%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO187+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 23:22:01 EDT 2023 % Result : Theorem 16.62s 3.11s % Output : Proof 29.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO187+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 21:50:25 EDT 2023 % 0.12/0.34 % CPUTime : % 0.63/0.62 ________ _____ % 0.63/0.62 ___ __ \_________(_)________________________________ % 0.63/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.62 % 0.63/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.62 (2023-06-19) % 0.63/0.62 % 0.63/0.62 (c) Philipp Rümmer, 2009-2023 % 0.63/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.62 Amanda Stjerna. % 0.63/0.62 Free software under BSD-3-Clause. % 0.63/0.62 % 0.63/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.62 % 0.63/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.64 Running up to 7 provers in parallel. % 0.70/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.68/1.27 Prover 4: Preprocessing ... % 3.68/1.27 Prover 1: Preprocessing ... % 3.68/1.31 Prover 2: Preprocessing ... % 3.68/1.31 Prover 0: Preprocessing ... % 3.68/1.31 Prover 5: Preprocessing ... % 3.68/1.31 Prover 6: Preprocessing ... % 3.68/1.31 Prover 3: Preprocessing ... % 7.39/1.77 Prover 5: Proving ... % 7.39/1.79 Prover 2: Proving ... % 7.97/1.90 Prover 6: Constructing countermodel ... % 8.55/1.93 Prover 1: Constructing countermodel ... % 8.55/1.97 Prover 3: Constructing countermodel ... % 9.86/2.13 Prover 6: gave up % 9.86/2.14 Prover 3: gave up % 9.86/2.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.86/2.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.05/2.19 Prover 1: gave up % 10.05/2.21 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.05/2.23 Prover 7: Preprocessing ... % 10.58/2.23 Prover 8: Preprocessing ... % 10.58/2.27 Prover 9: Preprocessing ... % 10.58/2.28 Prover 7: Warning: ignoring some quantifiers % 11.03/2.30 Prover 7: Constructing countermodel ... % 11.03/2.35 Prover 4: Constructing countermodel ... % 11.61/2.37 Prover 0: Proving ... % 12.05/2.44 Prover 8: Warning: ignoring some quantifiers % 12.18/2.45 Prover 8: Constructing countermodel ... % 13.20/2.63 Prover 8: gave up % 13.20/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.81/2.68 Prover 9: Constructing countermodel ... % 13.97/2.71 Prover 10: Preprocessing ... % 14.42/2.74 Prover 10: Warning: ignoring some quantifiers % 14.42/2.78 Prover 10: Constructing countermodel ... % 15.64/2.96 Prover 10: gave up % 15.64/2.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.47/3.01 Prover 11: Preprocessing ... % 16.62/3.11 Prover 0: proved (2456ms) % 16.62/3.11 % 16.62/3.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.62/3.11 % 16.62/3.11 Prover 9: stopped % 16.62/3.11 Prover 2: stopped % 17.26/3.13 Prover 5: stopped % 17.26/3.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.26/3.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.26/3.13 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.26/3.14 Prover 16: Preprocessing ... % 17.26/3.16 Prover 13: Preprocessing ... % 17.26/3.18 Prover 19: Preprocessing ... % 17.26/3.19 Prover 16: Warning: ignoring some quantifiers % 17.82/3.20 Prover 16: Constructing countermodel ... % 17.82/3.23 Prover 13: Warning: ignoring some quantifiers % 17.82/3.24 Prover 13: Constructing countermodel ... % 17.82/3.26 Prover 19: Warning: ignoring some quantifiers % 18.43/3.27 Prover 19: Constructing countermodel ... % 18.88/3.33 Prover 11: Constructing countermodel ... % 18.88/3.41 Prover 7: gave up % 19.60/3.48 Prover 19: gave up % 20.18/3.51 Prover 16: gave up % 20.68/3.65 Prover 13: gave up % 27.91/4.95 Prover 11: Found proof (size 369) % 27.91/4.95 Prover 11: proved (1989ms) % 27.91/4.96 Prover 4: stopped % 27.91/4.96 % 27.91/4.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.91/4.96 % 28.21/4.98 % SZS output start Proof for theBenchmark % 28.21/4.98 Assumptions after simplification: % 28.21/4.98 --------------------------------- % 28.21/4.98 % 28.21/4.98 (a4) % 28.21/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.21/5.01 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.21/5.01 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 28.21/5.01 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.21/5.01 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 28.21/5.01 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 28.21/5.01 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 28.21/5.01 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 28.21/5.01 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 28.21/5.01 % 28.21/5.01 (ceq2) % 28.21/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 28.21/5.02 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 28.21/5.02 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 28.21/5.02 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 28.21/5.02 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 28.21/5.02 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.21/5.02 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.21/5.02 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 28.21/5.02 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.21/5.02 apart_point_and_line(v0, v2) = 0) % 28.21/5.02 % 28.21/5.02 (ci1) % 28.21/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 28.21/5.02 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 28.21/5.02 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 28.21/5.02 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 28.21/5.02 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.21/5.02 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 28.21/5.02 $i(v2))) % 28.21/5.02 % 28.21/5.02 (ci2) % 28.21/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 28.21/5.02 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 28.21/5.02 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 28.21/5.02 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 28.21/5.02 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.21/5.02 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 28.21/5.02 $i(v2))) % 28.21/5.02 % 28.21/5.02 (con) % 28.21/5.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 28.21/5.03 $i] : ? [v6: int] : ? [v7: int] : (incident_point_and_line(v1, v4) = 0 & % 28.21/5.03 incident_point_and_line(v0, v4) = 0 & line_connecting(v2, v3) = v4 & % 28.21/5.03 line_connecting(v0, v1) = v5 & distinct_points(v2, v3) = 0 & % 28.21/5.03 distinct_points(v0, v1) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 28.21/5.03 $i(v0) & (( ~ (v7 = 0) & incident_point_and_line(v3, v5) = v7) | ( ~ (v6 = % 28.21/5.03 0) & incident_point_and_line(v2, v5) = v6))) % 28.21/5.03 % 28.21/5.03 (cu1) % 28.21/5.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 28.21/5.04 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 28.21/5.04 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 28.21/5.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 28.21/5.04 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 28.21/5.04 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 28.21/5.04 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 28.21/5.04 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 28.21/5.04 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 28.21/5.04 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 28.21/5.04 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 28.21/5.04 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 28.21/5.04 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 28.21/5.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 28.21/5.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 28.21/5.04 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 28.21/5.04 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 28.21/5.04 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 28.21/5.04 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 28.21/5.04 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 28.21/5.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 28.21/5.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 28.21/5.04 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 28.21/5.04 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 28.21/5.04 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 28.21/5.04 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 28.21/5.04 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 28.21/5.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 28.21/5.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 28.21/5.04 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 28.21/5.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 28.21/5.04 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 28.21/5.04 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 28.21/5.04 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 28.21/5.04 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 28.21/5.05 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 28.21/5.05 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 28.21/5.05 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 28.21/5.05 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 28.21/5.05 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 28.21/5.05 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 28.21/5.05 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 28.21/5.05 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 28.21/5.05 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 28.21/5.05 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 28.21/5.05 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 28.21/5.05 % 28.21/5.05 (function-axioms) % 28.61/5.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 28.61/5.05 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 28.61/5.05 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.61/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.05 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 28.61/5.05 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.61/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 28.61/5.05 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.61/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.05 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 28.61/5.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.61/5.05 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 28.61/5.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.05 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 28.61/5.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 28.61/5.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 28.61/5.05 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.61/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 28.61/5.05 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.61/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 28.61/5.05 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 28.61/5.05 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 28.61/5.05 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.61/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.05 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 28.61/5.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.61/5.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 28.61/5.05 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.61/5.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.05 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 28.61/5.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.61/5.05 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 28.61/5.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.61/5.05 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 28.61/5.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 28.61/5.05 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 28.61/5.05 % 28.61/5.05 Further assumptions not needed in the proof: % 28.61/5.05 -------------------------------------------- % 28.61/5.05 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq3, ci3, % 28.61/5.05 ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, % 28.61/5.05 orth1, ouo1, p1, par1 % 28.61/5.05 % 28.61/5.05 Those formulas are unsatisfiable: % 28.61/5.05 --------------------------------- % 28.61/5.05 % 28.61/5.05 Begin of proof % 28.61/5.06 | % 28.61/5.06 | ALPHA: (ci1) implies: % 28.61/5.06 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 28.61/5.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.61/5.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 28.61/5.06 | $i(v2))) % 28.61/5.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 28.61/5.06 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 28.61/5.06 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & % 28.61/5.06 | distinct_points(v0, v1) = v3))) % 28.61/5.06 | % 28.61/5.06 | ALPHA: (ci2) implies: % 28.61/5.06 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 28.61/5.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.61/5.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 28.61/5.06 | $i(v2))) % 28.61/5.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 28.61/5.06 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 28.61/5.06 | (v4 = 0) & apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & % 28.61/5.06 | distinct_points(v0, v1) = v3))) % 28.61/5.06 | % 28.61/5.06 | ALPHA: (cu1) implies: % 28.61/5.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 28.61/5.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 28.61/5.06 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 28.61/5.06 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.61/5.06 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 28.61/5.06 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 28.61/5.06 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 28.61/5.06 | distinct_lines(v2, v3) = v6))) % 28.61/5.07 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 28.61/5.07 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 28.61/5.07 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 28.61/5.07 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 28.61/5.07 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 28.61/5.07 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 28.61/5.07 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 28.61/5.07 | v1) = v6))) % 28.61/5.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 28.61/5.07 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 28.61/5.07 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 28.61/5.07 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 28.61/5.07 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 28.61/5.07 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 28.61/5.07 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 28.61/5.07 | v1) = v6))) % 28.61/5.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 28.61/5.07 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 28.61/5.07 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 28.61/5.07 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.61/5.07 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 28.61/5.07 | apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 28.61/5.07 | apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.61/5.07 | distinct_lines(v2, v3) = v6))) % 28.61/5.07 | % 28.61/5.07 | ALPHA: (ceq2) implies: % 28.61/5.07 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 28.61/5.07 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 28.61/5.07 | (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.61/5.07 | ? [v5: int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 28.61/5.07 | % 28.61/5.07 | ALPHA: (a4) implies: % 28.61/5.07 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) % 28.61/5.07 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 28.61/5.07 | apart_point_and_line(v0, v1) = v2)) % 28.61/5.07 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.61/5.07 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.61/5.07 | apart_point_and_line(v0, v1) = 0) % 28.61/5.07 | % 28.61/5.07 | ALPHA: (function-axioms) implies: % 28.61/5.07 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.61/5.07 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 28.61/5.07 | (distinct_points(v3, v2) = v0)) % 28.61/5.07 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.61/5.08 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 28.61/5.08 | (distinct_lines(v3, v2) = v0)) % 28.61/5.08 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.61/5.08 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 28.61/5.08 | (apart_point_and_line(v3, v2) = v0)) % 28.61/5.08 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.61/5.08 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 28.61/5.08 | % 28.61/5.08 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 28.61/5.08 | all_38_3, all_38_4, all_38_5, all_38_6, all_38_7 gives: % 28.61/5.08 | (16) incident_point_and_line(all_38_6, all_38_3) = 0 & % 28.61/5.08 | incident_point_and_line(all_38_7, all_38_3) = 0 & % 28.61/5.08 | line_connecting(all_38_5, all_38_4) = all_38_3 & % 28.61/5.08 | line_connecting(all_38_7, all_38_6) = all_38_2 & % 28.61/5.08 | distinct_points(all_38_5, all_38_4) = 0 & distinct_points(all_38_7, % 28.61/5.08 | all_38_6) = 0 & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 28.61/5.08 | $i(all_38_5) & $i(all_38_6) & $i(all_38_7) & (( ~ (all_38_0 = 0) & % 28.61/5.08 | incident_point_and_line(all_38_4, all_38_2) = all_38_0) | ( ~ % 28.61/5.08 | (all_38_1 = 0) & incident_point_and_line(all_38_5, all_38_2) = % 28.61/5.08 | all_38_1)) % 28.61/5.08 | % 28.61/5.08 | ALPHA: (16) implies: % 28.61/5.08 | (17) $i(all_38_7) % 28.61/5.08 | (18) $i(all_38_6) % 28.61/5.08 | (19) $i(all_38_5) % 28.61/5.08 | (20) $i(all_38_4) % 28.61/5.08 | (21) $i(all_38_3) % 28.61/5.08 | (22) distinct_points(all_38_7, all_38_6) = 0 % 28.61/5.08 | (23) distinct_points(all_38_5, all_38_4) = 0 % 28.61/5.08 | (24) line_connecting(all_38_7, all_38_6) = all_38_2 % 28.61/5.08 | (25) line_connecting(all_38_5, all_38_4) = all_38_3 % 28.61/5.08 | (26) incident_point_and_line(all_38_7, all_38_3) = 0 % 28.61/5.08 | (27) incident_point_and_line(all_38_6, all_38_3) = 0 % 28.61/5.08 | (28) ( ~ (all_38_0 = 0) & incident_point_and_line(all_38_4, all_38_2) = % 28.61/5.08 | all_38_0) | ( ~ (all_38_1 = 0) & incident_point_and_line(all_38_5, % 28.61/5.08 | all_38_2) = all_38_1) % 28.61/5.08 | % 28.61/5.08 | GROUND_INST: instantiating (3) with all_38_7, all_38_6, simplifying with (17), % 28.61/5.08 | (18), (22) gives: % 28.61/5.08 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_7, % 28.61/5.08 | all_38_6) = v0 & apart_point_and_line(all_38_6, v0) = v1 & $i(v0)) % 28.61/5.08 | % 28.61/5.08 | GROUND_INST: instantiating (1) with all_38_7, all_38_6, simplifying with (17), % 28.61/5.08 | (18), (22) gives: % 28.77/5.08 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_7, % 28.77/5.08 | all_38_6) = v0 & apart_point_and_line(all_38_7, v0) = v1 & $i(v0)) % 28.77/5.08 | % 28.77/5.08 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (19), % 28.77/5.08 | (20), (23) gives: % 28.77/5.09 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 28.77/5.09 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (19), % 28.77/5.09 | (20), (23) gives: % 28.77/5.09 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 28.77/5.09 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (4) with all_38_7, all_38_6, all_38_2, simplifying % 28.77/5.09 | with (17), (18), (24) gives: % 28.77/5.09 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 28.77/5.09 | apart_point_and_line(all_38_6, all_38_2) = v1) | ( ~ (v0 = 0) & % 28.77/5.09 | distinct_points(all_38_7, all_38_6) = v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (2) with all_38_7, all_38_6, all_38_2, simplifying % 28.77/5.09 | with (17), (18), (24) gives: % 28.77/5.09 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 28.77/5.09 | apart_point_and_line(all_38_7, all_38_2) = v1) | ( ~ (v0 = 0) & % 28.77/5.09 | distinct_points(all_38_7, all_38_6) = v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_3, simplifying % 28.77/5.09 | with (19), (20), (25) gives: % 28.77/5.09 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 28.77/5.09 | apart_point_and_line(all_38_4, all_38_3) = v1) | ( ~ (v0 = 0) & % 28.77/5.09 | distinct_points(all_38_5, all_38_4) = v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_3, simplifying % 28.77/5.09 | with (19), (20), (25) gives: % 28.77/5.09 | (36) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 28.77/5.09 | apart_point_and_line(all_38_5, all_38_3) = v1) | ( ~ (v0 = 0) & % 28.77/5.09 | distinct_points(all_38_5, all_38_4) = v0)) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (10) with all_38_7, all_38_3, simplifying with % 28.77/5.09 | (17), (21), (26) gives: % 28.77/5.09 | (37) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_7, all_38_3) % 28.77/5.09 | = v0) % 28.77/5.09 | % 28.77/5.09 | GROUND_INST: instantiating (10) with all_38_6, all_38_3, simplifying with % 28.77/5.09 | (18), (21), (27) gives: % 28.77/5.09 | (38) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_6, all_38_3) % 28.77/5.09 | = v0) % 28.77/5.09 | % 28.77/5.09 | DELTA: instantiating (38) with fresh symbol all_45_0 gives: % 28.77/5.09 | (39) ~ (all_45_0 = 0) & apart_point_and_line(all_38_6, all_38_3) = % 28.77/5.09 | all_45_0 % 28.77/5.09 | % 28.77/5.09 | ALPHA: (39) implies: % 28.77/5.09 | (40) ~ (all_45_0 = 0) % 28.77/5.09 | (41) apart_point_and_line(all_38_6, all_38_3) = all_45_0 % 28.77/5.09 | % 28.77/5.09 | DELTA: instantiating (37) with fresh symbol all_47_0 gives: % 28.77/5.09 | (42) ~ (all_47_0 = 0) & apart_point_and_line(all_38_7, all_38_3) = % 28.77/5.09 | all_47_0 % 28.77/5.09 | % 28.77/5.09 | ALPHA: (42) implies: % 28.77/5.09 | (43) ~ (all_47_0 = 0) % 28.77/5.09 | (44) apart_point_and_line(all_38_7, all_38_3) = all_47_0 % 28.77/5.09 | % 28.77/5.09 | DELTA: instantiating (34) with fresh symbols all_53_0, all_53_1 gives: % 28.77/5.09 | (45) ( ~ (all_53_0 = 0) & apart_point_and_line(all_38_7, all_38_2) = % 28.77/5.09 | all_53_0) | ( ~ (all_53_1 = 0) & distinct_points(all_38_7, all_38_6) % 28.77/5.09 | = all_53_1) % 28.77/5.09 | % 28.77/5.09 | DELTA: instantiating (30) with fresh symbols all_54_0, all_54_1 gives: % 28.77/5.10 | (46) ~ (all_54_0 = 0) & line_connecting(all_38_7, all_38_6) = all_54_1 & % 28.77/5.10 | apart_point_and_line(all_38_7, all_54_1) = all_54_0 & $i(all_54_1) % 28.77/5.10 | % 28.77/5.10 | ALPHA: (46) implies: % 28.77/5.10 | (47) ~ (all_54_0 = 0) % 28.77/5.10 | (48) $i(all_54_1) % 28.77/5.10 | (49) apart_point_and_line(all_38_7, all_54_1) = all_54_0 % 28.77/5.10 | (50) line_connecting(all_38_7, all_38_6) = all_54_1 % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (29) with fresh symbols all_56_0, all_56_1 gives: % 28.77/5.10 | (51) ~ (all_56_0 = 0) & line_connecting(all_38_7, all_38_6) = all_56_1 & % 28.77/5.10 | apart_point_and_line(all_38_6, all_56_1) = all_56_0 & $i(all_56_1) % 28.77/5.10 | % 28.77/5.10 | ALPHA: (51) implies: % 28.77/5.10 | (52) apart_point_and_line(all_38_6, all_56_1) = all_56_0 % 28.77/5.10 | (53) line_connecting(all_38_7, all_38_6) = all_56_1 % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (36) with fresh symbols all_58_0, all_58_1 gives: % 28.77/5.10 | (54) ( ~ (all_58_0 = 0) & apart_point_and_line(all_38_5, all_38_3) = % 28.77/5.10 | all_58_0) | ( ~ (all_58_1 = 0) & distinct_points(all_38_5, all_38_4) % 28.77/5.10 | = all_58_1) % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (33) with fresh symbols all_59_0, all_59_1 gives: % 28.77/5.10 | (55) ( ~ (all_59_0 = 0) & apart_point_and_line(all_38_6, all_38_2) = % 28.77/5.10 | all_59_0) | ( ~ (all_59_1 = 0) & distinct_points(all_38_7, all_38_6) % 28.77/5.10 | = all_59_1) % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (35) with fresh symbols all_60_0, all_60_1 gives: % 28.77/5.10 | (56) ( ~ (all_60_0 = 0) & apart_point_and_line(all_38_4, all_38_3) = % 28.77/5.10 | all_60_0) | ( ~ (all_60_1 = 0) & distinct_points(all_38_5, all_38_4) % 28.77/5.10 | = all_60_1) % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (32) with fresh symbols all_61_0, all_61_1 gives: % 28.77/5.10 | (57) ~ (all_61_0 = 0) & line_connecting(all_38_5, all_38_4) = all_61_1 & % 28.77/5.10 | apart_point_and_line(all_38_5, all_61_1) = all_61_0 & $i(all_61_1) % 28.77/5.10 | % 28.77/5.10 | ALPHA: (57) implies: % 28.77/5.10 | (58) ~ (all_61_0 = 0) % 28.77/5.10 | (59) $i(all_61_1) % 28.77/5.10 | (60) apart_point_and_line(all_38_5, all_61_1) = all_61_0 % 28.77/5.10 | (61) line_connecting(all_38_5, all_38_4) = all_61_1 % 28.77/5.10 | % 28.77/5.10 | DELTA: instantiating (31) with fresh symbols all_63_0, all_63_1 gives: % 28.77/5.10 | (62) ~ (all_63_0 = 0) & line_connecting(all_38_5, all_38_4) = all_63_1 & % 28.77/5.10 | apart_point_and_line(all_38_4, all_63_1) = all_63_0 & $i(all_63_1) % 28.77/5.10 | % 28.77/5.10 | ALPHA: (62) implies: % 28.77/5.10 | (63) ~ (all_63_0 = 0) % 28.77/5.10 | (64) apart_point_and_line(all_38_4, all_63_1) = all_63_0 % 28.77/5.10 | (65) line_connecting(all_38_5, all_38_4) = all_63_1 % 28.77/5.10 | % 28.77/5.10 | BETA: splitting (55) gives: % 28.77/5.10 | % 28.77/5.10 | Case 1: % 28.77/5.10 | | % 28.77/5.10 | | (66) ~ (all_59_0 = 0) & apart_point_and_line(all_38_6, all_38_2) = % 28.77/5.10 | | all_59_0 % 28.77/5.10 | | % 28.77/5.10 | | ALPHA: (66) implies: % 28.77/5.10 | | (67) ~ (all_59_0 = 0) % 28.77/5.10 | | (68) apart_point_and_line(all_38_6, all_38_2) = all_59_0 % 28.77/5.10 | | % 28.77/5.10 | | BETA: splitting (54) gives: % 28.77/5.10 | | % 28.77/5.10 | | Case 1: % 28.77/5.10 | | | % 28.77/5.10 | | | (69) ~ (all_58_0 = 0) & apart_point_and_line(all_38_5, all_38_3) = % 28.77/5.10 | | | all_58_0 % 28.77/5.10 | | | % 28.77/5.10 | | | ALPHA: (69) implies: % 28.77/5.10 | | | (70) apart_point_and_line(all_38_5, all_38_3) = all_58_0 % 28.77/5.10 | | | % 28.77/5.10 | | | BETA: splitting (45) gives: % 28.77/5.10 | | | % 28.77/5.10 | | | Case 1: % 28.77/5.10 | | | | % 28.77/5.10 | | | | (71) ~ (all_53_0 = 0) & apart_point_and_line(all_38_7, all_38_2) = % 28.77/5.10 | | | | all_53_0 % 28.77/5.10 | | | | % 28.77/5.10 | | | | ALPHA: (71) implies: % 28.77/5.10 | | | | (72) apart_point_and_line(all_38_7, all_38_2) = all_53_0 % 28.77/5.10 | | | | % 28.77/5.10 | | | | BETA: splitting (56) gives: % 28.77/5.10 | | | | % 28.77/5.10 | | | | Case 1: % 28.77/5.10 | | | | | % 28.77/5.10 | | | | | (73) ~ (all_60_0 = 0) & apart_point_and_line(all_38_4, all_38_3) = % 28.77/5.10 | | | | | all_60_0 % 28.77/5.10 | | | | | % 28.77/5.11 | | | | | ALPHA: (73) implies: % 28.77/5.11 | | | | | (74) apart_point_and_line(all_38_4, all_38_3) = all_60_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (15) with all_38_2, all_56_1, all_38_6, % 28.77/5.11 | | | | | all_38_7, simplifying with (24), (53) gives: % 28.77/5.11 | | | | | (75) all_56_1 = all_38_2 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (15) with all_54_1, all_56_1, all_38_6, % 28.77/5.11 | | | | | all_38_7, simplifying with (50), (53) gives: % 28.77/5.11 | | | | | (76) all_56_1 = all_54_1 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (15) with all_38_3, all_63_1, all_38_4, % 28.77/5.11 | | | | | all_38_5, simplifying with (25), (65) gives: % 28.77/5.11 | | | | | (77) all_63_1 = all_38_3 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (15) with all_61_1, all_63_1, all_38_4, % 28.77/5.11 | | | | | all_38_5, simplifying with (61), (65) gives: % 28.77/5.11 | | | | | (78) all_63_1 = all_61_1 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | COMBINE_EQS: (77), (78) imply: % 28.77/5.11 | | | | | (79) all_61_1 = all_38_3 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | COMBINE_EQS: (75), (76) imply: % 28.77/5.11 | | | | | (80) all_54_1 = all_38_2 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | SIMP: (80) implies: % 28.77/5.11 | | | | | (81) all_54_1 = all_38_2 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (64), (77) imply: % 28.77/5.11 | | | | | (82) apart_point_and_line(all_38_4, all_38_3) = all_63_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (60), (79) imply: % 28.77/5.11 | | | | | (83) apart_point_and_line(all_38_5, all_38_3) = all_61_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (52), (75) imply: % 28.77/5.11 | | | | | (84) apart_point_and_line(all_38_6, all_38_2) = all_56_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (49), (81) imply: % 28.77/5.11 | | | | | (85) apart_point_and_line(all_38_7, all_38_2) = all_54_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (48), (81) imply: % 28.77/5.11 | | | | | (86) $i(all_38_2) % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (14) with all_53_0, all_54_0, all_38_2, % 28.77/5.11 | | | | | all_38_7, simplifying with (72), (85) gives: % 28.77/5.11 | | | | | (87) all_54_0 = all_53_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (14) with all_59_0, all_56_0, all_38_2, % 28.77/5.11 | | | | | all_38_6, simplifying with (68), (84) gives: % 28.77/5.11 | | | | | (88) all_59_0 = all_56_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (14) with all_58_0, all_61_0, all_38_3, % 28.77/5.11 | | | | | all_38_5, simplifying with (70), (83) gives: % 28.77/5.11 | | | | | (89) all_61_0 = all_58_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (14) with all_60_0, all_63_0, all_38_3, % 28.77/5.11 | | | | | all_38_4, simplifying with (74), (82) gives: % 28.77/5.11 | | | | | (90) all_63_0 = all_60_0 % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (63), (90) imply: % 28.77/5.11 | | | | | (91) ~ (all_60_0 = 0) % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (58), (89) imply: % 28.77/5.11 | | | | | (92) ~ (all_58_0 = 0) % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (67), (88) imply: % 28.77/5.11 | | | | | (93) ~ (all_56_0 = 0) % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | REDUCE: (47), (87) imply: % 28.77/5.11 | | | | | (94) ~ (all_53_0 = 0) % 28.77/5.11 | | | | | % 28.77/5.11 | | | | | GROUND_INST: instantiating (5) with all_38_7, all_38_6, all_38_2, % 28.77/5.11 | | | | | all_38_3, all_53_0, all_47_0, simplifying with (17), % 28.77/5.11 | | | | | (18), (21), (22), (44), (72), (86) gives: % 28.77/5.11 | | | | | (95) all_53_0 = 0 | all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.11 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_38_6, % 28.77/5.11 | | | | | all_38_3) = 0) | (v1 = 0 & % 28.77/5.11 | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | ( ~ (v0 = % 28.77/5.11 | | | | | 0) & distinct_lines(all_38_2, all_38_3) = v0)) % 28.77/5.11 | | | | | % 28.77/5.12 | | | | | GROUND_INST: instantiating (7) with all_38_7, all_38_7, all_38_3, % 28.77/5.12 | | | | | all_38_2, all_47_0, all_53_0, simplifying with (17), % 28.77/5.12 | | | | | (21), (44), (72), (86) gives: % 28.77/5.12 | | | | | (96) all_53_0 = 0 | all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.12 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) | (v2 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | ( ~ (v1 = % 28.77/5.12 | | | | | 0) & distinct_lines(all_38_3, all_38_2) = v1) | ( ~ (v0 % 28.77/5.12 | | | | | = 0) & distinct_points(all_38_7, all_38_7) = v0)) % 28.77/5.12 | | | | | % 28.77/5.12 | | | | | GROUND_INST: instantiating (7) with all_38_7, all_38_6, all_38_2, % 28.77/5.12 | | | | | all_38_3, all_53_0, all_45_0, simplifying with (17), % 28.77/5.12 | | | | | (18), (21), (41), (72), (86) gives: % 28.77/5.12 | | | | | (97) all_53_0 = 0 | all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.12 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | (v2 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) | ( ~ (v1 = % 28.77/5.12 | | | | | 0) & distinct_lines(all_38_2, all_38_3) = v1) | ( ~ (v0 % 28.77/5.12 | | | | | = 0) & distinct_points(all_38_7, all_38_6) = v0)) % 28.77/5.12 | | | | | % 28.77/5.12 | | | | | GROUND_INST: instantiating (8) with all_38_7, all_38_6, all_38_2, % 28.77/5.12 | | | | | all_38_3, all_56_0, all_45_0, simplifying with (17), % 28.77/5.12 | | | | | (18), (21), (22), (41), (84), (86) gives: % 28.77/5.12 | | | | | (98) all_56_0 = 0 | all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.12 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.12 | | | | | all_38_3) = 0) | (v1 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | ( ~ (v0 = % 28.77/5.12 | | | | | 0) & distinct_lines(all_38_2, all_38_3) = v0)) % 28.77/5.12 | | | | | % 28.77/5.12 | | | | | GROUND_INST: instantiating (6) with all_38_7, all_38_6, all_38_2, % 28.77/5.12 | | | | | all_38_3, all_47_0, all_56_0, simplifying with (17), % 28.77/5.12 | | | | | (18), (21), (44), (84), (86) gives: % 28.77/5.12 | | | | | (99) all_56_0 = 0 | all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.12 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) | (v2 = 0 & % 28.77/5.12 | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | ( ~ (v1 = % 28.77/5.12 | | | | | 0) & distinct_lines(all_38_2, all_38_3) = v1) | ( ~ (v0 % 28.77/5.12 | | | | | = 0) & distinct_points(all_38_7, all_38_6) = v0)) % 28.77/5.12 | | | | | % 28.77/5.12 | | | | | BETA: splitting (28) gives: % 28.77/5.12 | | | | | % 28.77/5.12 | | | | | Case 1: % 28.77/5.12 | | | | | | % 28.77/5.12 | | | | | | (100) ~ (all_38_0 = 0) & incident_point_and_line(all_38_4, % 28.77/5.12 | | | | | | all_38_2) = all_38_0 % 28.77/5.12 | | | | | | % 28.77/5.12 | | | | | | ALPHA: (100) implies: % 28.77/5.12 | | | | | | (101) ~ (all_38_0 = 0) % 28.77/5.13 | | | | | | (102) incident_point_and_line(all_38_4, all_38_2) = all_38_0 % 28.77/5.13 | | | | | | % 28.77/5.13 | | | | | | BETA: splitting (95) gives: % 28.77/5.13 | | | | | | % 28.77/5.13 | | | | | | Case 1: % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | (103) all_53_0 = 0 % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | REDUCE: (94), (103) imply: % 28.77/5.13 | | | | | | | (104) $false % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | CLOSE: (104) is inconsistent. % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | Case 2: % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | (105) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 28.77/5.13 | | | | | | | : ((v2 = 0 & apart_point_and_line(all_38_6, all_38_3) = % 28.77/5.13 | | | | | | | 0) | (v1 = 0 & apart_point_and_line(all_38_6, % 28.77/5.13 | | | | | | | all_38_2) = 0) | ( ~ (v0 = 0) & % 28.77/5.13 | | | | | | | distinct_lines(all_38_2, all_38_3) = v0)) % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | BETA: splitting (97) gives: % 28.77/5.13 | | | | | | | % 28.77/5.13 | | | | | | | Case 1: % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | (106) all_53_0 = 0 % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | REDUCE: (94), (106) imply: % 28.77/5.13 | | | | | | | | (107) $false % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | CLOSE: (107) is inconsistent. % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | Case 2: % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | (108) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 28.77/5.13 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.13 | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | (v2 % 28.77/5.13 | | | | | | | | = 0 & apart_point_and_line(all_38_7, all_38_3) = 0) % 28.77/5.13 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_38_2, all_38_3) = % 28.77/5.13 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_38_7, % 28.77/5.13 | | | | | | | | all_38_6) = v0)) % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | BETA: splitting (98) gives: % 28.77/5.13 | | | | | | | | % 28.77/5.13 | | | | | | | | Case 1: % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | (109) all_56_0 = 0 % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | REDUCE: (93), (109) imply: % 28.77/5.13 | | | | | | | | | (110) $false % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | CLOSE: (110) is inconsistent. % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | Case 2: % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | (111) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 28.77/5.13 | | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.13 | | | | | | | | | all_38_3) = 0) | (v1 = 0 & % 28.77/5.13 | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | ( % 28.77/5.13 | | | | | | | | | ~ (v0 = 0) & distinct_lines(all_38_2, all_38_3) = % 28.77/5.13 | | | | | | | | | v0)) % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | BETA: splitting (99) gives: % 28.77/5.13 | | | | | | | | | % 28.77/5.13 | | | | | | | | | Case 1: % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | (112) all_56_0 = 0 % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | REDUCE: (93), (112) imply: % 28.77/5.13 | | | | | | | | | | (113) $false % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | CLOSE: (113) is inconsistent. % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | Case 2: % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | (114) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.13 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.13 | | | | | | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) | % 28.77/5.13 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.13 | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 28.77/5.13 | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 28.77/5.13 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 28.77/5.13 | | | | | | | | | | = v0)) % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | BETA: splitting (96) gives: % 28.77/5.13 | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | Case 1: % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | (115) all_53_0 = 0 % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | REDUCE: (94), (115) imply: % 28.77/5.13 | | | | | | | | | | | (116) $false % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | CLOSE: (116) is inconsistent. % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | Case 2: % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | (117) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 28.77/5.13 | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.77/5.13 | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) % 28.77/5.13 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.13 | | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 28.77/5.13 | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1) | ( ~ % 28.77/5.13 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_7) % 28.77/5.13 | | | | | | | | | | | = v0)) % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | BETA: splitting (105) gives: % 28.77/5.13 | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | Case 1: % 28.77/5.13 | | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | | (118) all_47_0 = 0 % 28.77/5.13 | | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | | REDUCE: (43), (118) imply: % 28.77/5.13 | | | | | | | | | | | | (119) $false % 28.77/5.13 | | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 28.77/5.13 | | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | Case 2: % 28.77/5.13 | | | | | | | | | | | | % 28.77/5.13 | | | | | | | | | | | | (120) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 28.77/5.13 | | | | | | | | | | | | = 0 & apart_point_and_line(all_38_6, all_38_3) % 28.77/5.13 | | | | | | | | | | | | = 0) | (v1 = 0 & % 28.77/5.13 | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) % 28.77/5.13 | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | all_38_3) = v0)) % 28.77/5.14 | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | DELTA: instantiating (120) with fresh symbols all_378_0, % 28.77/5.14 | | | | | | | | | | | | all_378_1, all_378_2 gives: % 28.77/5.14 | | | | | | | | | | | | (121) (all_378_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.14 | | | | | | | | | | | | all_38_3) = 0) | (all_378_1 = 0 & % 28.77/5.14 | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | % 28.77/5.14 | | | | | | | | | | | | ( ~ (all_378_2 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | all_38_3) = all_378_2) % 28.77/5.14 | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | BETA: splitting (108) gives: % 28.77/5.14 | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | (122) all_45_0 = 0 % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | REDUCE: (40), (122) imply: % 28.77/5.14 | | | | | | | | | | | | | (123) $false % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | (124) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 28.77/5.14 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 28.77/5.14 | | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) % 28.77/5.14 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (v1 = 0) & % 28.77/5.14 | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 28.77/5.14 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 28.77/5.14 | | | | | | | | | | | | | = v0)) % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | DELTA: instantiating (124) with fresh symbols all_382_0, % 28.77/5.14 | | | | | | | | | | | | | all_382_1, all_382_2, all_382_3 gives: % 28.77/5.14 | | | | | | | | | | | | | (125) (all_382_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.14 | | | | | | | | | | | | | all_38_2) = 0) | (all_382_1 = 0 & % 28.77/5.14 | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) | % 28.77/5.14 | | | | | | | | | | | | | ( ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | | all_38_3) = all_382_2) | ( ~ (all_382_3 = 0) & % 28.77/5.14 | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_382_3) % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | BETA: splitting (111) gives: % 28.77/5.14 | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | (126) all_45_0 = 0 % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | REDUCE: (40), (126) imply: % 28.77/5.14 | | | | | | | | | | | | | | (127) $false % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | CLOSE: (127) is inconsistent. % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | (128) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 28.77/5.14 | | | | | | | | | | | | | | = 0 & apart_point_and_line(all_38_7, all_38_3) % 28.77/5.14 | | | | | | | | | | | | | | = 0) | (v1 = 0 & % 28.77/5.14 | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) % 28.77/5.14 | | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | | | all_38_3) = v0)) % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | DELTA: instantiating (128) with fresh symbols all_434_0, % 28.77/5.14 | | | | | | | | | | | | | | all_434_1, all_434_2 gives: % 28.77/5.14 | | | | | | | | | | | | | | (129) (all_434_0 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | all_38_3) = 0) | (all_434_1 = 0 & % 28.77/5.14 | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | % 28.77/5.14 | | | | | | | | | | | | | | ( ~ (all_434_2 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | | | all_38_3) = all_434_2) % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | BETA: splitting (114) gives: % 28.77/5.14 | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | (130) all_47_0 = 0 % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | REDUCE: (43), (130) imply: % 28.77/5.14 | | | | | | | | | | | | | | | (131) $false % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | (132) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 28.77/5.14 | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 28.77/5.14 | | | | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) % 28.77/5.14 | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 28.77/5.14 | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 28.77/5.14 | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 28.77/5.14 | | | | | | | | | | | | | | | = v0)) % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_438_0, % 28.77/5.14 | | | | | | | | | | | | | | | all_438_1, all_438_2, all_438_3 gives: % 28.77/5.14 | | | | | | | | | | | | | | | (133) (all_438_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.14 | | | | | | | | | | | | | | | all_38_3) = 0) | (all_438_1 = 0 & % 28.77/5.14 | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | % 28.77/5.14 | | | | | | | | | | | | | | | ( ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | | | | all_38_3) = all_438_2) | ( ~ (all_438_3 = 0) & % 28.77/5.14 | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_438_3) % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 28.77/5.14 | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | (134) all_434_0 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | | | all_38_3) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | ALPHA: (134) implies: % 28.77/5.14 | | | | | | | | | | | | | | | | (135) apart_point_and_line(all_38_7, all_38_3) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (43), (44), (135) are inconsistent by % 28.77/5.14 | | | | | | | | | | | | | | | | sub-proof #4. % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | (136) (all_434_1 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_434_2 = 0) & % 28.77/5.14 | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_434_2) % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 28.77/5.14 | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | (137) all_434_1 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | | | | all_38_2) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | ALPHA: (137) implies: % 28.77/5.14 | | | | | | | | | | | | | | | | | (138) apart_point_and_line(all_38_7, all_38_2) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (72), (94), (138) are inconsistent by % 28.77/5.14 | | | | | | | | | | | | | | | | | sub-proof #3. % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | (139) ~ (all_434_2 = 0) & distinct_lines(all_38_2, % 28.77/5.14 | | | | | | | | | | | | | | | | | all_38_3) = all_434_2 % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | ALPHA: (139) implies: % 28.77/5.14 | | | | | | | | | | | | | | | | | (140) distinct_lines(all_38_2, all_38_3) = all_434_2 % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 28.77/5.14 | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | (141) (all_382_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.14 | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_382_1 = 0 & % 28.77/5.14 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) % 28.77/5.14 | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 28.77/5.14 | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | Case 1: % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | | (142) all_382_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.14 | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies: % 28.77/5.14 | | | | | | | | | | | | | | | | | | | (143) apart_point_and_line(all_38_6, all_38_2) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (84), (93), (143) are inconsistent by % 28.77/5.14 | | | | | | | | | | | | | | | | | | | sub-proof #2. % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | Case 2: % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | | (144) all_382_1 = 0 & apart_point_and_line(all_38_7, % 28.77/5.14 | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 28.77/5.14 | | | | | | | | | | | | | | | | | | | % 28.77/5.14 | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | (145) apart_point_and_line(all_38_7, all_38_3) = 0 % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (43), (44), (145) are inconsistent by % 28.77/5.15 | | | | | | | | | | | | | | | | | | | sub-proof #4. % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | End of split % 28.77/5.15 | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | Case 2: % 28.77/5.15 | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | (146) ( ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 28.77/5.15 | | | | | | | | | | | | | | | | | | all_38_3) = all_382_2) | ( ~ (all_382_3 = 0) & % 28.77/5.15 | | | | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_382_3) % 28.77/5.15 | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 28.77/5.15 | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | Case 1: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | (147) ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 28.77/5.15 | | | | | | | | | | | | | | | | | | | all_38_3) = all_382_2 % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | (148) ~ (all_382_2 = 0) % 28.77/5.15 | | | | | | | | | | | | | | | | | | | (149) distinct_lines(all_38_2, all_38_3) = all_382_2 % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | Case 1: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | (150) (all_438_0 = 0 & apart_point_and_line(all_38_6, % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | (all_438_1 = 0 & % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 28.77/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (151) all_438_0 = 0 & apart_point_and_line(all_38_6, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (152) apart_point_and_line(all_38_6, all_38_3) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (41), (152) are inconsistent by % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (153) all_438_1 = 0 & apart_point_and_line(all_38_7, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (154) apart_point_and_line(all_38_7, all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (72), (94), (154) are inconsistent by % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | (155) ( ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | all_38_3) = all_438_2) | ( ~ (all_438_3 = 0) & % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_438_3) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (156) ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_438_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | (157) distinct_lines(all_38_2, all_38_3) = all_438_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | (158) all_378_0 = 0 & apart_point_and_line(all_38_6, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | (159) apart_point_and_line(all_38_6, all_38_3) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (41), (159) are inconsistent by % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | (160) (all_378_1 = 0 & apart_point_and_line(all_38_6, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_378_2 = 0) & % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_378_2) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | (161) all_378_1 = 0 & apart_point_and_line(all_38_6, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | (162) apart_point_and_line(all_38_6, all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (84), (93), (162) are inconsistent by % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | (163) ~ (all_378_2 = 0) & distinct_lines(all_38_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | (164) distinct_lines(all_38_2, all_38_3) = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (165) all_47_0 = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (165) imply: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (166) $false % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_382_2, all_434_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (140), (149) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (167) all_434_2 = all_382_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_434_2, all_438_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (140), (157) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (168) all_438_2 = all_434_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_378_2, all_438_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (157), (164) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (169) all_438_2 = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (169) imply: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (170) all_434_2 = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (170) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (171) all_434_2 = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (171) imply: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (172) all_382_2 = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (172) implies: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (173) all_382_2 = all_378_2 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (173) imply: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (174) ~ (all_378_2 = 0) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_38_4, all_38_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_378_2, all_60_0, simplifying with % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (74), (86), (164) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (175) all_378_2 = 0 | all_60_0 = 0 | ? [v0: int] : ( ~ % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & apart_point_and_line(all_38_4, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v0) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_38_4, all_38_2, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_0, simplifying with (20), (86), (102) % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | (176) all_38_0 = 0 | apart_point_and_line(all_38_4, % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | (177) apart_point_and_line(all_38_4, all_38_2) = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_378_2 = 0 % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (178) imply: % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (179) $false % 29.06/5.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v0) % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_60_0 = 0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (181) imply: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) $false % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) ? [v0: int] : ( ~ (v0 = 0) & % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v0) % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (183) with fresh symbol all_641_0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_641_0 = 0) & % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_641_0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_641_0 = 0) % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) apart_point_and_line(all_38_4, all_38_2) = % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_641_0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_641_0, all_38_2, % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_4, simplifying with (177), (186) gives: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_641_0 = 0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (187) imply: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) $false % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_38_0 = 0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (189) imply: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | (190) $false % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent. % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_438_3 = 0) & distinct_points(all_38_7, % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | all_38_6) = all_438_3 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_438_3 = 0) % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | (193) distinct_points(all_38_7, all_38_6) = all_438_3 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_438_3, all_38_6, % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | all_38_7, simplifying with (22), (193) gives: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | (194) all_438_3 = 0 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (194) imply: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | (195) $false % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent. % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | End of split % 29.06/5.16 | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | Case 2: % 29.06/5.16 | | | | | | | | | | | | | | | | | | | % 29.06/5.16 | | | | | | | | | | | | | | | | | | | (196) ~ (all_382_3 = 0) & distinct_points(all_38_7, % 29.06/5.16 | | | | | | | | | | | | | | | | | | | all_38_6) = all_382_3 % 29.06/5.16 | | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies: % 29.15/5.16 | | | | | | | | | | | | | | | | | | | (197) ~ (all_382_3 = 0) % 29.15/5.16 | | | | | | | | | | | | | | | | | | | (198) distinct_points(all_38_7, all_38_6) = all_382_3 % 29.15/5.16 | | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_382_3, all_38_6, % 29.15/5.16 | | | | | | | | | | | | | | | | | | | all_38_7, simplifying with (22), (198) gives: % 29.15/5.16 | | | | | | | | | | | | | | | | | | | (199) all_382_3 = 0 % 29.15/5.16 | | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | | | REDUCE: (197), (199) imply: % 29.15/5.16 | | | | | | | | | | | | | | | | | | | (200) $false % 29.15/5.16 | | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 29.15/5.16 | | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | | % 29.15/5.16 | | | | | | | | | End of split % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | End of split % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | End of split % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | End of split % 29.15/5.16 | | | | | | % 29.15/5.16 | | | | | Case 2: % 29.15/5.16 | | | | | | % 29.15/5.16 | | | | | | (201) ~ (all_38_1 = 0) & incident_point_and_line(all_38_5, % 29.15/5.16 | | | | | | all_38_2) = all_38_1 % 29.15/5.16 | | | | | | % 29.15/5.16 | | | | | | ALPHA: (201) implies: % 29.15/5.16 | | | | | | (202) ~ (all_38_1 = 0) % 29.15/5.16 | | | | | | (203) incident_point_and_line(all_38_5, all_38_2) = all_38_1 % 29.15/5.16 | | | | | | % 29.15/5.16 | | | | | | BETA: splitting (95) gives: % 29.15/5.16 | | | | | | % 29.15/5.16 | | | | | | Case 1: % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | (204) all_53_0 = 0 % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | REDUCE: (94), (204) imply: % 29.15/5.16 | | | | | | | (205) $false % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | CLOSE: (205) is inconsistent. % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | Case 2: % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | (206) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 29.15/5.16 | | | | | | | : ((v2 = 0 & apart_point_and_line(all_38_6, all_38_3) = % 29.15/5.16 | | | | | | | 0) | (v1 = 0 & apart_point_and_line(all_38_6, % 29.15/5.16 | | | | | | | all_38_2) = 0) | ( ~ (v0 = 0) & % 29.15/5.16 | | | | | | | distinct_lines(all_38_2, all_38_3) = v0)) % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | BETA: splitting (97) gives: % 29.15/5.16 | | | | | | | % 29.15/5.16 | | | | | | | Case 1: % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | (207) all_53_0 = 0 % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | REDUCE: (94), (207) imply: % 29.15/5.16 | | | | | | | | (208) $false % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | CLOSE: (208) is inconsistent. % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | Case 2: % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | (209) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 29.15/5.16 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 29.15/5.16 | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | (v2 % 29.15/5.16 | | | | | | | | = 0 & apart_point_and_line(all_38_7, all_38_3) = 0) % 29.15/5.16 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_38_2, all_38_3) = % 29.15/5.16 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_38_7, % 29.15/5.16 | | | | | | | | all_38_6) = v0)) % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | BETA: splitting (98) gives: % 29.15/5.16 | | | | | | | | % 29.15/5.16 | | | | | | | | Case 1: % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | (210) all_56_0 = 0 % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | REDUCE: (93), (210) imply: % 29.15/5.16 | | | | | | | | | (211) $false % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | CLOSE: (211) is inconsistent. % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | Case 2: % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | (212) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 29.15/5.16 | | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_38_7, % 29.15/5.16 | | | | | | | | | all_38_3) = 0) | (v1 = 0 & % 29.15/5.16 | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | ( % 29.15/5.16 | | | | | | | | | ~ (v0 = 0) & distinct_lines(all_38_2, all_38_3) = % 29.15/5.16 | | | | | | | | | v0)) % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | BETA: splitting (99) gives: % 29.15/5.16 | | | | | | | | | % 29.15/5.16 | | | | | | | | | Case 1: % 29.15/5.16 | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | (213) all_56_0 = 0 % 29.15/5.16 | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | REDUCE: (93), (213) imply: % 29.15/5.16 | | | | | | | | | | (214) $false % 29.15/5.16 | | | | | | | | | | % 29.15/5.16 | | | | | | | | | | CLOSE: (214) is inconsistent. % 29.15/5.16 | | | | | | | | | | % 29.15/5.16 | | | | | | | | | Case 2: % 29.15/5.16 | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | (215) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 29.15/5.17 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 29.15/5.17 | | | | | | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) | % 29.15/5.17 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 29.15/5.17 | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 29.15/5.17 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 29.15/5.17 | | | | | | | | | | = v0)) % 29.15/5.17 | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | BETA: splitting (96) gives: % 29.15/5.17 | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | (216) all_53_0 = 0 % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | REDUCE: (94), (216) imply: % 29.15/5.17 | | | | | | | | | | | (217) $false % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | CLOSE: (217) is inconsistent. % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | (218) all_47_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 29.15/5.17 | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 29.15/5.17 | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) % 29.15/5.17 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 29.15/5.17 | | | | | | | | | | | distinct_lines(all_38_3, all_38_2) = v1) | ( ~ % 29.15/5.17 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_7) % 29.15/5.17 | | | | | | | | | | | = v0)) % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | BETA: splitting (206) gives: % 29.15/5.17 | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | (219) all_47_0 = 0 % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | REDUCE: (43), (219) imply: % 29.15/5.17 | | | | | | | | | | | | (220) $false % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | (221) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 29.15/5.17 | | | | | | | | | | | | = 0 & apart_point_and_line(all_38_6, all_38_3) % 29.15/5.17 | | | | | | | | | | | | = 0) | (v1 = 0 & % 29.15/5.17 | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) % 29.15/5.17 | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | all_38_3) = v0)) % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | DELTA: instantiating (221) with fresh symbols all_378_0, % 29.15/5.17 | | | | | | | | | | | | all_378_1, all_378_2 gives: % 29.15/5.17 | | | | | | | | | | | | (222) (all_378_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.17 | | | | | | | | | | | | all_38_3) = 0) | (all_378_1 = 0 & % 29.15/5.17 | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) | % 29.15/5.17 | | | | | | | | | | | | ( ~ (all_378_2 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | all_38_3) = all_378_2) % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | BETA: splitting (209) gives: % 29.15/5.17 | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | (223) all_45_0 = 0 % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | REDUCE: (40), (223) imply: % 29.15/5.17 | | | | | | | | | | | | | (224) $false % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | (225) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.15/5.17 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 29.15/5.17 | | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_2) = 0) % 29.15/5.17 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (v1 = 0) & % 29.15/5.17 | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 29.15/5.17 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 29.15/5.17 | | | | | | | | | | | | | = v0)) % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | DELTA: instantiating (225) with fresh symbols all_382_0, % 29.15/5.17 | | | | | | | | | | | | | all_382_1, all_382_2, all_382_3 gives: % 29.15/5.17 | | | | | | | | | | | | | (226) (all_382_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.17 | | | | | | | | | | | | | all_38_2) = 0) | (all_382_1 = 0 & % 29.15/5.17 | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) | % 29.15/5.17 | | | | | | | | | | | | | ( ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | | all_38_3) = all_382_2) | ( ~ (all_382_3 = 0) & % 29.15/5.17 | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_382_3) % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | BETA: splitting (212) gives: % 29.15/5.17 | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | (227) all_45_0 = 0 % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | REDUCE: (40), (227) imply: % 29.15/5.17 | | | | | | | | | | | | | | (228) $false % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | (229) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 29.15/5.17 | | | | | | | | | | | | | | = 0 & apart_point_and_line(all_38_7, all_38_3) % 29.15/5.17 | | | | | | | | | | | | | | = 0) | (v1 = 0 & % 29.15/5.17 | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) % 29.15/5.17 | | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | | | all_38_3) = v0)) % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_434_0, % 29.15/5.17 | | | | | | | | | | | | | | all_434_1, all_434_2 gives: % 29.15/5.17 | | | | | | | | | | | | | | (230) (all_434_0 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | | all_38_3) = 0) | (all_434_1 = 0 & % 29.15/5.17 | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | % 29.15/5.17 | | | | | | | | | | | | | | ( ~ (all_434_2 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | | | all_38_3) = all_434_2) % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | BETA: splitting (215) gives: % 29.15/5.17 | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | (231) all_47_0 = 0 % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | REDUCE: (43), (231) imply: % 29.15/5.17 | | | | | | | | | | | | | | | (232) $false % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | (233) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.15/5.17 | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 29.15/5.17 | | | | | | | | | | | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) % 29.15/5.17 | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (v1 = 0) & % 29.15/5.17 | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = v1) | ( ~ % 29.15/5.17 | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_7, all_38_6) % 29.15/5.17 | | | | | | | | | | | | | | | = v0)) % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_438_0, % 29.15/5.17 | | | | | | | | | | | | | | | all_438_1, all_438_2, all_438_3 gives: % 29.15/5.17 | | | | | | | | | | | | | | | (234) (all_438_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.17 | | | | | | | | | | | | | | | all_38_3) = 0) | (all_438_1 = 0 & % 29.15/5.17 | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) | % 29.15/5.17 | | | | | | | | | | | | | | | ( ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | | | | all_38_3) = all_438_2) | ( ~ (all_438_3 = 0) & % 29.15/5.17 | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_438_3) % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 29.15/5.17 | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | (235) all_434_0 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | ALPHA: (235) implies: % 29.15/5.17 | | | | | | | | | | | | | | | | (236) apart_point_and_line(all_38_7, all_38_3) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (43), (44), (236) are inconsistent by % 29.15/5.17 | | | | | | | | | | | | | | | | sub-proof #4. % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | (237) (all_434_1 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_434_2 = 0) & % 29.15/5.17 | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_434_2) % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 29.15/5.17 | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | (238) all_434_1 = 0 & apart_point_and_line(all_38_7, % 29.15/5.17 | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 29.15/5.17 | | | | | | | | | | | | | | | | | (239) apart_point_and_line(all_38_7, all_38_2) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (72), (94), (239) are inconsistent by % 29.15/5.17 | | | | | | | | | | | | | | | | | sub-proof #3. % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | Case 2: % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | (240) ~ (all_434_2 = 0) & distinct_lines(all_38_2, % 29.15/5.17 | | | | | | | | | | | | | | | | | all_38_3) = all_434_2 % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 29.15/5.17 | | | | | | | | | | | | | | | | | (241) distinct_lines(all_38_2, all_38_3) = all_434_2 % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 29.15/5.17 | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | (242) (all_382_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.17 | | | | | | | | | | | | | | | | | | all_38_2) = 0) | (all_382_1 = 0 & % 29.15/5.17 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_3) = 0) % 29.15/5.17 | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 29.15/5.17 | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.17 | | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | | (243) all_382_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.17 | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 29.15/5.17 | | | | | | | | | | | | | | | | | | | (244) apart_point_and_line(all_38_6, all_38_2) = 0 % 29.15/5.17 | | | | | | | | | | | | | | | | | | | % 29.15/5.17 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (84), (93), (244) are inconsistent by % 29.15/5.17 | | | | | | | | | | | | | | | | | | | sub-proof #2. % 29.15/5.17 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | (245) all_382_1 = 0 & apart_point_and_line(all_38_7, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | (246) apart_point_and_line(all_38_7, all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (43), (44), (246) are inconsistent by % 29.15/5.18 | | | | | | | | | | | | | | | | | | | sub-proof #4. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | End of split % 29.15/5.18 | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | (247) ( ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | all_38_3) = all_382_2) | ( ~ (all_382_3 = 0) & % 29.15/5.18 | | | | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_382_3) % 29.15/5.18 | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | (248) ~ (all_382_2 = 0) & distinct_lines(all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | all_38_3) = all_382_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | (249) ~ (all_382_2 = 0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | (250) distinct_lines(all_38_2, all_38_3) = all_382_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | (251) (all_438_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | (all_438_1 = 0 & % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_7, all_38_2) = 0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (252) all_438_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (253) apart_point_and_line(all_38_6, all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (41), (253) are inconsistent by % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (254) all_438_1 = 0 & apart_point_and_line(all_38_7, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (255) apart_point_and_line(all_38_7, all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (72), (94), (255) are inconsistent by % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | (256) ( ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | all_38_3) = all_438_2) | ( ~ (all_438_3 = 0) & % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_7, all_38_6) = all_438_3) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_438_2 = 0) & distinct_lines(all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_438_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | (258) distinct_lines(all_38_2, all_38_3) = all_438_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | (259) all_378_0 = 0 & apart_point_and_line(all_38_6, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | (260) apart_point_and_line(all_38_6, all_38_3) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (41), (260) are inconsistent by % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | (261) (all_378_1 = 0 & apart_point_and_line(all_38_6, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_378_2 = 0) & % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_3) = all_378_2) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | (262) all_378_1 = 0 & apart_point_and_line(all_38_6, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | (263) apart_point_and_line(all_38_6, all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (84), (93), (263) are inconsistent by % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | (264) ~ (all_378_2 = 0) & distinct_lines(all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | (265) distinct_lines(all_38_2, all_38_3) = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (266) all_47_0 = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (266) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (267) $false % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_382_2, all_434_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (241), (250) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (268) all_434_2 = all_382_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_434_2, all_438_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (241), (258) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (269) all_438_2 = all_434_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_378_2, all_438_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_2, simplifying with (258), (265) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (270) all_438_2 = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (270) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (271) all_434_2 = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (272) all_434_2 = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (272) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (273) all_382_2 = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (274) all_382_2 = all_378_2 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (274) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (275) ~ (all_378_2 = 0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_38_5, all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_3, all_378_2, all_58_0, simplifying with % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (19), (21), (70), (86), (265) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (276) all_378_2 = 0 | all_58_0 = 0 | ? [v0: int] : ( ~ % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & apart_point_and_line(all_38_5, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_38_5, all_38_2, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (19), (86), (203) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | (277) all_38_1 = 0 | apart_point_and_line(all_38_5, % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | (278) apart_point_and_line(all_38_5, all_38_2) = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_378_2 = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (279) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (280) $false % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_0 = 0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (282) imply: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) $false % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) ? [v0: int] : ( ~ (v0 = 0) & % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v0) % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbol all_638_0 % 29.15/5.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) ~ (all_638_0 = 0) & % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_638_0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_638_0 = 0) % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) apart_point_and_line(all_38_5, all_38_2) = % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_638_0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_638_0, all_38_2, % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (278), (287) gives: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_638_0 = 0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (288) imply: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) $false % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent. % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_38_1 = 0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (290) imply: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | (291) $false % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_438_3 = 0) & distinct_points(all_38_7, % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | all_38_6) = all_438_3 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | (293) ~ (all_438_3 = 0) % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | (294) distinct_points(all_38_7, all_38_6) = all_438_3 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_438_3, all_38_6, % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | all_38_7, simplifying with (22), (294) gives: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | (295) all_438_3 = 0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (293), (295) imply: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | (296) $false % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | Case 2: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | (297) ~ (all_382_3 = 0) & distinct_points(all_38_7, % 29.15/5.19 | | | | | | | | | | | | | | | | | | | all_38_6) = all_382_3 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | (298) ~ (all_382_3 = 0) % 29.15/5.19 | | | | | | | | | | | | | | | | | | | (299) distinct_points(all_38_7, all_38_6) = all_382_3 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_382_3, all_38_6, % 29.15/5.19 | | | | | | | | | | | | | | | | | | | all_38_7, simplifying with (22), (299) gives: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | (300) all_382_3 = 0 % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | REDUCE: (298), (300) imply: % 29.15/5.19 | | | | | | | | | | | | | | | | | | | (301) $false % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 29.15/5.19 | | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | | % 29.15/5.19 | | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | | % 29.15/5.19 | | | | | | | | | End of split % 29.15/5.19 | | | | | | | | | % 29.15/5.19 | | | | | | | | End of split % 29.15/5.19 | | | | | | | | % 29.15/5.19 | | | | | | | End of split % 29.15/5.19 | | | | | | | % 29.15/5.19 | | | | | | End of split % 29.15/5.19 | | | | | | % 29.15/5.19 | | | | | End of split % 29.15/5.19 | | | | | % 29.15/5.19 | | | | Case 2: % 29.15/5.19 | | | | | % 29.15/5.19 | | | | | (302) ~ (all_60_1 = 0) & distinct_points(all_38_5, all_38_4) = % 29.15/5.19 | | | | | all_60_1 % 29.15/5.19 | | | | | % 29.15/5.19 | | | | | ALPHA: (302) implies: % 29.15/5.19 | | | | | (303) ~ (all_60_1 = 0) % 29.15/5.19 | | | | | (304) distinct_points(all_38_5, all_38_4) = all_60_1 % 29.15/5.19 | | | | | % 29.15/5.19 | | | | | GROUND_INST: instantiating (12) with 0, all_60_1, all_38_4, all_38_5, % 29.15/5.19 | | | | | simplifying with (23), (304) gives: % 29.15/5.19 | | | | | (305) all_60_1 = 0 % 29.15/5.19 | | | | | % 29.15/5.19 | | | | | REDUCE: (303), (305) imply: % 29.15/5.19 | | | | | (306) $false % 29.15/5.19 | | | | | % 29.15/5.19 | | | | | CLOSE: (306) is inconsistent. % 29.15/5.19 | | | | | % 29.15/5.19 | | | | End of split % 29.15/5.19 | | | | % 29.15/5.19 | | | Case 2: % 29.15/5.19 | | | | % 29.15/5.19 | | | | (307) ~ (all_53_1 = 0) & distinct_points(all_38_7, all_38_6) = % 29.15/5.19 | | | | all_53_1 % 29.15/5.19 | | | | % 29.15/5.19 | | | | ALPHA: (307) implies: % 29.15/5.19 | | | | (308) ~ (all_53_1 = 0) % 29.15/5.19 | | | | (309) distinct_points(all_38_7, all_38_6) = all_53_1 % 29.15/5.19 | | | | % 29.15/5.19 | | | | GROUND_INST: instantiating (12) with 0, all_53_1, all_38_6, all_38_7, % 29.15/5.19 | | | | simplifying with (22), (309) gives: % 29.15/5.19 | | | | (310) all_53_1 = 0 % 29.15/5.19 | | | | % 29.15/5.19 | | | | REDUCE: (308), (310) imply: % 29.15/5.19 | | | | (311) $false % 29.15/5.19 | | | | % 29.15/5.19 | | | | CLOSE: (311) is inconsistent. % 29.15/5.19 | | | | % 29.15/5.19 | | | End of split % 29.15/5.19 | | | % 29.15/5.19 | | Case 2: % 29.15/5.19 | | | % 29.15/5.19 | | | (312) ~ (all_58_1 = 0) & distinct_points(all_38_5, all_38_4) = % 29.15/5.19 | | | all_58_1 % 29.15/5.19 | | | % 29.15/5.19 | | | ALPHA: (312) implies: % 29.15/5.19 | | | (313) ~ (all_58_1 = 0) % 29.15/5.19 | | | (314) distinct_points(all_38_5, all_38_4) = all_58_1 % 29.15/5.19 | | | % 29.15/5.19 | | | GROUND_INST: instantiating (12) with 0, all_58_1, all_38_4, all_38_5, % 29.15/5.19 | | | simplifying with (23), (314) gives: % 29.15/5.19 | | | (315) all_58_1 = 0 % 29.15/5.19 | | | % 29.15/5.19 | | | REDUCE: (313), (315) imply: % 29.15/5.19 | | | (316) $false % 29.15/5.19 | | | % 29.15/5.19 | | | CLOSE: (316) is inconsistent. % 29.15/5.19 | | | % 29.15/5.19 | | End of split % 29.15/5.19 | | % 29.15/5.19 | Case 2: % 29.15/5.19 | | % 29.15/5.19 | | (317) ~ (all_59_1 = 0) & distinct_points(all_38_7, all_38_6) = all_59_1 % 29.15/5.19 | | % 29.15/5.19 | | ALPHA: (317) implies: % 29.15/5.19 | | (318) ~ (all_59_1 = 0) % 29.15/5.19 | | (319) distinct_points(all_38_7, all_38_6) = all_59_1 % 29.15/5.19 | | % 29.15/5.19 | | GROUND_INST: instantiating (12) with 0, all_59_1, all_38_6, all_38_7, % 29.15/5.19 | | simplifying with (22), (319) gives: % 29.15/5.19 | | (320) all_59_1 = 0 % 29.15/5.19 | | % 29.15/5.19 | | REDUCE: (318), (320) imply: % 29.15/5.19 | | (321) $false % 29.15/5.19 | | % 29.15/5.19 | | CLOSE: (321) is inconsistent. % 29.15/5.19 | | % 29.15/5.19 | End of split % 29.15/5.19 | % 29.15/5.19 End of proof % 29.15/5.19 % 29.15/5.19 Sub-proof #1 shows that the following formulas are inconsistent: % 29.15/5.19 ---------------------------------------------------------------- % 29.15/5.19 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.15/5.19 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 29.15/5.19 (apart_point_and_line(v3, v2) = v0)) % 29.15/5.19 (2) apart_point_and_line(all_38_6, all_38_3) = all_45_0 % 29.15/5.19 (3) apart_point_and_line(all_38_6, all_38_3) = 0 % 29.15/5.19 (4) ~ (all_45_0 = 0) % 29.15/5.19 % 29.15/5.19 Begin of proof % 29.15/5.19 | % 29.15/5.19 | GROUND_INST: instantiating (1) with all_45_0, 0, all_38_3, all_38_6, % 29.15/5.19 | simplifying with (2), (3) gives: % 29.15/5.19 | (5) all_45_0 = 0 % 29.15/5.19 | % 29.15/5.19 | REDUCE: (4), (5) imply: % 29.15/5.19 | (6) $false % 29.15/5.19 | % 29.15/5.19 | CLOSE: (6) is inconsistent. % 29.15/5.19 | % 29.15/5.20 End of proof % 29.15/5.20 % 29.15/5.20 Sub-proof #2 shows that the following formulas are inconsistent: % 29.15/5.20 ---------------------------------------------------------------- % 29.15/5.20 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.15/5.20 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 29.15/5.20 (apart_point_and_line(v3, v2) = v0)) % 29.15/5.20 (2) apart_point_and_line(all_38_6, all_38_2) = all_56_0 % 29.15/5.20 (3) apart_point_and_line(all_38_6, all_38_2) = 0 % 29.15/5.20 (4) ~ (all_56_0 = 0) % 29.15/5.20 % 29.15/5.20 Begin of proof % 29.15/5.20 | % 29.15/5.20 | GROUND_INST: instantiating (1) with all_56_0, 0, all_38_2, all_38_6, % 29.15/5.20 | simplifying with (2), (3) gives: % 29.15/5.20 | (5) all_56_0 = 0 % 29.15/5.20 | % 29.15/5.20 | REDUCE: (4), (5) imply: % 29.15/5.20 | (6) $false % 29.15/5.20 | % 29.15/5.20 | CLOSE: (6) is inconsistent. % 29.15/5.20 | % 29.15/5.20 End of proof % 29.15/5.20 % 29.15/5.20 Sub-proof #3 shows that the following formulas are inconsistent: % 29.15/5.20 ---------------------------------------------------------------- % 29.15/5.20 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.15/5.20 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 29.15/5.20 (apart_point_and_line(v3, v2) = v0)) % 29.15/5.20 (2) apart_point_and_line(all_38_7, all_38_2) = all_53_0 % 29.15/5.20 (3) apart_point_and_line(all_38_7, all_38_2) = 0 % 29.15/5.20 (4) ~ (all_53_0 = 0) % 29.15/5.20 % 29.15/5.20 Begin of proof % 29.15/5.20 | % 29.15/5.20 | GROUND_INST: instantiating (1) with all_53_0, 0, all_38_2, all_38_7, % 29.15/5.20 | simplifying with (2), (3) gives: % 29.15/5.20 | (5) all_53_0 = 0 % 29.15/5.20 | % 29.15/5.20 | REDUCE: (4), (5) imply: % 29.15/5.20 | (6) $false % 29.15/5.20 | % 29.15/5.20 | CLOSE: (6) is inconsistent. % 29.15/5.20 | % 29.15/5.20 End of proof % 29.15/5.20 % 29.15/5.20 Sub-proof #4 shows that the following formulas are inconsistent: % 29.15/5.20 ---------------------------------------------------------------- % 29.15/5.20 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.15/5.20 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 29.15/5.20 (apart_point_and_line(v3, v2) = v0)) % 29.15/5.20 (2) apart_point_and_line(all_38_7, all_38_3) = all_47_0 % 29.15/5.20 (3) apart_point_and_line(all_38_7, all_38_3) = 0 % 29.15/5.20 (4) ~ (all_47_0 = 0) % 29.15/5.20 % 29.15/5.20 Begin of proof % 29.15/5.20 | % 29.15/5.20 | GROUND_INST: instantiating (1) with all_47_0, 0, all_38_3, all_38_7, % 29.15/5.20 | simplifying with (2), (3) gives: % 29.15/5.20 | (5) all_47_0 = 0 % 29.15/5.20 | % 29.15/5.20 | REDUCE: (4), (5) imply: % 29.15/5.20 | (6) $false % 29.15/5.20 | % 29.15/5.20 | CLOSE: (6) is inconsistent. % 29.15/5.20 | % 29.15/5.20 End of proof % 29.15/5.20 % SZS output end Proof for theBenchmark % 29.15/5.20 % 29.15/5.20 4576ms %------------------------------------------------------------------------------