%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO189+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 : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:03 EDT 2023 % Result : Theorem 14.87s 2.76s % Output : Proof 21.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO189+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 21:16:22 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.47/1.22 Prover 4: Preprocessing ... % 3.47/1.22 Prover 1: Preprocessing ... % 3.47/1.26 Prover 5: Preprocessing ... % 3.47/1.26 Prover 2: Preprocessing ... % 3.47/1.26 Prover 0: Preprocessing ... % 3.47/1.26 Prover 3: Preprocessing ... % 3.47/1.26 Prover 6: Preprocessing ... % 6.36/1.64 Prover 5: Proving ... % 6.79/1.69 Prover 2: Proving ... % 6.79/1.74 Prover 3: Constructing countermodel ... % 6.79/1.76 Prover 6: Constructing countermodel ... % 7.82/1.82 Prover 1: Constructing countermodel ... % 7.88/1.90 Prover 3: gave up % 7.88/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.88/1.94 Prover 6: gave up % 7.88/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.77/1.99 Prover 7: Preprocessing ... % 8.77/2.02 Prover 8: Preprocessing ... % 9.62/2.08 Prover 7: Warning: ignoring some quantifiers % 9.62/2.11 Prover 7: Constructing countermodel ... % 9.62/2.12 Prover 0: Proving ... % 9.62/2.15 Prover 4: Constructing countermodel ... % 9.62/2.16 Prover 1: gave up % 10.30/2.16 Prover 8: Warning: ignoring some quantifiers % 10.30/2.17 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.30/2.18 Prover 8: Constructing countermodel ... % 10.54/2.22 Prover 9: Preprocessing ... % 11.92/2.42 Prover 8: gave up % 11.92/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.62/2.48 Prover 10: Preprocessing ... % 13.14/2.53 Prover 10: Warning: ignoring some quantifiers % 13.14/2.57 Prover 10: Constructing countermodel ... % 13.14/2.60 Prover 9: Constructing countermodel ... % 14.38/2.70 Prover 10: gave up % 14.38/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.38/2.75 Prover 11: Preprocessing ... % 14.87/2.76 Prover 0: proved (2116ms) % 14.87/2.76 % 14.87/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.87/2.76 % 14.87/2.77 Prover 9: stopped % 14.87/2.77 Prover 5: stopped % 14.87/2.77 Prover 2: stopped % 14.87/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.87/2.78 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.87/2.78 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.13/2.81 Prover 19: Preprocessing ... % 15.41/2.84 Prover 16: Preprocessing ... % 15.41/2.85 Prover 13: Preprocessing ... % 16.16/2.94 Prover 13: Warning: ignoring some quantifiers % 16.16/2.94 Prover 16: Warning: ignoring some quantifiers % 16.16/2.94 Prover 19: Warning: ignoring some quantifiers % 16.16/2.95 Prover 16: Constructing countermodel ... % 16.16/2.95 Prover 13: Constructing countermodel ... % 16.16/2.96 Prover 19: Constructing countermodel ... % 16.64/3.01 Prover 11: Constructing countermodel ... % 17.43/3.15 Prover 19: gave up % 17.98/3.27 Prover 13: gave up % 19.39/3.44 Prover 16: gave up % 20.29/3.51 Prover 7: gave up % 20.96/3.64 Prover 4: Found proof (size 339) % 20.96/3.64 Prover 4: proved (2995ms) % 20.96/3.64 Prover 11: stopped % 20.96/3.65 % 20.96/3.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.96/3.65 % 21.30/3.70 % SZS output start Proof for theBenchmark % 21.30/3.70 Assumptions after simplification: % 21.30/3.70 --------------------------------- % 21.30/3.70 % 21.30/3.70 (a4) % 21.30/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.30/3.73 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.30/3.73 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 21.30/3.73 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.30/3.73 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.30/3.73 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 21.30/3.73 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 21.30/3.73 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 21.30/3.73 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 21.30/3.73 % 21.30/3.73 (ceq2) % 21.30/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.30/3.73 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 21.30/3.73 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 21.30/3.73 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 21.30/3.73 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 21.30/3.73 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.30/3.73 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.30/3.73 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 21.30/3.73 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.30/3.73 apart_point_and_line(v0, v2) = 0) % 21.30/3.73 % 21.30/3.73 (ci1) % 21.30/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 21.30/3.74 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.30/3.74 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 21.30/3.74 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.30/3.74 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.30/3.74 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 21.30/3.74 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 21.30/3.74 % 21.30/3.74 (ci2) % 21.30/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 21.30/3.74 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.30/3.74 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 21.30/3.74 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.30/3.74 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.30/3.74 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 21.30/3.74 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 21.30/3.74 % 21.30/3.74 (con) % 21.30/3.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 21.30/3.74 int] : ( ~ (v5 = 0) & incident_point_and_line(v2, v3) = 0 & % 21.30/3.74 incident_point_and_line(v1, v4) = v5 & line_connecting(v0, v2) = v4 & % 21.30/3.74 line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & % 21.30/3.74 distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) % 21.30/3.74 & $i(v2) & $i(v1) & $i(v0)) % 21.30/3.74 % 21.30/3.74 (con1) % 21.30/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 21.30/3.74 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 21.30/3.74 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 21.30/3.74 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 21.30/3.74 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 21.30/3.74 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 21.30/3.74 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 21.30/3.74 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 21.30/3.74 0))) % 21.30/3.74 % 21.30/3.74 (cu1) % 21.30/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 21.30/3.75 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 21.30/3.75 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.30/3.75 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.30/3.75 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 21.30/3.75 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.30/3.75 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.30/3.75 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 21.30/3.75 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 21.30/3.75 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 21.30/3.75 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 21.30/3.75 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 21.30/3.75 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.30/3.75 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.30/3.75 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.30/3.75 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 21.30/3.75 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 21.30/3.75 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 21.30/3.75 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 21.30/3.75 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.30/3.75 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 21.30/3.75 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.30/3.75 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 21.30/3.75 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 21.30/3.75 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 21.30/3.75 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 21.30/3.75 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.30/3.75 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.30/3.75 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.30/3.75 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.30/3.75 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 21.30/3.75 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 21.30/3.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 21.30/3.75 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 21.30/3.75 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.30/3.75 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.30/3.75 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 21.30/3.75 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.30/3.75 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 21.30/3.75 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 21.30/3.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 21.30/3.75 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 21.30/3.75 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 21.30/3.75 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 21.30/3.75 % 21.30/3.75 (cup1) % 21.30/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.30/3.76 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 21.30/3.76 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.30/3.76 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 & % 21.30/3.76 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 21.30/3.76 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 21.30/3.76 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 21.30/3.76 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 21.30/3.76 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = % 21.30/3.76 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.30/3.76 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 21.30/3.76 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 21.30/3.76 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 & % 21.30/3.76 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 21.30/3.76 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 21.30/3.76 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 21.30/3.76 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 & % 21.30/3.76 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! % 21.30/3.76 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 21.30/3.76 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 21.30/3.76 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 & % 21.30/3.76 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 21.30/3.76 % 21.30/3.76 (function-axioms) % 21.72/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.72/3.76 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 21.72/3.76 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.72/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.76 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 21.72/3.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.72/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 21.72/3.76 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.72/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.76 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 21.72/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.72/3.76 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 21.72/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.76 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 21.72/3.76 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 21.72/3.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 21.72/3.76 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.72/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 21.72/3.76 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.72/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 21.72/3.76 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.72/3.76 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 21.72/3.76 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.72/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.76 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 21.72/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.72/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 21.72/3.76 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.72/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.76 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 21.72/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.72/3.76 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 21.72/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.72/3.76 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 21.72/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.72/3.76 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 21.72/3.76 % 21.72/3.76 Further assumptions not needed in the proof: % 21.72/3.76 -------------------------------------------- % 21.72/3.77 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq3, ci3, % 21.72/3.77 ci4, coipo1, cotno1, couo1, cp1, cp2, int1, oac1, occu1, ooc1, ooc2, orth1, % 21.72/3.77 ouo1, p1, par1 % 21.72/3.77 % 21.72/3.77 Those formulas are unsatisfiable: % 21.72/3.77 --------------------------------- % 21.72/3.77 % 21.72/3.77 Begin of proof % 21.72/3.77 | % 21.72/3.77 | ALPHA: (ci1) implies: % 21.72/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 21.72/3.77 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 21.72/3.77 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 21.72/3.77 | $i(v2))) % 21.72/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 21.72/3.77 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.72/3.77 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 21.72/3.77 | ~ (v4 = 0) | ~ (v3 = 0)))) % 21.72/3.77 | % 21.72/3.77 | ALPHA: (ci2) implies: % 21.72/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 21.72/3.77 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 21.72/3.77 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 21.72/3.77 | $i(v2))) % 21.72/3.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 21.72/3.77 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.72/3.77 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 21.72/3.77 | ~ (v4 = 0) | ~ (v3 = 0)))) % 21.72/3.77 | % 21.72/3.77 | ALPHA: (cu1) implies: % 21.72/3.77 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 21.72/3.77 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 21.72/3.77 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.72/3.77 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 21.72/3.77 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 21.72/3.77 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 21.72/3.77 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 21.72/3.77 | | v8 = 0))) % 21.72/3.78 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 21.72/3.78 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 21.72/3.78 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.72/3.78 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 21.72/3.78 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 21.72/3.78 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 21.72/3.78 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 21.72/3.78 | | v8 = 0))) % 21.72/3.78 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 21.72/3.78 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 21.72/3.78 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 21.72/3.78 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/3.78 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 21.72/3.78 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 21.72/3.78 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 21.72/3.78 | % 21.72/3.78 | ALPHA: (ceq2) implies: % 21.72/3.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.72/3.78 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 21.72/3.78 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 21.72/3.78 | v2) = 0) % 21.72/3.78 | % 21.72/3.78 | ALPHA: (cup1) implies: % 21.72/3.78 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 21.72/3.78 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 21.72/3.78 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.72/3.78 | $i(v0) | ? [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 % 21.72/3.78 | & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 21.72/3.78 | % 21.72/3.78 | ALPHA: (con1) implies: % 21.72/3.78 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 21.72/3.78 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 21.72/3.78 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 21.72/3.78 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 21.72/3.78 | | v5 = 0))) % 21.72/3.78 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 21.72/3.78 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 21.72/3.78 | [v5: any] : ? [v6: any] : (point(v1) = v4 & point(v0) = v3 & % 21.72/3.78 | line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ % 21.72/3.78 | (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 21.72/3.78 | % 21.72/3.78 | ALPHA: (a4) implies: % 21.72/3.78 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) % 21.72/3.78 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 21.72/3.78 | apart_point_and_line(v0, v1) = v2)) % 21.72/3.78 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.72/3.78 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/3.78 | apart_point_and_line(v0, v1) = 0) % 21.72/3.78 | % 21.72/3.78 | ALPHA: (function-axioms) implies: % 21.72/3.78 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.72/3.78 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 21.72/3.78 | (distinct_points(v3, v2) = v0)) % 21.72/3.79 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.72/3.79 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 21.72/3.79 | (distinct_lines(v3, v2) = v0)) % 21.72/3.79 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.72/3.79 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 21.72/3.79 | (apart_point_and_line(v3, v2) = v0)) % 21.72/3.79 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.72/3.79 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 21.72/3.79 | % 21.72/3.79 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 21.72/3.79 | all_38_3, all_38_4, all_38_5 gives: % 21.72/3.79 | (18) ~ (all_38_0 = 0) & incident_point_and_line(all_38_3, all_38_2) = 0 & % 21.72/3.79 | incident_point_and_line(all_38_4, all_38_1) = all_38_0 & % 21.72/3.79 | line_connecting(all_38_5, all_38_3) = all_38_1 & % 21.72/3.79 | line_connecting(all_38_5, all_38_4) = all_38_2 & % 21.72/3.79 | distinct_points(all_38_4, all_38_3) = 0 & distinct_points(all_38_5, % 21.72/3.79 | all_38_3) = 0 & distinct_points(all_38_5, all_38_4) = 0 & % 21.72/3.79 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 21.72/3.79 | $i(all_38_5) % 21.72/3.79 | % 21.72/3.79 | ALPHA: (18) implies: % 21.72/3.79 | (19) ~ (all_38_0 = 0) % 21.72/3.79 | (20) $i(all_38_5) % 21.72/3.79 | (21) $i(all_38_4) % 21.72/3.79 | (22) $i(all_38_3) % 21.72/3.79 | (23) $i(all_38_2) % 21.72/3.79 | (24) $i(all_38_1) % 21.72/3.79 | (25) distinct_points(all_38_5, all_38_4) = 0 % 21.87/3.79 | (26) distinct_points(all_38_5, all_38_3) = 0 % 21.87/3.79 | (27) distinct_points(all_38_4, all_38_3) = 0 % 21.87/3.79 | (28) line_connecting(all_38_5, all_38_4) = all_38_2 % 21.87/3.79 | (29) line_connecting(all_38_5, all_38_3) = all_38_1 % 21.87/3.79 | (30) incident_point_and_line(all_38_4, all_38_1) = all_38_0 % 21.87/3.79 | (31) incident_point_and_line(all_38_3, all_38_2) = 0 % 21.87/3.79 | % 21.87/3.79 | GROUND_INST: instantiating (10) with all_38_5, all_38_4, simplifying with % 21.87/3.79 | (20), (21), (25) gives: % 21.87/3.79 | (32) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 21.87/3.79 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(v2) = v3 & % 21.87/3.79 | line_connecting(all_38_5, all_38_4) = v2 & $i(v2) & ( ~ (v1 = 0) | % 21.87/3.79 | ~ (v0 = 0) | v3 = 0)) % 21.87/3.79 | % 21.87/3.80 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (20), % 21.87/3.80 | (21), (25) gives: % 21.87/3.80 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 21.87/3.80 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (20), % 21.87/3.80 | (21), (25) gives: % 21.87/3.80 | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 21.87/3.80 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (10) with all_38_5, all_38_3, simplifying with % 21.87/3.80 | (20), (22), (26) gives: % 21.87/3.80 | (35) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 21.87/3.80 | (point(all_38_3) = v1 & point(all_38_5) = v0 & line(v2) = v3 & % 21.87/3.80 | line_connecting(all_38_5, all_38_3) = v2 & $i(v2) & ( ~ (v1 = 0) | % 21.87/3.80 | ~ (v0 = 0) | v3 = 0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (3) with all_38_5, all_38_3, simplifying with (20), % 21.87/3.80 | (22), (26) gives: % 21.87/3.80 | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 21.87/3.80 | all_38_3) = v0 & apart_point_and_line(all_38_3, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (1) with all_38_5, all_38_3, simplifying with (20), % 21.87/3.80 | (22), (26) gives: % 21.87/3.80 | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 21.87/3.80 | all_38_3) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (10) with all_38_4, all_38_3, simplifying with % 21.87/3.80 | (21), (22), (27) gives: % 21.87/3.80 | (38) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 21.87/3.80 | (point(all_38_3) = v1 & point(all_38_4) = v0 & line(v2) = v3 & % 21.87/3.80 | line_connecting(all_38_4, all_38_3) = v2 & $i(v2) & ( ~ (v1 = 0) | % 21.87/3.80 | ~ (v0 = 0) | v3 = 0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (3) with all_38_4, all_38_3, simplifying with (21), % 21.87/3.80 | (22), (27) gives: % 21.87/3.80 | (39) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_4, % 21.87/3.80 | all_38_3) = v0 & apart_point_and_line(all_38_3, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (1) with all_38_4, all_38_3, simplifying with (21), % 21.87/3.80 | (22), (27) gives: % 21.87/3.80 | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_4, % 21.87/3.80 | all_38_3) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (11) with all_38_5, all_38_4, all_38_2, simplifying % 21.87/3.80 | with (20), (21), (28) gives: % 21.87/3.80 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 21.87/3.80 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_2) = v3 & % 21.87/3.80 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 21.87/3.80 | 0) | ~ (v0 = 0) | v3 = 0)) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 21.87/3.80 | with (20), (21), (28) gives: % 21.87/3.80 | (42) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 21.87/3.80 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 21.87/3.80 | (v1 = 0) | ~ (v0 = 0))) % 21.87/3.80 | % 21.87/3.80 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 21.87/3.80 | with (20), (21), (28) gives: % 21.87/3.80 | (43) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5, % 21.87/3.80 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 21.87/3.80 | (v1 = 0) | ~ (v0 = 0))) % 21.87/3.81 | % 21.87/3.81 | GROUND_INST: instantiating (11) with all_38_5, all_38_3, all_38_1, simplifying % 21.87/3.81 | with (20), (22), (29) gives: % 21.87/3.81 | (44) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 21.87/3.81 | (point(all_38_3) = v1 & point(all_38_5) = v0 & line(all_38_1) = v3 & % 21.87/3.81 | distinct_points(all_38_5, all_38_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 21.87/3.81 | 0) | ~ (v0 = 0) | v3 = 0)) % 21.87/3.81 | % 21.87/3.81 | GROUND_INST: instantiating (4) with all_38_5, all_38_3, all_38_1, simplifying % 21.87/3.81 | with (20), (22), (29) gives: % 21.87/3.81 | (45) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 21.87/3.81 | all_38_1) = v1 & distinct_points(all_38_5, all_38_3) = v0 & ( ~ % 21.87/3.81 | (v1 = 0) | ~ (v0 = 0))) % 21.87/3.81 | % 21.87/3.81 | GROUND_INST: instantiating (2) with all_38_5, all_38_3, all_38_1, simplifying % 21.87/3.81 | with (20), (22), (29) gives: % 21.87/3.81 | (46) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5, % 21.87/3.81 | all_38_1) = v1 & distinct_points(all_38_5, all_38_3) = v0 & ( ~ % 21.87/3.81 | (v1 = 0) | ~ (v0 = 0))) % 21.87/3.81 | % 21.87/3.81 | GROUND_INST: instantiating (13) with all_38_4, all_38_1, all_38_0, simplifying % 21.87/3.81 | with (21), (24), (30) gives: % 21.87/3.81 | (47) all_38_0 = 0 | apart_point_and_line(all_38_4, all_38_1) = 0 % 21.87/3.81 | % 21.87/3.81 | GROUND_INST: instantiating (12) with all_38_3, all_38_2, simplifying with % 21.87/3.81 | (22), (23), (31) gives: % 21.87/3.81 | (48) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_3, all_38_2) % 21.87/3.81 | = v0) % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (48) with fresh symbol all_45_0 gives: % 21.87/3.81 | (49) ~ (all_45_0 = 0) & apart_point_and_line(all_38_3, all_38_2) = % 21.87/3.81 | all_45_0 % 21.87/3.81 | % 21.87/3.81 | ALPHA: (49) implies: % 21.87/3.81 | (50) ~ (all_45_0 = 0) % 21.87/3.81 | (51) apart_point_and_line(all_38_3, all_38_2) = all_45_0 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (39) with fresh symbols all_53_0, all_53_1 gives: % 21.87/3.81 | (52) ~ (all_53_0 = 0) & line_connecting(all_38_4, all_38_3) = all_53_1 & % 21.87/3.81 | apart_point_and_line(all_38_3, all_53_1) = all_53_0 & $i(all_53_1) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (52) implies: % 21.87/3.81 | (53) ~ (all_53_0 = 0) % 21.87/3.81 | (54) apart_point_and_line(all_38_3, all_53_1) = all_53_0 % 21.87/3.81 | (55) line_connecting(all_38_4, all_38_3) = all_53_1 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (43) with fresh symbols all_55_0, all_55_1 gives: % 21.87/3.81 | (56) apart_point_and_line(all_38_5, all_38_2) = all_55_0 & % 21.87/3.81 | distinct_points(all_38_5, all_38_4) = all_55_1 & ( ~ (all_55_0 = 0) | % 21.87/3.81 | ~ (all_55_1 = 0)) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (56) implies: % 21.87/3.81 | (57) distinct_points(all_38_5, all_38_4) = all_55_1 % 21.87/3.81 | (58) apart_point_and_line(all_38_5, all_38_2) = all_55_0 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (40) with fresh symbols all_57_0, all_57_1 gives: % 21.87/3.81 | (59) ~ (all_57_0 = 0) & line_connecting(all_38_4, all_38_3) = all_57_1 & % 21.87/3.81 | apart_point_and_line(all_38_4, all_57_1) = all_57_0 & $i(all_57_1) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (59) implies: % 21.87/3.81 | (60) ~ (all_57_0 = 0) % 21.87/3.81 | (61) $i(all_57_1) % 21.87/3.81 | (62) apart_point_and_line(all_38_4, all_57_1) = all_57_0 % 21.87/3.81 | (63) line_connecting(all_38_4, all_38_3) = all_57_1 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (36) with fresh symbols all_59_0, all_59_1 gives: % 21.87/3.81 | (64) ~ (all_59_0 = 0) & line_connecting(all_38_5, all_38_3) = all_59_1 & % 21.87/3.81 | apart_point_and_line(all_38_3, all_59_1) = all_59_0 & $i(all_59_1) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (64) implies: % 21.87/3.81 | (65) $i(all_59_1) % 21.87/3.81 | (66) apart_point_and_line(all_38_3, all_59_1) = all_59_0 % 21.87/3.81 | (67) line_connecting(all_38_5, all_38_3) = all_59_1 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (33) with fresh symbols all_61_0, all_61_1 gives: % 21.87/3.81 | (68) ~ (all_61_0 = 0) & line_connecting(all_38_5, all_38_4) = all_61_1 & % 21.87/3.81 | apart_point_and_line(all_38_4, all_61_1) = all_61_0 & $i(all_61_1) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (68) implies: % 21.87/3.81 | (69) $i(all_61_1) % 21.87/3.81 | (70) apart_point_and_line(all_38_4, all_61_1) = all_61_0 % 21.87/3.81 | (71) line_connecting(all_38_5, all_38_4) = all_61_1 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (46) with fresh symbols all_63_0, all_63_1 gives: % 21.87/3.81 | (72) apart_point_and_line(all_38_5, all_38_1) = all_63_0 & % 21.87/3.81 | distinct_points(all_38_5, all_38_3) = all_63_1 & ( ~ (all_63_0 = 0) | % 21.87/3.81 | ~ (all_63_1 = 0)) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (72) implies: % 21.87/3.81 | (73) distinct_points(all_38_5, all_38_3) = all_63_1 % 21.87/3.81 | (74) apart_point_and_line(all_38_5, all_38_1) = all_63_0 % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (42) with fresh symbols all_65_0, all_65_1 gives: % 21.87/3.81 | (75) apart_point_and_line(all_38_4, all_38_2) = all_65_0 & % 21.87/3.81 | distinct_points(all_38_5, all_38_4) = all_65_1 & ( ~ (all_65_0 = 0) | % 21.87/3.81 | ~ (all_65_1 = 0)) % 21.87/3.81 | % 21.87/3.81 | ALPHA: (75) implies: % 21.87/3.81 | (76) distinct_points(all_38_5, all_38_4) = all_65_1 % 21.87/3.81 | (77) apart_point_and_line(all_38_4, all_38_2) = all_65_0 % 21.87/3.81 | (78) ~ (all_65_0 = 0) | ~ (all_65_1 = 0) % 21.87/3.81 | % 21.87/3.81 | DELTA: instantiating (37) with fresh symbols all_67_0, all_67_1 gives: % 21.87/3.82 | (79) ~ (all_67_0 = 0) & line_connecting(all_38_5, all_38_3) = all_67_1 & % 21.87/3.82 | apart_point_and_line(all_38_5, all_67_1) = all_67_0 & $i(all_67_1) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (79) implies: % 21.87/3.82 | (80) ~ (all_67_0 = 0) % 21.87/3.82 | (81) apart_point_and_line(all_38_5, all_67_1) = all_67_0 % 21.87/3.82 | (82) line_connecting(all_38_5, all_38_3) = all_67_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (45) with fresh symbols all_69_0, all_69_1 gives: % 21.87/3.82 | (83) apart_point_and_line(all_38_3, all_38_1) = all_69_0 & % 21.87/3.82 | distinct_points(all_38_5, all_38_3) = all_69_1 & ( ~ (all_69_0 = 0) | % 21.87/3.82 | ~ (all_69_1 = 0)) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (83) implies: % 21.87/3.82 | (84) distinct_points(all_38_5, all_38_3) = all_69_1 % 21.87/3.82 | (85) apart_point_and_line(all_38_3, all_38_1) = all_69_0 % 21.87/3.82 | (86) ~ (all_69_0 = 0) | ~ (all_69_1 = 0) % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (34) with fresh symbols all_71_0, all_71_1 gives: % 21.87/3.82 | (87) ~ (all_71_0 = 0) & line_connecting(all_38_5, all_38_4) = all_71_1 & % 21.87/3.82 | apart_point_and_line(all_38_5, all_71_1) = all_71_0 & $i(all_71_1) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (87) implies: % 21.87/3.82 | (88) ~ (all_71_0 = 0) % 21.87/3.82 | (89) apart_point_and_line(all_38_5, all_71_1) = all_71_0 % 21.87/3.82 | (90) line_connecting(all_38_5, all_38_4) = all_71_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (38) with fresh symbols all_73_0, all_73_1, all_73_2, % 21.87/3.82 | all_73_3 gives: % 21.87/3.82 | (91) point(all_38_3) = all_73_2 & point(all_38_4) = all_73_3 & % 21.87/3.82 | line(all_73_1) = all_73_0 & line_connecting(all_38_4, all_38_3) = % 21.87/3.82 | all_73_1 & $i(all_73_1) & ( ~ (all_73_2 = 0) | ~ (all_73_3 = 0) | % 21.87/3.82 | all_73_0 = 0) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (91) implies: % 21.87/3.82 | (92) line_connecting(all_38_4, all_38_3) = all_73_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (41) with fresh symbols all_75_0, all_75_1, all_75_2, % 21.87/3.82 | all_75_3 gives: % 21.87/3.82 | (93) point(all_38_4) = all_75_2 & point(all_38_5) = all_75_3 & % 21.87/3.82 | line(all_38_2) = all_75_0 & distinct_points(all_38_5, all_38_4) = % 21.87/3.82 | all_75_1 & ( ~ (all_75_1 = 0) | ~ (all_75_2 = 0) | ~ (all_75_3 = 0) % 21.87/3.82 | | all_75_0 = 0) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (93) implies: % 21.87/3.82 | (94) distinct_points(all_38_5, all_38_4) = all_75_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (35) with fresh symbols all_77_0, all_77_1, all_77_2, % 21.87/3.82 | all_77_3 gives: % 21.87/3.82 | (95) point(all_38_3) = all_77_2 & point(all_38_5) = all_77_3 & % 21.87/3.82 | line(all_77_1) = all_77_0 & line_connecting(all_38_5, all_38_3) = % 21.87/3.82 | all_77_1 & $i(all_77_1) & ( ~ (all_77_2 = 0) | ~ (all_77_3 = 0) | % 21.87/3.82 | all_77_0 = 0) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (95) implies: % 21.87/3.82 | (96) line_connecting(all_38_5, all_38_3) = all_77_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (32) with fresh symbols all_79_0, all_79_1, all_79_2, % 21.87/3.82 | all_79_3 gives: % 21.87/3.82 | (97) point(all_38_4) = all_79_2 & point(all_38_5) = all_79_3 & % 21.87/3.82 | line(all_79_1) = all_79_0 & line_connecting(all_38_5, all_38_4) = % 21.87/3.82 | all_79_1 & $i(all_79_1) & ( ~ (all_79_2 = 0) | ~ (all_79_3 = 0) | % 21.87/3.82 | all_79_0 = 0) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (97) implies: % 21.87/3.82 | (98) line_connecting(all_38_5, all_38_4) = all_79_1 % 21.87/3.82 | % 21.87/3.82 | DELTA: instantiating (44) with fresh symbols all_81_0, all_81_1, all_81_2, % 21.87/3.82 | all_81_3 gives: % 21.87/3.82 | (99) point(all_38_3) = all_81_2 & point(all_38_5) = all_81_3 & % 21.87/3.82 | line(all_38_1) = all_81_0 & distinct_points(all_38_5, all_38_3) = % 21.87/3.82 | all_81_1 & ( ~ (all_81_1 = 0) | ~ (all_81_2 = 0) | ~ (all_81_3 = 0) % 21.87/3.82 | | all_81_0 = 0) % 21.87/3.82 | % 21.87/3.82 | ALPHA: (99) implies: % 21.87/3.82 | (100) distinct_points(all_38_5, all_38_3) = all_81_1 % 21.87/3.82 | % 21.87/3.82 | BETA: splitting (47) gives: % 21.87/3.82 | % 21.87/3.82 | Case 1: % 21.87/3.82 | | % 21.87/3.82 | | (101) apart_point_and_line(all_38_4, all_38_1) = 0 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with 0, all_65_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (25), (76) gives: % 21.87/3.82 | | (102) all_65_1 = 0 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with all_65_1, all_75_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (76), (94) gives: % 21.87/3.82 | | (103) all_75_1 = all_65_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with all_55_1, all_75_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (57), (94) gives: % 21.87/3.82 | | (104) all_75_1 = all_55_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with 0, all_69_1, all_38_3, all_38_5, % 21.87/3.82 | | simplifying with (26), (84) gives: % 21.87/3.82 | | (105) all_69_1 = 0 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with all_69_1, all_81_1, all_38_3, all_38_5, % 21.87/3.82 | | simplifying with (84), (100) gives: % 21.87/3.82 | | (106) all_81_1 = all_69_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (14) with all_63_1, all_81_1, all_38_3, all_38_5, % 21.87/3.82 | | simplifying with (73), (100) gives: % 21.87/3.82 | | (107) all_81_1 = all_63_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (17) with all_38_2, all_71_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (28), (90) gives: % 21.87/3.82 | | (108) all_71_1 = all_38_2 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (17) with all_71_1, all_79_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (90), (98) gives: % 21.87/3.82 | | (109) all_79_1 = all_71_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (17) with all_61_1, all_79_1, all_38_4, all_38_5, % 21.87/3.82 | | simplifying with (71), (98) gives: % 21.87/3.82 | | (110) all_79_1 = all_61_1 % 21.87/3.82 | | % 21.87/3.82 | | GROUND_INST: instantiating (17) with all_38_1, all_77_1, all_38_3, all_38_5, % 21.87/3.82 | | simplifying with (29), (96) gives: % 21.87/3.82 | | (111) all_77_1 = all_38_1 % 21.87/3.82 | | % 21.87/3.83 | | GROUND_INST: instantiating (17) with all_67_1, all_77_1, all_38_3, all_38_5, % 21.87/3.83 | | simplifying with (82), (96) gives: % 21.87/3.83 | | (112) all_77_1 = all_67_1 % 21.87/3.83 | | % 21.87/3.83 | | GROUND_INST: instantiating (17) with all_59_1, all_77_1, all_38_3, all_38_5, % 21.87/3.83 | | simplifying with (67), (96) gives: % 21.87/3.83 | | (113) all_77_1 = all_59_1 % 21.87/3.83 | | % 21.87/3.83 | | GROUND_INST: instantiating (17) with all_57_1, all_73_1, all_38_3, all_38_4, % 21.87/3.83 | | simplifying with (63), (92) gives: % 21.87/3.83 | | (114) all_73_1 = all_57_1 % 21.87/3.83 | | % 21.87/3.83 | | GROUND_INST: instantiating (17) with all_53_1, all_73_1, all_38_3, all_38_4, % 21.87/3.83 | | simplifying with (55), (92) gives: % 21.87/3.83 | | (115) all_73_1 = all_53_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (106), (107) imply: % 21.87/3.83 | | (116) all_69_1 = all_63_1 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (116) implies: % 21.87/3.83 | | (117) all_69_1 = all_63_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (109), (110) imply: % 21.87/3.83 | | (118) all_71_1 = all_61_1 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (118) implies: % 21.87/3.83 | | (119) all_71_1 = all_61_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (111), (112) imply: % 21.87/3.83 | | (120) all_67_1 = all_38_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (112), (113) imply: % 21.87/3.83 | | (121) all_67_1 = all_59_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (103), (104) imply: % 21.87/3.83 | | (122) all_65_1 = all_55_1 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (122) implies: % 21.87/3.83 | | (123) all_65_1 = all_55_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (114), (115) imply: % 21.87/3.83 | | (124) all_57_1 = all_53_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (108), (119) imply: % 21.87/3.83 | | (125) all_61_1 = all_38_2 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (125) implies: % 21.87/3.83 | | (126) all_61_1 = all_38_2 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (105), (117) imply: % 21.87/3.83 | | (127) all_63_1 = 0 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (127) implies: % 21.87/3.83 | | (128) all_63_1 = 0 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (120), (121) imply: % 21.87/3.83 | | (129) all_59_1 = all_38_1 % 21.87/3.83 | | % 21.87/3.83 | | SIMP: (129) implies: % 21.87/3.83 | | (130) all_59_1 = all_38_1 % 21.87/3.83 | | % 21.87/3.83 | | COMBINE_EQS: (102), (123) imply: % 21.87/3.83 | | (131) all_55_1 = 0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (66), (130) imply: % 21.87/3.83 | | (132) apart_point_and_line(all_38_3, all_38_1) = all_59_0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (70), (126) imply: % 21.87/3.83 | | (133) apart_point_and_line(all_38_4, all_38_2) = all_61_0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (62), (124) imply: % 21.87/3.83 | | (134) apart_point_and_line(all_38_4, all_53_1) = all_57_0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (89), (108) imply: % 21.87/3.83 | | (135) apart_point_and_line(all_38_5, all_38_2) = all_71_0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (81), (120) imply: % 21.87/3.83 | | (136) apart_point_and_line(all_38_5, all_38_1) = all_67_0 % 21.87/3.83 | | % 21.87/3.83 | | REDUCE: (61), (124) imply: % 21.87/3.83 | | (137) $i(all_53_1) % 21.87/3.83 | | % 21.87/3.83 | | BETA: splitting (86) gives: % 21.87/3.83 | | % 21.87/3.83 | | Case 1: % 21.87/3.83 | | | % 21.87/3.83 | | | (138) ~ (all_69_0 = 0) % 21.87/3.83 | | | % 21.87/3.83 | | | BETA: splitting (78) gives: % 21.87/3.83 | | | % 21.87/3.83 | | | Case 1: % 21.87/3.83 | | | | % 21.87/3.83 | | | | (139) ~ (all_65_0 = 0) % 21.87/3.83 | | | | % 21.87/3.83 | | | | GROUND_INST: instantiating (16) with all_55_0, all_71_0, all_38_2, % 21.87/3.83 | | | | all_38_5, simplifying with (58), (135) gives: % 21.87/3.83 | | | | (140) all_71_0 = all_55_0 % 21.87/3.83 | | | | % 21.87/3.83 | | | | GROUND_INST: instantiating (16) with all_63_0, all_67_0, all_38_1, % 21.87/3.83 | | | | all_38_5, simplifying with (74), (136) gives: % 21.87/3.83 | | | | (141) all_67_0 = all_63_0 % 21.87/3.83 | | | | % 21.87/3.83 | | | | GROUND_INST: instantiating (16) with all_65_0, all_61_0, all_38_2, % 21.87/3.83 | | | | all_38_4, simplifying with (77), (133) gives: % 21.87/3.83 | | | | (142) all_65_0 = all_61_0 % 21.87/3.83 | | | | % 21.87/3.83 | | | | GROUND_INST: instantiating (16) with all_69_0, all_59_0, all_38_1, % 21.87/3.83 | | | | all_38_3, simplifying with (85), (132) gives: % 21.87/3.83 | | | | (143) all_69_0 = all_59_0 % 21.87/3.83 | | | | % 21.87/3.83 | | | | REDUCE: (88), (140) imply: % 21.87/3.83 | | | | (144) ~ (all_55_0 = 0) % 21.87/3.83 | | | | % 21.87/3.83 | | | | REDUCE: (138), (143) imply: % 21.87/3.83 | | | | (145) ~ (all_59_0 = 0) % 21.87/3.83 | | | | % 21.87/3.83 | | | | REDUCE: (80), (141) imply: % 21.87/3.83 | | | | (146) ~ (all_63_0 = 0) % 21.87/3.83 | | | | % 21.87/3.83 | | | | REDUCE: (139), (142) imply: % 21.87/3.83 | | | | (147) ~ (all_61_0 = 0) % 21.87/3.83 | | | | % 21.87/3.83 | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_5, all_38_1, % 21.87/3.83 | | | | all_38_1, all_63_0, all_63_0, simplifying with (20), (24), % 21.87/3.83 | | | | (74) gives: % 21.87/3.84 | | | | (148) all_63_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.84 | | | | [v3: any] : (apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.84 | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 21.87/3.84 | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_4, all_38_2, % 21.87/3.84 | | | | all_38_2, all_61_0, all_61_0, simplifying with (20), (21), % 21.87/3.84 | | | | (23), (25), (133) gives: % 21.87/3.84 | | | | (149) all_61_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 21.87/3.84 | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.84 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 21.87/3.84 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 21.87/3.84 | | | | 0 | v1 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_4, all_38_5, all_38_2, % 21.87/3.84 | | | | all_38_1, all_61_0, all_63_0, simplifying with (20), (21), % 21.87/3.84 | | | | (23), (24), (74), (133) gives: % 21.87/3.84 | | | | (150) all_63_0 = 0 | all_61_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.84 | | | | all_38_1) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.84 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_2, % 21.87/3.84 | | | | all_38_1, all_63_0, all_61_0, simplifying with (20), (21), % 21.87/3.84 | | | | (23), (24), (74), (133) gives: % 21.87/3.84 | | | | (151) all_63_0 = 0 | all_61_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.84 | | | | all_38_1) = v3 & apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.84 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_1, all_38_2, % 21.87/3.84 | | | | all_61_0, simplifying with (21), (23), (24), (101), (133) % 21.87/3.84 | | | | gives: % 21.87/3.84 | | | | (152) all_61_0 = 0 | distinct_lines(all_38_1, all_38_2) = 0 % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_4, all_38_2, % 21.87/3.84 | | | | all_53_1, all_45_0, all_57_0, simplifying with (21), (22), % 21.87/3.84 | | | | (23), (51), (134), (137) gives: % 21.87/3.84 | | | | (153) all_57_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.84 | | | | all_53_1) = v2 & apart_point_and_line(all_38_4, all_38_2) = % 21.87/3.84 | | | | v3 & distinct_lines(all_38_2, all_53_1) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_5, all_38_2, % 21.87/3.84 | | | | all_38_2, all_45_0, all_55_0, simplifying with (20), (22), % 21.87/3.84 | | | | (23), (51), (58) gives: % 21.87/3.84 | | | | (154) all_55_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.84 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.84 | | | | v3 & distinct_lines(all_38_2, all_38_2) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_3, all_38_1, % 21.87/3.84 | | | | all_38_2, all_59_0, all_45_0, simplifying with (20), (22), % 21.87/3.84 | | | | (23), (24), (26), (51), (132) gives: % 21.87/3.84 | | | | (155) all_59_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_38_1) = v1 & % 21.87/3.84 | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.84 | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 21.87/3.84 | | | | 0 | v1 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (9) with all_38_3, all_38_1, all_38_2, % 21.87/3.84 | | | | all_59_0, all_45_0, simplifying with (22), (23), (24), % 21.87/3.84 | | | | (51), (132) gives: % 21.87/3.84 | | | | (156) all_59_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 21.87/3.84 | | | | (convergent_lines(all_38_1, all_38_2) = v1 & % 21.87/3.84 | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v1 = % 21.87/3.84 | | | | 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_4, all_38_1, % 21.87/3.84 | | | | all_38_2, all_59_0, all_61_0, simplifying with (21), (22), % 21.87/3.84 | | | | (23), (24), (132), (133) gives: % 21.87/3.84 | | | | (157) all_61_0 = 0 | all_59_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.84 | | | | all_38_2) = v2 & apart_point_and_line(all_38_4, all_38_1) = % 21.87/3.84 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_5, all_38_1, % 21.87/3.84 | | | | all_38_1, all_59_0, all_63_0, simplifying with (20), (22), % 21.87/3.84 | | | | (24), (74), (132) gives: % 21.87/3.84 | | | | (158) all_63_0 = 0 | all_59_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.84 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.84 | | | | all_38_1) = v2 & apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.84 | | | | v3 & distinct_lines(all_38_1, all_38_1) = v1 & % 21.87/3.84 | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.84 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.84 | | | | % 21.87/3.84 | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_5, all_38_1, % 21.87/3.84 | | | | all_38_2, all_59_0, all_55_0, simplifying with (20), (22), % 21.87/3.84 | | | | (23), (24), (58), (132) gives: % 21.87/3.85 | | | | (159) all_59_0 = 0 | all_55_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.85 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.85 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.85 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.85 | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.85 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.85 | | | | % 21.87/3.85 | | | | GROUND_INST: instantiating (5) with all_38_3, all_38_5, all_38_2, % 21.87/3.85 | | | | all_38_1, all_59_0, all_55_0, simplifying with (20), (22), % 21.87/3.85 | | | | (23), (24), (58), (132) gives: % 21.87/3.85 | | | | (160) all_59_0 = 0 | all_55_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.85 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.85 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.85 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.85 | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 21.87/3.85 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.85 | | | | % 21.87/3.85 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_3, all_53_1, % 21.87/3.85 | | | | all_38_1, all_53_0, all_59_0, simplifying with (20), (22), % 21.87/3.85 | | | | (24), (26), (54), (132), (137) gives: % 21.87/3.85 | | | | (161) all_59_0 = 0 | all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.85 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_53_1) = v1 & % 21.87/3.85 | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 21.87/3.85 | | | | distinct_lines(all_53_1, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = % 21.87/3.85 | | | | 0 | v1 = 0)) % 21.87/3.85 | | | | % 21.87/3.85 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_3, all_38_2, % 21.87/3.85 | | | | all_53_1, all_45_0, all_53_0, simplifying with (20), (22), % 21.87/3.85 | | | | (23), (26), (51), (54), (137) gives: % 21.87/3.85 | | | | (162) all_53_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.85 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_53_1) = v2 & % 21.87/3.85 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 21.87/3.85 | | | | distinct_lines(all_38_2, all_53_1) = v0 & ( ~ (v0 = 0) | v2 = % 21.87/3.85 | | | | 0 | v1 = 0)) % 21.87/3.85 | | | | % 21.87/3.85 | | | | BETA: splitting (152) gives: % 21.87/3.85 | | | | % 21.87/3.85 | | | | Case 1: % 21.87/3.85 | | | | | % 21.87/3.85 | | | | | (163) distinct_lines(all_38_1, all_38_2) = 0 % 21.87/3.85 | | | | | % 21.87/3.85 | | | | | BETA: splitting (148) gives: % 21.87/3.85 | | | | | % 21.87/3.85 | | | | | Case 1: % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | (164) all_63_0 = 0 % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | REDUCE: (146), (164) imply: % 21.87/3.85 | | | | | | (165) $false % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | CLOSE: (165) is inconsistent. % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | Case 2: % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | (166) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 21.87/3.85 | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.85 | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 21.87/3.85 | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 21.87/3.85 | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | % 21.87/3.85 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | DELTA: instantiating (166) with fresh symbols all_141_0, all_141_1, % 21.87/3.85 | | | | | | all_141_2, all_141_3 gives: % 21.87/3.85 | | | | | | (167) apart_point_and_line(all_38_5, all_38_1) = all_141_0 & % 21.87/3.85 | | | | | | apart_point_and_line(all_38_5, all_38_1) = all_141_1 & % 21.87/3.85 | | | | | | distinct_lines(all_38_1, all_38_1) = all_141_2 & % 21.87/3.85 | | | | | | distinct_points(all_38_5, all_38_5) = all_141_3 & ( ~ % 21.87/3.85 | | | | | | (all_141_2 = 0) | ~ (all_141_3 = 0) | all_141_0 = 0 | % 21.87/3.85 | | | | | | all_141_1 = 0) % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | ALPHA: (167) implies: % 21.87/3.85 | | | | | | (168) apart_point_and_line(all_38_5, all_38_1) = all_141_1 % 21.87/3.85 | | | | | | (169) apart_point_and_line(all_38_5, all_38_1) = all_141_0 % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | BETA: splitting (151) gives: % 21.87/3.85 | | | | | | % 21.87/3.85 | | | | | | Case 1: % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | (170) all_63_0 = 0 % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | REDUCE: (146), (170) imply: % 21.87/3.85 | | | | | | | (171) $false % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | CLOSE: (171) is inconsistent. % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | Case 2: % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | (172) all_61_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 21.87/3.85 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.85 | | | | | | | all_38_1) = v3 & apart_point_and_line(all_38_5, % 21.87/3.85 | | | | | | | all_38_2) = v2 & distinct_lines(all_38_2, all_38_1) = % 21.87/3.85 | | | | | | | v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 % 21.87/3.85 | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | BETA: splitting (150) gives: % 21.87/3.85 | | | | | | | % 21.87/3.85 | | | | | | | Case 1: % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | (173) all_63_0 = 0 % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | REDUCE: (146), (173) imply: % 21.87/3.85 | | | | | | | | (174) $false % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | CLOSE: (174) is inconsistent. % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | Case 2: % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | (175) all_61_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 21.87/3.85 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.85 | | | | | | | | all_38_1) = v2 & apart_point_and_line(all_38_5, % 21.87/3.85 | | | | | | | | all_38_2) = v3 & distinct_lines(all_38_2, all_38_1) % 21.87/3.85 | | | | | | | | = v1 & distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 21.87/3.85 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | BETA: splitting (162) gives: % 21.87/3.85 | | | | | | | | % 21.87/3.85 | | | | | | | | Case 1: % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | (176) all_53_0 = 0 % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | REDUCE: (53), (176) imply: % 21.87/3.85 | | | | | | | | | (177) $false % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | CLOSE: (177) is inconsistent. % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | Case 2: % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | (178) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 21.87/3.85 | | | | | | | | | any] : (apart_point_and_line(all_38_5, all_53_1) = % 21.87/3.85 | | | | | | | | | v2 & apart_point_and_line(all_38_5, all_38_2) = v1 % 21.87/3.85 | | | | | | | | | & distinct_lines(all_38_2, all_53_1) = v0 & ( ~ (v0 % 21.87/3.85 | | | | | | | | | = 0) | v2 = 0 | v1 = 0)) % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | BETA: splitting (161) gives: % 21.87/3.85 | | | | | | | | | % 21.87/3.85 | | | | | | | | | Case 1: % 21.87/3.85 | | | | | | | | | | % 21.87/3.85 | | | | | | | | | | (179) all_59_0 = 0 % 21.87/3.85 | | | | | | | | | | % 21.87/3.85 | | | | | | | | | | REDUCE: (145), (179) imply: % 21.87/3.85 | | | | | | | | | | (180) $false % 21.87/3.85 | | | | | | | | | | % 21.87/3.85 | | | | | | | | | | CLOSE: (180) is inconsistent. % 21.87/3.85 | | | | | | | | | | % 21.87/3.85 | | | | | | | | | Case 2: % 21.87/3.85 | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | (181) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_5, % 21.87/3.86 | | | | | | | | | | all_53_1) = v1 & apart_point_and_line(all_38_5, % 21.87/3.86 | | | | | | | | | | all_38_1) = v2 & distinct_lines(all_53_1, % 21.87/3.86 | | | | | | | | | | all_38_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = % 21.87/3.86 | | | | | | | | | | 0)) % 21.87/3.86 | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | BETA: splitting (155) gives: % 21.87/3.86 | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | (182) all_59_0 = 0 % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | REDUCE: (145), (182) imply: % 21.87/3.86 | | | | | | | | | | | (183) $false % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | CLOSE: (183) is inconsistent. % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | (184) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_5, % 21.87/3.86 | | | | | | | | | | | all_38_1) = v1 & % 21.87/3.86 | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | BETA: splitting (184) gives: % 21.87/3.86 | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | (185) all_45_0 = 0 % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | REDUCE: (50), (185) imply: % 21.87/3.86 | | | | | | | | | | | | (186) $false % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | CLOSE: (186) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | (187) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 21.87/3.86 | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v1 & % 21.87/3.86 | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | DELTA: instantiating (187) with fresh symbols all_250_0, % 21.87/3.86 | | | | | | | | | | | | all_250_1, all_250_2 gives: % 21.87/3.86 | | | | | | | | | | | | (188) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.86 | | | | | | | | | | | | all_250_1 & apart_point_and_line(all_38_5, % 21.87/3.86 | | | | | | | | | | | | all_38_2) = all_250_0 & distinct_lines(all_38_1, % 21.87/3.86 | | | | | | | | | | | | all_38_2) = all_250_2 & ( ~ (all_250_2 = 0) | % 21.87/3.86 | | | | | | | | | | | | all_250_0 = 0 | all_250_1 = 0) % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | ALPHA: (188) implies: % 21.87/3.86 | | | | | | | | | | | | (189) distinct_lines(all_38_1, all_38_2) = all_250_2 % 21.87/3.86 | | | | | | | | | | | | (190) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.86 | | | | | | | | | | | | all_250_0 % 21.87/3.86 | | | | | | | | | | | | (191) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.86 | | | | | | | | | | | | all_250_1 % 21.87/3.86 | | | | | | | | | | | | (192) ~ (all_250_2 = 0) | all_250_0 = 0 | all_250_1 = 0 % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | BETA: splitting (154) gives: % 21.87/3.86 | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | (193) all_55_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | REDUCE: (144), (193) imply: % 21.87/3.86 | | | | | | | | | | | | | (194) $false % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | (195) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.86 | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 21.87/3.86 | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 21.87/3.86 | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | BETA: splitting (149) gives: % 21.87/3.86 | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | (196) all_61_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | REDUCE: (147), (196) imply: % 21.87/3.86 | | | | | | | | | | | | | | (197) $false % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | (198) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 21.87/3.86 | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 21.87/3.86 | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | DELTA: instantiating (198) with fresh symbols all_269_0, % 21.87/3.86 | | | | | | | | | | | | | | all_269_1, all_269_2 gives: % 21.87/3.86 | | | | | | | | | | | | | | (199) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.86 | | | | | | | | | | | | | | all_269_0 & apart_point_and_line(all_38_5, % 21.87/3.86 | | | | | | | | | | | | | | all_38_2) = all_269_1 & distinct_lines(all_38_2, % 21.87/3.86 | | | | | | | | | | | | | | all_38_2) = all_269_2 & ( ~ (all_269_2 = 0) | % 21.87/3.86 | | | | | | | | | | | | | | all_269_0 = 0 | all_269_1 = 0) % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | ALPHA: (199) implies: % 21.87/3.86 | | | | | | | | | | | | | | (200) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.86 | | | | | | | | | | | | | | all_269_1 % 21.87/3.86 | | | | | | | | | | | | | | (201) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.86 | | | | | | | | | | | | | | all_269_0 % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | BETA: splitting (156) gives: % 21.87/3.86 | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | (202) all_59_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | REDUCE: (145), (202) imply: % 21.87/3.86 | | | | | | | | | | | | | | | (203) $false % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | (204) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 21.87/3.86 | | | | | | | | | | | | | | | (convergent_lines(all_38_1, all_38_2) = v1 & % 21.87/3.86 | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 21.87/3.86 | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | (205) all_59_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | REDUCE: (145), (205) imply: % 21.87/3.86 | | | | | | | | | | | | | | | | (206) $false % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | (207) all_55_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.86 | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.86 | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.86 | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 21.87/3.86 | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | (208) all_63_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | REDUCE: (146), (208) imply: % 21.87/3.86 | | | | | | | | | | | | | | | | | (209) $false % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | (210) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.86 | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_1) = v2 & % 21.87/3.86 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.86 | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 21.87/3.86 | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 21.87/3.86 | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | (211) all_59_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | REDUCE: (145), (211) imply: % 21.87/3.86 | | | | | | | | | | | | | | | | | | (212) $false % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | (213) all_55_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.86 | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.86 | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 21.87/3.86 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.86 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.86 | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.86 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 21.87/3.86 | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.86 | | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | | (214) all_61_0 = 0 % 21.87/3.86 | | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | | REDUCE: (147), (214) imply: % 21.87/3.86 | | | | | | | | | | | | | | | | | | | (215) $false % 21.87/3.86 | | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 21.87/3.86 | | | | | | | | | | | | | | | | | | | % 21.87/3.86 | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.86 | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | (216) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.87 | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (216) with fresh symbols all_317_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_317_1, all_317_2, all_317_3 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | (217) apart_point_and_line(all_38_4, all_38_1) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_317_0 & apart_point_and_line(all_38_5, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_38_2) = all_317_1 & distinct_lines(all_38_2, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_38_1) = all_317_2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = all_317_3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | ( ~ (all_317_2 = 0) | ~ (all_317_3 = 0) | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_317_0 = 0 | all_317_1 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | (218) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | all_317_1 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (219) all_61_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (219) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (220) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (221) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (221) with fresh symbols all_322_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_322_1, all_322_2, all_322_3 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (222) apart_point_and_line(all_38_4, all_38_1) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_322_1 & apart_point_and_line(all_38_5, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_38_2) = all_322_0 & distinct_lines(all_38_2, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_38_1) = all_322_2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_5) = all_322_3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | ( ~ (all_322_2 = 0) | ~ (all_322_3 = 0) | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_322_0 = 0 | all_322_1 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | (223) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | all_322_0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (224) all_45_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (224) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (225) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (226) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_53_1) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_53_1) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (226) with fresh symbols all_337_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_337_1, all_337_2 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (227) apart_point_and_line(all_38_5, all_53_1) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_337_0 & apart_point_and_line(all_38_5, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_337_1 & distinct_lines(all_38_2, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_53_1) = all_337_2 & ( ~ (all_337_2 = 0) | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_337_0 = 0 | all_337_1 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | (228) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | all_337_1 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (229) all_53_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (229) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (230) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (231) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_53_1) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_53_1, all_38_1) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_342_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_342_1, all_342_2 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (232) apart_point_and_line(all_38_5, all_53_1) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_342_1 & apart_point_and_line(all_38_5, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_342_0 & distinct_lines(all_53_1, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_342_2 & ( ~ (all_342_2 = 0) | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_342_0 = 0 | all_342_1 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | (233) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | all_342_0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | (234) all_61_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (234) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | (235) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | (236) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | (237) all_57_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (237) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | (238) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | (239) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_53_1) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_53_1) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_45_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (240) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (241) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (242) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (242) with fresh symbols all_443_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_443_1, all_443_2, all_443_3 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (243) apart_point_and_line(all_38_3, all_38_2) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_443_1 & apart_point_and_line(all_38_5, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_443_0 & distinct_lines(all_38_2, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_443_2 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = all_443_3 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_443_2 = 0) | ~ (all_443_3 = 0) | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_443_0 = 0 | all_443_1 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | (244) apart_point_and_line(all_38_5, all_38_2) = % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | all_443_0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_45_0 = 0 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (245) imply: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent. % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (convergent_lines(all_38_1, all_38_2) = v1 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_453_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | all_453_1 gives: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (248) convergent_lines(all_38_1, all_38_2) = all_453_0 & % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = all_453_1 & ( % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_453_1 = 0) | all_453_0 = 0) % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) distinct_lines(all_38_1, all_38_2) = all_453_1 % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_458_0, % 21.87/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | all_458_1 gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (250) convergent_lines(all_38_1, all_38_2) = all_458_0 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = all_458_1 & ( % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_458_1 = 0) | all_458_0 = 0) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (251) distinct_lines(all_38_1, all_38_2) = all_458_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_55_0 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (252) imply: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_463_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_463_1, all_463_2, all_463_3 gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) apart_point_and_line(all_38_3, all_38_2) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_463_1 & apart_point_and_line(all_38_5, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_463_0 & distinct_lines(all_38_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_463_2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = all_463_3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_463_2 = 0) | ~ (all_463_3 = 0) | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_463_0 = 0 | all_463_1 = 0) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) distinct_lines(all_38_1, all_38_2) = all_463_2 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_463_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_59_0 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (258) imply: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_1) = v1 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbols all_468_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_1, all_468_2, all_468_3 gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) apart_point_and_line(all_38_3, all_38_1) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_1 & apart_point_and_line(all_38_5, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_468_0 & distinct_lines(all_38_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_468_2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = all_468_3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_468_2 = 0) | ~ (all_468_3 = 0) | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_0 = 0 | all_468_1 = 0) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_55_0 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (263) imply: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) $false % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_473_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_473_1, all_473_2, all_473_3 gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) apart_point_and_line(all_38_3, all_38_2) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_473_1 & apart_point_and_line(all_38_5, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_473_0 & distinct_lines(all_38_2, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_473_2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = all_473_3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_473_2 = 0) | ~ (all_473_3 = 0) | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_473_0 = 0 | all_473_1 = 0) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) apart_point_and_line(all_38_5, all_38_1) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_473_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_59_0 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (268) imply: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) $false % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent. % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (270) with fresh symbols all_534_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_534_1, all_534_2, all_534_3 gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) apart_point_and_line(all_38_3, all_38_2) = % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_534_1 & apart_point_and_line(all_38_4, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_534_0 & distinct_lines(all_38_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_534_2 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = all_534_3 & % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_534_2 = 0) | ~ (all_534_3 = 0) | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_534_0 = 0 | all_534_1 = 0) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) distinct_lines(all_38_1, all_38_2) = all_534_2 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_45_0 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (273) imply: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) $false % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_250_2, all_453_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (189), (249) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_453_1 = all_250_2 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_463_2, all_38_2, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (163), (256) gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_463_2 = 0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_463_2, all_534_2, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (256), (272) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_534_2 = all_463_2 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_458_1, all_534_2, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (251), (272) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_534_2 = all_458_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_453_1, all_534_2, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_1, simplifying with (249), (272) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_534_2 = all_453_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_250_0, all_269_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (190), (200) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_269_1 = all_250_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_269_0, all_322_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (201), (223) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_322_0 = all_269_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_55_0, all_443_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (58), (244) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_443_0 = all_55_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_337_1, all_443_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (228), (244) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_443_0 = all_337_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_322_0, all_443_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (223), (244) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_443_0 = all_322_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_317_1, all_443_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (218), (244) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_443_0 = all_317_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_269_1, all_443_0, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (200), (244) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_443_0 = all_269_1 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_63_0, all_250_1, % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (74), (191) % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_250_1 = all_63_0 % 21.87/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_141_0, all_250_1, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (169), (191) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_250_1 = all_141_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_250_1, all_342_0, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (191), (233) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_342_0 = all_250_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_141_1, all_468_0, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (168), (262) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_468_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_468_0, all_473_0, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (262), (267) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_473_0 = all_468_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_463_0, all_473_0, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (257), (267) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_473_0 = all_463_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_342_0, all_473_0, % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (233), (267) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_473_0 = all_342_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (279) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_458_1 = all_453_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (278) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_463_2 = all_458_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (295) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_463_2 = all_458_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (292) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_468_0 = all_463_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (297) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_468_0 = all_463_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (293) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_463_0 = all_342_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (298) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_463_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_463_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (301) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_342_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_342_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (296) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_458_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (304) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_458_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (305) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_453_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_453_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (307) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_250_2 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_250_2 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_337_1 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (285) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_337_1 = all_317_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (286) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_337_1 = all_269_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (284) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_337_1 = all_322_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (303) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_250_1 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_250_1 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (312) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_317_1 = all_269_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (311) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_317_1 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (313) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_322_0 = all_317_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_322_0 = all_317_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (319) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_317_1 = all_269_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (320) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_317_1 = all_269_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (321) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_269_0 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (321) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_269_0 = all_269_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (323) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_269_1 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (324) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_269_1 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (325) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_250_0 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (326) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_250_0 = all_55_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (288) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_141_0 = all_63_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (315) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_141_0 = all_141_1 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (329) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_141_1 = all_63_0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_250_2 = 0) % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (331) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) $false % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent. % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_250_0 = 0 | all_250_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_250_0 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (334) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_55_0 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (335) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_55_0 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (336) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) $false % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent. % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_250_1 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (338) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_63_0 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_63_0 = 0 % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (340) imply: % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) $false % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (341) is inconsistent. % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | | % 21.87/3.89 | | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | | % 21.87/3.89 | | | | | | | | | End of split % 21.87/3.89 | | | | | | | | | % 21.87/3.89 | | | | | | | | End of split % 21.87/3.89 | | | | | | | | % 21.87/3.89 | | | | | | | End of split % 21.87/3.89 | | | | | | | % 21.87/3.89 | | | | | | End of split % 21.87/3.89 | | | | | | % 21.87/3.89 | | | | | End of split % 21.87/3.89 | | | | | % 21.87/3.89 | | | | Case 2: % 21.87/3.89 | | | | | % 21.87/3.89 | | | | | (342) all_61_0 = 0 % 21.87/3.89 | | | | | % 21.87/3.89 | | | | | REDUCE: (147), (342) imply: % 21.87/3.89 | | | | | (343) $false % 21.87/3.89 | | | | | % 21.87/3.89 | | | | | CLOSE: (343) is inconsistent. % 21.87/3.89 | | | | | % 21.87/3.89 | | | | End of split % 21.87/3.89 | | | | % 21.87/3.89 | | | Case 2: % 21.87/3.89 | | | | % 21.87/3.89 | | | | (344) ~ (all_65_1 = 0) % 21.87/3.89 | | | | % 21.87/3.89 | | | | REDUCE: (102), (344) imply: % 21.87/3.89 | | | | (345) $false % 21.87/3.89 | | | | % 21.87/3.89 | | | | CLOSE: (345) is inconsistent. % 21.87/3.89 | | | | % 21.87/3.89 | | | End of split % 21.87/3.89 | | | % 21.87/3.89 | | Case 2: % 21.87/3.89 | | | % 21.87/3.89 | | | (346) ~ (all_69_1 = 0) % 21.87/3.89 | | | % 21.87/3.89 | | | REDUCE: (105), (346) imply: % 21.87/3.89 | | | (347) $false % 21.87/3.89 | | | % 21.87/3.89 | | | CLOSE: (347) is inconsistent. % 21.87/3.89 | | | % 21.87/3.89 | | End of split % 21.87/3.89 | | % 21.87/3.89 | Case 2: % 21.87/3.89 | | % 21.87/3.89 | | (348) all_38_0 = 0 % 21.87/3.89 | | % 21.87/3.89 | | REDUCE: (19), (348) imply: % 21.87/3.89 | | (349) $false % 21.87/3.89 | | % 21.87/3.89 | | CLOSE: (349) is inconsistent. % 21.87/3.89 | | % 21.87/3.89 | End of split % 21.87/3.89 | % 21.87/3.89 End of proof % 21.87/3.89 % SZS output end Proof for theBenchmark % 21.87/3.89 % 21.87/3.89 3268ms %------------------------------------------------------------------------------