all_17_5) = all_17_4 % 16.19/3.25 | (24) apart_point_and_line(all_17_8, all_17_5) = all_17_3 % 16.19/3.25 | (25) line_connecting(all_17_9, all_17_8) = all_17_2 % 16.19/3.25 | (26) line_connecting(all_17_7, all_17_6) = all_17_5 % 16.19/3.25 | (27) (all_17_0 = 0 & apart_point_and_line(all_17_6, all_17_2) = 0) | % 16.19/3.25 | (all_17_1 = 0 & apart_point_and_line(all_17_7, all_17_2) = 0) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (3) with all_17_9, all_17_8, simplifying with (17), % 16.19/3.25 | (18), (21) gives: % 16.19/3.25 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9, % 16.19/3.25 | all_17_8) = v0 & apart_point_and_line(all_17_8, v0) = v1 & $i(v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (1) with all_17_9, all_17_8, simplifying with (17), % 16.19/3.25 | (18), (21) gives: % 16.19/3.25 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9, % 16.19/3.25 | all_17_8) = v0 & apart_point_and_line(all_17_9, v0) = v1 & $i(v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (3) with all_17_7, all_17_6, simplifying with (19), % 16.19/3.25 | (20), (22) gives: % 16.19/3.25 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7, % 16.19/3.25 | all_17_6) = v0 & apart_point_and_line(all_17_6, v0) = v1 & $i(v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (1) with all_17_7, all_17_6, simplifying with (19), % 16.19/3.25 | (20), (22) gives: % 16.19/3.25 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7, % 16.19/3.25 | all_17_6) = v0 & apart_point_and_line(all_17_7, v0) = v1 & $i(v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (4) with all_17_9, all_17_8, all_17_2, simplifying % 16.19/3.25 | with (17), (18), (25) gives: % 16.19/3.25 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.19/3.25 | apart_point_and_line(all_17_8, all_17_2) = v1) | ( ~ (v0 = 0) & % 16.19/3.25 | distinct_points(all_17_9, all_17_8) = v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (2) with all_17_9, all_17_8, all_17_2, simplifying % 16.19/3.25 | with (17), (18), (25) gives: % 16.19/3.25 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.19/3.25 | apart_point_and_line(all_17_9, all_17_2) = v1) | ( ~ (v0 = 0) & % 16.19/3.25 | distinct_points(all_17_9, all_17_8) = v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (4) with all_17_7, all_17_6, all_17_5, simplifying % 16.19/3.25 | with (19), (20), (26) gives: % 16.19/3.25 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.19/3.25 | apart_point_and_line(all_17_6, all_17_5) = v1) | ( ~ (v0 = 0) & % 16.19/3.25 | distinct_points(all_17_7, all_17_6) = v0)) % 16.19/3.25 | % 16.19/3.25 | GROUND_INST: instantiating (2) with all_17_7, all_17_6, all_17_5, simplifying % 16.19/3.25 | with (19), (20), (26) gives: % 16.19/3.25 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.19/3.25 | apart_point_and_line(all_17_7, all_17_5) = v1) | ( ~ (v0 = 0) & % 16.19/3.25 | distinct_points(all_17_7, all_17_6) = v0)) % 16.19/3.25 | % 16.19/3.25 | DELTA: instantiating (35) with fresh symbols all_24_0, all_24_1 gives: % 16.19/3.26 | (36) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) = % 16.19/3.26 | all_24_0) | ( ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6) % 16.19/3.26 | = all_24_1) % 16.19/3.26 | % 16.19/3.26 | DELTA: instantiating (34) with fresh symbols all_25_0, all_25_1 gives: % 16.19/3.26 | (37) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) = % 16.19/3.26 | all_25_0) | ( ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6) % 16.19/3.26 | = all_25_1) % 16.19/3.26 | % 16.19/3.26 | DELTA: instantiating (33) with fresh symbols all_26_0, all_26_1 gives: % 16.19/3.26 | (38) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) = % 16.19/3.26 | all_26_0) | ( ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8) % 16.19/3.26 | = all_26_1) % 16.19/3.26 | % 16.19/3.26 | DELTA: instantiating (31) with fresh symbols all_27_0, all_27_1 gives: % 16.19/3.26 | (39) ~ (all_27_0 = 0) & line_connecting(all_17_7, all_17_6) = all_27_1 & % 16.19/3.26 | apart_point_and_line(all_17_7, all_27_1) = all_27_0 & $i(all_27_1) % 16.19/3.26 | % 16.19/3.26 | ALPHA: (39) implies: % 16.19/3.26 | (40) ~ (all_27_0 = 0) % 16.19/3.26 | (41) $i(all_27_1) % 16.19/3.26 | (42) apart_point_and_line(all_17_7, all_27_1) = all_27_0 % 16.19/3.26 | (43) line_connecting(all_17_7, all_17_6) = all_27_1 % 16.19/3.26 | % 16.19/3.26 | DELTA: instantiating (30) with fresh symbols all_29_0, all_29_1 gives: % 16.19/3.26 | (44) ~ (all_29_0 = 0) & line_connecting(all_17_7, all_17_6) = all_29_1 & % 16.19/3.26 | apart_point_and_line(all_17_6, all_29_1) = all_29_0 & $i(all_29_1) % 16.19/3.26 | % 16.19/3.26 | ALPHA: (44) implies: % 16.19/3.26 | (45) ~ (all_29_0 = 0) % 16.19/3.26 | (46) apart_point_and_line(all_17_6, all_29_1) = all_29_0 % 16.19/3.26 | (47) line_connecting(all_17_7, all_17_6) = all_29_1 % 16.19/3.26 | % 16.19/3.26 | DELTA: instantiating (28) with fresh symbols all_31_0, all_31_1 gives: % 16.19/3.26 | (48) ~ (all_31_0 = 0) & line_connecting(all_17_9, all_17_8) = all_31_1 & % 16.19/3.26 | apart_point_and_line(all_17_8, all_31_1) = all_31_0 & $i(all_31_1) % 16.19/3.26 | % 16.19/3.26 | ALPHA: (48) implies: % 16.85/3.26 | (49) $i(all_31_1) % 16.85/3.26 | (50) apart_point_and_line(all_17_8, all_31_1) = all_31_0 % 16.85/3.26 | (51) line_connecting(all_17_9, all_17_8) = all_31_1 % 16.85/3.26 | % 16.85/3.26 | DELTA: instantiating (29) with fresh symbols all_33_0, all_33_1 gives: % 16.85/3.26 | (52) ~ (all_33_0 = 0) & line_connecting(all_17_9, all_17_8) = all_33_1 & % 16.85/3.26 | apart_point_and_line(all_17_9, all_33_1) = all_33_0 & $i(all_33_1) % 16.85/3.26 | % 16.85/3.26 | ALPHA: (52) implies: % 16.85/3.26 | (53) ~ (all_33_0 = 0) % 16.85/3.26 | (54) apart_point_and_line(all_17_9, all_33_1) = all_33_0 % 16.85/3.26 | (55) line_connecting(all_17_9, all_17_8) = all_33_1 % 16.85/3.26 | % 16.85/3.26 | DELTA: instantiating (32) with fresh symbols all_35_0, all_35_1 gives: % 16.85/3.26 | (56) ( ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) = % 16.85/3.26 | all_35_0) | ( ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8) % 16.85/3.26 | = all_35_1) % 16.85/3.26 | % 16.85/3.26 | BETA: splitting (56) gives: % 16.85/3.26 | % 16.85/3.26 | Case 1: % 16.85/3.26 | | % 16.85/3.26 | | (57) ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) = % 16.85/3.26 | | all_35_0 % 16.85/3.26 | | % 16.85/3.26 | | ALPHA: (57) implies: % 16.85/3.26 | | (58) ~ (all_35_0 = 0) % 16.85/3.26 | | (59) apart_point_and_line(all_17_8, all_17_2) = all_35_0 % 16.85/3.26 | | % 16.85/3.26 | | BETA: splitting (36) gives: % 16.85/3.26 | | % 16.85/3.26 | | Case 1: % 16.85/3.26 | | | % 16.85/3.26 | | | (60) ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) = % 16.85/3.26 | | | all_24_0 % 16.85/3.26 | | | % 16.85/3.26 | | | ALPHA: (60) implies: % 16.85/3.26 | | | (61) apart_point_and_line(all_17_7, all_17_5) = all_24_0 % 16.85/3.26 | | | % 16.85/3.26 | | | BETA: splitting (38) gives: % 16.85/3.26 | | | % 16.85/3.26 | | | Case 1: % 16.85/3.26 | | | | % 16.85/3.26 | | | | (62) ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) = % 16.85/3.26 | | | | all_26_0 % 16.85/3.26 | | | | % 16.85/3.26 | | | | ALPHA: (62) implies: % 16.85/3.26 | | | | (63) apart_point_and_line(all_17_9, all_17_2) = all_26_0 % 16.85/3.26 | | | | % 16.85/3.26 | | | | BETA: splitting (37) gives: % 16.85/3.26 | | | | % 16.85/3.26 | | | | Case 1: % 16.85/3.26 | | | | | % 16.85/3.26 | | | | | (64) ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) = % 16.85/3.26 | | | | | all_25_0 % 16.85/3.26 | | | | | % 16.85/3.26 | | | | | ALPHA: (64) implies: % 16.85/3.26 | | | | | (65) apart_point_and_line(all_17_6, all_17_5) = all_25_0 % 16.85/3.26 | | | | | % 16.85/3.26 | | | | | GROUND_INST: instantiating (13) with all_17_2, all_33_1, all_17_8, % 16.85/3.26 | | | | | all_17_9, simplifying with (25), (55) gives: % 16.85/3.26 | | | | | (66) all_33_1 = all_17_2 % 16.85/3.26 | | | | | % 16.85/3.26 | | | | | GROUND_INST: instantiating (13) with all_31_1, all_33_1, all_17_8, % 16.85/3.26 | | | | | all_17_9, simplifying with (51), (55) gives: % 16.85/3.26 | | | | | (67) all_33_1 = all_31_1 % 16.85/3.26 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (13) with all_17_5, all_29_1, all_17_6, % 16.85/3.27 | | | | | all_17_7, simplifying with (26), (47) gives: % 16.85/3.27 | | | | | (68) all_29_1 = all_17_5 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (13) with all_27_1, all_29_1, all_17_6, % 16.85/3.27 | | | | | all_17_7, simplifying with (43), (47) gives: % 16.85/3.27 | | | | | (69) all_29_1 = all_27_1 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | COMBINE_EQS: (66), (67) imply: % 16.85/3.27 | | | | | (70) all_31_1 = all_17_2 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | SIMP: (70) implies: % 16.85/3.27 | | | | | (71) all_31_1 = all_17_2 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | COMBINE_EQS: (68), (69) imply: % 16.85/3.27 | | | | | (72) all_27_1 = all_17_5 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | SIMP: (72) implies: % 16.85/3.27 | | | | | (73) all_27_1 = all_17_5 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (46), (68) imply: % 16.85/3.27 | | | | | (74) apart_point_and_line(all_17_6, all_17_5) = all_29_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (42), (73) imply: % 16.85/3.27 | | | | | (75) apart_point_and_line(all_17_7, all_17_5) = all_27_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (50), (71) imply: % 16.85/3.27 | | | | | (76) apart_point_and_line(all_17_8, all_17_2) = all_31_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (54), (66) imply: % 16.85/3.27 | | | | | (77) apart_point_and_line(all_17_9, all_17_2) = all_33_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (49), (71) imply: % 16.85/3.27 | | | | | (78) $i(all_17_2) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (41), (73) imply: % 16.85/3.27 | | | | | (79) $i(all_17_5) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (12) with all_26_0, all_33_0, all_17_2, % 16.85/3.27 | | | | | all_17_9, simplifying with (63), (77) gives: % 16.85/3.27 | | | | | (80) all_33_0 = all_26_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (12) with all_35_0, all_31_0, all_17_2, % 16.85/3.27 | | | | | all_17_8, simplifying with (59), (76) gives: % 16.85/3.27 | | | | | (81) all_35_0 = all_31_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (12) with all_24_0, all_27_0, all_17_5, % 16.85/3.27 | | | | | all_17_7, simplifying with (61), (75) gives: % 16.85/3.27 | | | | | (82) all_27_0 = all_24_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (12) with all_25_0, all_29_0, all_17_5, % 16.85/3.27 | | | | | all_17_6, simplifying with (65), (74) gives: % 16.85/3.27 | | | | | (83) all_29_0 = all_25_0 % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (58), (81) imply: % 16.85/3.27 | | | | | (84) ~ (all_31_0 = 0) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (53), (80) imply: % 16.85/3.27 | | | | | (85) ~ (all_26_0 = 0) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (45), (83) imply: % 16.85/3.27 | | | | | (86) ~ (all_25_0 = 0) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | REDUCE: (40), (82) imply: % 16.85/3.27 | | | | | (87) ~ (all_24_0 = 0) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (7) with all_17_9, all_17_8, all_17_2, % 16.85/3.27 | | | | | all_17_5, all_26_0, all_17_3, simplifying with (17), % 16.85/3.27 | | | | | (18), (24), (63), (78), (79) gives: % 16.85/3.27 | | | | | (88) all_26_0 = 0 | all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? % 16.85/3.27 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 16.85/3.27 | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) | (v2 = 0 & % 16.85/3.27 | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | ( ~ (v1 = % 16.85/3.27 | | | | | 0) & distinct_lines(all_17_2, all_17_5) = v1) | ( ~ (v0 % 16.85/3.27 | | | | | = 0) & distinct_points(all_17_9, all_17_8) = v0)) % 16.85/3.27 | | | | | % 16.85/3.27 | | | | | GROUND_INST: instantiating (5) with all_17_9, all_17_8, all_17_2, % 16.85/3.27 | | | | | all_17_5, all_26_0, all_17_4, simplifying with (17), % 16.85/3.27 | | | | | (18), (21), (23), (63), (78), (79) gives: % 17.16/3.27 | | | | | (89) all_26_0 = 0 | all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.16/3.27 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_8, % 17.16/3.27 | | | | | all_17_5) = 0) | (v1 = 0 & % 17.16/3.27 | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) | ( ~ (v0 = % 17.16/3.27 | | | | | 0) & distinct_lines(all_17_2, all_17_5) = v0)) % 17.16/3.27 | | | | | % 17.16/3.28 | | | | | GROUND_INST: instantiating (8) with all_17_9, all_17_8, all_17_2, % 17.16/3.28 | | | | | all_17_5, all_31_0, all_17_3, simplifying with (17), % 17.16/3.28 | | | | | (18), (21), (24), (76), (78), (79) gives: % 17.16/3.28 | | | | | (90) all_31_0 = 0 | all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.16/3.28 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.28 | | | | | all_17_5) = 0) | (v1 = 0 & % 17.16/3.28 | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | ( ~ (v0 = % 17.16/3.28 | | | | | 0) & distinct_lines(all_17_2, all_17_5) = v0)) % 17.16/3.28 | | | | | % 17.16/3.28 | | | | | GROUND_INST: instantiating (6) with all_17_9, all_17_8, all_17_2, % 17.16/3.28 | | | | | all_17_5, all_17_4, all_31_0, simplifying with (17), % 17.16/3.28 | | | | | (18), (23), (76), (78), (79) gives: % 17.16/3.28 | | | | | (91) all_31_0 = 0 | all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.16/3.28 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 17.16/3.28 | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) | (v2 = 0 & % 17.16/3.28 | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | ( ~ (v1 = % 17.16/3.28 | | | | | 0) & distinct_lines(all_17_2, all_17_5) = v1) | ( ~ (v0 % 17.16/3.28 | | | | | = 0) & distinct_points(all_17_9, all_17_8) = v0)) % 17.16/3.28 | | | | | % 17.16/3.28 | | | | | BETA: splitting (27) gives: % 17.16/3.28 | | | | | % 17.16/3.28 | | | | | Case 1: % 17.16/3.28 | | | | | | % 17.16/3.28 | | | | | | (92) all_17_0 = 0 & apart_point_and_line(all_17_6, all_17_2) = 0 % 17.16/3.28 | | | | | | % 17.16/3.28 | | | | | | ALPHA: (92) implies: % 17.16/3.28 | | | | | | (93) apart_point_and_line(all_17_6, all_17_2) = 0 % 17.16/3.28 | | | | | | % 17.16/3.28 | | | | | | BETA: splitting (88) gives: % 17.16/3.28 | | | | | | % 17.16/3.28 | | | | | | Case 1: % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | (94) all_26_0 = 0 % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | REDUCE: (85), (94) imply: % 17.16/3.28 | | | | | | | (95) $false % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | CLOSE: (95) is inconsistent. % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | Case 2: % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | (96) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 17.16/3.28 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_8, % 17.16/3.28 | | | | | | | all_17_2) = 0) | (v2 = 0 & % 17.16/3.28 | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | ( ~ % 17.16/3.28 | | | | | | | (v1 = 0) & distinct_lines(all_17_2, all_17_5) = v1) | % 17.16/3.28 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_9, all_17_8) = % 17.16/3.28 | | | | | | | v0)) % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | BETA: splitting (90) gives: % 17.16/3.28 | | | | | | | % 17.16/3.28 | | | | | | | Case 1: % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | (97) all_31_0 = 0 % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | REDUCE: (84), (97) imply: % 17.16/3.28 | | | | | | | | (98) $false % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | CLOSE: (98) is inconsistent. % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | Case 2: % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | (99) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.16/3.28 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.28 | | | | | | | | all_17_5) = 0) | (v1 = 0 & % 17.16/3.28 | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | ( ~ % 17.16/3.28 | | | | | | | | (v0 = 0) & distinct_lines(all_17_2, all_17_5) = v0)) % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | BETA: splitting (91) gives: % 17.16/3.28 | | | | | | | | % 17.16/3.28 | | | | | | | | Case 1: % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | (100) all_31_0 = 0 % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | REDUCE: (84), (100) imply: % 17.16/3.28 | | | | | | | | | (101) $false % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | CLOSE: (101) is inconsistent. % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | Case 2: % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | (102) all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.16/3.28 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 17.16/3.28 | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) | % 17.16/3.28 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, all_17_2) % 17.16/3.28 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_2, % 17.16/3.28 | | | | | | | | | all_17_5) = v1) | ( ~ (v0 = 0) & % 17.16/3.28 | | | | | | | | | distinct_points(all_17_9, all_17_8) = v0)) % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | BETA: splitting (89) gives: % 17.16/3.28 | | | | | | | | | % 17.16/3.28 | | | | | | | | | Case 1: % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | (103) all_26_0 = 0 % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | REDUCE: (85), (103) imply: % 17.16/3.28 | | | | | | | | | | (104) $false % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | CLOSE: (104) is inconsistent. % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | Case 2: % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | (105) all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.16/3.28 | | | | | | | | | | [v2: int] : ((v2 = 0 & % 17.16/3.28 | | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) | % 17.16/3.28 | | | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.28 | | | | | | | | | | all_17_2) = 0) | ( ~ (v0 = 0) & % 17.16/3.28 | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v0)) % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | BETA: splitting (96) gives: % 17.16/3.28 | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | Case 1: % 17.16/3.28 | | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | | (106) all_17_3 = 0 % 17.16/3.28 | | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | | REDUCE: (16), (106) imply: % 17.16/3.28 | | | | | | | | | | | (107) $false % 17.16/3.28 | | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | | CLOSE: (107) is inconsistent. % 17.16/3.28 | | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | Case 2: % 17.16/3.28 | | | | | | | | | | | % 17.16/3.28 | | | | | | | | | | | (108) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.16/3.28 | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.16/3.28 | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) % 17.16/3.28 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.28 | | | | | | | | | | | all_17_5) = 0) | ( ~ (v1 = 0) & % 17.16/3.29 | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v1) | ( ~ % 17.16/3.29 | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_9, all_17_8) % 17.16/3.29 | | | | | | | | | | | = v0)) % 17.16/3.29 | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_306_0, % 17.16/3.29 | | | | | | | | | | | all_306_1, all_306_2, all_306_3 gives: % 17.16/3.29 | | | | | | | | | | | (109) (all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | all_17_2) = 0) | (all_306_1 = 0 & % 17.16/3.29 | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | % 17.16/3.29 | | | | | | | | | | | ( ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | all_17_5) = all_306_2) | ( ~ (all_306_3 = 0) & % 17.16/3.29 | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_306_3) % 17.16/3.29 | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | BETA: splitting (99) gives: % 17.16/3.29 | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | (110) all_17_3 = 0 % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | REDUCE: (16), (110) imply: % 17.16/3.29 | | | | | | | | | | | | (111) $false % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | (112) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.16/3.29 | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_9, all_17_5) % 17.16/3.29 | | | | | | | | | | | | = 0) | (v1 = 0 & % 17.16/3.29 | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) % 17.16/3.29 | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | all_17_5) = v0)) % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | DELTA: instantiating (112) with fresh symbols all_314_0, % 17.16/3.29 | | | | | | | | | | | | all_314_1, all_314_2 gives: % 17.16/3.29 | | | | | | | | | | | | (113) (all_314_0 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | all_17_5) = 0) | (all_314_1 = 0 & % 17.16/3.29 | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | % 17.16/3.29 | | | | | | | | | | | | ( ~ (all_314_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | all_17_5) = all_314_2) % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | BETA: splitting (102) gives: % 17.16/3.29 | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | (114) all_17_4 = 0 % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | REDUCE: (15), (114) imply: % 17.16/3.29 | | | | | | | | | | | | | (115) $false % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | CLOSE: (115) is inconsistent. % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | (116) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.16/3.29 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.16/3.29 | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) % 17.16/3.29 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) & % 17.16/3.29 | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v1) | ( ~ % 17.16/3.29 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_9, all_17_8) % 17.16/3.29 | | | | | | | | | | | | | = v0)) % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_322_0, % 17.16/3.29 | | | | | | | | | | | | | all_322_1, all_322_2, all_322_3 gives: % 17.16/3.29 | | | | | | | | | | | | | (117) (all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | all_17_5) = 0) | (all_322_1 = 0 & % 17.16/3.29 | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | % 17.16/3.29 | | | | | | | | | | | | | ( ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | all_17_5) = all_322_2) | ( ~ (all_322_3 = 0) & % 17.16/3.29 | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_322_3) % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | BETA: splitting (105) gives: % 17.16/3.29 | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | (118) all_17_4 = 0 % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | REDUCE: (15), (118) imply: % 17.16/3.29 | | | | | | | | | | | | | | (119) $false % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | (120) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.16/3.29 | | | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_8, all_17_5) % 17.16/3.29 | | | | | | | | | | | | | | = 0) | (v1 = 0 & % 17.16/3.29 | | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) % 17.16/3.29 | | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | all_17_5) = v0)) % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | DELTA: instantiating (120) with fresh symbols all_326_0, % 17.16/3.29 | | | | | | | | | | | | | | all_326_1, all_326_2 gives: % 17.16/3.29 | | | | | | | | | | | | | | (121) (all_326_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | all_17_5) = 0) | (all_326_1 = 0 & % 17.16/3.29 | | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) | % 17.16/3.29 | | | | | | | | | | | | | | ( ~ (all_326_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | all_17_5) = all_326_2) % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | BETA: splitting (113) gives: % 17.16/3.29 | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | (122) all_314_0 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | ALPHA: (122) implies: % 17.16/3.29 | | | | | | | | | | | | | | | (123) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (123) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | sub-proof #4. % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | (124) (all_314_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_314_2 = 0) & % 17.16/3.29 | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = all_314_2) % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 17.16/3.29 | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | (125) all_314_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | ALPHA: (125) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | (126) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (85), (126) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | | sub-proof #3. % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | (127) ~ (all_314_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | | | all_17_5) = all_314_2 % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | (128) ~ (all_314_2 = 0) % 17.16/3.29 | | | | | | | | | | | | | | | | (129) distinct_lines(all_17_2, all_17_5) = all_314_2 % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | (130) all_326_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | ALPHA: (130) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | (131) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (24), (131) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | | | sub-proof #2. % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | (132) (all_326_1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_326_2 = 0) & % 17.16/3.29 | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = all_326_2) % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | (133) all_326_1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | ALPHA: (133) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | | (134) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (76), (84), (134) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | | | | sub-proof #1. % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | (135) ~ (all_326_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | | | | | all_17_5) = all_326_2 % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | ALPHA: (135) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | | (136) distinct_lines(all_17_2, all_17_5) = all_326_2 % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | (137) (all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | | | | | | all_17_5) = 0) | (all_322_1 = 0 & % 17.16/3.29 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (138) all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (139) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (24), (139) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (140) all_322_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (141) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (85), (141) are inconsistent by % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | (142) ( ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | | | | | | all_17_5) = all_322_2) | ( ~ (all_322_3 = 0) & % 17.16/3.29 | | | | | | | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_322_3) % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (143) ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | all_17_5) = all_322_2 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | (144) distinct_lines(all_17_2, all_17_5) = all_322_2 % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.29 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | (145) (all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0) | (all_306_1 = 0 & % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (146) all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (147) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (76), (84), (147) are inconsistent by % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (148) all_306_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (149) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (149) are inconsistent by % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | (150) ( ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_306_2) | ( ~ (all_306_3 = 0) & % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_306_3) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (152) distinct_lines(all_17_2, all_17_5) = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_314_2, all_322_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (129), (144) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (153) all_322_2 = all_314_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_322_2, all_326_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (136), (144) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (154) all_326_2 = all_322_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_306_2, all_326_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (136), (152) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (155) all_326_2 = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (155) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (156) all_322_2 = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | SIMP: (156) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (157) all_322_2 = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (157) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (158) all_314_2 = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | SIMP: (158) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (159) all_314_2 = all_306_2 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (159) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (160) ~ (all_306_2 = 0) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_17_6, all_17_2, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_306_2, simplifying with (20), (78), % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (79), (93), (152) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (161) all_306_2 = 0 | apart_point_and_line(all_17_6, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | (162) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_25_0, 0, all_17_5, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | all_17_6, simplifying with (65), (162) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | (163) all_25_0 = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (163) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | (164) $false % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | (165) all_306_2 = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (165) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | (166) $false % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_306_3 = 0) & distinct_points(all_17_9, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_8) = all_306_3 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (168) ~ (all_306_3 = 0) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (169) distinct_points(all_17_9, all_17_8) = all_306_3 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_306_3, all_17_8, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | all_17_9, simplifying with (21), (169) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (170) all_306_3 = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (170) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | (171) $false % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | (172) ~ (all_322_3 = 0) & distinct_points(all_17_9, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | all_17_8) = all_322_3 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | (173) ~ (all_322_3 = 0) % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | (174) distinct_points(all_17_9, all_17_8) = all_322_3 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_322_3, all_17_8, % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | all_17_9, simplifying with (21), (174) gives: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | (175) all_322_3 = 0 % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (175) imply: % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | (176) $false % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 17.16/3.30 | | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | End of split % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | End of split % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | End of split % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | End of split % 17.16/3.30 | | | | | | % 17.16/3.30 | | | | | Case 2: % 17.16/3.30 | | | | | | % 17.16/3.30 | | | | | | (177) all_17_1 = 0 & apart_point_and_line(all_17_7, all_17_2) = 0 % 17.16/3.30 | | | | | | % 17.16/3.30 | | | | | | ALPHA: (177) implies: % 17.16/3.30 | | | | | | (178) apart_point_and_line(all_17_7, all_17_2) = 0 % 17.16/3.30 | | | | | | % 17.16/3.30 | | | | | | BETA: splitting (88) gives: % 17.16/3.30 | | | | | | % 17.16/3.30 | | | | | | Case 1: % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | (179) all_26_0 = 0 % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | REDUCE: (85), (179) imply: % 17.16/3.30 | | | | | | | (180) $false % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | CLOSE: (180) is inconsistent. % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | Case 2: % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | (181) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 17.16/3.30 | | | | | | | : ? [v3: int] : ((v3 = 0 & % 17.16/3.30 | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) | (v2 = % 17.16/3.30 | | | | | | | 0 & apart_point_and_line(all_17_9, all_17_5) = 0) | ( % 17.16/3.30 | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_2, all_17_5) = v1) % 17.16/3.30 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_9, all_17_8) = % 17.16/3.30 | | | | | | | v0)) % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | BETA: splitting (90) gives: % 17.16/3.30 | | | | | | | % 17.16/3.30 | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | (182) all_31_0 = 0 % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | REDUCE: (84), (182) imply: % 17.16/3.30 | | | | | | | | (183) $false % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | CLOSE: (183) is inconsistent. % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | (184) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.16/3.30 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.30 | | | | | | | | all_17_5) = 0) | (v1 = 0 & % 17.16/3.30 | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | ( ~ % 17.16/3.30 | | | | | | | | (v0 = 0) & distinct_lines(all_17_2, all_17_5) = % 17.16/3.30 | | | | | | | | v0)) % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | BETA: splitting (91) gives: % 17.16/3.30 | | | | | | | | % 17.16/3.30 | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | (185) all_31_0 = 0 % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | REDUCE: (84), (185) imply: % 17.16/3.30 | | | | | | | | | (186) $false % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | CLOSE: (186) is inconsistent. % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | (187) all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.16/3.30 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 17.16/3.30 | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) | % 17.16/3.30 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, all_17_2) % 17.16/3.30 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_2, % 17.16/3.30 | | | | | | | | | all_17_5) = v1) | ( ~ (v0 = 0) & % 17.16/3.30 | | | | | | | | | distinct_points(all_17_9, all_17_8) = v0)) % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | BETA: splitting (89) gives: % 17.16/3.30 | | | | | | | | | % 17.16/3.30 | | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | (188) all_26_0 = 0 % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | REDUCE: (85), (188) imply: % 17.16/3.30 | | | | | | | | | | (189) $false % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | CLOSE: (189) is inconsistent. % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | Case 2: % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | (190) all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.16/3.30 | | | | | | | | | | [v2: int] : ((v2 = 0 & % 17.16/3.30 | | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) | % 17.16/3.30 | | | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.30 | | | | | | | | | | all_17_2) = 0) | ( ~ (v0 = 0) & % 17.16/3.30 | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v0)) % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | BETA: splitting (181) gives: % 17.16/3.30 | | | | | | | | | | % 17.16/3.30 | | | | | | | | | | Case 1: % 17.16/3.30 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | (191) all_17_3 = 0 % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | REDUCE: (16), (191) imply: % 17.16/3.31 | | | | | | | | | | | (192) $false % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | CLOSE: (192) is inconsistent. % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | (193) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.16/3.31 | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.16/3.31 | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) % 17.16/3.31 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | all_17_5) = 0) | ( ~ (v1 = 0) & % 17.16/3.31 | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v1) | ( ~ % 17.16/3.31 | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_9, all_17_8) % 17.16/3.31 | | | | | | | | | | | = v0)) % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | DELTA: instantiating (193) with fresh symbols all_306_0, % 17.16/3.31 | | | | | | | | | | | all_306_1, all_306_2, all_306_3 gives: % 17.16/3.31 | | | | | | | | | | | (194) (all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | all_17_2) = 0) | (all_306_1 = 0 & % 17.16/3.31 | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | % 17.16/3.31 | | | | | | | | | | | ( ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | all_17_5) = all_306_2) | ( ~ (all_306_3 = 0) & % 17.16/3.31 | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_306_3) % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | BETA: splitting (184) gives: % 17.16/3.31 | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | (195) all_17_3 = 0 % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | REDUCE: (16), (195) imply: % 17.16/3.31 | | | | | | | | | | | | (196) $false % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | (197) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.16/3.31 | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_9, all_17_5) % 17.16/3.31 | | | | | | | | | | | | = 0) | (v1 = 0 & % 17.16/3.31 | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) % 17.16/3.31 | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | all_17_5) = v0)) % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_314_0, % 17.16/3.31 | | | | | | | | | | | | all_314_1, all_314_2 gives: % 17.16/3.31 | | | | | | | | | | | | (198) (all_314_0 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | all_17_5) = 0) | (all_314_1 = 0 & % 17.16/3.31 | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | % 17.16/3.31 | | | | | | | | | | | | ( ~ (all_314_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | all_17_5) = all_314_2) % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | BETA: splitting (187) gives: % 17.16/3.31 | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | (199) all_17_4 = 0 % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | REDUCE: (15), (199) imply: % 17.16/3.31 | | | | | | | | | | | | | (200) $false % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | (201) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.16/3.31 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.16/3.31 | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_5) = 0) % 17.16/3.31 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) & % 17.16/3.31 | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = v1) | ( ~ % 17.16/3.31 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_9, all_17_8) % 17.16/3.31 | | | | | | | | | | | | | = v0)) % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | DELTA: instantiating (201) with fresh symbols all_322_0, % 17.16/3.31 | | | | | | | | | | | | | all_322_1, all_322_2, all_322_3 gives: % 17.16/3.31 | | | | | | | | | | | | | (202) (all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | all_17_5) = 0) | (all_322_1 = 0 & % 17.16/3.31 | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) | % 17.16/3.31 | | | | | | | | | | | | | ( ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | all_17_5) = all_322_2) | ( ~ (all_322_3 = 0) & % 17.16/3.31 | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_322_3) % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | BETA: splitting (190) gives: % 17.16/3.31 | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | (203) all_17_4 = 0 % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | REDUCE: (15), (203) imply: % 17.16/3.31 | | | | | | | | | | | | | | (204) $false % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | CLOSE: (204) is inconsistent. % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | (205) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.16/3.31 | | | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_8, all_17_5) % 17.16/3.31 | | | | | | | | | | | | | | = 0) | (v1 = 0 & % 17.16/3.31 | | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) % 17.16/3.31 | | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | all_17_5) = v0)) % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_326_0, % 17.16/3.31 | | | | | | | | | | | | | | all_326_1, all_326_2 gives: % 17.16/3.31 | | | | | | | | | | | | | | (206) (all_326_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | all_17_5) = 0) | (all_326_1 = 0 & % 17.16/3.31 | | | | | | | | | | | | | | apart_point_and_line(all_17_8, all_17_2) = 0) | % 17.16/3.31 | | | | | | | | | | | | | | ( ~ (all_326_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | all_17_5) = all_326_2) % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | BETA: splitting (198) gives: % 17.16/3.31 | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | (207) all_314_0 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | ALPHA: (207) implies: % 17.16/3.31 | | | | | | | | | | | | | | | (208) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (208) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | sub-proof #4. % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | (209) (all_314_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_314_2 = 0) & % 17.16/3.31 | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = all_314_2) % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 17.16/3.31 | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | (210) all_314_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | (211) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (85), (211) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | sub-proof #3. % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | (212) ~ (all_314_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | | | all_17_5) = all_314_2 % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | (213) ~ (all_314_2 = 0) % 17.16/3.31 | | | | | | | | | | | | | | | | (214) distinct_lines(all_17_2, all_17_5) = all_314_2 % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | (215) all_326_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | (216) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (24), (216) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | | sub-proof #2. % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | (217) (all_326_1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_326_2 = 0) & % 17.16/3.31 | | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_5) = all_326_2) % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | (218) all_326_1 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | (219) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (76), (84), (219) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | | | sub-proof #1. % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | (220) ~ (all_326_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | | | | | all_17_5) = all_326_2 % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | (221) distinct_lines(all_17_2, all_17_5) = all_326_2 % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | (222) (all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | all_17_5) = 0) | (all_322_1 = 0 & % 17.16/3.31 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_2) = 0) % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (223) all_322_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (224) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (24), (224) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (225) all_322_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (226) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (85), (226) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | (227) ( ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | all_17_5) = all_322_2) | ( ~ (all_322_3 = 0) & % 17.16/3.31 | | | | | | | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_322_3) % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (228) ~ (all_322_2 = 0) & distinct_lines(all_17_2, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | all_17_5) = all_322_2 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | (229) distinct_lines(all_17_2, all_17_5) = all_322_2 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | (230) (all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0) | (all_306_1 = 0 & % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | (231) all_306_0 = 0 & apart_point_and_line(all_17_8, % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | (232) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (76), (84), (232) are inconsistent by % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.31 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (233) all_306_1 = 0 & apart_point_and_line(all_17_9, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (234) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (234) are inconsistent by % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | End of split % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | Case 2: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | (235) ( ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_306_2) | ( ~ (all_306_3 = 0) & % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_9, all_17_8) = all_306_3) % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_306_2 = 0) & distinct_lines(all_17_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (237) distinct_lines(all_17_2, all_17_5) = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_314_2, all_322_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (214), (229) % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (238) all_322_2 = all_314_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_322_2, all_326_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (221), (229) % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (239) all_326_2 = all_322_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_306_2, all_326_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_17_2, simplifying with (221), (237) % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | gives: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (240) all_326_2 = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (240) imply: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (241) all_322_2 = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (242) all_322_2 = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (242) imply: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (243) all_314_2 = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | SIMP: (243) implies: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (244) all_314_2 = all_306_2 % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (244) imply: % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_306_2 = 0) % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_17_7, all_17_2, % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5, all_306_2, simplifying with (19), (78), % 17.16/3.32 | | | | | | | | | | | | | | | | | | | | | | (79), (178), (237) gives: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (246) all_306_2 = 0 | apart_point_and_line(all_17_7, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | (247) apart_point_and_line(all_17_7, all_17_5) = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_24_0, 0, all_17_5, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | all_17_7, simplifying with (61), (247) gives: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | (248) all_24_0 = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (248) imply: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | (249) $false % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent. % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | (250) all_306_2 = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (250) imply: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | (251) $false % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | Case 2: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_306_3 = 0) & distinct_points(all_17_9, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_8) = all_306_3 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_306_3 = 0) % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (254) distinct_points(all_17_9, all_17_8) = all_306_3 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_306_3, all_17_8, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | all_17_9, simplifying with (21), (254) gives: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (255) all_306_3 = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (255) imply: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | (256) $false % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | Case 2: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | (257) ~ (all_322_3 = 0) & distinct_points(all_17_9, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | all_17_8) = all_322_3 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | (258) ~ (all_322_3 = 0) % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | (259) distinct_points(all_17_9, all_17_8) = all_322_3 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_322_3, all_17_8, % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | all_17_9, simplifying with (21), (259) gives: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | (260) all_322_3 = 0 % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (260) imply: % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | (261) $false % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 17.38/3.32 | | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | | % 17.38/3.32 | | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | | % 17.38/3.32 | | | | | | | | | End of split % 17.38/3.32 | | | | | | | | | % 17.38/3.32 | | | | | | | | End of split % 17.38/3.32 | | | | | | | | % 17.38/3.32 | | | | | | | End of split % 17.38/3.32 | | | | | | | % 17.38/3.32 | | | | | | End of split % 17.38/3.32 | | | | | | % 17.38/3.32 | | | | | End of split % 17.38/3.32 | | | | | % 17.38/3.32 | | | | Case 2: % 17.38/3.32 | | | | | % 17.38/3.32 | | | | | (262) ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6) = % 17.38/3.32 | | | | | all_25_1 % 17.38/3.32 | | | | | % 17.38/3.32 | | | | | ALPHA: (262) implies: % 17.38/3.32 | | | | | (263) ~ (all_25_1 = 0) % 17.38/3.32 | | | | | (264) distinct_points(all_17_7, all_17_6) = all_25_1 % 17.38/3.32 | | | | | % 17.38/3.32 | | | | | GROUND_INST: instantiating (10) with 0, all_25_1, all_17_6, all_17_7, % 17.38/3.32 | | | | | simplifying with (22), (264) gives: % 17.38/3.32 | | | | | (265) all_25_1 = 0 % 17.38/3.32 | | | | | % 17.38/3.32 | | | | | REDUCE: (263), (265) imply: % 17.38/3.32 | | | | | (266) $false % 17.38/3.32 | | | | | % 17.38/3.32 | | | | | CLOSE: (266) is inconsistent. % 17.38/3.32 | | | | | % 17.38/3.32 | | | | End of split % 17.38/3.32 | | | | % 17.38/3.32 | | | Case 2: % 17.38/3.32 | | | | % 17.38/3.32 | | | | (267) ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8) = % 17.38/3.32 | | | | all_26_1 % 17.38/3.32 | | | | % 17.38/3.32 | | | | ALPHA: (267) implies: % 17.38/3.32 | | | | (268) ~ (all_26_1 = 0) % 17.38/3.32 | | | | (269) distinct_points(all_17_9, all_17_8) = all_26_1 % 17.38/3.32 | | | | % 17.38/3.32 | | | | GROUND_INST: instantiating (10) with 0, all_26_1, all_17_8, all_17_9, % 17.38/3.32 | | | | simplifying with (21), (269) gives: % 17.38/3.32 | | | | (270) all_26_1 = 0 % 17.38/3.32 | | | | % 17.38/3.32 | | | | REDUCE: (268), (270) imply: % 17.38/3.32 | | | | (271) $false % 17.38/3.32 | | | | % 17.38/3.32 | | | | CLOSE: (271) is inconsistent. % 17.38/3.32 | | | | % 17.38/3.32 | | | End of split % 17.38/3.32 | | | % 17.38/3.32 | | Case 2: % 17.38/3.32 | | | % 17.38/3.32 | | | (272) ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6) = % 17.38/3.32 | | | all_24_1 % 17.38/3.32 | | | % 17.38/3.32 | | | ALPHA: (272) implies: % 17.38/3.32 | | | (273) ~ (all_24_1 = 0) % 17.38/3.32 | | | (274) distinct_points(all_17_7, all_17_6) = all_24_1 % 17.38/3.32 | | | % 17.38/3.32 | | | GROUND_INST: instantiating (10) with 0, all_24_1, all_17_6, all_17_7, % 17.38/3.32 | | | simplifying with (22), (274) gives: % 17.38/3.32 | | | (275) all_24_1 = 0 % 17.38/3.32 | | | % 17.38/3.32 | | | REDUCE: (273), (275) imply: % 17.38/3.32 | | | (276) $false % 17.38/3.32 | | | % 17.38/3.32 | | | CLOSE: (276) is inconsistent. % 17.38/3.32 | | | % 17.38/3.32 | | End of split % 17.38/3.32 | | % 17.38/3.32 | Case 2: % 17.38/3.32 | | % 17.38/3.32 | | (277) ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8) = all_35_1 % 17.38/3.32 | | % 17.38/3.32 | | ALPHA: (277) implies: % 17.38/3.32 | | (278) ~ (all_35_1 = 0) % 17.38/3.32 | | (279) distinct_points(all_17_9, all_17_8) = all_35_1 % 17.38/3.32 | | % 17.38/3.32 | | GROUND_INST: instantiating (10) with 0, all_35_1, all_17_8, all_17_9, % 17.38/3.32 | | simplifying with (21), (279) gives: % 17.38/3.32 | | (280) all_35_1 = 0 % 17.38/3.32 | | % 17.38/3.32 | | REDUCE: (278), (280) imply: % 17.38/3.32 | | (281) $false % 17.38/3.32 | | % 17.38/3.32 | | CLOSE: (281) is inconsistent. % 17.38/3.32 | | % 17.38/3.32 | End of split % 17.38/3.32 | % 17.38/3.32 End of proof % 17.38/3.32 % 17.38/3.32 Sub-proof #1 shows that the following formulas are inconsistent: % 17.38/3.32 ---------------------------------------------------------------- % 17.38/3.32 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.38/3.32 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.38/3.32 (apart_point_and_line(v3, v2) = v0)) % 17.38/3.32 (2) apart_point_and_line(all_17_8, all_17_2) = all_31_0 % 17.38/3.32 (3) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.38/3.32 (4) ~ (all_31_0 = 0) % 17.38/3.33 % 17.38/3.33 Begin of proof % 17.38/3.33 | % 17.38/3.33 | GROUND_INST: instantiating (1) with all_31_0, 0, all_17_2, all_17_8, % 17.38/3.33 | simplifying with (2), (3) gives: % 17.38/3.33 | (5) all_31_0 = 0 % 17.38/3.33 | % 17.38/3.33 | REDUCE: (4), (5) imply: % 17.38/3.33 | (6) $false % 17.38/3.33 | % 17.38/3.33 | CLOSE: (6) is inconsistent. % 17.38/3.33 | % 17.38/3.33 End of proof % 17.38/3.33 % 17.38/3.33 Sub-proof #2 shows that the following formulas are inconsistent: % 17.38/3.33 ---------------------------------------------------------------- % 17.38/3.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.38/3.33 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.38/3.33 (apart_point_and_line(v3, v2) = v0)) % 17.38/3.33 (2) apart_point_and_line(all_17_8, all_17_5) = all_17_3 % 17.38/3.33 (3) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.38/3.33 (4) ~ (all_17_3 = 0) % 17.38/3.33 % 17.38/3.33 Begin of proof % 17.38/3.33 | % 17.38/3.33 | GROUND_INST: instantiating (1) with all_17_3, 0, all_17_5, all_17_8, % 17.38/3.33 | simplifying with (2), (3) gives: % 17.38/3.33 | (5) all_17_3 = 0 % 17.38/3.33 | % 17.38/3.33 | REDUCE: (4), (5) imply: % 17.38/3.33 | (6) $false % 17.38/3.33 | % 17.38/3.33 | CLOSE: (6) is inconsistent. % 17.38/3.33 | % 17.38/3.33 End of proof % 17.38/3.33 % 17.38/3.33 Sub-proof #3 shows that the following formulas are inconsistent: % 17.38/3.33 ---------------------------------------------------------------- % 17.38/3.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.38/3.33 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.38/3.33 (apart_point_and_line(v3, v2) = v0)) % 17.38/3.33 (2) apart_point_and_line(all_17_9, all_17_2) = all_26_0 % 17.38/3.33 (3) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.38/3.33 (4) ~ (all_26_0 = 0) % 17.38/3.33 % 17.38/3.33 Begin of proof % 17.38/3.33 | % 17.38/3.33 | GROUND_INST: instantiating (1) with all_26_0, 0, all_17_2, all_17_9, % 17.38/3.33 | simplifying with (2), (3) gives: % 17.38/3.33 | (5) all_26_0 = 0 % 17.38/3.33 | % 17.38/3.33 | REDUCE: (4), (5) imply: % 17.38/3.33 | (6) $false % 17.38/3.33 | % 17.38/3.33 | CLOSE: (6) is inconsistent. % 17.38/3.33 | % 17.38/3.33 End of proof % 17.38/3.33 % 17.38/3.33 Sub-proof #4 shows that the following formulas are inconsistent: % 17.38/3.33 ---------------------------------------------------------------- % 17.38/3.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.38/3.33 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.38/3.33 (apart_point_and_line(v3, v2) = v0)) % 17.38/3.33 (2) apart_point_and_line(all_17_9, all_17_5) = all_17_4 % 17.38/3.33 (3) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.38/3.33 (4) ~ (all_17_4 = 0) % 17.38/3.33 % 17.38/3.33 Begin of proof % 17.38/3.33 | % 17.38/3.33 | GROUND_INST: instantiating (1) with all_17_4, 0, all_17_5, all_17_9, % 17.38/3.33 | simplifying with (2), (3) gives: % 17.38/3.33 | (5) all_17_4 = 0 % 17.38/3.33 | % 17.38/3.33 | REDUCE: (4), (5) imply: % 17.38/3.33 | (6) $false % 17.38/3.33 | % 17.38/3.33 | CLOSE: (6) is inconsistent. % 17.38/3.33 | % 17.38/3.33 End of proof % 17.38/3.33 % SZS output end Proof for theBenchmark % 17.38/3.33 % 17.38/3.33 2717ms %------------------------------------------------------------------------------