%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO196+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.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 23:22:09 EDT 2023 % Result : Theorem 14.26s 2.68s % Output : Proof 38.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO196+1 : TPTP v8.1.2. Released v3.3.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n022.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 19:23:53 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.63 Running up to 7 provers in parallel. % 0.67/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.21/1.02 Prover 4: Preprocessing ... % 2.21/1.02 Prover 1: Preprocessing ... % 2.21/1.06 Prover 2: Preprocessing ... % 2.60/1.06 Prover 3: Preprocessing ... % 2.60/1.06 Prover 6: Preprocessing ... % 2.60/1.06 Prover 5: Preprocessing ... % 2.60/1.06 Prover 0: Preprocessing ... % 4.01/1.31 Prover 5: Proving ... % 4.01/1.33 Prover 2: Proving ... % 4.60/1.35 Prover 6: Constructing countermodel ... % 4.60/1.36 Prover 3: Constructing countermodel ... % 4.60/1.36 Prover 1: Constructing countermodel ... % 5.42/1.49 Prover 4: Constructing countermodel ... % 5.42/1.50 Prover 3: gave up % 5.42/1.50 Prover 1: gave up % 5.42/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.42/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.84/1.54 Prover 6: gave up % 5.84/1.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.84/1.55 Prover 0: Proving ... % 5.84/1.55 Prover 8: Preprocessing ... % 6.15/1.58 Prover 7: Preprocessing ... % 6.15/1.58 Prover 9: Preprocessing ... % 6.15/1.63 Prover 7: Warning: ignoring some quantifiers % 6.15/1.64 Prover 7: Constructing countermodel ... % 7.10/1.69 Prover 8: Warning: ignoring some quantifiers % 7.10/1.72 Prover 8: Constructing countermodel ... % 7.72/1.78 Prover 8: gave up % 7.72/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.72/1.81 Prover 9: Constructing countermodel ... % 7.72/1.81 Prover 10: Preprocessing ... % 8.16/1.83 Prover 7: gave up % 8.16/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.35/1.87 Prover 11: Preprocessing ... % 8.35/1.89 Prover 10: Warning: ignoring some quantifiers % 8.35/1.90 Prover 10: Constructing countermodel ... % 8.81/1.95 Prover 10: gave up % 8.81/1.96 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.10/2.00 Prover 12: Preprocessing ... % 9.82/2.07 Prover 11: Constructing countermodel ... % 9.82/2.12 Prover 12: Proving ... % 14.26/2.68 Prover 9: proved (1134ms) % 14.26/2.68 % 14.26/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.26/2.68 % 14.26/2.69 Prover 2: stopped % 14.26/2.69 Prover 12: stopped % 14.26/2.69 Prover 0: stopped % 14.26/2.70 Prover 5: stopped % 14.26/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.26/2.70 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.26/2.70 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.26/2.72 Prover 13: Preprocessing ... % 14.67/2.75 Prover 19: Preprocessing ... % 14.67/2.76 Prover 16: Preprocessing ... % 14.67/2.78 Prover 13: Warning: ignoring some quantifiers % 14.67/2.79 Prover 16: Warning: ignoring some quantifiers % 14.67/2.79 Prover 13: Constructing countermodel ... % 14.67/2.79 Prover 16: Constructing countermodel ... % 14.67/2.82 Prover 19: Warning: ignoring some quantifiers % 14.67/2.83 Prover 19: Constructing countermodel ... % 15.55/2.91 Prover 19: gave up % 16.27/3.00 Prover 16: gave up % 16.40/3.05 Prover 13: gave up % 37.56/7.16 Prover 11: Found proof (size 225) % 37.56/7.16 Prover 11: proved (5329ms) % 37.56/7.17 Prover 4: stopped % 37.56/7.17 % 37.56/7.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 37.56/7.17 % 37.56/7.19 % SZS output start Proof for theBenchmark % 37.56/7.19 Assumptions after simplification: % 37.56/7.19 --------------------------------- % 37.56/7.19 % 37.56/7.19 (apart3) % 37.56/7.22 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 37.56/7.22 % 37.56/7.22 (ceq1) % 38.04/7.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 38.04/7.23 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 38.04/7.23 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 38.04/7.23 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 38.04/7.23 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.04/7.23 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 38.04/7.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 38.04/7.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.04/7.23 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 38.04/7.23 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 38.04/7.23 % 38.04/7.23 (ceq3) % 38.04/7.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 38.04/7.23 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 38.04/7.23 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 38.04/7.23 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 38.04/7.23 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 38.04/7.23 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.04/7.23 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 38.04/7.23 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 38.04/7.23 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.04/7.23 convergent_lines(v0, v2) = 0) % 38.04/7.23 % 38.04/7.23 (ci3) % 38.04/7.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 38.04/7.24 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 38.04/7.24 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 38.04/7.24 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 38.04/7.24 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 38.04/7.24 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 38.04/7.24 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 38.04/7.24 % 38.04/7.24 (ci4) % 38.04/7.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 38.04/7.24 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 38.04/7.24 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 38.04/7.24 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 38.04/7.24 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 38.04/7.24 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 38.04/7.24 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 38.04/7.24 % 38.04/7.24 (con) % 38.04/7.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 38.04/7.25 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ( ~ (v6 = % 38.04/7.25 0) & ~ (v5 = 0) & intersection_point(v2, v3) = v7 & % 38.04/7.25 intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v3) = v6 & % 38.04/7.25 apart_point_and_line(v4, v2) = v5 & convergent_lines(v2, v3) = 0 & % 38.04/7.25 convergent_lines(v0, v1) = 0 & $i(v7) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 38.04/7.25 $i(v0) & ((v9 = 0 & apart_point_and_line(v7, v1) = 0) | (v8 = 0 & % 38.04/7.25 apart_point_and_line(v7, v0) = 0))) % 38.04/7.25 % 38.04/7.25 (cu1) % 38.04/7.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 38.04/7.26 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 38.04/7.26 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 38.04/7.26 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 38.04/7.26 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 38.04/7.26 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 38.04/7.26 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 38.04/7.26 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 38.04/7.26 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 38.04/7.26 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 38.04/7.26 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 38.04/7.26 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 38.04/7.26 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 38.04/7.26 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 38.04/7.26 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 38.04/7.26 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.04/7.26 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 38.04/7.26 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 38.04/7.26 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 38.04/7.26 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 38.04/7.26 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 38.04/7.26 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 38.04/7.26 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.04/7.26 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 38.04/7.26 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 38.04/7.26 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 38.04/7.26 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 38.04/7.26 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 38.04/7.26 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 38.04/7.26 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 38.04/7.26 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 38.04/7.26 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 38.04/7.26 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 38.04/7.26 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 38.04/7.26 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 38.04/7.26 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 38.04/7.26 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.04/7.26 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 38.04/7.26 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 38.04/7.26 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 38.04/7.26 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 38.04/7.26 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 38.04/7.26 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 38.04/7.26 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 38.04/7.26 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 38.04/7.26 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 38.04/7.26 % 38.04/7.26 (function-axioms) % 38.04/7.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.04/7.26 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 38.04/7.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.04/7.26 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 38.04/7.26 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.04/7.26 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 38.04/7.26 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.04/7.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.04/7.26 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 38.04/7.26 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.04/7.26 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 38.04/7.26 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 38.04/7.26 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 38.04/7.26 (distinct_points(v3, v2) = v0)) % 38.04/7.26 % 38.04/7.26 Further assumptions not needed in the proof: % 38.04/7.26 -------------------------------------------- % 38.04/7.26 apart1, apart2, apart4, apart5, ax6, ceq2, ci1, ci2 % 38.04/7.26 % 38.04/7.26 Those formulas are unsatisfiable: % 38.04/7.26 --------------------------------- % 38.04/7.26 % 38.04/7.26 Begin of proof % 38.04/7.26 | % 38.04/7.27 | ALPHA: (ci3) implies: % 38.04/7.27 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 38.04/7.27 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 38.04/7.27 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 38.04/7.27 | & $i(v2))) % 38.04/7.27 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 38.04/7.27 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 38.04/7.27 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 38.04/7.27 | convergent_lines(v0, v1) = v3))) % 38.04/7.27 | % 38.04/7.27 | ALPHA: (ci4) implies: % 38.04/7.27 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 38.04/7.27 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 38.04/7.27 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 38.04/7.27 | & $i(v2))) % 38.04/7.27 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 38.04/7.27 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 38.04/7.27 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 38.04/7.27 | convergent_lines(v0, v1) = v3))) % 38.04/7.27 | % 38.04/7.27 | ALPHA: (cu1) implies: % 38.04/7.27 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 38.04/7.27 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 38.04/7.27 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 38.04/7.27 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 38.04/7.27 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 38.04/7.27 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 38.04/7.27 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 38.04/7.27 | v1) = v6))) % 38.04/7.27 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 38.04/7.27 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 38.04/7.27 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 38.04/7.27 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 38.04/7.27 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 38.04/7.27 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 38.04/7.27 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 38.04/7.27 | v1) = v6))) % 38.04/7.27 | % 38.04/7.27 | ALPHA: (ceq1) implies: % 38.04/7.27 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.04/7.27 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 38.04/7.27 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 38.04/7.27 | distinct_points(v0, v2) = 0) % 38.04/7.27 | % 38.04/7.27 | ALPHA: (ceq3) implies: % 38.04/7.28 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 38.04/7.28 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 38.04/7.28 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 38.04/7.28 | % 38.04/7.28 | ALPHA: (function-axioms) implies: % 38.04/7.28 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.04/7.28 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 38.04/7.28 | (distinct_points(v3, v2) = v0)) % 38.04/7.28 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.04/7.28 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 38.04/7.28 | (distinct_lines(v3, v2) = v0)) % 38.04/7.28 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.04/7.28 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 38.04/7.28 | (convergent_lines(v3, v2) = v0)) % 38.04/7.28 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 38.04/7.28 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 38.04/7.28 | (apart_point_and_line(v3, v2) = v0)) % 38.04/7.28 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.04/7.28 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 38.04/7.28 | v0)) % 38.04/7.28 | % 38.04/7.28 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 38.04/7.28 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8, all_17_9 % 38.04/7.28 | gives: % 38.04/7.28 | (14) ~ (all_17_3 = 0) & ~ (all_17_4 = 0) & intersection_point(all_17_7, % 38.04/7.28 | all_17_6) = all_17_2 & intersection_point(all_17_9, all_17_8) = % 38.04/7.28 | all_17_5 & apart_point_and_line(all_17_5, all_17_6) = all_17_3 & % 38.04/7.28 | apart_point_and_line(all_17_5, all_17_7) = all_17_4 & % 38.04/7.28 | convergent_lines(all_17_7, all_17_6) = 0 & convergent_lines(all_17_9, % 38.04/7.28 | all_17_8) = 0 & $i(all_17_2) & $i(all_17_5) & $i(all_17_6) & % 38.04/7.28 | $i(all_17_7) & $i(all_17_8) & $i(all_17_9) & ((all_17_0 = 0 & % 38.04/7.28 | apart_point_and_line(all_17_2, all_17_8) = 0) | (all_17_1 = 0 & % 38.04/7.28 | apart_point_and_line(all_17_2, all_17_9) = 0)) % 38.04/7.28 | % 38.04/7.28 | ALPHA: (14) implies: % 38.04/7.28 | (15) ~ (all_17_4 = 0) % 38.04/7.28 | (16) ~ (all_17_3 = 0) % 38.04/7.28 | (17) $i(all_17_9) % 38.04/7.28 | (18) $i(all_17_8) % 38.04/7.28 | (19) $i(all_17_7) % 38.04/7.28 | (20) $i(all_17_6) % 38.04/7.28 | (21) convergent_lines(all_17_9, all_17_8) = 0 % 38.04/7.28 | (22) convergent_lines(all_17_7, all_17_6) = 0 % 38.04/7.28 | (23) apart_point_and_line(all_17_5, all_17_7) = all_17_4 % 38.04/7.28 | (24) apart_point_and_line(all_17_5, all_17_6) = all_17_3 % 38.04/7.28 | (25) intersection_point(all_17_9, all_17_8) = all_17_5 % 38.04/7.28 | (26) intersection_point(all_17_7, all_17_6) = all_17_2 % 38.04/7.28 | (27) (all_17_0 = 0 & apart_point_and_line(all_17_2, all_17_8) = 0) | % 38.04/7.28 | (all_17_1 = 0 & apart_point_and_line(all_17_2, all_17_9) = 0) % 38.04/7.28 | % 38.04/7.29 | GROUND_INST: instantiating (3) with all_17_9, all_17_8, simplifying with (17), % 38.04/7.29 | (18), (21) gives: % 38.04/7.29 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 38.04/7.29 | intersection_point(all_17_9, all_17_8) = v0 & % 38.04/7.29 | apart_point_and_line(v0, all_17_8) = v1 & $i(v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (1) with all_17_9, all_17_8, simplifying with (17), % 38.04/7.29 | (18), (21) gives: % 38.04/7.29 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 38.04/7.29 | intersection_point(all_17_9, all_17_8) = v0 & % 38.04/7.29 | apart_point_and_line(v0, all_17_9) = v1 & $i(v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (3) with all_17_7, all_17_6, simplifying with (19), % 38.04/7.29 | (20), (22) gives: % 38.04/7.29 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 38.04/7.29 | intersection_point(all_17_7, all_17_6) = v0 & % 38.04/7.29 | apart_point_and_line(v0, all_17_6) = v1 & $i(v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (1) with all_17_7, all_17_6, simplifying with (19), % 38.04/7.29 | (20), (22) gives: % 38.04/7.29 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 38.04/7.29 | intersection_point(all_17_7, all_17_6) = v0 & % 38.04/7.29 | apart_point_and_line(v0, all_17_7) = v1 & $i(v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (4) with all_17_9, all_17_8, all_17_5, simplifying % 38.04/7.29 | with (17), (18), (25) gives: % 38.04/7.29 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 38.04/7.29 | apart_point_and_line(all_17_5, all_17_8) = v1) | ( ~ (v0 = 0) & % 38.04/7.29 | convergent_lines(all_17_9, all_17_8) = v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (2) with all_17_9, all_17_8, all_17_5, simplifying % 38.04/7.29 | with (17), (18), (25) gives: % 38.04/7.29 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 38.04/7.29 | apart_point_and_line(all_17_5, all_17_9) = v1) | ( ~ (v0 = 0) & % 38.04/7.29 | convergent_lines(all_17_9, all_17_8) = v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (4) with all_17_7, all_17_6, all_17_2, simplifying % 38.04/7.29 | with (19), (20), (26) gives: % 38.04/7.29 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 38.04/7.29 | apart_point_and_line(all_17_2, all_17_6) = v1) | ( ~ (v0 = 0) & % 38.04/7.29 | convergent_lines(all_17_7, all_17_6) = v0)) % 38.04/7.29 | % 38.04/7.29 | GROUND_INST: instantiating (2) with all_17_7, all_17_6, all_17_2, simplifying % 38.04/7.29 | with (19), (20), (26) gives: % 38.04/7.29 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 38.04/7.29 | apart_point_and_line(all_17_2, all_17_7) = v1) | ( ~ (v0 = 0) & % 38.04/7.29 | convergent_lines(all_17_7, all_17_6) = v0)) % 38.04/7.29 | % 38.04/7.29 | DELTA: instantiating (35) with fresh symbols all_24_0, all_24_1 gives: % 38.04/7.29 | (36) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_7) = % 38.04/7.29 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_7, % 38.04/7.29 | all_17_6) = all_24_1) % 38.04/7.29 | % 38.04/7.29 | DELTA: instantiating (34) with fresh symbols all_25_0, all_25_1 gives: % 38.04/7.30 | (37) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_6) = % 38.04/7.30 | all_25_0) | ( ~ (all_25_1 = 0) & convergent_lines(all_17_7, % 38.04/7.30 | all_17_6) = all_25_1) % 38.04/7.30 | % 38.04/7.30 | DELTA: instantiating (33) with fresh symbols all_26_0, all_26_1 gives: % 38.04/7.30 | (38) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_9) = % 38.04/7.30 | all_26_0) | ( ~ (all_26_1 = 0) & convergent_lines(all_17_9, % 38.04/7.30 | all_17_8) = all_26_1) % 38.04/7.30 | % 38.04/7.30 | DELTA: instantiating (31) with fresh symbols all_27_0, all_27_1 gives: % 38.39/7.30 | (39) ~ (all_27_0 = 0) & intersection_point(all_17_7, all_17_6) = all_27_1 % 38.39/7.30 | & apart_point_and_line(all_27_1, all_17_7) = all_27_0 & $i(all_27_1) % 38.39/7.30 | % 38.39/7.30 | ALPHA: (39) implies: % 38.39/7.30 | (40) ~ (all_27_0 = 0) % 38.39/7.30 | (41) $i(all_27_1) % 38.39/7.30 | (42) apart_point_and_line(all_27_1, all_17_7) = all_27_0 % 38.39/7.30 | (43) intersection_point(all_17_7, all_17_6) = all_27_1 % 38.39/7.30 | % 38.39/7.30 | DELTA: instantiating (30) with fresh symbols all_29_0, all_29_1 gives: % 38.39/7.30 | (44) ~ (all_29_0 = 0) & intersection_point(all_17_7, all_17_6) = all_29_1 % 38.39/7.30 | & apart_point_and_line(all_29_1, all_17_6) = all_29_0 & $i(all_29_1) % 38.39/7.30 | % 38.39/7.30 | ALPHA: (44) implies: % 38.39/7.30 | (45) ~ (all_29_0 = 0) % 38.39/7.30 | (46) apart_point_and_line(all_29_1, all_17_6) = all_29_0 % 38.39/7.30 | (47) intersection_point(all_17_7, all_17_6) = all_29_1 % 38.39/7.30 | % 38.39/7.30 | DELTA: instantiating (28) with fresh symbols all_31_0, all_31_1 gives: % 38.39/7.30 | (48) ~ (all_31_0 = 0) & intersection_point(all_17_9, all_17_8) = all_31_1 % 38.39/7.30 | & apart_point_and_line(all_31_1, all_17_8) = all_31_0 & $i(all_31_1) % 38.39/7.30 | % 38.39/7.30 | ALPHA: (48) implies: % 38.39/7.30 | (49) $i(all_31_1) % 38.39/7.30 | (50) apart_point_and_line(all_31_1, all_17_8) = all_31_0 % 38.39/7.30 | (51) intersection_point(all_17_9, all_17_8) = all_31_1 % 38.39/7.30 | % 38.39/7.30 | DELTA: instantiating (29) with fresh symbols all_33_0, all_33_1 gives: % 38.39/7.30 | (52) ~ (all_33_0 = 0) & intersection_point(all_17_9, all_17_8) = all_33_1 % 38.39/7.30 | & apart_point_and_line(all_33_1, all_17_9) = all_33_0 & $i(all_33_1) % 38.39/7.30 | % 38.39/7.30 | ALPHA: (52) implies: % 38.39/7.30 | (53) ~ (all_33_0 = 0) % 38.39/7.30 | (54) apart_point_and_line(all_33_1, all_17_9) = all_33_0 % 38.39/7.30 | (55) intersection_point(all_17_9, all_17_8) = all_33_1 % 38.39/7.30 | % 38.39/7.30 | DELTA: instantiating (32) with fresh symbols all_35_0, all_35_1 gives: % 38.39/7.30 | (56) ( ~ (all_35_0 = 0) & apart_point_and_line(all_17_5, all_17_8) = % 38.39/7.30 | all_35_0) | ( ~ (all_35_1 = 0) & convergent_lines(all_17_9, % 38.39/7.30 | all_17_8) = all_35_1) % 38.39/7.30 | % 38.39/7.30 | BETA: splitting (56) gives: % 38.39/7.30 | % 38.39/7.30 | Case 1: % 38.39/7.30 | | % 38.39/7.30 | | (57) ~ (all_35_0 = 0) & apart_point_and_line(all_17_5, all_17_8) = % 38.39/7.30 | | all_35_0 % 38.39/7.30 | | % 38.39/7.30 | | ALPHA: (57) implies: % 38.39/7.30 | | (58) ~ (all_35_0 = 0) % 38.39/7.30 | | (59) apart_point_and_line(all_17_5, all_17_8) = all_35_0 % 38.39/7.30 | | % 38.39/7.30 | | BETA: splitting (36) gives: % 38.39/7.30 | | % 38.39/7.30 | | Case 1: % 38.39/7.30 | | | % 38.39/7.30 | | | (60) ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_7) = % 38.39/7.30 | | | all_24_0 % 38.39/7.30 | | | % 38.39/7.30 | | | ALPHA: (60) implies: % 38.39/7.30 | | | (61) apart_point_and_line(all_17_2, all_17_7) = all_24_0 % 38.39/7.30 | | | % 38.39/7.30 | | | BETA: splitting (37) gives: % 38.39/7.30 | | | % 38.39/7.30 | | | Case 1: % 38.39/7.30 | | | | % 38.39/7.30 | | | | (62) ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_6) = % 38.39/7.30 | | | | all_25_0 % 38.39/7.30 | | | | % 38.39/7.30 | | | | ALPHA: (62) implies: % 38.39/7.30 | | | | (63) apart_point_and_line(all_17_2, all_17_6) = all_25_0 % 38.39/7.30 | | | | % 38.39/7.30 | | | | BETA: splitting (38) gives: % 38.39/7.30 | | | | % 38.39/7.30 | | | | Case 1: % 38.39/7.30 | | | | | % 38.39/7.30 | | | | | (64) ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_9) = % 38.39/7.30 | | | | | all_26_0 % 38.39/7.30 | | | | | % 38.39/7.30 | | | | | ALPHA: (64) implies: % 38.39/7.30 | | | | | (65) apart_point_and_line(all_17_5, all_17_9) = all_26_0 % 38.39/7.30 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (13) with all_17_5, all_33_1, all_17_8, % 38.39/7.31 | | | | | all_17_9, simplifying with (25), (55) gives: % 38.39/7.31 | | | | | (66) all_33_1 = all_17_5 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (13) with all_31_1, all_33_1, all_17_8, % 38.39/7.31 | | | | | all_17_9, simplifying with (51), (55) gives: % 38.39/7.31 | | | | | (67) all_33_1 = all_31_1 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (13) with all_17_2, all_29_1, all_17_6, % 38.39/7.31 | | | | | all_17_7, simplifying with (26), (47) gives: % 38.39/7.31 | | | | | (68) all_29_1 = all_17_2 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (13) with all_27_1, all_29_1, all_17_6, % 38.39/7.31 | | | | | all_17_7, simplifying with (43), (47) gives: % 38.39/7.31 | | | | | (69) all_29_1 = all_27_1 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | COMBINE_EQS: (66), (67) imply: % 38.39/7.31 | | | | | (70) all_31_1 = all_17_5 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | COMBINE_EQS: (68), (69) imply: % 38.39/7.31 | | | | | (71) all_27_1 = all_17_2 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (54), (66) imply: % 38.39/7.31 | | | | | (72) apart_point_and_line(all_17_5, all_17_9) = all_33_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (50), (70) imply: % 38.39/7.31 | | | | | (73) apart_point_and_line(all_17_5, all_17_8) = all_31_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (46), (68) imply: % 38.39/7.31 | | | | | (74) apart_point_and_line(all_17_2, all_17_6) = all_29_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (42), (71) imply: % 38.39/7.31 | | | | | (75) apart_point_and_line(all_17_2, all_17_7) = all_27_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (49), (70) imply: % 38.39/7.31 | | | | | (76) $i(all_17_5) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (41), (71) imply: % 38.39/7.31 | | | | | (77) $i(all_17_2) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (12) with all_26_0, all_33_0, all_17_9, % 38.39/7.31 | | | | | all_17_5, simplifying with (65), (72) gives: % 38.39/7.31 | | | | | (78) all_33_0 = all_26_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (12) with all_35_0, all_31_0, all_17_8, % 38.39/7.31 | | | | | all_17_5, simplifying with (59), (73) gives: % 38.39/7.31 | | | | | (79) all_35_0 = all_31_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (12) with all_24_0, all_27_0, all_17_7, % 38.39/7.31 | | | | | all_17_2, simplifying with (61), (75) gives: % 38.39/7.31 | | | | | (80) all_27_0 = all_24_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (12) with all_25_0, all_29_0, all_17_6, % 38.39/7.31 | | | | | all_17_2, simplifying with (63), (74) gives: % 38.39/7.31 | | | | | (81) all_29_0 = all_25_0 % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (58), (79) imply: % 38.39/7.31 | | | | | (82) ~ (all_31_0 = 0) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (53), (78) imply: % 38.39/7.31 | | | | | (83) ~ (all_26_0 = 0) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (45), (81) imply: % 38.39/7.31 | | | | | (84) ~ (all_25_0 = 0) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | REDUCE: (40), (80) imply: % 38.39/7.31 | | | | | (85) ~ (all_24_0 = 0) % 38.39/7.31 | | | | | % 38.39/7.31 | | | | | GROUND_INST: instantiating (5) with all_17_2, all_17_5, all_17_6, % 38.39/7.31 | | | | | all_17_7, all_24_0, all_17_3, simplifying with (19), % 38.39/7.31 | | | | | (20), (24), (61), (76), (77) gives: % 38.39/7.31 | | | | | (86) all_24_0 = 0 | all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? % 38.39/7.31 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.31 | | | | | apart_point_and_line(all_17_5, all_17_7) = 0) | (v2 = 0 & % 38.39/7.31 | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) | ( ~ (v1 = % 38.39/7.31 | | | | | 0) & distinct_lines(all_17_6, all_17_7) = v1) | ( ~ (v0 % 38.39/7.31 | | | | | = 0) & distinct_points(all_17_2, all_17_5) = v0)) % 38.39/7.31 | | | | | % 38.39/7.32 | | | | | GROUND_INST: instantiating (5) with all_17_5, all_17_2, all_17_6, % 38.39/7.32 | | | | | all_17_7, all_17_4, all_25_0, simplifying with (19), % 38.39/7.32 | | | | | (20), (23), (63), (76), (77) gives: % 38.39/7.32 | | | | | (87) all_25_0 = 0 | all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? % 38.39/7.32 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_2, all_17_7) = 0) | (v2 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) | ( ~ (v1 = % 38.39/7.32 | | | | | 0) & distinct_lines(all_17_6, all_17_7) = v1) | ( ~ (v0 % 38.39/7.32 | | | | | = 0) & distinct_points(all_17_5, all_17_2) = v0)) % 38.39/7.32 | | | | | % 38.39/7.32 | | | | | GROUND_INST: instantiating (6) with all_17_5, all_17_2, all_17_8, % 38.39/7.32 | | | | | all_17_6, all_31_0, all_25_0, simplifying with (18), % 38.39/7.32 | | | | | (20), (63), (73), (76), (77) gives: % 38.39/7.32 | | | | | (88) all_31_0 = 0 | all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 38.39/7.32 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_2, all_17_8) = 0) | (v2 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) | ( ~ (v1 = % 38.39/7.32 | | | | | 0) & distinct_lines(all_17_8, all_17_6) = v1) | ( ~ (v0 % 38.39/7.32 | | | | | = 0) & distinct_points(all_17_5, all_17_2) = v0)) % 38.39/7.32 | | | | | % 38.39/7.32 | | | | | GROUND_INST: instantiating (5) with all_17_2, all_17_5, all_17_8, % 38.39/7.32 | | | | | all_17_6, all_25_0, all_31_0, simplifying with (18), % 38.39/7.32 | | | | | (20), (63), (73), (76), (77) gives: % 38.39/7.32 | | | | | (89) all_31_0 = 0 | all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 38.39/7.32 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) | (v2 = 0 & % 38.39/7.32 | | | | | apart_point_and_line(all_17_2, all_17_8) = 0) | ( ~ (v1 = % 38.39/7.32 | | | | | 0) & distinct_lines(all_17_8, all_17_6) = v1) | ( ~ (v0 % 38.39/7.32 | | | | | = 0) & distinct_points(all_17_2, all_17_5) = v0)) % 38.39/7.32 | | | | | % 38.39/7.32 | | | | | BETA: splitting (27) gives: % 38.39/7.32 | | | | | % 38.39/7.32 | | | | | Case 1: % 38.39/7.32 | | | | | | % 38.39/7.32 | | | | | | (90) all_17_0 = 0 & apart_point_and_line(all_17_2, all_17_8) = 0 % 38.39/7.32 | | | | | | % 38.39/7.32 | | | | | | ALPHA: (90) implies: % 38.39/7.32 | | | | | | (91) apart_point_and_line(all_17_2, all_17_8) = 0 % 38.39/7.32 | | | | | | % 38.39/7.32 | | | | | | BETA: splitting (86) gives: % 38.39/7.32 | | | | | | % 38.39/7.32 | | | | | | Case 1: % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | (92) all_24_0 = 0 % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | REDUCE: (85), (92) imply: % 38.39/7.32 | | | | | | | (93) $false % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | CLOSE: (93) is inconsistent. % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | Case 2: % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | (94) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 38.39/7.32 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_5, % 38.39/7.32 | | | | | | | all_17_7) = 0) | (v2 = 0 & % 38.39/7.32 | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) | ( ~ % 38.39/7.32 | | | | | | | (v1 = 0) & distinct_lines(all_17_6, all_17_7) = v1) | % 38.39/7.32 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_2, all_17_5) = % 38.39/7.32 | | | | | | | v0)) % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | BETA: splitting (87) gives: % 38.39/7.32 | | | | | | | % 38.39/7.32 | | | | | | | Case 1: % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | (95) all_25_0 = 0 % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | REDUCE: (84), (95) imply: % 38.39/7.32 | | | | | | | | (96) $false % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | CLOSE: (96) is inconsistent. % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | Case 2: % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | (97) all_17_4 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 38.39/7.32 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.32 | | | | | | | | apart_point_and_line(all_17_2, all_17_7) = 0) | (v2 % 38.39/7.32 | | | | | | | | = 0 & apart_point_and_line(all_17_5, all_17_6) = 0) % 38.39/7.32 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_17_6, all_17_7) = % 38.39/7.32 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_5, % 38.39/7.32 | | | | | | | | all_17_2) = v0)) % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | BETA: splitting (89) gives: % 38.39/7.32 | | | | | | | | % 38.39/7.32 | | | | | | | | Case 1: % 38.39/7.32 | | | | | | | | | % 38.39/7.32 | | | | | | | | | (98) all_31_0 = 0 % 38.39/7.32 | | | | | | | | | % 38.39/7.32 | | | | | | | | | REDUCE: (82), (98) imply: % 38.39/7.33 | | | | | | | | | (99) $false % 38.39/7.33 | | | | | | | | | % 38.39/7.33 | | | | | | | | | CLOSE: (99) is inconsistent. % 38.39/7.33 | | | | | | | | | % 38.39/7.33 | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | % 38.39/7.33 | | | | | | | | | (100) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 38.39/7.33 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.33 | | | | | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) | % 38.39/7.33 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_2, all_17_8) % 38.39/7.33 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_8, % 38.39/7.33 | | | | | | | | | all_17_6) = v1) | ( ~ (v0 = 0) & % 38.39/7.33 | | | | | | | | | distinct_points(all_17_2, all_17_5) = v0)) % 38.39/7.33 | | | | | | | | | % 38.39/7.33 | | | | | | | | | BETA: splitting (94) gives: % 38.39/7.33 | | | | | | | | | % 38.39/7.33 | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | (101) all_17_3 = 0 % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | REDUCE: (16), (101) imply: % 38.39/7.33 | | | | | | | | | | (102) $false % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | CLOSE: (102) is inconsistent. % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 38.39/7.33 | | | | | | | | | | [v3: int] : ((v3 = 0 & % 38.39/7.33 | | | | | | | | | | apart_point_and_line(all_17_5, all_17_7) = 0) | % 38.39/7.33 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_2, % 38.39/7.33 | | | | | | | | | | all_17_6) = 0) | ( ~ (v1 = 0) & % 38.39/7.33 | | | | | | | | | | distinct_lines(all_17_6, all_17_7) = v1) | ( ~ % 38.39/7.33 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_2, all_17_5) % 38.39/7.33 | | | | | | | | | | = v0)) % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_298_0, % 38.39/7.33 | | | | | | | | | | all_298_1, all_298_2, all_298_3 gives: % 38.39/7.33 | | | | | | | | | | (104) (all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.33 | | | | | | | | | | all_17_7) = 0) | (all_298_1 = 0 & % 38.39/7.33 | | | | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) | ( % 38.39/7.33 | | | | | | | | | | ~ (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.33 | | | | | | | | | | all_17_7) = all_298_2) | ( ~ (all_298_3 = 0) & % 38.39/7.33 | | | | | | | | | | distinct_points(all_17_2, all_17_5) = all_298_3) % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | BETA: splitting (97) gives: % 38.39/7.33 | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | (105) all_17_4 = 0 % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | REDUCE: (15), (105) imply: % 38.39/7.33 | | | | | | | | | | | (106) $false % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | CLOSE: (106) is inconsistent. % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | (107) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 38.39/7.33 | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 38.39/7.33 | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_7) = 0) % 38.39/7.33 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_5, % 38.39/7.33 | | | | | | | | | | | all_17_6) = 0) | ( ~ (v1 = 0) & % 38.39/7.33 | | | | | | | | | | | distinct_lines(all_17_6, all_17_7) = v1) | ( ~ % 38.39/7.33 | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_5, all_17_2) % 38.39/7.33 | | | | | | | | | | | = v0)) % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | DELTA: instantiating (107) with fresh symbols all_346_0, % 38.39/7.33 | | | | | | | | | | | all_346_1, all_346_2, all_346_3 gives: % 38.39/7.33 | | | | | | | | | | | (108) (all_346_0 = 0 & apart_point_and_line(all_17_2, % 38.39/7.33 | | | | | | | | | | | all_17_7) = 0) | (all_346_1 = 0 & % 38.39/7.33 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) | % 38.39/7.33 | | | | | | | | | | | ( ~ (all_346_2 = 0) & distinct_lines(all_17_6, % 38.39/7.33 | | | | | | | | | | | all_17_7) = all_346_2) | ( ~ (all_346_3 = 0) & % 38.39/7.33 | | | | | | | | | | | distinct_points(all_17_5, all_17_2) = all_346_3) % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | BETA: splitting (100) gives: % 38.39/7.33 | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | (109) all_25_0 = 0 % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | REDUCE: (84), (109) imply: % 38.39/7.33 | | | | | | | | | | | | (110) $false % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | CLOSE: (110) is inconsistent. % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_2, all_17_8, % 38.39/7.33 | | | | | | | | | | | | all_17_5, all_31_0, simplifying with (18), (73), % 38.39/7.33 | | | | | | | | | | | | (76), (77), (91) gives: % 38.39/7.33 | | | | | | | | | | | | (111) all_31_0 = 0 | distinct_points(all_17_2, all_17_5) % 38.39/7.33 | | | | | | | | | | | | = 0 % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | BETA: splitting (111) gives: % 38.39/7.33 | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | (112) distinct_points(all_17_2, all_17_5) = 0 % 38.39/7.33 | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | BETA: splitting (104) gives: % 38.39/7.33 | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | (113) (all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.33 | | | | | | | | | | | | | | all_17_7) = 0) | (all_298_1 = 0 & % 38.39/7.33 | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | BETA: splitting (113) gives: % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | (114) all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.33 | | | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | ALPHA: (114) implies: % 38.39/7.33 | | | | | | | | | | | | | | | (115) apart_point_and_line(all_17_5, all_17_7) = 0 % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (115) are inconsistent by % 38.39/7.33 | | | | | | | | | | | | | | | sub-proof #3. % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | (116) all_298_1 = 0 & apart_point_and_line(all_17_2, % 38.39/7.33 | | | | | | | | | | | | | | | all_17_6) = 0 % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | ALPHA: (116) implies: % 38.39/7.33 | | | | | | | | | | | | | | | (117) apart_point_and_line(all_17_2, all_17_6) = 0 % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (84), (117) are inconsistent by % 38.39/7.33 | | | | | | | | | | | | | | | sub-proof #2. % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | End of split % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | Case 2: % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | (118) ( ~ (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.33 | | | | | | | | | | | | | | all_17_7) = all_298_2) | ( ~ (all_298_3 = 0) & % 38.39/7.33 | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_5) = all_298_3) % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | BETA: splitting (118) gives: % 38.39/7.33 | | | | | | | | | | | | | | % 38.39/7.33 | | | | | | | | | | | | | | Case 1: % 38.39/7.33 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | (119) ~ (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | all_17_7) = all_298_2 % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | ALPHA: (119) implies: % 38.39/7.34 | | | | | | | | | | | | | | | (120) ~ (all_298_2 = 0) % 38.39/7.34 | | | | | | | | | | | | | | | (121) distinct_lines(all_17_6, all_17_7) = all_298_2 % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | (122) (all_346_0 = 0 & apart_point_and_line(all_17_2, % 38.39/7.34 | | | | | | | | | | | | | | | | all_17_7) = 0) | (all_346_1 = 0 & % 38.39/7.34 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_6) = 0) % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | (123) all_346_0 = 0 & apart_point_and_line(all_17_2, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | ALPHA: (123) implies: % 38.39/7.34 | | | | | | | | | | | | | | | | | (124) apart_point_and_line(all_17_2, all_17_7) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_24_0, 0, all_17_7, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_2, simplifying with (61), (124) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | | (125) all_24_0 = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | REDUCE: (85), (125) imply: % 38.39/7.34 | | | | | | | | | | | | | | | | | (126) $false % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | (127) all_346_1 = 0 & apart_point_and_line(all_17_5, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_6) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 38.39/7.34 | | | | | | | | | | | | | | | | | (128) apart_point_and_line(all_17_5, all_17_6) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_17_3, 0, all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_5, simplifying with (24), (128) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | | (129) all_17_3 = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | REDUCE: (16), (129) imply: % 38.39/7.34 | | | | | | | | | | | | | | | | | (130) $false % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | (131) ( ~ (all_346_2 = 0) & distinct_lines(all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | | all_17_7) = all_346_2) | ( ~ (all_346_3 = 0) & % 38.39/7.34 | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_2) = all_346_3) % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | (132) ~ (all_346_2 = 0) & distinct_lines(all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7) = all_346_2 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | ALPHA: (132) implies: % 38.39/7.34 | | | | | | | | | | | | | | | | | (133) ~ (all_346_2 = 0) % 38.39/7.34 | | | | | | | | | | | | | | | | | (134) distinct_lines(all_17_6, all_17_7) = all_346_2 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_298_2, all_346_2, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7, all_17_6, simplifying with (121), (134) % 38.39/7.34 | | | | | | | | | | | | | | | | | gives: % 38.39/7.34 | | | | | | | | | | | | | | | | | (135) all_346_2 = all_298_2 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_17_7, all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7, all_298_2, simplifying with (19), (20), % 38.39/7.34 | | | | | | | | | | | | | | | | | (22), (121) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | | (136) all_298_2 = 0 | convergent_lines(all_17_7, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (120), (136), (apart3) are inconsistent by % 38.39/7.34 | | | | | | | | | | | | | | | | | sub-proof #1. % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_17_7, all_17_6, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7, all_298_2, simplifying with (19), (20), % 38.39/7.34 | | | | | | | | | | | | | | | | | (22), (121) gives: % 38.39/7.34 | | | | | | | | | | | | | | | | | (137) all_298_2 = 0 | convergent_lines(all_17_7, % 38.39/7.34 | | | | | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (120), (137), (apart3) are inconsistent by % 38.39/7.34 | | | | | | | | | | | | | | | | | sub-proof #1. % 38.39/7.34 | | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | (138) ~ (all_298_3 = 0) & distinct_points(all_17_2, % 38.39/7.34 | | | | | | | | | | | | | | | all_17_5) = all_298_3 % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | ALPHA: (138) implies: % 38.39/7.34 | | | | | | | | | | | | | | | (139) ~ (all_298_3 = 0) % 38.39/7.34 | | | | | | | | | | | | | | | (140) distinct_points(all_17_2, all_17_5) = all_298_3 % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_298_3, all_17_5, % 38.39/7.34 | | | | | | | | | | | | | | | all_17_2, simplifying with (112), (140) gives: % 38.39/7.34 | | | | | | | | | | | | | | | (141) all_298_3 = 0 % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | REDUCE: (139), (141) imply: % 38.39/7.34 | | | | | | | | | | | | | | | (142) $false % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent. % 38.39/7.34 | | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | (143) all_31_0 = 0 % 38.39/7.34 | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | REDUCE: (82), (143) imply: % 38.39/7.34 | | | | | | | | | | | | | (144) $false % 38.39/7.34 | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 38.39/7.34 | | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | End of split % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | End of split % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | End of split % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | End of split % 38.39/7.34 | | | | | | % 38.39/7.34 | | | | | Case 2: % 38.39/7.34 | | | | | | % 38.39/7.34 | | | | | | (145) all_17_1 = 0 & apart_point_and_line(all_17_2, all_17_9) = 0 % 38.39/7.34 | | | | | | % 38.39/7.34 | | | | | | ALPHA: (145) implies: % 38.39/7.34 | | | | | | (146) apart_point_and_line(all_17_2, all_17_9) = 0 % 38.39/7.34 | | | | | | % 38.39/7.34 | | | | | | BETA: splitting (86) gives: % 38.39/7.34 | | | | | | % 38.39/7.34 | | | | | | Case 1: % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | (147) all_24_0 = 0 % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | REDUCE: (85), (147) imply: % 38.39/7.34 | | | | | | | (148) $false % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | CLOSE: (148) is inconsistent. % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | Case 2: % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | (149) all_17_3 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 38.39/7.34 | | | | | | | : ? [v3: int] : ((v3 = 0 & % 38.39/7.34 | | | | | | | apart_point_and_line(all_17_5, all_17_7) = 0) | (v2 = % 38.39/7.34 | | | | | | | 0 & apart_point_and_line(all_17_2, all_17_6) = 0) | ( % 38.39/7.34 | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_6, all_17_7) = v1) % 38.39/7.34 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_2, all_17_5) = % 38.39/7.34 | | | | | | | v0)) % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | BETA: splitting (88) gives: % 38.39/7.34 | | | | | | | % 38.39/7.34 | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | (150) all_31_0 = 0 % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | REDUCE: (82), (150) imply: % 38.39/7.34 | | | | | | | | (151) $false % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | CLOSE: (151) is inconsistent. % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | (152) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 38.39/7.34 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 38.39/7.34 | | | | | | | | apart_point_and_line(all_17_2, all_17_8) = 0) | (v2 % 38.39/7.34 | | | | | | | | = 0 & apart_point_and_line(all_17_5, all_17_6) = 0) % 38.39/7.34 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_17_8, all_17_6) = % 38.39/7.34 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_5, % 38.39/7.34 | | | | | | | | all_17_2) = v0)) % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | BETA: splitting (149) gives: % 38.39/7.34 | | | | | | | | % 38.39/7.34 | | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | (153) all_17_3 = 0 % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | REDUCE: (16), (153) imply: % 38.39/7.34 | | | | | | | | | (154) $false % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | CLOSE: (154) is inconsistent. % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | (155) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 38.39/7.34 | | | | | | | | | int] : ((v3 = 0 & apart_point_and_line(all_17_5, % 38.39/7.34 | | | | | | | | | all_17_7) = 0) | (v2 = 0 & % 38.39/7.34 | | | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) | ( % 38.39/7.34 | | | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_6, all_17_7) = % 38.39/7.34 | | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_2, % 38.39/7.34 | | | | | | | | | all_17_5) = v0)) % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | DELTA: instantiating (155) with fresh symbols all_298_0, % 38.39/7.34 | | | | | | | | | all_298_1, all_298_2, all_298_3 gives: % 38.39/7.34 | | | | | | | | | (156) (all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.34 | | | | | | | | | all_17_7) = 0) | (all_298_1 = 0 & % 38.39/7.34 | | | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) | ( ~ % 38.39/7.34 | | | | | | | | | (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.34 | | | | | | | | | all_17_7) = all_298_2) | ( ~ (all_298_3 = 0) & % 38.39/7.34 | | | | | | | | | distinct_points(all_17_2, all_17_5) = all_298_3) % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | BETA: splitting (152) gives: % 38.39/7.34 | | | | | | | | | % 38.39/7.34 | | | | | | | | | Case 1: % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | (157) all_25_0 = 0 % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | REDUCE: (84), (157) imply: % 38.39/7.34 | | | | | | | | | | (158) $false % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | CLOSE: (158) is inconsistent. % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | Case 2: % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | % 38.39/7.34 | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_2, all_17_9, % 38.39/7.34 | | | | | | | | | | all_17_5, all_26_0, simplifying with (17), (65), % 38.39/7.34 | | | | | | | | | | (76), (77), (146) gives: % 38.39/7.35 | | | | | | | | | | (159) all_26_0 = 0 | distinct_points(all_17_2, all_17_5) % 38.39/7.35 | | | | | | | | | | = 0 % 38.39/7.35 | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | BETA: splitting (159) gives: % 38.39/7.35 | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | Case 1: % 38.39/7.35 | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | (160) distinct_points(all_17_2, all_17_5) = 0 % 38.39/7.35 | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | BETA: splitting (156) gives: % 38.39/7.35 | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | Case 1: % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | (161) (all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.35 | | | | | | | | | | | | all_17_7) = 0) | (all_298_1 = 0 & % 38.39/7.35 | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_6) = 0) % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | BETA: splitting (161) gives: % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | Case 1: % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | (162) all_298_0 = 0 & apart_point_and_line(all_17_5, % 38.39/7.35 | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | ALPHA: (162) implies: % 38.39/7.35 | | | | | | | | | | | | | (163) apart_point_and_line(all_17_5, all_17_7) = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | REF_CLOSE: (12), (15), (23), (163) are inconsistent by % 38.39/7.35 | | | | | | | | | | | | | sub-proof #3. % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | Case 2: % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | (164) all_298_1 = 0 & apart_point_and_line(all_17_2, % 38.39/7.35 | | | | | | | | | | | | | all_17_6) = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | ALPHA: (164) implies: % 38.39/7.35 | | | | | | | | | | | | | (165) apart_point_and_line(all_17_2, all_17_6) = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | REF_CLOSE: (12), (63), (84), (165) are inconsistent by % 38.39/7.35 | | | | | | | | | | | | | sub-proof #2. % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | End of split % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | Case 2: % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | (166) ( ~ (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.35 | | | | | | | | | | | | all_17_7) = all_298_2) | ( ~ (all_298_3 = 0) & % 38.39/7.35 | | | | | | | | | | | | distinct_points(all_17_2, all_17_5) = all_298_3) % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | BETA: splitting (166) gives: % 38.39/7.35 | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | Case 1: % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | (167) ~ (all_298_2 = 0) & distinct_lines(all_17_6, % 38.39/7.35 | | | | | | | | | | | | | all_17_7) = all_298_2 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | ALPHA: (167) implies: % 38.39/7.35 | | | | | | | | | | | | | (168) ~ (all_298_2 = 0) % 38.39/7.35 | | | | | | | | | | | | | (169) distinct_lines(all_17_6, all_17_7) = all_298_2 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_17_7, all_17_6, % 38.39/7.35 | | | | | | | | | | | | | all_17_7, all_298_2, simplifying with (19), (20), % 38.39/7.35 | | | | | | | | | | | | | (22), (169) gives: % 38.39/7.35 | | | | | | | | | | | | | (170) all_298_2 = 0 | convergent_lines(all_17_7, % 38.39/7.35 | | | | | | | | | | | | | all_17_7) = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | BETA: splitting (170) gives: % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | Case 1: % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | (171) convergent_lines(all_17_7, all_17_7) = 0 % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_7, simplifying % 38.39/7.35 | | | | | | | | | | | | | | with (19), (171) gives: % 38.39/7.35 | | | | | | | | | | | | | | (172) $false % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | Case 2: % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | (173) all_298_2 = 0 % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | REDUCE: (168), (173) imply: % 38.39/7.35 | | | | | | | | | | | | | | (174) $false % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | | CLOSE: (174) is inconsistent. % 38.39/7.35 | | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | End of split % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | Case 2: % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | (175) ~ (all_298_3 = 0) & distinct_points(all_17_2, % 38.39/7.35 | | | | | | | | | | | | | all_17_5) = all_298_3 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | ALPHA: (175) implies: % 38.39/7.35 | | | | | | | | | | | | | (176) ~ (all_298_3 = 0) % 38.39/7.35 | | | | | | | | | | | | | (177) distinct_points(all_17_2, all_17_5) = all_298_3 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_298_3, all_17_5, % 38.39/7.35 | | | | | | | | | | | | | all_17_2, simplifying with (160), (177) gives: % 38.39/7.35 | | | | | | | | | | | | | (178) all_298_3 = 0 % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.35 | | | | | | | | | | | | | REDUCE: (176), (178) imply: % 38.39/7.35 | | | | | | | | | | | | | (179) $false % 38.39/7.35 | | | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 38.39/7.36 | | | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | | End of split % 38.39/7.36 | | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | End of split % 38.39/7.36 | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | Case 2: % 38.39/7.36 | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | (180) all_26_0 = 0 % 38.39/7.36 | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | REDUCE: (83), (180) imply: % 38.39/7.36 | | | | | | | | | | | (181) $false % 38.39/7.36 | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | | CLOSE: (181) is inconsistent. % 38.39/7.36 | | | | | | | | | | | % 38.39/7.36 | | | | | | | | | | End of split % 38.39/7.36 | | | | | | | | | | % 38.39/7.36 | | | | | | | | | End of split % 38.39/7.36 | | | | | | | | | % 38.39/7.36 | | | | | | | | End of split % 38.39/7.36 | | | | | | | | % 38.39/7.36 | | | | | | | End of split % 38.39/7.36 | | | | | | | % 38.39/7.36 | | | | | | End of split % 38.39/7.36 | | | | | | % 38.39/7.36 | | | | | End of split % 38.39/7.36 | | | | | % 38.39/7.36 | | | | Case 2: % 38.39/7.36 | | | | | % 38.39/7.36 | | | | | (182) ~ (all_26_1 = 0) & convergent_lines(all_17_9, all_17_8) = % 38.39/7.36 | | | | | all_26_1 % 38.39/7.36 | | | | | % 38.39/7.36 | | | | | ALPHA: (182) implies: % 38.39/7.36 | | | | | (183) ~ (all_26_1 = 0) % 38.39/7.36 | | | | | (184) convergent_lines(all_17_9, all_17_8) = all_26_1 % 38.39/7.36 | | | | | % 38.39/7.36 | | | | | GROUND_INST: instantiating (11) with 0, all_26_1, all_17_8, all_17_9, % 38.39/7.36 | | | | | simplifying with (21), (184) gives: % 38.39/7.36 | | | | | (185) all_26_1 = 0 % 38.39/7.36 | | | | | % 38.39/7.36 | | | | | REDUCE: (183), (185) imply: % 38.39/7.36 | | | | | (186) $false % 38.39/7.36 | | | | | % 38.39/7.36 | | | | | CLOSE: (186) is inconsistent. % 38.39/7.36 | | | | | % 38.39/7.36 | | | | End of split % 38.39/7.36 | | | | % 38.39/7.36 | | | Case 2: % 38.39/7.36 | | | | % 38.39/7.36 | | | | (187) ~ (all_25_1 = 0) & convergent_lines(all_17_7, all_17_6) = % 38.39/7.36 | | | | all_25_1 % 38.39/7.36 | | | | % 38.39/7.36 | | | | ALPHA: (187) implies: % 38.39/7.36 | | | | (188) ~ (all_25_1 = 0) % 38.39/7.36 | | | | (189) convergent_lines(all_17_7, all_17_6) = all_25_1 % 38.39/7.36 | | | | % 38.39/7.36 | | | | GROUND_INST: instantiating (11) with 0, all_25_1, all_17_6, all_17_7, % 38.39/7.36 | | | | simplifying with (22), (189) gives: % 38.39/7.36 | | | | (190) all_25_1 = 0 % 38.39/7.36 | | | | % 38.39/7.36 | | | | REDUCE: (188), (190) imply: % 38.39/7.36 | | | | (191) $false % 38.39/7.36 | | | | % 38.39/7.36 | | | | CLOSE: (191) is inconsistent. % 38.39/7.36 | | | | % 38.39/7.36 | | | End of split % 38.39/7.36 | | | % 38.39/7.36 | | Case 2: % 38.39/7.36 | | | % 38.39/7.36 | | | (192) ~ (all_24_1 = 0) & convergent_lines(all_17_7, all_17_6) = % 38.39/7.36 | | | all_24_1 % 38.39/7.36 | | | % 38.39/7.36 | | | ALPHA: (192) implies: % 38.39/7.36 | | | (193) ~ (all_24_1 = 0) % 38.39/7.36 | | | (194) convergent_lines(all_17_7, all_17_6) = all_24_1 % 38.39/7.36 | | | % 38.39/7.36 | | | GROUND_INST: instantiating (11) with 0, all_24_1, all_17_6, all_17_7, % 38.39/7.36 | | | simplifying with (22), (194) gives: % 38.39/7.36 | | | (195) all_24_1 = 0 % 38.39/7.36 | | | % 38.39/7.36 | | | REDUCE: (193), (195) imply: % 38.39/7.36 | | | (196) $false % 38.39/7.36 | | | % 38.39/7.36 | | | CLOSE: (196) is inconsistent. % 38.39/7.36 | | | % 38.39/7.36 | | End of split % 38.39/7.36 | | % 38.39/7.36 | Case 2: % 38.39/7.36 | | % 38.39/7.36 | | (197) ~ (all_35_1 = 0) & convergent_lines(all_17_9, all_17_8) = all_35_1 % 38.39/7.36 | | % 38.39/7.36 | | ALPHA: (197) implies: % 38.39/7.36 | | (198) ~ (all_35_1 = 0) % 38.39/7.36 | | (199) convergent_lines(all_17_9, all_17_8) = all_35_1 % 38.39/7.36 | | % 38.39/7.36 | | GROUND_INST: instantiating (11) with 0, all_35_1, all_17_8, all_17_9, % 38.39/7.36 | | simplifying with (21), (199) gives: % 38.39/7.36 | | (200) all_35_1 = 0 % 38.39/7.36 | | % 38.39/7.36 | | REDUCE: (198), (200) imply: % 38.39/7.36 | | (201) $false % 38.39/7.36 | | % 38.39/7.36 | | CLOSE: (201) is inconsistent. % 38.39/7.36 | | % 38.39/7.36 | End of split % 38.39/7.36 | % 38.39/7.36 End of proof % 38.39/7.36 % 38.39/7.36 Sub-proof #1 shows that the following formulas are inconsistent: % 38.39/7.36 ---------------------------------------------------------------- % 38.39/7.36 (1) all_298_2 = 0 | convergent_lines(all_17_7, all_17_7) = 0 % 38.39/7.36 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 38.39/7.36 (3) $i(all_17_7) % 38.39/7.36 (4) ~ (all_298_2 = 0) % 38.39/7.36 % 38.39/7.36 Begin of proof % 38.39/7.36 | % 38.39/7.36 | BETA: splitting (1) gives: % 38.39/7.36 | % 38.39/7.36 | Case 1: % 38.39/7.36 | | % 38.39/7.36 | | (5) convergent_lines(all_17_7, all_17_7) = 0 % 38.39/7.36 | | % 38.39/7.36 | | GROUND_INST: instantiating (2) with all_17_7, simplifying with (3), (5) % 38.39/7.36 | | gives: % 38.39/7.36 | | (6) $false % 38.39/7.36 | | % 38.39/7.36 | | CLOSE: (6) is inconsistent. % 38.39/7.36 | | % 38.39/7.36 | Case 2: % 38.39/7.36 | | % 38.39/7.36 | | (7) all_298_2 = 0 % 38.39/7.36 | | % 38.39/7.36 | | REDUCE: (4), (7) imply: % 38.39/7.36 | | (8) $false % 38.39/7.36 | | % 38.39/7.36 | | CLOSE: (8) is inconsistent. % 38.39/7.36 | | % 38.39/7.36 | End of split % 38.39/7.36 | % 38.39/7.36 End of proof % 38.39/7.36 % 38.39/7.36 Sub-proof #2 shows that the following formulas are inconsistent: % 38.39/7.36 ---------------------------------------------------------------- % 38.39/7.36 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.39/7.36 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 38.39/7.36 (apart_point_and_line(v3, v2) = v0)) % 38.39/7.36 (2) apart_point_and_line(all_17_2, all_17_6) = all_25_0 % 38.39/7.36 (3) apart_point_and_line(all_17_2, all_17_6) = 0 % 38.39/7.36 (4) ~ (all_25_0 = 0) % 38.39/7.36 % 38.39/7.36 Begin of proof % 38.39/7.36 | % 38.39/7.36 | GROUND_INST: instantiating (1) with all_25_0, 0, all_17_6, all_17_2, % 38.39/7.36 | simplifying with (2), (3) gives: % 38.39/7.36 | (5) all_25_0 = 0 % 38.39/7.36 | % 38.39/7.36 | REDUCE: (4), (5) imply: % 38.39/7.36 | (6) $false % 38.39/7.36 | % 38.39/7.36 | CLOSE: (6) is inconsistent. % 38.39/7.36 | % 38.39/7.36 End of proof % 38.39/7.36 % 38.39/7.36 Sub-proof #3 shows that the following formulas are inconsistent: % 38.39/7.36 ---------------------------------------------------------------- % 38.39/7.36 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.39/7.36 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 38.39/7.36 (apart_point_and_line(v3, v2) = v0)) % 38.39/7.36 (2) apart_point_and_line(all_17_5, all_17_7) = all_17_4 % 38.39/7.36 (3) apart_point_and_line(all_17_5, all_17_7) = 0 % 38.39/7.36 (4) ~ (all_17_4 = 0) % 38.39/7.36 % 38.39/7.36 Begin of proof % 38.39/7.36 | % 38.39/7.36 | GROUND_INST: instantiating (1) with all_17_4, 0, all_17_7, all_17_5, % 38.39/7.36 | simplifying with (2), (3) gives: % 38.39/7.36 | (5) all_17_4 = 0 % 38.39/7.36 | % 38.39/7.36 | REDUCE: (4), (5) imply: % 38.39/7.37 | (6) $false % 38.39/7.37 | % 38.39/7.37 | CLOSE: (6) is inconsistent. % 38.39/7.37 | % 38.39/7.37 End of proof % 38.39/7.37 % SZS output end Proof for theBenchmark % 38.39/7.37 % 38.39/7.37 6744ms %------------------------------------------------------------------------------