%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO201+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 : n032.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 23:22:13 EDT 2023 % Result : Theorem 10.89s 2.10s % Output : Proof 17.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : GEO201+1 : TPTP v8.1.2. Released v3.3.0. % 0.08/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 300 % 0.08/0.28 % DateTime : Tue Aug 29 19:02:47 EDT 2023 % 0.08/0.28 % CPUTime : % 0.13/0.48 ________ _____ % 0.13/0.48 ___ __ \_________(_)________________________________ % 0.13/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.48 % 0.13/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.48 (2023-06-19) % 0.13/0.48 % 0.13/0.48 (c) Philipp Rümmer, 2009-2023 % 0.13/0.48 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.48 Amanda Stjerna. % 0.13/0.48 Free software under BSD-3-Clause. % 0.13/0.48 % 0.13/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.48 % 0.13/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.13/0.50 Running up to 7 provers in parallel. % 0.13/0.51 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.51 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.51 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.51 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.95/0.89 Prover 1: Preprocessing ... % 1.95/0.90 Prover 4: Preprocessing ... % 2.52/0.93 Prover 6: Preprocessing ... % 2.52/0.93 Prover 3: Preprocessing ... % 2.52/0.93 Prover 0: Preprocessing ... % 2.52/0.93 Prover 5: Preprocessing ... % 2.52/0.93 Prover 2: Preprocessing ... % 3.84/1.18 Prover 2: Proving ... % 3.84/1.18 Prover 5: Proving ... % 4.15/1.21 Prover 6: Constructing countermodel ... % 4.15/1.22 Prover 1: Constructing countermodel ... % 4.15/1.22 Prover 3: Constructing countermodel ... % 5.07/1.31 Prover 1: gave up % 5.07/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.07/1.32 Prover 3: gave up % 5.07/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.07/1.34 Prover 6: gave up % 5.49/1.35 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.49/1.35 Prover 7: Preprocessing ... % 5.49/1.35 Prover 0: Proving ... % 5.53/1.36 Prover 8: Preprocessing ... % 5.53/1.36 Prover 4: Constructing countermodel ... % 5.53/1.39 Prover 9: Preprocessing ... % 5.87/1.43 Prover 7: Warning: ignoring some quantifiers % 6.14/1.46 Prover 8: Warning: ignoring some quantifiers % 6.14/1.46 Prover 7: Constructing countermodel ... % 6.14/1.46 Prover 8: Constructing countermodel ... % 6.14/1.53 Prover 8: gave up % 6.84/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.84/1.57 Prover 10: Preprocessing ... % 6.84/1.58 Prover 7: gave up % 6.84/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.26/1.60 Prover 9: Constructing countermodel ... % 7.26/1.60 Prover 10: Warning: ignoring some quantifiers % 7.26/1.61 Prover 10: Constructing countermodel ... % 7.26/1.62 Prover 11: Preprocessing ... % 7.26/1.65 Prover 10: gave up % 7.76/1.68 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.06/1.72 Prover 12: Preprocessing ... % 8.06/1.78 Prover 11: Constructing countermodel ... % 8.44/1.85 Prover 12: Proving ... % 10.89/2.10 Prover 9: proved (751ms) % 10.89/2.10 % 10.89/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.89/2.10 % 10.89/2.11 Prover 0: stopped % 10.89/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.89/2.11 Prover 2: stopped % 10.89/2.11 Prover 5: stopped % 10.89/2.11 Prover 12: stopped % 10.89/2.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.89/2.11 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.89/2.12 Prover 16: Preprocessing ... % 10.89/2.13 Prover 13: Preprocessing ... % 11.24/2.13 Prover 19: Preprocessing ... % 11.31/2.16 Prover 16: Warning: ignoring some quantifiers % 11.31/2.16 Prover 16: Constructing countermodel ... % 11.31/2.17 Prover 13: Warning: ignoring some quantifiers % 11.31/2.17 Prover 13: Constructing countermodel ... % 11.31/2.18 Prover 19: Warning: ignoring some quantifiers % 11.31/2.19 Prover 19: Constructing countermodel ... % 11.80/2.22 Prover 19: gave up % 12.24/2.31 Prover 13: gave up % 12.24/2.33 Prover 16: gave up % 16.38/3.07 Prover 11: Found proof (size 188) % 16.38/3.07 Prover 11: proved (1489ms) % 16.38/3.07 Prover 4: stopped % 16.38/3.07 % 16.38/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.38/3.07 % 16.38/3.08 % SZS output start Proof for theBenchmark % 16.38/3.08 Assumptions after simplification: % 16.38/3.08 --------------------------------- % 16.38/3.08 % 16.38/3.08 (apart3) % 16.90/3.11 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 16.90/3.11 % 16.90/3.11 (ax6) % 16.90/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.90/3.11 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 16.90/3.11 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 16.90/3.11 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 16.90/3.11 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 16.90/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.90/3.11 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.90/3.11 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 16.90/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.90/3.11 convergent_lines(v1, v2) = 0) % 16.90/3.11 % 16.90/3.11 (ceq3) % 16.90/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 16.90/3.12 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 16.90/3.12 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 16.90/3.12 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.90/3.12 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 16.90/3.12 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.90/3.12 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.90/3.12 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 16.90/3.12 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.90/3.12 convergent_lines(v0, v2) = 0) % 16.90/3.12 % 16.90/3.12 (ci1) % 16.90/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.90/3.12 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.90/3.12 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.90/3.12 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.90/3.12 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.12 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.90/3.12 $i(v2))) % 16.90/3.12 % 16.90/3.12 (ci2) % 16.90/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 16.90/3.12 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 16.90/3.12 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 16.90/3.12 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 16.90/3.12 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.12 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.90/3.12 $i(v2))) % 16.90/3.12 % 16.90/3.12 (ci3) % 16.90/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 16.90/3.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 16.90/3.13 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 16.90/3.13 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.90/3.13 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 16.90/3.13 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 16.90/3.13 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 16.90/3.13 % 16.90/3.13 (ci4) % 16.90/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 16.90/3.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 16.90/3.13 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 16.90/3.13 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.90/3.13 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 16.90/3.13 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 16.90/3.13 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 16.90/3.13 % 16.90/3.13 (con) % 16.90/3.13 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 16.90/3.13 (intersection_point(v1, v0) = v3 & intersection_point(v0, v1) = v2 & % 16.90/3.13 convergent_lines(v0, v1) = 0 & distinct_points(v2, v3) = 0 & $i(v3) & $i(v2) % 16.90/3.13 & $i(v1) & $i(v0)) % 16.90/3.13 % 16.90/3.13 (cu1) % 16.90/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.90/3.14 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.90/3.14 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.90/3.14 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.90/3.14 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 16.90/3.14 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 16.90/3.14 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.90/3.14 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 16.90/3.14 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 16.90/3.14 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 16.90/3.14 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.90/3.14 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 16.90/3.14 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.90/3.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.90/3.14 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.90/3.14 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.90/3.14 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.90/3.14 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.90/3.14 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.90/3.14 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.90/3.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.90/3.14 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.90/3.14 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.90/3.14 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.90/3.14 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 16.90/3.14 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.90/3.14 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.90/3.14 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.90/3.14 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.90/3.14 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 16.90/3.14 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.90/3.14 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.90/3.14 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 16.90/3.14 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.90/3.14 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 16.90/3.14 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 16.90/3.14 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.90/3.14 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.90/3.14 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 16.90/3.14 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 16.90/3.14 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 16.90/3.14 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.90/3.14 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 16.90/3.14 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 16.90/3.14 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 16.90/3.14 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 16.90/3.14 % 16.90/3.14 (function-axioms) % 16.90/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.90/3.14 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.90/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.90/3.14 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.90/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.90/3.14 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.90/3.14 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.90/3.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.90/3.14 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.90/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.90/3.14 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.90/3.14 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.90/3.14 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.90/3.14 (distinct_points(v3, v2) = v0)) % 16.90/3.14 % 16.90/3.14 Further assumptions not needed in the proof: % 16.90/3.14 -------------------------------------------- % 16.90/3.14 apart1, apart2, apart4, apart5, ceq1, ceq2 % 16.90/3.14 % 16.90/3.14 Those formulas are unsatisfiable: % 16.90/3.14 --------------------------------- % 16.90/3.14 % 16.90/3.14 Begin of proof % 16.90/3.15 | % 16.90/3.15 | ALPHA: (ax6) implies: % 16.90/3.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.90/3.15 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 16.90/3.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 16.90/3.15 | % 16.90/3.15 | ALPHA: (ci1) implies: % 16.90/3.15 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.90/3.15 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.15 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 16.90/3.15 | $i(v2))) % 16.90/3.15 | % 16.90/3.15 | ALPHA: (ci2) implies: % 16.90/3.15 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 16.90/3.15 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.15 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 16.90/3.15 | $i(v2))) % 16.90/3.15 | % 16.90/3.15 | ALPHA: (ci3) implies: % 16.90/3.15 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 16.90/3.15 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.15 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 16.90/3.15 | & $i(v2))) % 16.90/3.15 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 16.90/3.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 16.90/3.15 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 16.90/3.15 | convergent_lines(v0, v1) = v3))) % 16.90/3.15 | % 16.90/3.15 | ALPHA: (ci4) implies: % 16.90/3.15 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 16.90/3.15 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 16.90/3.15 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 16.90/3.15 | & $i(v2))) % 16.90/3.15 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 16.90/3.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 16.90/3.15 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 16.90/3.15 | convergent_lines(v0, v1) = v3))) % 16.90/3.15 | % 16.90/3.15 | ALPHA: (cu1) implies: % 16.90/3.15 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.90/3.15 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 16.90/3.15 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 16.90/3.15 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.90/3.15 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.90/3.15 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.90/3.15 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 16.90/3.15 | distinct_lines(v2, v3) = v6))) % 16.90/3.16 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.90/3.16 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 16.90/3.16 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.90/3.16 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 16.90/3.16 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.90/3.16 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 16.90/3.16 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 16.90/3.16 | v1) = v6))) % 16.90/3.16 | % 16.90/3.16 | ALPHA: (ceq3) implies: % 16.90/3.16 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.90/3.16 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 16.90/3.16 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 16.90/3.16 | % 16.90/3.16 | ALPHA: (function-axioms) implies: % 16.90/3.16 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.90/3.16 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.90/3.16 | (distinct_points(v3, v2) = v0)) % 16.90/3.16 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.90/3.16 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 16.90/3.16 | (distinct_lines(v3, v2) = v0)) % 16.90/3.16 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.90/3.16 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 16.90/3.16 | (convergent_lines(v3, v2) = v0)) % 16.90/3.16 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.90/3.16 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.90/3.16 | (apart_point_and_line(v3, v2) = v0)) % 16.90/3.16 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.90/3.16 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 16.90/3.16 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.90/3.16 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 16.90/3.16 | v0)) % 16.90/3.16 | % 16.90/3.16 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 16.90/3.16 | all_17_3 gives: % 16.90/3.16 | (17) intersection_point(all_17_2, all_17_3) = all_17_0 & % 16.90/3.16 | intersection_point(all_17_3, all_17_2) = all_17_1 & % 16.90/3.16 | convergent_lines(all_17_3, all_17_2) = 0 & distinct_points(all_17_1, % 16.90/3.16 | all_17_0) = 0 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & % 16.90/3.16 | $i(all_17_3) % 16.90/3.16 | % 16.90/3.16 | ALPHA: (17) implies: % 16.90/3.16 | (18) $i(all_17_3) % 16.90/3.16 | (19) $i(all_17_2) % 16.90/3.16 | (20) $i(all_17_1) % 16.90/3.16 | (21) $i(all_17_0) % 16.90/3.16 | (22) distinct_points(all_17_1, all_17_0) = 0 % 16.90/3.16 | (23) convergent_lines(all_17_3, all_17_2) = 0 % 16.90/3.16 | (24) intersection_point(all_17_3, all_17_2) = all_17_1 % 16.90/3.16 | (25) intersection_point(all_17_2, all_17_3) = all_17_0 % 16.90/3.16 | % 16.90/3.16 | GROUND_INST: instantiating (3) with all_17_1, all_17_0, simplifying with (20), % 16.90/3.16 | (21), (22) gives: % 16.90/3.16 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_1, % 16.90/3.16 | all_17_0) = v0 & apart_point_and_line(all_17_0, v0) = v1 & $i(v0)) % 16.90/3.16 | % 16.90/3.16 | GROUND_INST: instantiating (2) with all_17_1, all_17_0, simplifying with (20), % 16.90/3.16 | (21), (22) gives: % 16.90/3.16 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_1, % 16.90/3.16 | all_17_0) = v0 & apart_point_and_line(all_17_1, v0) = v1 & $i(v0)) % 16.90/3.16 | % 17.26/3.16 | GROUND_INST: instantiating (6) with all_17_3, all_17_2, simplifying with (18), % 17.26/3.16 | (19), (23) gives: % 17.26/3.17 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 17.26/3.17 | intersection_point(all_17_3, all_17_2) = v0 & % 17.26/3.17 | apart_point_and_line(v0, all_17_2) = v1 & $i(v0)) % 17.26/3.17 | % 17.26/3.17 | GROUND_INST: instantiating (4) with all_17_3, all_17_2, simplifying with (18), % 17.26/3.17 | (19), (23) gives: % 17.26/3.17 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 17.26/3.17 | intersection_point(all_17_3, all_17_2) = v0 & % 17.26/3.17 | apart_point_and_line(v0, all_17_3) = v1 & $i(v0)) % 17.26/3.17 | % 17.26/3.17 | GROUND_INST: instantiating (7) with all_17_3, all_17_2, all_17_1, simplifying % 17.26/3.17 | with (18), (19), (24) gives: % 17.26/3.17 | (30) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.26/3.17 | apart_point_and_line(all_17_1, all_17_2) = v1) | ( ~ (v0 = 0) & % 17.26/3.17 | convergent_lines(all_17_3, all_17_2) = v0)) % 17.26/3.17 | % 17.26/3.17 | GROUND_INST: instantiating (5) with all_17_3, all_17_2, all_17_1, simplifying % 17.26/3.17 | with (18), (19), (24) gives: % 17.27/3.17 | (31) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.17 | apart_point_and_line(all_17_1, all_17_3) = v1) | ( ~ (v0 = 0) & % 17.27/3.17 | convergent_lines(all_17_3, all_17_2) = v0)) % 17.27/3.17 | % 17.27/3.17 | GROUND_INST: instantiating (7) with all_17_2, all_17_3, all_17_0, simplifying % 17.27/3.17 | with (18), (19), (25) gives: % 17.27/3.17 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.17 | apart_point_and_line(all_17_0, all_17_3) = v1) | ( ~ (v0 = 0) & % 17.27/3.17 | convergent_lines(all_17_2, all_17_3) = v0)) % 17.27/3.17 | % 17.27/3.17 | GROUND_INST: instantiating (5) with all_17_2, all_17_3, all_17_0, simplifying % 17.27/3.17 | with (18), (19), (25) gives: % 17.27/3.17 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 17.27/3.17 | apart_point_and_line(all_17_0, all_17_2) = v1) | ( ~ (v0 = 0) & % 17.27/3.17 | convergent_lines(all_17_2, all_17_3) = v0)) % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (33) with fresh symbols all_24_0, all_24_1 gives: % 17.27/3.17 | (34) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_2) = % 17.27/3.17 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_2, % 17.27/3.17 | all_17_3) = all_24_1) % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (32) with fresh symbols all_25_0, all_25_1 gives: % 17.27/3.17 | (35) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_0, all_17_3) = % 17.27/3.17 | all_25_0) | ( ~ (all_25_1 = 0) & convergent_lines(all_17_2, % 17.27/3.17 | all_17_3) = all_25_1) % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (31) with fresh symbols all_26_0, all_26_1 gives: % 17.27/3.17 | (36) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_1, all_17_3) = % 17.27/3.17 | all_26_0) | ( ~ (all_26_1 = 0) & convergent_lines(all_17_3, % 17.27/3.17 | all_17_2) = all_26_1) % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (30) with fresh symbols all_27_0, all_27_1 gives: % 17.27/3.17 | (37) ( ~ (all_27_0 = 0) & apart_point_and_line(all_17_1, all_17_2) = % 17.27/3.17 | all_27_0) | ( ~ (all_27_1 = 0) & convergent_lines(all_17_3, % 17.27/3.17 | all_17_2) = all_27_1) % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (29) with fresh symbols all_28_0, all_28_1 gives: % 17.27/3.17 | (38) ~ (all_28_0 = 0) & intersection_point(all_17_3, all_17_2) = all_28_1 % 17.27/3.17 | & apart_point_and_line(all_28_1, all_17_3) = all_28_0 & $i(all_28_1) % 17.27/3.17 | % 17.27/3.17 | ALPHA: (38) implies: % 17.27/3.17 | (39) ~ (all_28_0 = 0) % 17.27/3.17 | (40) $i(all_28_1) % 17.27/3.17 | (41) apart_point_and_line(all_28_1, all_17_3) = all_28_0 % 17.27/3.17 | (42) intersection_point(all_17_3, all_17_2) = all_28_1 % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (27) with fresh symbols all_30_0, all_30_1 gives: % 17.27/3.17 | (43) ~ (all_30_0 = 0) & line_connecting(all_17_1, all_17_0) = all_30_1 & % 17.27/3.17 | apart_point_and_line(all_17_1, all_30_1) = all_30_0 & $i(all_30_1) % 17.27/3.17 | % 17.27/3.17 | ALPHA: (43) implies: % 17.27/3.17 | (44) ~ (all_30_0 = 0) % 17.27/3.17 | (45) apart_point_and_line(all_17_1, all_30_1) = all_30_0 % 17.27/3.17 | (46) line_connecting(all_17_1, all_17_0) = all_30_1 % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1 gives: % 17.27/3.17 | (47) ~ (all_32_0 = 0) & line_connecting(all_17_1, all_17_0) = all_32_1 & % 17.27/3.17 | apart_point_and_line(all_17_0, all_32_1) = all_32_0 & $i(all_32_1) % 17.27/3.17 | % 17.27/3.17 | ALPHA: (47) implies: % 17.27/3.17 | (48) ~ (all_32_0 = 0) % 17.27/3.17 | (49) $i(all_32_1) % 17.27/3.17 | (50) apart_point_and_line(all_17_0, all_32_1) = all_32_0 % 17.27/3.17 | (51) line_connecting(all_17_1, all_17_0) = all_32_1 % 17.27/3.17 | % 17.27/3.17 | DELTA: instantiating (28) with fresh symbols all_34_0, all_34_1 gives: % 17.27/3.18 | (52) ~ (all_34_0 = 0) & intersection_point(all_17_3, all_17_2) = all_34_1 % 17.27/3.18 | & apart_point_and_line(all_34_1, all_17_2) = all_34_0 & $i(all_34_1) % 17.27/3.18 | % 17.27/3.18 | ALPHA: (52) implies: % 17.27/3.18 | (53) ~ (all_34_0 = 0) % 17.27/3.18 | (54) apart_point_and_line(all_34_1, all_17_2) = all_34_0 % 17.27/3.18 | (55) intersection_point(all_17_3, all_17_2) = all_34_1 % 17.27/3.18 | % 17.27/3.18 | BETA: splitting (36) gives: % 17.27/3.18 | % 17.27/3.18 | Case 1: % 17.27/3.18 | | % 17.27/3.18 | | (56) ~ (all_26_0 = 0) & apart_point_and_line(all_17_1, all_17_3) = % 17.27/3.18 | | all_26_0 % 17.27/3.18 | | % 17.27/3.18 | | ALPHA: (56) implies: % 17.27/3.18 | | (57) apart_point_and_line(all_17_1, all_17_3) = all_26_0 % 17.27/3.18 | | % 17.27/3.18 | | BETA: splitting (37) gives: % 17.27/3.18 | | % 17.27/3.18 | | Case 1: % 17.27/3.18 | | | % 17.27/3.18 | | | (58) ~ (all_27_0 = 0) & apart_point_and_line(all_17_1, all_17_2) = % 17.27/3.18 | | | all_27_0 % 17.27/3.18 | | | % 17.27/3.18 | | | ALPHA: (58) implies: % 17.27/3.18 | | | (59) apart_point_and_line(all_17_1, all_17_2) = all_27_0 % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (15) with all_30_1, all_32_1, all_17_0, % 17.27/3.18 | | | all_17_1, simplifying with (46), (51) gives: % 17.27/3.18 | | | (60) all_32_1 = all_30_1 % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (16) with all_17_1, all_34_1, all_17_2, % 17.27/3.18 | | | all_17_3, simplifying with (24), (55) gives: % 17.27/3.18 | | | (61) all_34_1 = all_17_1 % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (16) with all_28_1, all_34_1, all_17_2, % 17.27/3.18 | | | all_17_3, simplifying with (42), (55) gives: % 17.27/3.18 | | | (62) all_34_1 = all_28_1 % 17.27/3.18 | | | % 17.27/3.18 | | | COMBINE_EQS: (61), (62) imply: % 17.27/3.18 | | | (63) all_28_1 = all_17_1 % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (54), (61) imply: % 17.27/3.18 | | | (64) apart_point_and_line(all_17_1, all_17_2) = all_34_0 % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (41), (63) imply: % 17.27/3.18 | | | (65) apart_point_and_line(all_17_1, all_17_3) = all_28_0 % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (50), (60) imply: % 17.27/3.18 | | | (66) apart_point_and_line(all_17_0, all_30_1) = all_32_0 % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (49), (60) imply: % 17.27/3.18 | | | (67) $i(all_30_1) % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (14) with all_26_0, all_28_0, all_17_3, % 17.27/3.18 | | | all_17_1, simplifying with (57), (65) gives: % 17.27/3.18 | | | (68) all_28_0 = all_26_0 % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (14) with all_27_0, all_34_0, all_17_2, % 17.27/3.18 | | | all_17_1, simplifying with (59), (64) gives: % 17.27/3.18 | | | (69) all_34_0 = all_27_0 % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (53), (69) imply: % 17.27/3.18 | | | (70) ~ (all_27_0 = 0) % 17.27/3.18 | | | % 17.27/3.18 | | | REDUCE: (39), (68) imply: % 17.27/3.18 | | | (71) ~ (all_26_0 = 0) % 17.27/3.18 | | | % 17.27/3.18 | | | GROUND_INST: instantiating (8) with all_17_1, all_17_0, all_17_2, % 17.27/3.18 | | | all_30_1, all_27_0, all_30_0, simplifying with (19), (20), % 17.27/3.18 | | | (21), (22), (45), (59), (67) gives: % 17.27/3.18 | | | (72) all_30_0 = 0 | all_27_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.18 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_30_1) = % 17.27/3.18 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_0, all_17_2) = 0) | % 17.27/3.18 | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, all_30_1) = v0)) % 17.27/3.18 | | | % 17.27/3.19 | | | GROUND_INST: instantiating (8) with all_17_1, all_17_0, all_17_3, % 17.27/3.19 | | | all_30_1, all_26_0, all_30_0, simplifying with (18), (20), % 17.27/3.19 | | | (21), (22), (45), (57), (67) gives: % 17.27/3.19 | | | (73) all_30_0 = 0 | all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.19 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_30_1) = % 17.27/3.19 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_0, all_17_3) = 0) | % 17.27/3.19 | | | ( ~ (v0 = 0) & distinct_lines(all_17_3, all_30_1) = v0)) % 17.27/3.19 | | | % 17.27/3.19 | | | GROUND_INST: instantiating (8) with all_17_1, all_17_0, all_30_1, % 17.27/3.19 | | | all_17_3, all_30_0, all_26_0, simplifying with (18), (20), % 17.27/3.19 | | | (21), (22), (45), (57), (67) gives: % 17.27/3.19 | | | (74) all_30_0 = 0 | all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.19 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_17_3) = % 17.27/3.19 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_0, all_30_1) = 0) | % 17.27/3.19 | | | ( ~ (v0 = 0) & distinct_lines(all_30_1, all_17_3) = v0)) % 17.27/3.19 | | | % 17.27/3.19 | | | GROUND_INST: instantiating (9) with all_17_1, all_17_0, all_17_2, % 17.27/3.19 | | | all_30_1, all_27_0, all_32_0, simplifying with (19), (20), % 17.27/3.19 | | | (21), (59), (66), (67) gives: % 17.27/3.19 | | | (75) all_32_0 = 0 | all_27_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.27/3.19 | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 17.27/3.19 | | | apart_point_and_line(all_17_0, all_17_2) = 0) | (v2 = 0 & % 17.27/3.19 | | | apart_point_and_line(all_17_1, all_30_1) = 0) | ( ~ (v1 = 0) & % 17.27/3.19 | | | distinct_lines(all_17_2, all_30_1) = v1) | ( ~ (v0 = 0) & % 17.27/3.19 | | | distinct_points(all_17_1, all_17_0) = v0)) % 17.27/3.19 | | | % 17.27/3.19 | | | BETA: splitting (34) gives: % 17.27/3.19 | | | % 17.27/3.19 | | | Case 1: % 17.27/3.19 | | | | % 17.27/3.19 | | | | (76) ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_2) = % 17.27/3.19 | | | | all_24_0 % 17.27/3.19 | | | | % 17.27/3.19 | | | | ALPHA: (76) implies: % 17.27/3.19 | | | | (77) ~ (all_24_0 = 0) % 17.27/3.19 | | | | (78) apart_point_and_line(all_17_0, all_17_2) = all_24_0 % 17.27/3.19 | | | | % 17.27/3.19 | | | | BETA: splitting (75) gives: % 17.27/3.19 | | | | % 17.27/3.19 | | | | Case 1: % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | (79) all_32_0 = 0 % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | REDUCE: (48), (79) imply: % 17.27/3.19 | | | | | (80) $false % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | CLOSE: (80) is inconsistent. % 17.27/3.19 | | | | | % 17.27/3.19 | | | | Case 2: % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | (81) all_27_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 17.27/3.19 | | | | | [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_0, % 17.27/3.19 | | | | | all_17_2) = 0) | (v2 = 0 & % 17.27/3.19 | | | | | apart_point_and_line(all_17_1, all_30_1) = 0) | ( ~ (v1 = % 17.27/3.19 | | | | | 0) & distinct_lines(all_17_2, all_30_1) = v1) | ( ~ (v0 % 17.27/3.19 | | | | | = 0) & distinct_points(all_17_1, all_17_0) = v0)) % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | BETA: splitting (72) gives: % 17.27/3.19 | | | | | % 17.27/3.19 | | | | | Case 1: % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | (82) all_30_0 = 0 % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | REDUCE: (44), (82) imply: % 17.27/3.19 | | | | | | (83) $false % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | CLOSE: (83) is inconsistent. % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | Case 2: % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | (84) all_27_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 17.27/3.19 | | | | | | ((v2 = 0 & apart_point_and_line(all_17_0, all_30_1) = 0) | % 17.27/3.19 | | | | | | (v1 = 0 & apart_point_and_line(all_17_0, all_17_2) = 0) | % 17.27/3.19 | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, all_30_1) = v0)) % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | BETA: splitting (74) gives: % 17.27/3.19 | | | | | | % 17.27/3.19 | | | | | | Case 1: % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | (85) all_30_0 = 0 % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | REDUCE: (44), (85) imply: % 17.27/3.19 | | | | | | | (86) $false % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | CLOSE: (86) is inconsistent. % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | Case 2: % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | (87) all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 17.27/3.19 | | | | | | | : ((v2 = 0 & apart_point_and_line(all_17_0, all_17_3) = 0) % 17.27/3.19 | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_0, all_30_1) = % 17.27/3.19 | | | | | | | 0) | ( ~ (v0 = 0) & distinct_lines(all_30_1, all_17_3) % 17.27/3.19 | | | | | | | = v0)) % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | BETA: splitting (87) gives: % 17.27/3.19 | | | | | | | % 17.27/3.19 | | | | | | | Case 1: % 17.27/3.19 | | | | | | | | % 17.27/3.19 | | | | | | | | (88) all_26_0 = 0 % 17.27/3.19 | | | | | | | | % 17.27/3.19 | | | | | | | | REDUCE: (71), (88) imply: % 17.27/3.19 | | | | | | | | (89) $false % 17.27/3.19 | | | | | | | | % 17.27/3.19 | | | | | | | | CLOSE: (89) is inconsistent. % 17.27/3.19 | | | | | | | | % 17.27/3.19 | | | | | | | Case 2: % 17.27/3.19 | | | | | | | | % 17.27/3.20 | | | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 17.27/3.20 | | | | | | | | apart_point_and_line(all_17_0, all_17_3) = 0) | (v1 % 17.27/3.20 | | | | | | | | = 0 & apart_point_and_line(all_17_0, all_30_1) = 0) % 17.27/3.20 | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_30_1, all_17_3) = % 17.27/3.20 | | | | | | | | v0)) % 17.27/3.20 | | | | | | | | % 17.27/3.20 | | | | | | | | DELTA: instantiating (90) with fresh symbols all_239_0, % 17.27/3.20 | | | | | | | | all_239_1, all_239_2 gives: % 17.27/3.20 | | | | | | | | (91) (all_239_0 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | all_17_3) = 0) | (all_239_1 = 0 & % 17.27/3.20 | | | | | | | | apart_point_and_line(all_17_0, all_30_1) = 0) | ( ~ % 17.27/3.20 | | | | | | | | (all_239_2 = 0) & distinct_lines(all_30_1, all_17_3) = % 17.27/3.20 | | | | | | | | all_239_2) % 17.27/3.20 | | | | | | | | % 17.27/3.20 | | | | | | | | BETA: splitting (81) gives: % 17.27/3.20 | | | | | | | | % 17.27/3.20 | | | | | | | | Case 1: % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | (92) all_27_0 = 0 % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | REDUCE: (70), (92) imply: % 17.27/3.20 | | | | | | | | | (93) $false % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | CLOSE: (93) is inconsistent. % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | Case 2: % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | (94) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 17.27/3.20 | | | | | | | | | int] : ((v3 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | | all_17_2) = 0) | (v2 = 0 & % 17.27/3.20 | | | | | | | | | apart_point_and_line(all_17_1, all_30_1) = 0) | ( % 17.27/3.20 | | | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_2, all_30_1) = % 17.27/3.20 | | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_1, % 17.27/3.20 | | | | | | | | | all_17_0) = v0)) % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | DELTA: instantiating (94) with fresh symbols all_264_0, % 17.27/3.20 | | | | | | | | | all_264_1, all_264_2, all_264_3 gives: % 17.27/3.20 | | | | | | | | | (95) (all_264_0 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | | all_17_2) = 0) | (all_264_1 = 0 & % 17.27/3.20 | | | | | | | | | apart_point_and_line(all_17_1, all_30_1) = 0) | ( ~ % 17.27/3.20 | | | | | | | | | (all_264_2 = 0) & distinct_lines(all_17_2, all_30_1) % 17.27/3.20 | | | | | | | | | = all_264_2) | ( ~ (all_264_3 = 0) & % 17.27/3.20 | | | | | | | | | distinct_points(all_17_1, all_17_0) = all_264_3) % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | BETA: splitting (84) gives: % 17.27/3.20 | | | | | | | | | % 17.27/3.20 | | | | | | | | | Case 1: % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | (96) all_27_0 = 0 % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | REDUCE: (70), (96) imply: % 17.27/3.20 | | | | | | | | | | (97) $false % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | CLOSE: (97) is inconsistent. % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | Case 2: % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | (98) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = % 17.27/3.20 | | | | | | | | | | 0 & apart_point_and_line(all_17_0, all_30_1) = % 17.27/3.20 | | | | | | | | | | 0) | (v1 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | | | all_17_2) = 0) | ( ~ (v0 = 0) & % 17.27/3.20 | | | | | | | | | | distinct_lines(all_17_2, all_30_1) = v0)) % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_268_0, % 17.27/3.20 | | | | | | | | | | all_268_1, all_268_2 gives: % 17.27/3.20 | | | | | | | | | | (99) (all_268_0 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | | | all_30_1) = 0) | (all_268_1 = 0 & % 17.27/3.20 | | | | | | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) | ( % 17.27/3.20 | | | | | | | | | | ~ (all_268_2 = 0) & distinct_lines(all_17_2, % 17.27/3.20 | | | | | | | | | | all_30_1) = all_268_2) % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | BETA: splitting (95) gives: % 17.27/3.20 | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | Case 1: % 17.27/3.20 | | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | | (100) (all_264_0 = 0 & apart_point_and_line(all_17_0, % 17.27/3.20 | | | | | | | | | | | all_17_2) = 0) | (all_264_1 = 0 & % 17.27/3.20 | | | | | | | | | | | apart_point_and_line(all_17_1, all_30_1) = 0) % 17.27/3.20 | | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | | BETA: splitting (100) gives: % 17.27/3.20 | | | | | | | | | | | % 17.27/3.20 | | | | | | | | | | | Case 1: % 17.27/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | (101) all_264_0 = 0 & apart_point_and_line(all_17_0, % 17.44/3.20 | | | | | | | | | | | | all_17_2) = 0 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | ALPHA: (101) implies: % 17.44/3.20 | | | | | | | | | | | | (102) apart_point_and_line(all_17_0, all_17_2) = 0 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | REF_CLOSE: (14), (77), (78), (102) are inconsistent by % 17.44/3.20 | | | | | | | | | | | | sub-proof #2. % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | Case 2: % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | (103) all_264_1 = 0 & apart_point_and_line(all_17_1, % 17.44/3.20 | | | | | | | | | | | | all_30_1) = 0 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | ALPHA: (103) implies: % 17.44/3.20 | | | | | | | | | | | | (104) apart_point_and_line(all_17_1, all_30_1) = 0 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_30_0, 0, all_30_1, % 17.44/3.20 | | | | | | | | | | | | all_17_1, simplifying with (45), (104) gives: % 17.44/3.20 | | | | | | | | | | | | (105) all_30_0 = 0 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | REDUCE: (44), (105) imply: % 17.44/3.20 | | | | | | | | | | | | (106) $false % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | End of split % 17.44/3.20 | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | Case 2: % 17.44/3.20 | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | (107) ( ~ (all_264_2 = 0) & distinct_lines(all_17_2, % 17.44/3.20 | | | | | | | | | | | all_30_1) = all_264_2) | ( ~ (all_264_3 = 0) & % 17.44/3.20 | | | | | | | | | | | distinct_points(all_17_1, all_17_0) = all_264_3) % 17.44/3.20 | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | BETA: splitting (107) gives: % 17.44/3.20 | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | Case 1: % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | (108) ~ (all_264_2 = 0) & distinct_lines(all_17_2, % 17.44/3.20 | | | | | | | | | | | | all_30_1) = all_264_2 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | ALPHA: (108) implies: % 17.44/3.20 | | | | | | | | | | | | (109) distinct_lines(all_17_2, all_30_1) = all_264_2 % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | BETA: splitting (99) gives: % 17.44/3.20 | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | Case 1: % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | (110) all_268_0 = 0 & apart_point_and_line(all_17_0, % 17.44/3.20 | | | | | | | | | | | | | all_30_1) = 0 % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | ALPHA: (110) implies: % 17.44/3.20 | | | | | | | | | | | | | (111) apart_point_and_line(all_17_0, all_30_1) = 0 % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | REF_CLOSE: (14), (48), (66), (111) are inconsistent by % 17.44/3.20 | | | | | | | | | | | | | sub-proof #1. % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | Case 2: % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | (112) (all_268_1 = 0 & apart_point_and_line(all_17_0, % 17.44/3.20 | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_268_2 = 0) & % 17.44/3.20 | | | | | | | | | | | | | distinct_lines(all_17_2, all_30_1) = all_268_2) % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | BETA: splitting (112) gives: % 17.44/3.20 | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | Case 1: % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | | (113) all_268_1 = 0 & apart_point_and_line(all_17_0, % 17.44/3.20 | | | | | | | | | | | | | | all_17_2) = 0 % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | | ALPHA: (113) implies: % 17.44/3.20 | | | | | | | | | | | | | | (114) apart_point_and_line(all_17_0, all_17_2) = 0 % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | | REF_CLOSE: (14), (77), (78), (114) are inconsistent by % 17.44/3.20 | | | | | | | | | | | | | | sub-proof #2. % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | Case 2: % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | | (115) ~ (all_268_2 = 0) & distinct_lines(all_17_2, % 17.44/3.20 | | | | | | | | | | | | | | all_30_1) = all_268_2 % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.20 | | | | | | | | | | | | | | ALPHA: (115) implies: % 17.44/3.20 | | | | | | | | | | | | | | (116) ~ (all_268_2 = 0) % 17.44/3.20 | | | | | | | | | | | | | | (117) distinct_lines(all_17_2, all_30_1) = all_268_2 % 17.44/3.20 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_264_2, all_268_2, % 17.44/3.21 | | | | | | | | | | | | | | all_30_1, all_17_2, simplifying with (109), (117) % 17.44/3.21 | | | | | | | | | | | | | | gives: % 17.44/3.21 | | | | | | | | | | | | | | (118) all_268_2 = all_264_2 % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | REDUCE: (116), (118) imply: % 17.44/3.21 | | | | | | | | | | | | | | (119) ~ (all_264_2 = 0) % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_17_3, all_17_2, % 17.44/3.21 | | | | | | | | | | | | | | all_30_1, all_264_2, simplifying with (18), (19), % 17.44/3.21 | | | | | | | | | | | | | | (23), (67), (109) gives: % 17.44/3.21 | | | | | | | | | | | | | | (120) all_264_2 = 0 | convergent_lines(all_17_3, % 17.44/3.21 | | | | | | | | | | | | | | all_30_1) = 0 % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_17_0, all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | all_17_2, all_30_1, all_24_0, all_32_0, % 17.44/3.21 | | | | | | | | | | | | | | simplifying with (19), (21), (66), (67), (78) % 17.44/3.21 | | | | | | | | | | | | | | gives: % 17.44/3.21 | | | | | | | | | | | | | | (121) all_32_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? % 17.44/3.21 | | | | | | | | | | | | | | [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 17.44/3.21 | | | | | | | | | | | | | | & apart_point_and_line(all_17_0, all_17_2) = % 17.44/3.21 | | | | | | | | | | | | | | 0) | (v2 = 0 & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | all_30_1) = 0) | ( ~ (v1 = 0) & % 17.44/3.21 | | | | | | | | | | | | | | distinct_lines(all_17_2, all_30_1) = v1) | ( ~ % 17.44/3.21 | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_0, all_17_0) % 17.44/3.21 | | | | | | | | | | | | | | = v0)) % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | BETA: splitting (35) gives: % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | (122) ~ (all_25_0 = 0) & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | | all_17_3) = all_25_0 % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | ALPHA: (122) implies: % 17.44/3.21 | | | | | | | | | | | | | | | (123) ~ (all_25_0 = 0) % 17.44/3.21 | | | | | | | | | | | | | | | (124) apart_point_and_line(all_17_0, all_17_3) = % 17.44/3.21 | | | | | | | | | | | | | | | all_25_0 % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | (125) convergent_lines(all_17_3, all_30_1) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | (126) all_239_0 = 0 & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | | | | all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 17.44/3.21 | | | | | | | | | | | | | | | | | (127) apart_point_and_line(all_17_0, all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_25_0, all_17_3, % 17.44/3.21 | | | | | | | | | | | | | | | | | all_17_0, simplifying with (124), (127) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | (128) all_25_0 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | REDUCE: (123), (128) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | | (129) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | (130) (all_239_1 = 0 & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | | | | all_30_1) = 0) | ( ~ (all_239_2 = 0) & % 17.44/3.21 | | | | | | | | | | | | | | | | | distinct_lines(all_30_1, all_17_3) = all_239_2) % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | (131) all_239_1 = 0 & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | | | | | all_30_1) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (131) implies: % 17.44/3.21 | | | | | | | | | | | | | | | | | | (132) apart_point_and_line(all_17_0, all_30_1) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (48), (66), (132) are inconsistent by % 17.44/3.21 | | | | | | | | | | | | | | | | | | sub-proof #1. % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | (133) ~ (all_239_2 = 0) & distinct_lines(all_30_1, % 17.44/3.21 | | | | | | | | | | | | | | | | | | all_17_3) = all_239_2 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (133) implies: % 17.44/3.21 | | | | | | | | | | | | | | | | | | (134) ~ (all_239_2 = 0) % 17.44/3.21 | | | | | | | | | | | | | | | | | | (135) distinct_lines(all_30_1, all_17_3) = all_239_2 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_17_3, all_30_1, % 17.44/3.21 | | | | | | | | | | | | | | | | | | all_17_3, all_239_2, simplifying with (18), (67), % 17.44/3.21 | | | | | | | | | | | | | | | | | | (125), (135) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | | (136) all_239_2 = 0 | convergent_lines(all_17_3, % 17.44/3.21 | | | | | | | | | | | | | | | | | | all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | (137) convergent_lines(all_17_3, all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_3, simplifying % 17.44/3.21 | | | | | | | | | | | | | | | | | | | with (18), (137) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | | | (138) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | (139) all_239_2 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (139) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | | | | (140) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | (141) all_264_2 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | REDUCE: (119), (141) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | (142) $false % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | (143) ~ (all_25_1 = 0) & convergent_lines(all_17_2, % 17.44/3.21 | | | | | | | | | | | | | | | all_17_3) = all_25_1 % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | ALPHA: (143) implies: % 17.44/3.21 | | | | | | | | | | | | | | | (144) ~ (all_25_1 = 0) % 17.44/3.21 | | | | | | | | | | | | | | | (145) convergent_lines(all_17_2, all_17_3) = all_25_1 % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | (146) all_32_0 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | REDUCE: (48), (146) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | (147) $false % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | (148) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 17.44/3.21 | | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 17.44/3.21 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) % 17.44/3.21 | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_0, % 17.44/3.21 | | | | | | | | | | | | | | | | all_30_1) = 0) | ( ~ (v1 = 0) & % 17.44/3.21 | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_30_1) = v1) | ( ~ % 17.44/3.21 | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_0, all_17_0) % 17.44/3.21 | | | | | | | | | | | | | | | | = v0)) % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | (149) all_24_0 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | REDUCE: (77), (149) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | | (150) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_17_3, all_17_2, % 17.44/3.21 | | | | | | | | | | | | | | | | | all_17_3, all_25_1, simplifying with (18), (19), % 17.44/3.21 | | | | | | | | | | | | | | | | | (23), (145) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | (151) all_25_1 = 0 | convergent_lines(all_17_3, % 17.44/3.21 | | | | | | | | | | | | | | | | | all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | Case 1: % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | (152) convergent_lines(all_17_3, all_17_3) = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_3, simplifying % 17.44/3.21 | | | | | | | | | | | | | | | | | | with (18), (152) gives: % 17.44/3.21 | | | | | | | | | | | | | | | | | | (153) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | (154) all_25_1 = 0 % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | REDUCE: (144), (154) imply: % 17.44/3.21 | | | | | | | | | | | | | | | | | | (155) $false % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 17.44/3.21 | | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | End of split % 17.44/3.21 | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | Case 2: % 17.44/3.21 | | | | | | | | | | | | % 17.44/3.21 | | | | | | | | | | | | (156) ~ (all_264_3 = 0) & distinct_points(all_17_1, % 17.44/3.21 | | | | | | | | | | | | all_17_0) = all_264_3 % 17.44/3.21 | | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | | | ALPHA: (156) implies: % 17.44/3.22 | | | | | | | | | | | | (157) ~ (all_264_3 = 0) % 17.44/3.22 | | | | | | | | | | | | (158) distinct_points(all_17_1, all_17_0) = all_264_3 % 17.44/3.22 | | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_264_3, all_17_0, % 17.44/3.22 | | | | | | | | | | | | all_17_1, simplifying with (22), (158) gives: % 17.44/3.22 | | | | | | | | | | | | (159) all_264_3 = 0 % 17.44/3.22 | | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | | | REDUCE: (157), (159) imply: % 17.44/3.22 | | | | | | | | | | | | (160) $false % 17.44/3.22 | | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 17.44/3.22 | | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | | End of split % 17.44/3.22 | | | | | | | | | | | % 17.44/3.22 | | | | | | | | | | End of split % 17.44/3.22 | | | | | | | | | | % 17.44/3.22 | | | | | | | | | End of split % 17.44/3.22 | | | | | | | | | % 17.44/3.22 | | | | | | | | End of split % 17.44/3.22 | | | | | | | | % 17.44/3.22 | | | | | | | End of split % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | End of split % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | End of split % 17.44/3.22 | | | | | % 17.44/3.22 | | | | End of split % 17.44/3.22 | | | | % 17.44/3.22 | | | Case 2: % 17.44/3.22 | | | | % 17.44/3.22 | | | | (161) ~ (all_24_1 = 0) & convergent_lines(all_17_2, all_17_3) = % 17.44/3.22 | | | | all_24_1 % 17.44/3.22 | | | | % 17.44/3.22 | | | | ALPHA: (161) implies: % 17.44/3.22 | | | | (162) ~ (all_24_1 = 0) % 17.44/3.22 | | | | (163) convergent_lines(all_17_2, all_17_3) = all_24_1 % 17.44/3.22 | | | | % 17.44/3.22 | | | | BETA: splitting (73) gives: % 17.44/3.22 | | | | % 17.44/3.22 | | | | Case 1: % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | (164) all_30_0 = 0 % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | REDUCE: (44), (164) imply: % 17.44/3.22 | | | | | (165) $false % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | CLOSE: (165) is inconsistent. % 17.44/3.22 | | | | | % 17.44/3.22 | | | | Case 2: % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | (166) all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 17.44/3.22 | | | | | ((v2 = 0 & apart_point_and_line(all_17_0, all_30_1) = 0) | % 17.44/3.22 | | | | | (v1 = 0 & apart_point_and_line(all_17_0, all_17_3) = 0) | ( % 17.44/3.22 | | | | | ~ (v0 = 0) & distinct_lines(all_17_3, all_30_1) = v0)) % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | BETA: splitting (166) gives: % 17.44/3.22 | | | | | % 17.44/3.22 | | | | | Case 1: % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | (167) all_26_0 = 0 % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | REDUCE: (71), (167) imply: % 17.44/3.22 | | | | | | (168) $false % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | CLOSE: (168) is inconsistent. % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | Case 2: % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | GROUND_INST: instantiating (1) with all_17_3, all_17_2, all_17_3, % 17.44/3.22 | | | | | | all_24_1, simplifying with (18), (19), (23), (163) % 17.44/3.22 | | | | | | gives: % 17.44/3.22 | | | | | | (169) all_24_1 = 0 | convergent_lines(all_17_3, all_17_3) = 0 % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | BETA: splitting (169) gives: % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | | Case 1: % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | (170) convergent_lines(all_17_3, all_17_3) = 0 % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | GROUND_INST: instantiating (apart3) with all_17_3, simplifying % 17.44/3.22 | | | | | | | with (18), (170) gives: % 17.44/3.22 | | | | | | | (171) $false % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | CLOSE: (171) is inconsistent. % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | Case 2: % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | (172) all_24_1 = 0 % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | REDUCE: (162), (172) imply: % 17.44/3.22 | | | | | | | (173) $false % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | | CLOSE: (173) is inconsistent. % 17.44/3.22 | | | | | | | % 17.44/3.22 | | | | | | End of split % 17.44/3.22 | | | | | | % 17.44/3.22 | | | | | End of split % 17.44/3.22 | | | | | % 17.44/3.22 | | | | End of split % 17.44/3.22 | | | | % 17.44/3.22 | | | End of split % 17.44/3.22 | | | % 17.44/3.22 | | Case 2: % 17.44/3.22 | | | % 17.44/3.22 | | | (174) ~ (all_27_1 = 0) & convergent_lines(all_17_3, all_17_2) = % 17.44/3.22 | | | all_27_1 % 17.44/3.22 | | | % 17.44/3.22 | | | ALPHA: (174) implies: % 17.44/3.22 | | | (175) ~ (all_27_1 = 0) % 17.44/3.22 | | | (176) convergent_lines(all_17_3, all_17_2) = all_27_1 % 17.44/3.22 | | | % 17.44/3.22 | | | GROUND_INST: instantiating (13) with 0, all_27_1, all_17_2, all_17_3, % 17.44/3.22 | | | simplifying with (23), (176) gives: % 17.44/3.22 | | | (177) all_27_1 = 0 % 17.44/3.22 | | | % 17.44/3.22 | | | REDUCE: (175), (177) imply: % 17.44/3.22 | | | (178) $false % 17.44/3.22 | | | % 17.44/3.22 | | | CLOSE: (178) is inconsistent. % 17.44/3.22 | | | % 17.44/3.22 | | End of split % 17.44/3.22 | | % 17.44/3.22 | Case 2: % 17.44/3.22 | | % 17.44/3.22 | | (179) ~ (all_26_1 = 0) & convergent_lines(all_17_3, all_17_2) = all_26_1 % 17.44/3.22 | | % 17.44/3.22 | | ALPHA: (179) implies: % 17.44/3.22 | | (180) ~ (all_26_1 = 0) % 17.44/3.22 | | (181) convergent_lines(all_17_3, all_17_2) = all_26_1 % 17.44/3.22 | | % 17.44/3.22 | | GROUND_INST: instantiating (13) with 0, all_26_1, all_17_2, all_17_3, % 17.44/3.22 | | simplifying with (23), (181) gives: % 17.44/3.22 | | (182) all_26_1 = 0 % 17.44/3.22 | | % 17.44/3.22 | | REDUCE: (180), (182) imply: % 17.44/3.22 | | (183) $false % 17.44/3.22 | | % 17.44/3.22 | | CLOSE: (183) is inconsistent. % 17.44/3.22 | | % 17.44/3.22 | End of split % 17.44/3.22 | % 17.44/3.22 End of proof % 17.44/3.22 % 17.44/3.22 Sub-proof #1 shows that the following formulas are inconsistent: % 17.44/3.22 ---------------------------------------------------------------- % 17.44/3.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.44/3.22 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.44/3.22 (apart_point_and_line(v3, v2) = v0)) % 17.44/3.22 (2) apart_point_and_line(all_17_0, all_30_1) = all_32_0 % 17.44/3.22 (3) apart_point_and_line(all_17_0, all_30_1) = 0 % 17.44/3.22 (4) ~ (all_32_0 = 0) % 17.44/3.22 % 17.44/3.22 Begin of proof % 17.44/3.22 | % 17.44/3.22 | GROUND_INST: instantiating (1) with all_32_0, 0, all_30_1, all_17_0, % 17.44/3.22 | simplifying with (2), (3) gives: % 17.44/3.22 | (5) all_32_0 = 0 % 17.44/3.22 | % 17.44/3.22 | REDUCE: (4), (5) imply: % 17.44/3.22 | (6) $false % 17.44/3.22 | % 17.44/3.22 | CLOSE: (6) is inconsistent. % 17.44/3.22 | % 17.44/3.22 End of proof % 17.44/3.22 % 17.44/3.22 Sub-proof #2 shows that the following formulas are inconsistent: % 17.44/3.22 ---------------------------------------------------------------- % 17.44/3.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.44/3.22 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 17.44/3.22 (apart_point_and_line(v3, v2) = v0)) % 17.44/3.22 (2) apart_point_and_line(all_17_0, all_17_2) = all_24_0 % 17.44/3.22 (3) apart_point_and_line(all_17_0, all_17_2) = 0 % 17.44/3.22 (4) ~ (all_24_0 = 0) % 17.44/3.22 % 17.44/3.22 Begin of proof % 17.44/3.22 | % 17.44/3.22 | GROUND_INST: instantiating (1) with 0, all_24_0, all_17_2, all_17_0, % 17.44/3.22 | simplifying with (2), (3) gives: % 17.44/3.22 | (5) all_24_0 = 0 % 17.44/3.22 | % 17.44/3.22 | REDUCE: (4), (5) imply: % 17.44/3.22 | (6) $false % 17.44/3.22 | % 17.44/3.22 | CLOSE: (6) is inconsistent. % 17.44/3.22 | % 17.44/3.22 End of proof % 17.44/3.22 % SZS output end Proof for theBenchmark % 17.44/3.22 % 17.44/3.22 2737ms %------------------------------------------------------------------------------