%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO177+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 : n003.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 23:21:53 EDT 2023 % Result : Theorem 9.68s 2.02s % Output : Proof 17.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO177+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 20:32:11 EDT 2023 % 0.12/0.34 % CPUTime : % 0.51/0.60 ________ _____ % 0.51/0.60 ___ __ \_________(_)________________________________ % 0.51/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.60 % 0.51/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.60 (2023-06-19) % 0.51/0.60 % 0.51/0.60 (c) Philipp Rümmer, 2009-2023 % 0.51/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.60 Amanda Stjerna. % 0.51/0.60 Free software under BSD-3-Clause. % 0.51/0.60 % 0.51/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.60 % 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.62 Running up to 7 provers in parallel. % 0.51/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.64/1.05 Prover 4: Preprocessing ... % 2.64/1.05 Prover 1: Preprocessing ... % 2.96/1.09 Prover 2: Preprocessing ... % 2.96/1.09 Prover 3: Preprocessing ... % 2.96/1.09 Prover 5: Preprocessing ... % 2.96/1.09 Prover 0: Preprocessing ... % 2.96/1.09 Prover 6: Preprocessing ... % 4.53/1.31 Prover 6: Constructing countermodel ... % 4.53/1.31 Prover 5: Proving ... % 4.53/1.32 Prover 2: Proving ... % 4.53/1.33 Prover 1: Constructing countermodel ... % 4.53/1.34 Prover 3: Constructing countermodel ... % 5.48/1.47 Prover 4: Constructing countermodel ... % 5.48/1.48 Prover 0: Proving ... % 5.48/1.48 Prover 3: gave up % 5.48/1.48 Prover 6: gave up % 5.48/1.48 Prover 1: gave up % 5.48/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.48/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.48/1.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.89/1.53 Prover 9: Preprocessing ... % 5.89/1.53 Prover 8: Preprocessing ... % 6.37/1.57 Prover 7: Preprocessing ... % 6.37/1.60 Prover 7: Warning: ignoring some quantifiers % 6.73/1.60 Prover 7: Constructing countermodel ... % 7.04/1.64 Prover 8: Warning: ignoring some quantifiers % 7.04/1.65 Prover 8: Constructing countermodel ... % 7.04/1.71 Prover 9: Constructing countermodel ... % 7.04/1.72 Prover 8: gave up % 7.04/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.78/1.75 Prover 10: Preprocessing ... % 7.78/1.78 Prover 7: gave up % 7.78/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.78/1.80 Prover 11: Preprocessing ... % 7.78/1.82 Prover 10: Warning: ignoring some quantifiers % 7.78/1.83 Prover 10: Constructing countermodel ... % 8.34/1.87 Prover 10: gave up % 8.34/1.88 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.92/1.92 Prover 12: Preprocessing ... % 8.92/1.98 Prover 11: Constructing countermodel ... % 8.92/1.99 Prover 12: Proving ... % 9.68/2.02 Prover 0: proved (1395ms) % 9.68/2.02 % 9.68/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.68/2.02 % 9.68/2.02 Prover 9: stopped % 9.68/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.68/2.02 Prover 12: stopped % 9.68/2.02 Prover 5: stopped % 9.68/2.02 Prover 2: stopped % 9.68/2.02 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.68/2.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.68/2.04 Prover 16: Preprocessing ... % 9.68/2.04 Prover 19: Preprocessing ... % 9.68/2.04 Prover 13: Preprocessing ... % 9.68/2.07 Prover 13: Warning: ignoring some quantifiers % 9.68/2.07 Prover 16: Warning: ignoring some quantifiers % 9.68/2.07 Prover 13: Constructing countermodel ... % 9.68/2.07 Prover 16: Constructing countermodel ... % 9.68/2.09 Prover 19: Warning: ignoring some quantifiers % 9.68/2.10 Prover 19: Constructing countermodel ... % 10.40/2.14 Prover 19: gave up % 11.15/2.20 Prover 13: gave up % 11.15/2.26 Prover 16: gave up % 16.72/3.19 Prover 11: Found proof (size 234) % 16.72/3.19 Prover 11: proved (1411ms) % 16.72/3.19 Prover 4: stopped % 16.72/3.19 % 16.72/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.72/3.19 % 16.72/3.21 % SZS output start Proof for theBenchmark % 16.72/3.21 Assumptions after simplification: % 16.72/3.21 --------------------------------- % 16.72/3.21 % 16.72/3.21 (ceq2) % 16.72/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.72/3.24 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 16.72/3.24 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 16.72/3.24 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 16.72/3.24 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 16.72/3.24 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.72/3.24 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.72/3.24 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 16.72/3.24 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.72/3.24 apart_point_and_line(v0, v2) = 0) % 16.72/3.24 % 16.72/3.24 (ci1) % 16.72/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.72/3.24 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.72/3.24 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.72/3.24 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.72/3.24 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.72/3.24 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.72/3.24 $i(v2))) % 16.72/3.24 % 16.72/3.24 (ci2) % 16.72/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.72/3.25 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.72/3.25 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.72/3.25 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.72/3.25 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.72/3.25 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.72/3.25 $i(v2))) % 16.72/3.25 % 16.72/3.25 (con) % 16.72/3.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.72/3.25 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ( ~ (v9 = % 16.72/3.25 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) % 16.72/3.25 = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 % 16.72/3.25 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & $i(v7) & % 16.72/3.25 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & % 16.72/3.25 apart_point_and_line(v1, v4) = 0) | (v5 = 0 & apart_point_and_line(v0, % 16.72/3.25 v4) = 0))) % 16.72/3.25 % 16.72/3.25 (cu1) % 16.72/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.72/3.27 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.72/3.27 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.72/3.27 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.72/3.27 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 16.72/3.27 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 16.72/3.27 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.72/3.27 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 16.72/3.27 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 16.72/3.27 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 16.72/3.27 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.72/3.27 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 16.72/3.27 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.72/3.27 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.72/3.27 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.72/3.27 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.72/3.27 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.72/3.27 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.72/3.27 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 16.72/3.27 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.72/3.27 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.72/3.27 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 16.72/3.27 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.72/3.27 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.72/3.27 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 16.72/3.27 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.72/3.27 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 16.72/3.27 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 16.72/3.27 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.72/3.27 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 16.72/3.27 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 16.72/3.27 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 16.72/3.27 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.72/3.27 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 16.72/3.27 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 16.72/3.27 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 16.72/3.27 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 16.72/3.27 % 16.72/3.27 (function-axioms) % 16.72/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.72/3.28 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.72/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.72/3.28 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.72/3.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.72/3.28 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.72/3.28 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.72/3.28 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.72/3.28 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.72/3.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.72/3.28 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.72/3.28 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.72/3.28 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.72/3.28 (distinct_points(v3, v2) = v0)) % 16.72/3.28 % 16.72/3.28 Further assumptions not needed in the proof: % 16.72/3.28 -------------------------------------------- % 16.72/3.28 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq3, ci3, ci4 % 16.72/3.28 % 16.72/3.28 Those formulas are unsatisfiable: % 16.72/3.28 --------------------------------- % 16.72/3.28 % 16.72/3.28 Begin of proof % 16.72/3.28 | % 16.72/3.28 | ALPHA: (ci1) implies: % 16.72/3.28 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.72/3.28 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.72/3.28 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.72/3.28 | $i(v2))) % 16.72/3.28 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.72/3.28 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 16.72/3.28 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & % 16.72/3.28 | distinct_points(v0, v1) = v3))) % 16.72/3.28 | % 16.72/3.28 | ALPHA: (ci2) implies: % 16.72/3.28 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.72/3.28 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.72/3.28 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.72/3.28 | $i(v2))) % 16.72/3.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 16.72/3.28 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 16.72/3.28 | (v4 = 0) & apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & % 16.72/3.28 | distinct_points(v0, v1) = v3))) % 16.72/3.28 | % 16.72/3.28 | ALPHA: (cu1) implies: % 16.72/3.29 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.72/3.29 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 16.72/3.29 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 16.72/3.29 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.72/3.29 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.72/3.29 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.72/3.29 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 16.72/3.29 | distinct_lines(v2, v3) = v6))) % 16.72/3.29 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.72/3.29 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.72/3.29 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.72/3.29 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 16.72/3.29 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.72/3.29 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 16.72/3.29 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 16.72/3.29 | v1) = v6))) % 16.72/3.29 | % 16.72/3.29 | ALPHA: (ceq2) implies: % 16.72/3.29 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.72/3.29 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) % 16.72/3.29 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = % 16.72/3.29 | 0) % 16.72/3.29 | % 16.72/3.29 | ALPHA: (function-axioms) implies: % 16.72/3.29 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.72/3.29 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.72/3.29 | (distinct_points(v3, v2) = v0)) % 16.72/3.29 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.72/3.29 | ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 16.72/3.29 | (distinct_lines(v3, v2) = v0)) % 16.72/3.29 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.72/3.29 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.72/3.29 | (apart_point_and_line(v3, v2) = v0)) % 16.72/3.29 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.72/3.29 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 16.72/3.29 | % 16.72/3.29 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 16.72/3.29 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8, all_17_9 % 16.72/3.29 | gives: % 16.72/3.29 | (12) ~ (all_17_0 = 0) & ~ (all_17_1 = 0) & line_connecting(all_17_7, % 16.72/3.29 | all_17_6) = all_17_5 & line_connecting(all_17_9, all_17_8) = % 16.72/3.29 | all_17_2 & apart_point_and_line(all_17_6, all_17_2) = all_17_0 & % 16.72/3.29 | apart_point_and_line(all_17_7, all_17_2) = all_17_1 & % 16.72/3.29 | distinct_points(all_17_7, all_17_6) = 0 & distinct_points(all_17_9, % 16.72/3.29 | all_17_8) = 0 & $i(all_17_2) & $i(all_17_5) & $i(all_17_6) & % 16.72/3.29 | $i(all_17_7) & $i(all_17_8) & $i(all_17_9) & ((all_17_3 = 0 & % 16.72/3.29 | apart_point_and_line(all_17_8, all_17_5) = 0) | (all_17_4 = 0 & % 16.72/3.29 | apart_point_and_line(all_17_9, all_17_5) = 0)) % 16.72/3.29 | % 16.72/3.29 | ALPHA: (12) implies: % 16.72/3.30 | (13) ~ (all_17_1 = 0) % 16.72/3.30 | (14) ~ (all_17_0 = 0) % 16.72/3.30 | (15) $i(all_17_9) % 16.72/3.30 | (16) $i(all_17_8) % 16.72/3.30 | (17) $i(all_17_7) % 16.72/3.30 | (18) $i(all_17_6) % 16.72/3.30 | (19) distinct_points(all_17_9, all_17_8) = 0 % 16.72/3.30 | (20) distinct_points(all_17_7, all_17_6) = 0 % 16.72/3.30 | (21) apart_point_and_line(all_17_7, all_17_2) = all_17_1 % 16.72/3.30 | (22) apart_point_and_line(all_17_6, all_17_2) = all_17_0 % 16.72/3.30 | (23) line_connecting(all_17_9, all_17_8) = all_17_2 % 16.72/3.30 | (24) line_connecting(all_17_7, all_17_6) = all_17_5 % 17.27/3.30 | (25) (all_17_3 = 0 & apart_point_and_line(all_17_8, all_17_5) = 0) | % 17.27/3.30 | (all_17_4 = 0 & apart_point_and_line(all_17_9, all_17_5) = 0) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (3) with all_17_9, all_17_8, simplifying with (15), % 17.27/3.30 | (16), (19) gives: % 17.27/3.30 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9, % 17.27/3.30 | all_17_8) = v0 & apart_point_and_line(all_17_8, v0) = v1 & $i(v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (1) with all_17_9, all_17_8, simplifying with (15), % 17.27/3.30 | (16), (19) gives: % 17.27/3.30 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9, % 17.27/3.30 | all_17_8) = v0 & apart_point_and_line(all_17_9, v0) = v1 & $i(v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (3) with all_17_7, all_17_6, simplifying with (17), % 17.27/3.30 | (18), (20) gives: % 17.27/3.30 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7, % 17.27/3.30 | all_17_6) = v0 & apart_point_and_line(all_17_6, v0) = v1 & $i(v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (1) with all_17_7, all_17_6, simplifying with (17), % 17.27/3.30 | (18), (20) gives: % 17.27/3.30 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7, % 17.27/3.30 | all_17_6) = v0 & apart_point_and_line(all_17_7, v0) = v1 & $i(v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (4) with all_17_9, all_17_8, all_17_2, simplifying % 17.27/3.30 | with (15), (16), (23) gives: % 17.27/3.30 | (30) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.30 | apart_point_and_line(all_17_8, all_17_2) = v1) | ( ~ (v0 = 0) & % 17.27/3.30 | distinct_points(all_17_9, all_17_8) = v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (2) with all_17_9, all_17_8, all_17_2, simplifying % 17.27/3.30 | with (15), (16), (23) gives: % 17.27/3.30 | (31) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.30 | apart_point_and_line(all_17_9, all_17_2) = v1) | ( ~ (v0 = 0) & % 17.27/3.30 | distinct_points(all_17_9, all_17_8) = v0)) % 17.27/3.30 | % 17.27/3.30 | GROUND_INST: instantiating (4) with all_17_7, all_17_6, all_17_5, simplifying % 17.27/3.30 | with (17), (18), (24) gives: % 17.27/3.30 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.30 | apart_point_and_line(all_17_6, all_17_5) = v1) | ( ~ (v0 = 0) & % 17.27/3.30 | distinct_points(all_17_7, all_17_6) = v0)) % 17.27/3.31 | % 17.27/3.31 | GROUND_INST: instantiating (2) with all_17_7, all_17_6, all_17_5, simplifying % 17.27/3.31 | with (17), (18), (24) gives: % 17.27/3.31 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.31 | apart_point_and_line(all_17_7, all_17_5) = v1) | ( ~ (v0 = 0) & % 17.27/3.31 | distinct_points(all_17_7, all_17_6) = v0)) % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (33) with fresh symbols all_24_0, all_24_1 gives: % 17.27/3.31 | (34) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) = % 17.27/3.31 | all_24_0) | ( ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6) % 17.27/3.31 | = all_24_1) % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (32) with fresh symbols all_25_0, all_25_1 gives: % 17.27/3.31 | (35) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) = % 17.27/3.31 | all_25_0) | ( ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6) % 17.27/3.31 | = all_25_1) % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (31) with fresh symbols all_26_0, all_26_1 gives: % 17.27/3.31 | (36) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) = % 17.27/3.31 | all_26_0) | ( ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8) % 17.27/3.31 | = all_26_1) % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (29) with fresh symbols all_27_0, all_27_1 gives: % 17.27/3.31 | (37) ~ (all_27_0 = 0) & line_connecting(all_17_7, all_17_6) = all_27_1 & % 17.27/3.31 | apart_point_and_line(all_17_7, all_27_1) = all_27_0 & $i(all_27_1) % 17.27/3.31 | % 17.27/3.31 | ALPHA: (37) implies: % 17.27/3.31 | (38) ~ (all_27_0 = 0) % 17.27/3.31 | (39) $i(all_27_1) % 17.27/3.31 | (40) apart_point_and_line(all_17_7, all_27_1) = all_27_0 % 17.27/3.31 | (41) line_connecting(all_17_7, all_17_6) = all_27_1 % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1 gives: % 17.27/3.31 | (42) ~ (all_29_0 = 0) & line_connecting(all_17_7, all_17_6) = all_29_1 & % 17.27/3.31 | apart_point_and_line(all_17_6, all_29_1) = all_29_0 & $i(all_29_1) % 17.27/3.31 | % 17.27/3.31 | ALPHA: (42) implies: % 17.27/3.31 | (43) ~ (all_29_0 = 0) % 17.27/3.31 | (44) apart_point_and_line(all_17_6, all_29_1) = all_29_0 % 17.27/3.31 | (45) line_connecting(all_17_7, all_17_6) = all_29_1 % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (26) with fresh symbols all_31_0, all_31_1 gives: % 17.27/3.31 | (46) ~ (all_31_0 = 0) & line_connecting(all_17_9, all_17_8) = all_31_1 & % 17.27/3.31 | apart_point_and_line(all_17_8, all_31_1) = all_31_0 & $i(all_31_1) % 17.27/3.31 | % 17.27/3.31 | ALPHA: (46) implies: % 17.27/3.31 | (47) $i(all_31_1) % 17.27/3.31 | (48) apart_point_and_line(all_17_8, all_31_1) = all_31_0 % 17.27/3.31 | (49) line_connecting(all_17_9, all_17_8) = all_31_1 % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (27) with fresh symbols all_33_0, all_33_1 gives: % 17.27/3.31 | (50) ~ (all_33_0 = 0) & line_connecting(all_17_9, all_17_8) = all_33_1 & % 17.27/3.31 | apart_point_and_line(all_17_9, all_33_1) = all_33_0 & $i(all_33_1) % 17.27/3.31 | % 17.27/3.31 | ALPHA: (50) implies: % 17.27/3.31 | (51) ~ (all_33_0 = 0) % 17.27/3.31 | (52) apart_point_and_line(all_17_9, all_33_1) = all_33_0 % 17.27/3.31 | (53) line_connecting(all_17_9, all_17_8) = all_33_1 % 17.27/3.31 | % 17.27/3.31 | DELTA: instantiating (30) with fresh symbols all_35_0, all_35_1 gives: % 17.27/3.31 | (54) ( ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) = % 17.27/3.31 | all_35_0) | ( ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8) % 17.27/3.31 | = all_35_1) % 17.27/3.31 | % 17.27/3.31 | BETA: splitting (54) gives: % 17.27/3.31 | % 17.27/3.31 | Case 1: % 17.27/3.31 | | % 17.27/3.31 | | (55) ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) = % 17.27/3.31 | | all_35_0 % 17.27/3.31 | | % 17.27/3.31 | | ALPHA: (55) implies: % 17.27/3.31 | | (56) ~ (all_35_0 = 0) % 17.27/3.31 | | (57) apart_point_and_line(all_17_8, all_17_2) = all_35_0 % 17.27/3.31 | | % 17.27/3.31 | | BETA: splitting (34) gives: % 17.27/3.31 | | % 17.27/3.31 | | Case 1: % 17.27/3.31 | | | % 17.27/3.31 | | | (58) ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) = % 17.27/3.31 | | | all_24_0 % 17.27/3.31 | | | % 17.27/3.31 | | | ALPHA: (58) implies: % 17.27/3.31 | | | (59) apart_point_and_line(all_17_7, all_17_5) = all_24_0 % 17.27/3.31 | | | % 17.27/3.31 | | | BETA: splitting (36) gives: % 17.27/3.31 | | | % 17.27/3.31 | | | Case 1: % 17.27/3.31 | | | | % 17.27/3.32 | | | | (60) ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) = % 17.27/3.32 | | | | all_26_0 % 17.27/3.32 | | | | % 17.27/3.32 | | | | ALPHA: (60) implies: % 17.27/3.32 | | | | (61) apart_point_and_line(all_17_9, all_17_2) = all_26_0 % 17.27/3.32 | | | | % 17.27/3.32 | | | | BETA: splitting (35) gives: % 17.27/3.32 | | | | % 17.27/3.32 | | | | Case 1: % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | (62) ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) = % 17.27/3.32 | | | | | all_25_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | ALPHA: (62) implies: % 17.27/3.32 | | | | | (63) apart_point_and_line(all_17_6, all_17_5) = all_25_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_17_2, all_33_1, all_17_8, % 17.27/3.32 | | | | | all_17_9, simplifying with (23), (53) gives: % 17.27/3.32 | | | | | (64) all_33_1 = all_17_2 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_31_1, all_33_1, all_17_8, % 17.27/3.32 | | | | | all_17_9, simplifying with (49), (53) gives: % 17.27/3.32 | | | | | (65) all_33_1 = all_31_1 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_17_5, all_29_1, all_17_6, % 17.27/3.32 | | | | | all_17_7, simplifying with (24), (45) gives: % 17.27/3.32 | | | | | (66) all_29_1 = all_17_5 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_27_1, all_29_1, all_17_6, % 17.27/3.32 | | | | | all_17_7, simplifying with (41), (45) gives: % 17.27/3.32 | | | | | (67) all_29_1 = all_27_1 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | COMBINE_EQS: (64), (65) imply: % 17.27/3.32 | | | | | (68) all_31_1 = all_17_2 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | SIMP: (68) implies: % 17.27/3.32 | | | | | (69) all_31_1 = all_17_2 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | COMBINE_EQS: (66), (67) imply: % 17.27/3.32 | | | | | (70) all_27_1 = all_17_5 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | SIMP: (70) implies: % 17.27/3.32 | | | | | (71) all_27_1 = all_17_5 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (44), (66) imply: % 17.27/3.32 | | | | | (72) apart_point_and_line(all_17_6, all_17_5) = all_29_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (40), (71) imply: % 17.27/3.32 | | | | | (73) apart_point_and_line(all_17_7, all_17_5) = all_27_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (48), (69) imply: % 17.27/3.32 | | | | | (74) apart_point_and_line(all_17_8, all_17_2) = all_31_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (52), (64) imply: % 17.27/3.32 | | | | | (75) apart_point_and_line(all_17_9, all_17_2) = all_33_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (47), (69) imply: % 17.27/3.32 | | | | | (76) $i(all_17_2) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (39), (71) imply: % 17.27/3.32 | | | | | (77) $i(all_17_5) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_26_0, all_33_0, all_17_2, % 17.27/3.32 | | | | | all_17_9, simplifying with (61), (75) gives: % 17.27/3.32 | | | | | (78) all_33_0 = all_26_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_35_0, all_31_0, all_17_2, % 17.27/3.32 | | | | | all_17_8, simplifying with (57), (74) gives: % 17.27/3.32 | | | | | (79) all_35_0 = all_31_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_24_0, all_27_0, all_17_5, % 17.27/3.32 | | | | | all_17_7, simplifying with (59), (73) gives: % 17.27/3.32 | | | | | (80) all_27_0 = all_24_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_25_0, all_29_0, all_17_5, % 17.27/3.32 | | | | | all_17_6, simplifying with (63), (72) gives: % 17.27/3.32 | | | | | (81) all_29_0 = all_25_0 % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (56), (79) imply: % 17.27/3.32 | | | | | (82) ~ (all_31_0 = 0) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (51), (78) imply: % 17.27/3.32 | | | | | (83) ~ (all_26_0 = 0) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (43), (81) imply: % 17.27/3.32 | | | | | (84) ~ (all_25_0 = 0) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | REDUCE: (38), (80) imply: % 17.27/3.32 | | | | | (85) ~ (all_24_0 = 0) % 17.27/3.32 | | | | | % 17.27/3.32 | | | | | GROUND_INST: instantiating (6) with all_17_7, all_17_6, all_17_5, % 17.27/3.32 | | | | | all_17_2, all_24_0, all_17_0, simplifying with (17), % 17.27/3.32 | | | | | (18), (22), (59), (76), (77) gives: % 17.27/3.33 | | | | | (86) all_24_0 = 0 | all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.33 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | (v2 = 0 & % 17.27/3.33 | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( ~ (v1 = % 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v1) | ( ~ (v0 % 17.27/3.33 | | | | | = 0) & distinct_points(all_17_7, all_17_6) = v0)) % 17.27/3.33 | | | | | % 17.27/3.33 | | | | | GROUND_INST: instantiating (5) with all_17_7, all_17_6, all_17_5, % 17.27/3.33 | | | | | all_17_2, all_24_0, all_17_1, simplifying with (17), % 17.27/3.33 | | | | | (18), (20), (21), (59), (76), (77) gives: % 17.27/3.33 | | | | | (87) all_24_0 = 0 | all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.33 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_6, % 17.27/3.33 | | | | | all_17_2) = 0) | (v1 = 0 & % 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~ (v0 = % 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v0)) % 17.27/3.33 | | | | | % 17.27/3.33 | | | | | GROUND_INST: instantiating (6) with all_17_6, all_17_9, all_17_5, % 17.27/3.33 | | | | | all_17_2, all_25_0, all_26_0, simplifying with (15), % 17.27/3.33 | | | | | (18), (61), (63), (76), (77) gives: % 17.27/3.33 | | | | | (88) all_26_0 = 0 | all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.33 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 17.27/3.33 | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | (v2 = 0 & % 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_2) = 0) | ( ~ (v1 = % 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v1) | ( ~ (v0 % 17.27/3.33 | | | | | = 0) & distinct_points(all_17_6, all_17_9) = v0)) % 17.27/3.33 | | | | | % 17.27/3.33 | | | | | BETA: splitting (25) gives: % 17.27/3.33 | | | | | % 17.27/3.33 | | | | | Case 1: % 17.27/3.33 | | | | | | % 17.27/3.33 | | | | | | (89) all_17_3 = 0 & apart_point_and_line(all_17_8, all_17_5) = 0 % 17.27/3.33 | | | | | | % 17.27/3.33 | | | | | | ALPHA: (89) implies: % 17.27/3.33 | | | | | | (90) apart_point_and_line(all_17_8, all_17_5) = 0 % 17.27/3.33 | | | | | | % 17.27/3.33 | | | | | | BETA: splitting (86) gives: % 17.27/3.33 | | | | | | % 17.27/3.33 | | | | | | Case 1: % 17.27/3.33 | | | | | | | % 17.27/3.33 | | | | | | | (91) all_24_0 = 0 % 17.27/3.33 | | | | | | | % 17.27/3.33 | | | | | | | REDUCE: (85), (91) imply: % 17.27/3.33 | | | | | | | (92) $false % 17.27/3.33 | | | | | | | % 17.27/3.33 | | | | | | | CLOSE: (92) is inconsistent. % 17.27/3.33 | | | | | | | % 17.52/3.33 | | | | | | Case 2: % 17.52/3.33 | | | | | | | % 17.52/3.33 | | | | | | | (93) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 17.52/3.33 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6, % 17.52/3.33 | | | | | | | all_17_5) = 0) | (v2 = 0 & % 17.52/3.33 | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( ~ % 17.52/3.33 | | | | | | | (v1 = 0) & distinct_lines(all_17_5, all_17_2) = v1) | % 17.52/3.33 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_7, all_17_6) = % 17.52/3.33 | | | | | | | v0)) % 17.52/3.33 | | | | | | | % 17.52/3.33 | | | | | | | BETA: splitting (87) gives: % 17.52/3.33 | | | | | | | % 17.52/3.33 | | | | | | | Case 1: % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | (94) all_24_0 = 0 % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | REDUCE: (85), (94) imply: % 17.52/3.33 | | | | | | | | (95) $false % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | CLOSE: (95) is inconsistent. % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | Case 2: % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | (96) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.52/3.33 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_6, % 17.52/3.33 | | | | | | | | all_17_2) = 0) | (v1 = 0 & % 17.52/3.33 | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~ % 17.52/3.33 | | | | | | | | (v0 = 0) & distinct_lines(all_17_5, all_17_2) = v0)) % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | BETA: splitting (88) gives: % 17.52/3.33 | | | | | | | | % 17.52/3.33 | | | | | | | | Case 1: % 17.52/3.33 | | | | | | | | | % 17.52/3.33 | | | | | | | | | (97) all_26_0 = 0 % 17.52/3.33 | | | | | | | | | % 17.52/3.33 | | | | | | | | | REDUCE: (83), (97) imply: % 17.52/3.33 | | | | | | | | | (98) $false % 17.52/3.33 | | | | | | | | | % 17.52/3.33 | | | | | | | | | CLOSE: (98) is inconsistent. % 17.52/3.33 | | | | | | | | | % 17.52/3.33 | | | | | | | | Case 2: % 17.52/3.34 | | | | | | | | | % 17.52/3.34 | | | | | | | | | (99) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.52/3.34 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 17.52/3.34 | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | % 17.52/3.34 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_6, all_17_2) = % 17.52/3.34 | | | | | | | | | 0) | ( ~ (v1 = 0) & distinct_lines(all_17_5, % 17.52/3.34 | | | | | | | | | all_17_2) = v1) | ( ~ (v0 = 0) & % 17.52/3.34 | | | | | | | | | distinct_points(all_17_6, all_17_9) = v0)) % 17.52/3.34 | | | | | | | | | % 17.52/3.34 | | | | | | | | | BETA: splitting (93) gives: % 17.52/3.34 | | | | | | | | | % 17.52/3.34 | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | (100) all_17_0 = 0 % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | REDUCE: (14), (100) imply: % 17.52/3.34 | | | | | | | | | | (101) $false % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | CLOSE: (101) is inconsistent. % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | Case 2: % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | (102) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.52/3.34 | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.52/3.34 | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | % 17.52/3.34 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_7, % 17.52/3.34 | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) & % 17.52/3.34 | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = v1) | ( ~ % 17.52/3.34 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_7, all_17_6) % 17.52/3.34 | | | | | | | | | | = v0)) % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_286_0, % 17.52/3.34 | | | | | | | | | | all_286_1, all_286_2, all_286_3 gives: % 17.52/3.34 | | | | | | | | | | (103) (all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 & % 17.52/3.34 | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( % 17.52/3.34 | | | | | | | | | | ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.52/3.34 | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) & % 17.52/3.34 | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3) % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | BETA: splitting (96) gives: % 17.52/3.34 | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | (104) all_17_1 = 0 % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | REDUCE: (13), (104) imply: % 17.52/3.34 | | | | | | | | | | | (105) $false % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | CLOSE: (105) is inconsistent. % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | Case 2: % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | (106) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.52/3.34 | | | | | | | | | | | = 0 & apart_point_and_line(all_17_6, all_17_2) % 17.52/3.34 | | | | | | | | | | | = 0) | (v1 = 0 & % 17.52/3.34 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) % 17.52/3.34 | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_5, % 17.52/3.34 | | | | | | | | | | | all_17_2) = v0)) % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | DELTA: instantiating (106) with fresh symbols all_294_0, % 17.52/3.34 | | | | | | | | | | | all_294_1, all_294_2 gives: % 17.52/3.34 | | | | | | | | | | | (107) (all_294_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | | all_17_2) = 0) | (all_294_1 = 0 & % 17.52/3.34 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | % 17.52/3.34 | | | | | | | | | | | ( ~ (all_294_2 = 0) & distinct_lines(all_17_5, % 17.52/3.34 | | | | | | | | | | | all_17_2) = all_294_2) % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | BETA: splitting (107) gives: % 17.52/3.34 | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | (108) all_294_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | | | all_17_2) = 0 % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | ALPHA: (108) implies: % 17.52/3.34 | | | | | | | | | | | | (109) apart_point_and_line(all_17_6, all_17_2) = 0 % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | REF_CLOSE: (10), (14), (22), (109) are inconsistent by % 17.52/3.34 | | | | | | | | | | | | sub-proof #3. % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | Case 2: % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | (110) (all_294_1 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | | | all_17_5) = 0) | ( ~ (all_294_2 = 0) & % 17.52/3.34 | | | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = all_294_2) % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | BETA: splitting (110) gives: % 17.52/3.34 | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | (111) all_294_1 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | | | | all_17_5) = 0 % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | ALPHA: (111) implies: % 17.52/3.34 | | | | | | | | | | | | | (112) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (112) are inconsistent by % 17.52/3.34 | | | | | | | | | | | | | sub-proof #2. % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | Case 2: % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | (113) ~ (all_294_2 = 0) & distinct_lines(all_17_5, % 17.52/3.34 | | | | | | | | | | | | | all_17_2) = all_294_2 % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | ALPHA: (113) implies: % 17.52/3.34 | | | | | | | | | | | | | (114) ~ (all_294_2 = 0) % 17.52/3.34 | | | | | | | | | | | | | (115) distinct_lines(all_17_5, all_17_2) = all_294_2 % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | BETA: splitting (103) gives: % 17.52/3.34 | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | | (116) (all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.34 | | | | | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 & % 17.52/3.34 | | | | | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) % 17.52/3.34 | | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | | BETA: splitting (116) gives: % 17.52/3.34 | | | | | | | | | | | | | | % 17.52/3.34 | | | | | | | | | | | | | | Case 1: % 17.52/3.34 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | (117) all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.35 | | | | | | | | | | | | | | | all_17_5) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (117) implies: % 17.52/3.35 | | | | | | | | | | | | | | | (118) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (118) are inconsistent by % 17.52/3.35 | | | | | | | | | | | | | | | sub-proof #2. % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | Case 2: % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | (119) all_286_1 = 0 & apart_point_and_line(all_17_7, % 17.52/3.35 | | | | | | | | | | | | | | | all_17_2) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (119) implies: % 17.52/3.35 | | | | | | | | | | | | | | | (120) apart_point_and_line(all_17_7, all_17_2) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (21), (120) are inconsistent by % 17.52/3.35 | | | | | | | | | | | | | | | sub-proof #1. % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | End of split % 17.52/3.35 | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | Case 2: % 17.52/3.35 | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | (121) ( ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.52/3.35 | | | | | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) & % 17.52/3.35 | | | | | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3) % 17.52/3.35 | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | BETA: splitting (121) gives: % 17.52/3.35 | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | Case 1: % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | (122) ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.52/3.35 | | | | | | | | | | | | | | | all_17_2) = all_286_2 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (122) implies: % 17.52/3.35 | | | | | | | | | | | | | | | (123) distinct_lines(all_17_5, all_17_2) = all_286_2 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | Case 1: % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | (124) all_25_0 = 0 % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | REDUCE: (84), (124) imply: % 17.52/3.35 | | | | | | | | | | | | | | | | (125) $false % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | Case 2: % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_286_2, all_294_2, % 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (115), (123) % 17.52/3.35 | | | | | | | | | | | | | | | | gives: % 17.52/3.35 | | | | | | | | | | | | | | | | (126) all_294_2 = all_286_2 % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | REDUCE: (114), (126) imply: % 17.52/3.35 | | | | | | | | | | | | | | | | (127) ~ (all_286_2 = 0) % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_8, all_17_5, % 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2, all_286_2, simplifying with (16), (76), % 17.52/3.35 | | | | | | | | | | | | | | | | (77), (90), (123) gives: % 17.52/3.35 | | | | | | | | | | | | | | | | (128) all_286_2 = 0 | apart_point_and_line(all_17_8, % 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | Case 1: % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | (129) apart_point_and_line(all_17_8, all_17_2) = 0 % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_31_0, 0, all_17_2, % 17.52/3.35 | | | | | | | | | | | | | | | | | all_17_8, simplifying with (74), (129) gives: % 17.52/3.35 | | | | | | | | | | | | | | | | | (130) all_31_0 = 0 % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | REDUCE: (82), (130) imply: % 17.52/3.35 | | | | | | | | | | | | | | | | | (131) $false % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | Case 2: % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | (132) all_286_2 = 0 % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | REDUCE: (127), (132) imply: % 17.52/3.35 | | | | | | | | | | | | | | | | | (133) $false % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent. % 17.52/3.35 | | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | | End of split % 17.52/3.35 | | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | End of split % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | Case 2: % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | (134) ~ (all_286_3 = 0) & distinct_points(all_17_7, % 17.52/3.35 | | | | | | | | | | | | | | | all_17_6) = all_286_3 % 17.52/3.35 | | | | | | | | | | | | | | | % 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (134) implies: % 17.52/3.36 | | | | | | | | | | | | | | | (135) ~ (all_286_3 = 0) % 17.52/3.36 | | | | | | | | | | | | | | | (136) distinct_points(all_17_7, all_17_6) = all_286_3 % 17.52/3.36 | | | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_286_3, all_17_6, % 17.52/3.36 | | | | | | | | | | | | | | | all_17_7, simplifying with (20), (136) gives: % 17.52/3.36 | | | | | | | | | | | | | | | (137) all_286_3 = 0 % 17.52/3.36 | | | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | | | | REDUCE: (135), (137) imply: % 17.52/3.36 | | | | | | | | | | | | | | | (138) $false % 17.52/3.36 | | | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 17.52/3.36 | | | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | End of split % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | End of split % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | End of split % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | End of split % 17.52/3.36 | | | | | | % 17.52/3.36 | | | | | Case 2: % 17.52/3.36 | | | | | | % 17.52/3.36 | | | | | | (139) all_17_4 = 0 & apart_point_and_line(all_17_9, all_17_5) = 0 % 17.52/3.36 | | | | | | % 17.52/3.36 | | | | | | ALPHA: (139) implies: % 17.52/3.36 | | | | | | (140) apart_point_and_line(all_17_9, all_17_5) = 0 % 17.52/3.36 | | | | | | % 17.52/3.36 | | | | | | BETA: splitting (86) gives: % 17.52/3.36 | | | | | | % 17.52/3.36 | | | | | | Case 1: % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | (141) all_24_0 = 0 % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | REDUCE: (85), (141) imply: % 17.52/3.36 | | | | | | | (142) $false % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | CLOSE: (142) is inconsistent. % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | Case 2: % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | (143) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 17.52/3.36 | | | | | | | : ? [v3: int] : ((v3 = 0 & % 17.52/3.36 | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | (v2 = % 17.52/3.36 | | | | | | | 0 & apart_point_and_line(all_17_7, all_17_2) = 0) | ( % 17.52/3.36 | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_5, all_17_2) = v1) % 17.52/3.36 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_7, all_17_6) = % 17.52/3.36 | | | | | | | v0)) % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | BETA: splitting (87) gives: % 17.52/3.36 | | | | | | | % 17.52/3.36 | | | | | | | Case 1: % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | (144) all_24_0 = 0 % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | REDUCE: (85), (144) imply: % 17.52/3.36 | | | | | | | | (145) $false % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | CLOSE: (145) is inconsistent. % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | Case 2: % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | (146) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.52/3.36 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_6, % 17.52/3.36 | | | | | | | | all_17_2) = 0) | (v1 = 0 & % 17.52/3.36 | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~ % 17.52/3.36 | | | | | | | | (v0 = 0) & distinct_lines(all_17_5, all_17_2) = % 17.52/3.36 | | | | | | | | v0)) % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | BETA: splitting (88) gives: % 17.52/3.36 | | | | | | | | % 17.52/3.36 | | | | | | | | Case 1: % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | (147) all_26_0 = 0 % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | REDUCE: (83), (147) imply: % 17.52/3.36 | | | | | | | | | (148) $false % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | CLOSE: (148) is inconsistent. % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | Case 2: % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | (149) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 17.52/3.36 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 17.52/3.36 | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | % 17.52/3.36 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_6, all_17_2) % 17.52/3.36 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_5, % 17.52/3.36 | | | | | | | | | all_17_2) = v1) | ( ~ (v0 = 0) & % 17.52/3.36 | | | | | | | | | distinct_points(all_17_6, all_17_9) = v0)) % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | BETA: splitting (143) gives: % 17.52/3.36 | | | | | | | | | % 17.52/3.36 | | | | | | | | | Case 1: % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | (150) all_17_0 = 0 % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | REDUCE: (14), (150) imply: % 17.52/3.36 | | | | | | | | | | (151) $false % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | CLOSE: (151) is inconsistent. % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | Case 2: % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | (152) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.52/3.36 | | | | | | | | | | [v3: int] : ((v3 = 0 & % 17.52/3.36 | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | % 17.52/3.36 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_7, % 17.52/3.36 | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) & % 17.52/3.36 | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = v1) | ( ~ % 17.52/3.36 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_7, all_17_6) % 17.52/3.36 | | | | | | | | | | = v0)) % 17.52/3.36 | | | | | | | | | | % 17.52/3.36 | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_286_0, % 17.52/3.36 | | | | | | | | | | all_286_1, all_286_2, all_286_3 gives: % 17.52/3.36 | | | | | | | | | | (153) (all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.36 | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 & % 17.52/3.36 | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( % 17.52/3.37 | | | | | | | | | | ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.52/3.37 | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) & % 17.52/3.37 | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3) % 17.52/3.37 | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | BETA: splitting (146) gives: % 17.52/3.37 | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | Case 1: % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | (154) all_17_1 = 0 % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | REDUCE: (13), (154) imply: % 17.52/3.37 | | | | | | | | | | | (155) $false % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | CLOSE: (155) is inconsistent. % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | Case 2: % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | (156) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 17.52/3.37 | | | | | | | | | | | = 0 & apart_point_and_line(all_17_6, all_17_2) % 17.52/3.37 | | | | | | | | | | | = 0) | (v1 = 0 & % 17.52/3.37 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) % 17.52/3.37 | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_5, % 17.52/3.37 | | | | | | | | | | | all_17_2) = v0)) % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_294_0, % 17.52/3.37 | | | | | | | | | | | all_294_1, all_294_2 gives: % 17.52/3.37 | | | | | | | | | | | (157) (all_294_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.37 | | | | | | | | | | | all_17_2) = 0) | (all_294_1 = 0 & % 17.52/3.37 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | % 17.52/3.37 | | | | | | | | | | | ( ~ (all_294_2 = 0) & distinct_lines(all_17_5, % 17.52/3.37 | | | | | | | | | | | all_17_2) = all_294_2) % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | BETA: splitting (157) gives: % 17.52/3.37 | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | Case 1: % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | (158) all_294_0 = 0 & apart_point_and_line(all_17_6, % 17.52/3.37 | | | | | | | | | | | | all_17_2) = 0 % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | ALPHA: (158) implies: % 17.52/3.37 | | | | | | | | | | | | (159) apart_point_and_line(all_17_6, all_17_2) = 0 % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | REF_CLOSE: (10), (14), (22), (159) are inconsistent by % 17.52/3.37 | | | | | | | | | | | | sub-proof #3. % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | Case 2: % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | (160) (all_294_1 = 0 & apart_point_and_line(all_17_6, % 17.52/3.37 | | | | | | | | | | | | all_17_5) = 0) | ( ~ (all_294_2 = 0) & % 17.52/3.37 | | | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = all_294_2) % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | BETA: splitting (160) gives: % 17.52/3.37 | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | Case 1: % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | | (161) all_294_1 = 0 & apart_point_and_line(all_17_6, % 17.52/3.37 | | | | | | | | | | | | | all_17_5) = 0 % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | | ALPHA: (161) implies: % 17.52/3.37 | | | | | | | | | | | | | (162) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (162) are inconsistent by % 17.52/3.37 | | | | | | | | | | | | | sub-proof #2. % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | Case 2: % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | | (163) ~ (all_294_2 = 0) & distinct_lines(all_17_5, % 17.52/3.37 | | | | | | | | | | | | | all_17_2) = all_294_2 % 17.52/3.37 | | | | | | | | | | | | | % 17.52/3.37 | | | | | | | | | | | | | ALPHA: (163) implies: % 17.52/3.37 | | | | | | | | | | | | | (164) ~ (all_294_2 = 0) % 17.71/3.37 | | | | | | | | | | | | | (165) distinct_lines(all_17_5, all_17_2) = all_294_2 % 17.71/3.37 | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | BETA: splitting (153) gives: % 17.71/3.37 | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | Case 1: % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | (166) (all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.71/3.37 | | | | | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 & % 17.71/3.37 | | | | | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | BETA: splitting (166) gives: % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | Case 1: % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | (167) all_286_0 = 0 & apart_point_and_line(all_17_6, % 17.71/3.37 | | | | | | | | | | | | | | | all_17_5) = 0 % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | ALPHA: (167) implies: % 17.71/3.37 | | | | | | | | | | | | | | | (168) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (168) are inconsistent by % 17.71/3.37 | | | | | | | | | | | | | | | sub-proof #2. % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | Case 2: % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | (169) all_286_1 = 0 & apart_point_and_line(all_17_7, % 17.71/3.37 | | | | | | | | | | | | | | | all_17_2) = 0 % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | ALPHA: (169) implies: % 17.71/3.37 | | | | | | | | | | | | | | | (170) apart_point_and_line(all_17_7, all_17_2) = 0 % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (21), (170) are inconsistent by % 17.71/3.37 | | | | | | | | | | | | | | | sub-proof #1. % 17.71/3.37 | | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | End of split % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | Case 2: % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | (171) ( ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.71/3.37 | | | | | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) & % 17.71/3.37 | | | | | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3) % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | BETA: splitting (171) gives: % 17.71/3.37 | | | | | | | | | | | | | | % 17.71/3.37 | | | | | | | | | | | | | | Case 1: % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | (172) ~ (all_286_2 = 0) & distinct_lines(all_17_5, % 17.71/3.38 | | | | | | | | | | | | | | | all_17_2) = all_286_2 % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | ALPHA: (172) implies: % 17.71/3.38 | | | | | | | | | | | | | | | (173) distinct_lines(all_17_5, all_17_2) = all_286_2 % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | Case 1: % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | (174) all_25_0 = 0 % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | REDUCE: (84), (174) imply: % 17.71/3.38 | | | | | | | | | | | | | | | | (175) $false % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent. % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | Case 2: % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_286_2, all_294_2, % 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (165), (173) % 17.71/3.38 | | | | | | | | | | | | | | | | gives: % 17.71/3.38 | | | | | | | | | | | | | | | | (176) all_294_2 = all_286_2 % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | REDUCE: (164), (176) imply: % 17.71/3.38 | | | | | | | | | | | | | | | | (177) ~ (all_286_2 = 0) % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_9, all_17_5, % 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2, all_286_2, simplifying with (15), (76), % 17.71/3.38 | | | | | | | | | | | | | | | | (77), (140), (173) gives: % 17.71/3.38 | | | | | | | | | | | | | | | | (178) all_286_2 = 0 | apart_point_and_line(all_17_9, % 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2) = 0 % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | Case 1: % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | (179) apart_point_and_line(all_17_9, all_17_2) = 0 % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_26_0, 0, all_17_2, % 17.71/3.38 | | | | | | | | | | | | | | | | | all_17_9, simplifying with (61), (179) gives: % 17.71/3.38 | | | | | | | | | | | | | | | | | (180) all_26_0 = 0 % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | REDUCE: (83), (180) imply: % 17.71/3.38 | | | | | | | | | | | | | | | | | (181) $false % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | Case 2: % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | (182) all_286_2 = 0 % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | REDUCE: (177), (182) imply: % 17.71/3.38 | | | | | | | | | | | | | | | | | (183) $false % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent. % 17.71/3.38 | | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | Case 2: % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | (184) ~ (all_286_3 = 0) & distinct_points(all_17_7, % 17.71/3.38 | | | | | | | | | | | | | | | all_17_6) = all_286_3 % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | ALPHA: (184) implies: % 17.71/3.38 | | | | | | | | | | | | | | | (185) ~ (all_286_3 = 0) % 17.71/3.38 | | | | | | | | | | | | | | | (186) distinct_points(all_17_7, all_17_6) = all_286_3 % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_286_3, all_17_6, % 17.71/3.38 | | | | | | | | | | | | | | | all_17_7, simplifying with (20), (186) gives: % 17.71/3.38 | | | | | | | | | | | | | | | (187) all_286_3 = 0 % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | REDUCE: (185), (187) imply: % 17.71/3.38 | | | | | | | | | | | | | | | (188) $false % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 17.71/3.38 | | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | | % 17.71/3.38 | | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | | % 17.71/3.38 | | | | | | | | | End of split % 17.71/3.38 | | | | | | | | | % 17.71/3.38 | | | | | | | | End of split % 17.71/3.38 | | | | | | | | % 17.71/3.38 | | | | | | | End of split % 17.71/3.38 | | | | | | | % 17.71/3.38 | | | | | | End of split % 17.71/3.38 | | | | | | % 17.71/3.38 | | | | | End of split % 17.71/3.38 | | | | | % 17.71/3.38 | | | | Case 2: % 17.71/3.38 | | | | | % 17.71/3.38 | | | | | (189) ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6) = % 17.71/3.38 | | | | | all_25_1 % 17.71/3.38 | | | | | % 17.71/3.38 | | | | | ALPHA: (189) implies: % 17.71/3.38 | | | | | (190) ~ (all_25_1 = 0) % 17.71/3.38 | | | | | (191) distinct_points(all_17_7, all_17_6) = all_25_1 % 17.71/3.38 | | | | | % 17.71/3.38 | | | | | GROUND_INST: instantiating (8) with 0, all_25_1, all_17_6, all_17_7, % 17.71/3.38 | | | | | simplifying with (20), (191) gives: % 17.71/3.38 | | | | | (192) all_25_1 = 0 % 17.71/3.38 | | | | | % 17.71/3.38 | | | | | REDUCE: (190), (192) imply: % 17.71/3.38 | | | | | (193) $false % 17.71/3.38 | | | | | % 17.71/3.38 | | | | | CLOSE: (193) is inconsistent. % 17.71/3.38 | | | | | % 17.71/3.38 | | | | End of split % 17.71/3.38 | | | | % 17.71/3.38 | | | Case 2: % 17.71/3.38 | | | | % 17.71/3.38 | | | | (194) ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8) = % 17.71/3.38 | | | | all_26_1 % 17.71/3.38 | | | | % 17.71/3.38 | | | | ALPHA: (194) implies: % 17.71/3.38 | | | | (195) ~ (all_26_1 = 0) % 17.71/3.38 | | | | (196) distinct_points(all_17_9, all_17_8) = all_26_1 % 17.71/3.38 | | | | % 17.71/3.39 | | | | GROUND_INST: instantiating (8) with 0, all_26_1, all_17_8, all_17_9, % 17.71/3.39 | | | | simplifying with (19), (196) gives: % 17.71/3.39 | | | | (197) all_26_1 = 0 % 17.71/3.39 | | | | % 17.71/3.39 | | | | REDUCE: (195), (197) imply: % 17.71/3.39 | | | | (198) $false % 17.71/3.39 | | | | % 17.71/3.39 | | | | CLOSE: (198) is inconsistent. % 17.71/3.39 | | | | % 17.71/3.39 | | | End of split % 17.71/3.39 | | | % 17.71/3.39 | | Case 2: % 17.71/3.39 | | | % 17.71/3.39 | | | (199) ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6) = % 17.71/3.39 | | | all_24_1 % 17.71/3.39 | | | % 17.71/3.39 | | | ALPHA: (199) implies: % 17.71/3.39 | | | (200) ~ (all_24_1 = 0) % 17.71/3.39 | | | (201) distinct_points(all_17_7, all_17_6) = all_24_1 % 17.71/3.39 | | | % 17.71/3.39 | | | GROUND_INST: instantiating (8) with 0, all_24_1, all_17_6, all_17_7, % 17.71/3.39 | | | simplifying with (20), (201) gives: % 17.71/3.39 | | | (202) all_24_1 = 0 % 17.71/3.39 | | | % 17.71/3.39 | | | REDUCE: (200), (202) imply: % 17.71/3.39 | | | (203) $false % 17.71/3.39 | | | % 17.71/3.39 | | | CLOSE: (203) is inconsistent. % 17.71/3.39 | | | % 17.71/3.39 | | End of split % 17.71/3.39 | | % 17.71/3.39 | Case 2: % 17.71/3.39 | | % 17.71/3.39 | | (204) ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8) = all_35_1 % 17.71/3.39 | | % 17.71/3.39 | | ALPHA: (204) implies: % 17.71/3.39 | | (205) ~ (all_35_1 = 0) % 17.71/3.39 | | (206) distinct_points(all_17_9, all_17_8) = all_35_1 % 17.71/3.39 | | % 17.71/3.39 | | GROUND_INST: instantiating (8) with 0, all_35_1, all_17_8, all_17_9, % 17.71/3.39 | | simplifying with (19), (206) gives: % 17.71/3.39 | | (207) all_35_1 = 0 % 17.71/3.39 | | % 17.71/3.39 | | REDUCE: (205), (207) imply: % 17.71/3.39 | | (208) $false % 17.71/3.39 | | % 17.71/3.39 | | CLOSE: (208) is inconsistent. % 17.71/3.39 | | % 17.71/3.39 | End of split % 17.71/3.39 | % 17.71/3.39 End of proof % 17.71/3.39 % 17.71/3.39 Sub-proof #1 shows that the following formulas are inconsistent: % 17.71/3.39 ---------------------------------------------------------------- % 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.71/3.39 (apart_point_and_line(v3, v2) = v0)) % 17.71/3.39 (2) apart_point_and_line(all_17_7, all_17_2) = all_17_1 % 17.71/3.39 (3) apart_point_and_line(all_17_7, all_17_2) = 0 % 17.71/3.39 (4) ~ (all_17_1 = 0) % 17.71/3.39 % 17.71/3.39 Begin of proof % 17.71/3.39 | % 17.71/3.39 | GROUND_INST: instantiating (1) with all_17_1, 0, all_17_2, all_17_7, % 17.71/3.39 | simplifying with (2), (3) gives: % 17.71/3.39 | (5) all_17_1 = 0 % 17.71/3.39 | % 17.71/3.39 | REDUCE: (4), (5) imply: % 17.71/3.39 | (6) $false % 17.71/3.39 | % 17.71/3.39 | CLOSE: (6) is inconsistent. % 17.71/3.39 | % 17.71/3.39 End of proof % 17.71/3.39 % 17.71/3.39 Sub-proof #2 shows that the following formulas are inconsistent: % 17.71/3.39 ---------------------------------------------------------------- % 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.71/3.39 (apart_point_and_line(v3, v2) = v0)) % 17.71/3.39 (2) apart_point_and_line(all_17_6, all_17_5) = all_25_0 % 17.71/3.39 (3) apart_point_and_line(all_17_6, all_17_5) = 0 % 17.71/3.39 (4) ~ (all_25_0 = 0) % 17.71/3.39 % 17.71/3.39 Begin of proof % 17.71/3.39 | % 17.71/3.39 | GROUND_INST: instantiating (1) with all_25_0, 0, all_17_5, all_17_6, % 17.71/3.39 | simplifying with (2), (3) gives: % 17.71/3.39 | (5) all_25_0 = 0 % 17.71/3.39 | % 17.71/3.39 | REDUCE: (4), (5) imply: % 17.71/3.39 | (6) $false % 17.71/3.39 | % 17.71/3.39 | CLOSE: (6) is inconsistent. % 17.71/3.39 | % 17.71/3.39 End of proof % 17.71/3.39 % 17.71/3.39 Sub-proof #3 shows that the following formulas are inconsistent: % 17.71/3.39 ---------------------------------------------------------------- % 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.71/3.39 (apart_point_and_line(v3, v2) = v0)) % 17.71/3.39 (2) apart_point_and_line(all_17_6, all_17_2) = all_17_0 % 17.71/3.39 (3) apart_point_and_line(all_17_6, all_17_2) = 0 % 17.71/3.40 (4) ~ (all_17_0 = 0) % 17.71/3.40 % 17.71/3.40 Begin of proof % 17.71/3.40 | % 17.71/3.40 | GROUND_INST: instantiating (1) with all_17_0, 0, all_17_2, all_17_6, % 17.71/3.40 | simplifying with (2), (3) gives: % 17.71/3.40 | (5) all_17_0 = 0 % 17.71/3.40 | % 17.71/3.40 | REDUCE: (4), (5) imply: % 17.71/3.40 | (6) $false % 17.71/3.40 | % 17.71/3.40 | CLOSE: (6) is inconsistent. % 17.71/3.40 | % 17.71/3.40 End of proof % 17.71/3.40 % SZS output end Proof for theBenchmark % 17.71/3.40 % 17.71/3.40 2792ms %------------------------------------------------------------------------------