%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO197+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 23:22:10 EDT 2023 % Result : Theorem 19.03s 3.56s % Output : Proof 41.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO197+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 19:34:35 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.60 ________ _____ % 0.22/0.60 ___ __ \_________(_)________________________________ % 0.22/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.60 % 0.22/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.60 (2023-06-19) % 0.22/0.60 % 0.22/0.60 (c) Philipp Rümmer, 2009-2023 % 0.22/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.60 Amanda Stjerna. % 0.22/0.60 Free software under BSD-3-Clause. % 0.22/0.60 % 0.22/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.60 % 0.22/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.62 Running up to 7 provers in parallel. % 0.22/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.40/1.21 Prover 4: Preprocessing ... % 3.40/1.21 Prover 1: Preprocessing ... % 3.40/1.24 Prover 5: Preprocessing ... % 3.40/1.24 Prover 6: Preprocessing ... % 3.40/1.24 Prover 0: Preprocessing ... % 3.40/1.24 Prover 2: Preprocessing ... % 3.40/1.24 Prover 3: Preprocessing ... % 6.61/1.67 Prover 2: Proving ... % 6.61/1.68 Prover 5: Proving ... % 6.61/1.69 Prover 6: Constructing countermodel ... % 7.07/1.72 Prover 3: Constructing countermodel ... % 7.07/1.76 Prover 1: Constructing countermodel ... % 8.04/1.87 Prover 3: gave up % 8.04/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.67/1.97 Prover 7: Preprocessing ... % 8.67/2.03 Prover 4: Constructing countermodel ... % 8.67/2.03 Prover 6: gave up % 8.67/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.67/2.06 Prover 7: Warning: ignoring some quantifiers % 8.67/2.07 Prover 8: Preprocessing ... % 9.27/2.10 Prover 7: Constructing countermodel ... % 9.27/2.12 Prover 1: gave up % 9.27/2.13 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.95/2.16 Prover 0: Proving ... % 9.95/2.17 Prover 9: Preprocessing ... % 10.88/2.28 Prover 8: Warning: ignoring some quantifiers % 10.88/2.29 Prover 8: Constructing countermodel ... % 12.21/2.48 Prover 9: Constructing countermodel ... % 12.62/2.54 Prover 8: gave up % 13.16/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.16/2.63 Prover 7: gave up % 13.16/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.16/2.64 Prover 10: Preprocessing ... % 13.16/2.69 Prover 10: Warning: ignoring some quantifiers % 13.16/2.70 Prover 10: Constructing countermodel ... % 13.16/2.71 Prover 11: Preprocessing ... % 15.00/2.88 Prover 10: gave up % 15.00/2.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 15.70/2.96 Prover 12: Preprocessing ... % 16.92/3.08 Prover 11: Constructing countermodel ... % 17.84/3.23 Prover 12: Proving ... % 19.03/3.56 Prover 0: proved (2939ms) % 19.03/3.56 % 19.03/3.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.03/3.56 % 19.03/3.56 Prover 12: stopped % 19.03/3.56 Prover 5: stopped % 19.03/3.57 Prover 2: stopped % 19.03/3.57 Prover 9: stopped % 19.03/3.57 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 19.03/3.57 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 20.05/3.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.57/3.60 Prover 13: Preprocessing ... % 20.67/3.60 Prover 16: Preprocessing ... % 20.75/3.61 Prover 19: Preprocessing ... % 20.75/3.66 Prover 16: Warning: ignoring some quantifiers % 20.75/3.67 Prover 13: Warning: ignoring some quantifiers % 20.75/3.67 Prover 16: Constructing countermodel ... % 20.75/3.67 Prover 13: Constructing countermodel ... % 21.45/3.74 Prover 19: Warning: ignoring some quantifiers % 21.45/3.76 Prover 19: Constructing countermodel ... % 22.13/3.80 Prover 13: gave up % 22.98/3.93 Prover 19: gave up % 26.05/4.43 Prover 16: gave up % 39.73/7.13 Prover 11: Found proof (size 196) % 39.73/7.13 Prover 11: proved (4491ms) % 39.73/7.14 Prover 4: stopped % 39.73/7.14 % 39.73/7.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 39.73/7.14 % 39.73/7.15 % SZS output start Proof for theBenchmark % 39.73/7.15 Assumptions after simplification: % 39.73/7.15 --------------------------------- % 39.73/7.15 % 39.73/7.15 (a4) % 39.73/7.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.73/7.18 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.18 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 39.73/7.18 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.18 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 39.73/7.18 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 39.73/7.18 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 39.73/7.18 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 39.73/7.18 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 39.73/7.18 % 39.73/7.18 (apart3) % 39.73/7.18 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 39.73/7.18 % 39.73/7.18 (ceq1) % 39.73/7.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 39.73/7.19 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 39.73/7.19 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 39.73/7.19 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 39.73/7.19 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 39.73/7.19 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 39.73/7.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 39.73/7.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 39.73/7.19 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 39.73/7.19 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 39.73/7.19 % 39.73/7.19 (ceq2) % 39.73/7.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 39.73/7.19 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 39.73/7.19 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 39.73/7.19 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 39.73/7.19 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 39.73/7.19 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.19 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 39.73/7.19 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 39.73/7.19 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.19 apart_point_and_line(v0, v2) = 0) % 39.73/7.19 % 39.73/7.19 (ceq3) % 39.73/7.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 39.73/7.20 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 39.73/7.20 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 39.73/7.20 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 39.73/7.20 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 39.73/7.20 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.20 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 39.73/7.20 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 39.73/7.20 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.73/7.20 convergent_lines(v0, v2) = 0) % 39.73/7.20 % 39.73/7.20 (ci3) % 39.73/7.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 39.73/7.20 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 39.73/7.20 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 39.73/7.20 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 39.73/7.20 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 39.73/7.20 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 39.73/7.20 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 39.73/7.20 % 39.73/7.20 (ci4) % 39.73/7.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 39.73/7.21 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 39.73/7.21 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 39.73/7.21 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 39.73/7.21 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 39.73/7.21 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 39.73/7.21 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 39.73/7.21 % 39.73/7.21 (con) % 39.73/7.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 39.73/7.21 int] : ( ~ (v5 = 0) & incident_point_and_line(v4, v0) = v5 & % 39.73/7.21 incident_point_and_line(v3, v2) = 0 & intersection_point(v2, v1) = v4 & % 39.73/7.21 intersection_point(v0, v1) = v3 & convergent_lines(v2, v1) = 0 & % 39.73/7.21 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v4) & % 39.73/7.21 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 39.73/7.21 % 39.73/7.21 (cu1) % 40.67/7.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 40.67/7.22 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 40.67/7.22 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 40.67/7.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 40.67/7.22 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 40.67/7.22 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 40.67/7.22 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 40.67/7.22 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 40.67/7.22 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 40.67/7.22 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 40.67/7.22 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 40.67/7.22 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 40.67/7.22 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 40.67/7.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 40.67/7.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 40.67/7.22 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 40.67/7.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 40.67/7.22 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 40.67/7.22 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 40.67/7.22 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 40.67/7.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 40.67/7.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 40.67/7.22 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 40.67/7.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 40.67/7.22 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 40.67/7.22 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 40.67/7.22 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 40.67/7.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 40.67/7.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 40.67/7.22 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 40.67/7.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 40.67/7.22 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 40.67/7.22 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 40.67/7.22 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 40.67/7.22 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 40.67/7.22 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 40.67/7.22 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 40.67/7.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 40.67/7.22 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 40.67/7.22 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 40.67/7.22 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 40.67/7.22 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 40.67/7.22 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 40.67/7.22 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 40.67/7.22 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 40.67/7.22 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 40.67/7.22 % 40.67/7.22 (function-axioms) % 40.67/7.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 40.67/7.23 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 40.67/7.23 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 40.67/7.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.23 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 40.67/7.23 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 40.67/7.23 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 40.67/7.23 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 40.67/7.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.23 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 40.67/7.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 40.67/7.23 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 40.67/7.23 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.23 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 40.67/7.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 40.67/7.23 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 40.67/7.23 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 40.67/7.23 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 40.67/7.23 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 40.67/7.23 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 40.67/7.23 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 40.67/7.23 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 40.67/7.23 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 40.67/7.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.23 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 40.67/7.23 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 40.67/7.23 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 40.67/7.23 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 40.67/7.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.23 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 40.67/7.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 40.67/7.23 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 40.67/7.23 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 40.67/7.23 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 40.67/7.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 40.67/7.23 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 40.67/7.23 % 40.67/7.23 Further assumptions not needed in the proof: % 40.67/7.23 -------------------------------------------- % 40.67/7.23 a3, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ci1, ci2, coipo1, con1, % 40.67/7.23 cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, orth1, ouo1, p1, % 40.67/7.23 par1 % 40.67/7.23 % 40.67/7.23 Those formulas are unsatisfiable: % 40.67/7.23 --------------------------------- % 40.67/7.23 % 40.67/7.23 Begin of proof % 40.67/7.23 | % 40.67/7.23 | ALPHA: (ci3) implies: % 40.67/7.24 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 40.67/7.24 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 40.67/7.24 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 40.67/7.24 | & $i(v2))) % 40.67/7.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 40.67/7.24 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 40.67/7.24 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 40.67/7.24 | convergent_lines(v0, v1) = v3))) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (ci4) implies: % 40.67/7.24 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 40.67/7.24 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 40.67/7.24 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 40.67/7.24 | & $i(v2))) % 40.67/7.24 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 40.67/7.24 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 40.67/7.24 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 40.67/7.24 | convergent_lines(v0, v1) = v3))) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (cu1) implies: % 40.67/7.24 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 40.67/7.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 40.67/7.24 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 40.67/7.24 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 40.67/7.24 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 40.67/7.24 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 40.67/7.24 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 40.67/7.24 | v1) = v6))) % 40.67/7.24 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 40.67/7.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 40.67/7.24 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 40.67/7.24 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 40.67/7.24 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 40.67/7.24 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 40.67/7.24 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 40.67/7.24 | v1) = v6))) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (ceq1) implies: % 40.67/7.24 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 40.67/7.24 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 40.67/7.24 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 40.67/7.24 | distinct_points(v0, v2) = 0) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (ceq2) implies: % 40.67/7.24 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 40.67/7.24 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 40.67/7.24 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 40.67/7.24 | v2) = 0) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (ceq3) implies: % 40.67/7.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 40.67/7.24 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 40.67/7.24 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (a4) implies: % 40.67/7.24 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) % 40.67/7.24 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 40.67/7.24 | apart_point_and_line(v0, v1) = v2)) % 40.67/7.24 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 40.67/7.24 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 40.67/7.24 | apart_point_and_line(v0, v1) = 0) % 40.67/7.24 | % 40.67/7.24 | ALPHA: (function-axioms) implies: % 40.67/7.25 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 40.67/7.25 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 40.67/7.25 | (distinct_points(v3, v2) = v0)) % 40.67/7.25 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 40.67/7.25 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 40.67/7.25 | (distinct_lines(v3, v2) = v0)) % 40.67/7.25 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 40.67/7.25 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 40.67/7.25 | (convergent_lines(v3, v2) = v0)) % 40.67/7.25 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 40.67/7.25 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 40.67/7.25 | (apart_point_and_line(v3, v2) = v0)) % 40.67/7.25 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 40.67/7.25 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 40.67/7.25 | v0)) % 40.67/7.25 | % 40.67/7.25 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 40.67/7.25 | all_38_3, all_38_4, all_38_5 gives: % 40.67/7.25 | (17) ~ (all_38_0 = 0) & incident_point_and_line(all_38_1, all_38_5) = % 40.67/7.25 | all_38_0 & incident_point_and_line(all_38_2, all_38_3) = 0 & % 40.67/7.25 | intersection_point(all_38_3, all_38_4) = all_38_1 & % 40.67/7.25 | intersection_point(all_38_5, all_38_4) = all_38_2 & % 40.67/7.25 | convergent_lines(all_38_3, all_38_4) = 0 & convergent_lines(all_38_5, % 40.67/7.25 | all_38_3) = 0 & convergent_lines(all_38_5, all_38_4) = 0 & % 40.67/7.25 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 40.67/7.25 | $i(all_38_5) % 40.67/7.25 | % 40.67/7.25 | ALPHA: (17) implies: % 40.67/7.25 | (18) ~ (all_38_0 = 0) % 40.67/7.25 | (19) $i(all_38_5) % 40.67/7.25 | (20) $i(all_38_4) % 40.67/7.25 | (21) $i(all_38_3) % 40.67/7.25 | (22) $i(all_38_2) % 40.67/7.25 | (23) $i(all_38_1) % 40.67/7.25 | (24) convergent_lines(all_38_5, all_38_4) = 0 % 40.67/7.25 | (25) convergent_lines(all_38_3, all_38_4) = 0 % 40.67/7.25 | (26) intersection_point(all_38_5, all_38_4) = all_38_2 % 40.67/7.25 | (27) intersection_point(all_38_3, all_38_4) = all_38_1 % 40.67/7.25 | (28) incident_point_and_line(all_38_2, all_38_3) = 0 % 40.67/7.25 | (29) incident_point_and_line(all_38_1, all_38_5) = all_38_0 % 40.67/7.25 | % 40.67/7.25 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (19), % 40.67/7.25 | (20), (24) gives: % 40.67/7.25 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 40.67/7.25 | intersection_point(all_38_5, all_38_4) = v0 & % 40.67/7.25 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 40.67/7.25 | % 40.67/7.25 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (19), % 40.67/7.25 | (20), (24) gives: % 40.67/7.25 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 40.67/7.25 | intersection_point(all_38_5, all_38_4) = v0 & % 40.67/7.25 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 40.67/7.25 | % 40.67/7.25 | GROUND_INST: instantiating (3) with all_38_3, all_38_4, simplifying with (20), % 40.67/7.25 | (21), (25) gives: % 40.67/7.25 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 40.67/7.25 | intersection_point(all_38_3, all_38_4) = v0 & % 40.67/7.25 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 40.67/7.25 | % 40.67/7.25 | GROUND_INST: instantiating (1) with all_38_3, all_38_4, simplifying with (20), % 40.67/7.25 | (21), (25) gives: % 40.67/7.26 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 40.67/7.26 | intersection_point(all_38_3, all_38_4) = v0 & % 40.67/7.26 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 40.67/7.26 | with (19), (20), (26) gives: % 40.67/7.26 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 40.67/7.26 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) & % 40.67/7.26 | convergent_lines(all_38_5, all_38_4) = v0)) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 40.67/7.26 | with (19), (20), (26) gives: % 40.67/7.26 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 40.67/7.26 | apart_point_and_line(all_38_2, all_38_5) = v1) | ( ~ (v0 = 0) & % 40.67/7.26 | convergent_lines(all_38_5, all_38_4) = v0)) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (4) with all_38_3, all_38_4, all_38_1, simplifying % 40.67/7.26 | with (20), (21), (27) gives: % 40.67/7.26 | (36) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 40.67/7.26 | apart_point_and_line(all_38_1, all_38_4) = v1) | ( ~ (v0 = 0) & % 40.67/7.26 | convergent_lines(all_38_3, all_38_4) = v0)) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (2) with all_38_3, all_38_4, all_38_1, simplifying % 40.67/7.26 | with (20), (21), (27) gives: % 40.67/7.26 | (37) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 40.67/7.26 | apart_point_and_line(all_38_1, all_38_3) = v1) | ( ~ (v0 = 0) & % 40.67/7.26 | convergent_lines(all_38_3, all_38_4) = v0)) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (10) with all_38_2, all_38_3, simplifying with % 40.67/7.26 | (21), (22), (28) gives: % 40.67/7.26 | (38) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_2, all_38_3) % 40.67/7.26 | = v0) % 40.67/7.26 | % 40.67/7.26 | GROUND_INST: instantiating (11) with all_38_1, all_38_5, all_38_0, simplifying % 40.67/7.26 | with (19), (23), (29) gives: % 40.67/7.26 | (39) all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_5) = 0 % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (38) with fresh symbol all_45_0 gives: % 40.67/7.26 | (40) ~ (all_45_0 = 0) & apart_point_and_line(all_38_2, all_38_3) = % 40.67/7.26 | all_45_0 % 40.67/7.26 | % 40.67/7.26 | ALPHA: (40) implies: % 40.67/7.26 | (41) ~ (all_45_0 = 0) % 40.67/7.26 | (42) apart_point_and_line(all_38_2, all_38_3) = all_45_0 % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (32) with fresh symbols all_53_0, all_53_1 gives: % 40.67/7.26 | (43) ~ (all_53_0 = 0) & intersection_point(all_38_3, all_38_4) = all_53_1 % 40.67/7.26 | & apart_point_and_line(all_53_1, all_38_4) = all_53_0 & $i(all_53_1) % 40.67/7.26 | % 40.67/7.26 | ALPHA: (43) implies: % 40.67/7.26 | (44) $i(all_53_1) % 40.67/7.26 | (45) apart_point_and_line(all_53_1, all_38_4) = all_53_0 % 40.67/7.26 | (46) intersection_point(all_38_3, all_38_4) = all_53_1 % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (37) with fresh symbols all_57_0, all_57_1 gives: % 40.67/7.26 | (47) ( ~ (all_57_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 40.67/7.26 | all_57_0) | ( ~ (all_57_1 = 0) & convergent_lines(all_38_3, % 40.67/7.26 | all_38_4) = all_57_1) % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (35) with fresh symbols all_58_0, all_58_1 gives: % 40.67/7.26 | (48) ( ~ (all_58_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 40.67/7.26 | all_58_0) | ( ~ (all_58_1 = 0) & convergent_lines(all_38_5, % 40.67/7.26 | all_38_4) = all_58_1) % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (36) with fresh symbols all_59_0, all_59_1 gives: % 40.67/7.26 | (49) ( ~ (all_59_0 = 0) & apart_point_and_line(all_38_1, all_38_4) = % 40.67/7.26 | all_59_0) | ( ~ (all_59_1 = 0) & convergent_lines(all_38_3, % 40.67/7.26 | all_38_4) = all_59_1) % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (31) with fresh symbols all_62_0, all_62_1 gives: % 40.67/7.26 | (50) ~ (all_62_0 = 0) & intersection_point(all_38_5, all_38_4) = all_62_1 % 40.67/7.26 | & apart_point_and_line(all_62_1, all_38_5) = all_62_0 & $i(all_62_1) % 40.67/7.26 | % 40.67/7.26 | ALPHA: (50) implies: % 40.67/7.26 | (51) ~ (all_62_0 = 0) % 40.67/7.26 | (52) $i(all_62_1) % 40.67/7.26 | (53) apart_point_and_line(all_62_1, all_38_5) = all_62_0 % 40.67/7.26 | (54) intersection_point(all_38_5, all_38_4) = all_62_1 % 40.67/7.26 | % 40.67/7.26 | DELTA: instantiating (33) with fresh symbols all_64_0, all_64_1 gives: % 40.67/7.26 | (55) ~ (all_64_0 = 0) & intersection_point(all_38_3, all_38_4) = all_64_1 % 40.67/7.26 | & apart_point_and_line(all_64_1, all_38_3) = all_64_0 & $i(all_64_1) % 40.67/7.26 | % 40.67/7.26 | ALPHA: (55) implies: % 40.67/7.27 | (56) ~ (all_64_0 = 0) % 40.67/7.27 | (57) apart_point_and_line(all_64_1, all_38_3) = all_64_0 % 40.67/7.27 | (58) intersection_point(all_38_3, all_38_4) = all_64_1 % 40.67/7.27 | % 40.67/7.27 | DELTA: instantiating (30) with fresh symbols all_66_0, all_66_1 gives: % 40.67/7.27 | (59) ~ (all_66_0 = 0) & intersection_point(all_38_5, all_38_4) = all_66_1 % 40.67/7.27 | & apart_point_and_line(all_66_1, all_38_4) = all_66_0 & $i(all_66_1) % 40.67/7.27 | % 40.67/7.27 | ALPHA: (59) implies: % 40.67/7.27 | (60) apart_point_and_line(all_66_1, all_38_4) = all_66_0 % 40.67/7.27 | (61) intersection_point(all_38_5, all_38_4) = all_66_1 % 40.67/7.27 | % 40.67/7.27 | DELTA: instantiating (34) with fresh symbols all_68_0, all_68_1 gives: % 40.67/7.27 | (62) ( ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 40.67/7.27 | all_68_0) | ( ~ (all_68_1 = 0) & convergent_lines(all_38_5, % 40.67/7.27 | all_38_4) = all_68_1) % 40.67/7.27 | % 40.67/7.27 | BETA: splitting (49) gives: % 40.67/7.27 | % 40.67/7.27 | Case 1: % 40.67/7.27 | | % 40.67/7.27 | | (63) ~ (all_59_0 = 0) & apart_point_and_line(all_38_1, all_38_4) = % 40.67/7.27 | | all_59_0 % 40.67/7.27 | | % 40.67/7.27 | | ALPHA: (63) implies: % 40.67/7.27 | | (64) ~ (all_59_0 = 0) % 40.67/7.27 | | (65) apart_point_and_line(all_38_1, all_38_4) = all_59_0 % 40.67/7.27 | | % 40.67/7.27 | | BETA: splitting (39) gives: % 40.67/7.27 | | % 40.67/7.27 | | Case 1: % 40.67/7.27 | | | % 40.67/7.27 | | | (66) apart_point_and_line(all_38_1, all_38_5) = 0 % 40.67/7.27 | | | % 40.67/7.27 | | | BETA: splitting (47) gives: % 40.67/7.27 | | | % 40.67/7.27 | | | Case 1: % 40.67/7.27 | | | | % 40.67/7.27 | | | | (67) ~ (all_57_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 40.67/7.27 | | | | all_57_0 % 40.67/7.27 | | | | % 40.67/7.27 | | | | ALPHA: (67) implies: % 40.67/7.27 | | | | (68) apart_point_and_line(all_38_1, all_38_3) = all_57_0 % 40.67/7.27 | | | | % 40.67/7.27 | | | | BETA: splitting (62) gives: % 40.67/7.27 | | | | % 40.67/7.27 | | | | Case 1: % 40.67/7.27 | | | | | % 40.67/7.27 | | | | | (69) ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 40.67/7.27 | | | | | all_68_0 % 40.67/7.27 | | | | | % 40.67/7.27 | | | | | ALPHA: (69) implies: % 40.67/7.27 | | | | | (70) ~ (all_68_0 = 0) % 40.67/7.27 | | | | | (71) apart_point_and_line(all_38_2, all_38_4) = all_68_0 % 40.67/7.27 | | | | | % 40.67/7.27 | | | | | BETA: splitting (48) gives: % 40.67/7.27 | | | | | % 40.67/7.27 | | | | | Case 1: % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | (72) ~ (all_58_0 = 0) & apart_point_and_line(all_38_2, all_38_5) % 40.67/7.27 | | | | | | = all_58_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | ALPHA: (72) implies: % 40.67/7.27 | | | | | | (73) apart_point_and_line(all_38_2, all_38_5) = all_58_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (16) with all_38_2, all_66_1, all_38_4, % 40.67/7.27 | | | | | | all_38_5, simplifying with (26), (61) gives: % 40.67/7.27 | | | | | | (74) all_66_1 = all_38_2 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (16) with all_62_1, all_66_1, all_38_4, % 40.67/7.27 | | | | | | all_38_5, simplifying with (54), (61) gives: % 40.67/7.27 | | | | | | (75) all_66_1 = all_62_1 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (16) with all_38_1, all_64_1, all_38_4, % 40.67/7.27 | | | | | | all_38_3, simplifying with (27), (58) gives: % 40.67/7.27 | | | | | | (76) all_64_1 = all_38_1 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (16) with all_53_1, all_64_1, all_38_4, % 40.67/7.27 | | | | | | all_38_3, simplifying with (46), (58) gives: % 40.67/7.27 | | | | | | (77) all_64_1 = all_53_1 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | COMBINE_EQS: (74), (75) imply: % 40.67/7.27 | | | | | | (78) all_62_1 = all_38_2 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | COMBINE_EQS: (76), (77) imply: % 40.67/7.27 | | | | | | (79) all_53_1 = all_38_1 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | REDUCE: (60), (74) imply: % 40.67/7.27 | | | | | | (80) apart_point_and_line(all_38_2, all_38_4) = all_66_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | REDUCE: (57), (76) imply: % 40.67/7.27 | | | | | | (81) apart_point_and_line(all_38_1, all_38_3) = all_64_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | REDUCE: (53), (78) imply: % 40.67/7.27 | | | | | | (82) apart_point_and_line(all_38_2, all_38_5) = all_62_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | REDUCE: (45), (79) imply: % 40.67/7.27 | | | | | | (83) apart_point_and_line(all_38_1, all_38_4) = all_53_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (15) with all_58_0, all_62_0, all_38_5, % 40.67/7.27 | | | | | | all_38_2, simplifying with (73), (82) gives: % 40.67/7.27 | | | | | | (84) all_62_0 = all_58_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (15) with all_68_0, all_66_0, all_38_4, % 40.67/7.27 | | | | | | all_38_2, simplifying with (71), (80) gives: % 40.67/7.27 | | | | | | (85) all_68_0 = all_66_0 % 40.67/7.27 | | | | | | % 40.67/7.27 | | | | | | GROUND_INST: instantiating (15) with all_59_0, all_53_0, all_38_4, % 40.67/7.27 | | | | | | all_38_1, simplifying with (65), (83) gives: % 40.67/7.27 | | | | | | (86) all_59_0 = all_53_0 % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (15) with all_57_0, all_64_0, all_38_3, % 40.67/7.28 | | | | | | all_38_1, simplifying with (68), (81) gives: % 40.67/7.28 | | | | | | (87) all_64_0 = all_57_0 % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | REDUCE: (70), (85) imply: % 40.67/7.28 | | | | | | (88) ~ (all_66_0 = 0) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | REDUCE: (56), (87) imply: % 40.67/7.28 | | | | | | (89) ~ (all_57_0 = 0) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | REDUCE: (51), (84) imply: % 40.67/7.28 | | | | | | (90) ~ (all_58_0 = 0) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | REDUCE: (64), (86) imply: % 40.67/7.28 | | | | | | (91) ~ (all_53_0 = 0) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (5) with all_38_2, all_38_2, all_38_5, % 40.67/7.28 | | | | | | all_38_4, all_66_0, all_58_0, simplifying with (19), % 40.67/7.28 | | | | | | (20), (22), (73), (80) gives: % 40.67/7.28 | | | | | | (92) all_66_0 = 0 | all_58_0 = 0 | ? [v0: int] : ? [v1: int] : % 40.67/7.28 | | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 40.67/7.28 | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | (v2 = 0 % 40.67/7.28 | | | | | | & apart_point_and_line(all_38_2, all_38_5) = 0) | ( ~ % 40.67/7.28 | | | | | | (v1 = 0) & distinct_lines(all_38_5, all_38_4) = v1) | ( % 40.67/7.28 | | | | | | ~ (v0 = 0) & distinct_points(all_38_2, all_38_2) = v0)) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (7) with all_38_1, all_38_5, all_38_2, % 40.67/7.28 | | | | | | all_58_0, simplifying with (19), (22), (23), (66), (73) % 40.67/7.28 | | | | | | gives: % 40.67/7.28 | | | | | | (93) all_58_0 = 0 | distinct_points(all_38_1, all_38_2) = 0 % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (8) with all_38_1, all_38_5, all_38_4, % 40.67/7.28 | | | | | | all_53_0, simplifying with (19), (20), (23), (66), (83) % 40.67/7.28 | | | | | | gives: % 40.67/7.28 | | | | | | (94) all_53_0 = 0 | distinct_lines(all_38_5, all_38_4) = 0 % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (6) with all_38_1, all_38_2, all_38_4, % 40.67/7.28 | | | | | | all_38_3, all_53_0, all_45_0, simplifying with (20), % 40.67/7.28 | | | | | | (21), (22), (23), (42), (83) gives: % 40.67/7.28 | | | | | | (95) all_53_0 = 0 | all_45_0 = 0 | ? [v0: int] : ? [v1: int] : % 40.67/7.28 | | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 40.67/7.28 | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | (v2 = 0 % 40.67/7.28 | | | | | | & apart_point_and_line(all_38_1, all_38_3) = 0) | ( ~ % 40.67/7.28 | | | | | | (v1 = 0) & distinct_lines(all_38_4, all_38_3) = v1) | ( % 40.67/7.28 | | | | | | ~ (v0 = 0) & distinct_points(all_38_1, all_38_2) = v0)) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | GROUND_INST: instantiating (5) with all_38_1, all_38_2, all_38_4, % 40.67/7.28 | | | | | | all_38_3, all_57_0, all_66_0, simplifying with (20), % 40.67/7.28 | | | | | | (21), (22), (23), (68), (80) gives: % 40.67/7.28 | | | | | | (96) all_66_0 = 0 | all_57_0 = 0 | ? [v0: int] : ? [v1: int] : % 40.67/7.28 | | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 40.67/7.28 | | | | | | apart_point_and_line(all_38_2, all_38_3) = 0) | (v2 = 0 % 40.67/7.28 | | | | | | & apart_point_and_line(all_38_1, all_38_4) = 0) | ( ~ % 40.67/7.28 | | | | | | (v1 = 0) & distinct_lines(all_38_4, all_38_3) = v1) | ( % 40.67/7.28 | | | | | | ~ (v0 = 0) & distinct_points(all_38_1, all_38_2) = v0)) % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | BETA: splitting (96) gives: % 40.67/7.28 | | | | | | % 40.67/7.28 | | | | | | Case 1: % 40.67/7.28 | | | | | | | % 40.67/7.28 | | | | | | | (97) all_66_0 = 0 % 40.67/7.28 | | | | | | | % 40.67/7.28 | | | | | | | REDUCE: (88), (97) imply: % 40.67/7.28 | | | | | | | (98) $false % 40.67/7.29 | | | | | | | % 40.67/7.29 | | | | | | | CLOSE: (98) is inconsistent. % 40.67/7.29 | | | | | | | % 40.67/7.29 | | | | | | Case 2: % 40.67/7.29 | | | | | | | % 40.67/7.29 | | | | | | | (99) all_57_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 40.67/7.29 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_38_2, % 40.67/7.29 | | | | | | | all_38_3) = 0) | (v2 = 0 & % 40.67/7.29 | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | ( ~ % 40.67/7.29 | | | | | | | (v1 = 0) & distinct_lines(all_38_4, all_38_3) = v1) | % 40.67/7.29 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_1, all_38_2) = % 40.67/7.29 | | | | | | | v0)) % 40.67/7.29 | | | | | | | % 40.67/7.29 | | | | | | | BETA: splitting (94) gives: % 40.67/7.29 | | | | | | | % 40.67/7.29 | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | % 40.67/7.29 | | | | | | | | (100) distinct_lines(all_38_5, all_38_4) = 0 % 40.67/7.29 | | | | | | | | % 40.67/7.29 | | | | | | | | BETA: splitting (93) gives: % 40.67/7.29 | | | | | | | | % 40.67/7.29 | | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | | % 40.67/7.29 | | | | | | | | | (101) distinct_points(all_38_1, all_38_2) = 0 % 40.67/7.29 | | | | | | | | | % 40.67/7.29 | | | | | | | | | BETA: splitting (95) gives: % 40.67/7.29 | | | | | | | | | % 40.67/7.29 | | | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | (102) all_53_0 = 0 % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | REDUCE: (91), (102) imply: % 40.67/7.29 | | | | | | | | | | (103) $false % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | CLOSE: (103) is inconsistent. % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | Case 2: % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | (104) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 40.67/7.29 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 40.67/7.29 | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | % 40.67/7.29 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_1, % 40.67/7.29 | | | | | | | | | | all_38_3) = 0) | ( ~ (v1 = 0) & % 40.67/7.29 | | | | | | | | | | distinct_lines(all_38_4, all_38_3) = v1) | ( ~ % 40.67/7.29 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_1, all_38_2) % 40.67/7.29 | | | | | | | | | | = v0)) % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | BETA: splitting (92) gives: % 40.67/7.29 | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | (105) all_66_0 = 0 % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | REDUCE: (88), (105) imply: % 40.67/7.29 | | | | | | | | | | | (106) $false % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | CLOSE: (106) is inconsistent. % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | Case 2: % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | (107) all_58_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 40.67/7.29 | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 40.67/7.29 | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) % 40.67/7.29 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_2, % 40.67/7.29 | | | | | | | | | | | all_38_5) = 0) | ( ~ (v1 = 0) & % 40.67/7.29 | | | | | | | | | | | distinct_lines(all_38_5, all_38_4) = v1) | ( ~ % 40.67/7.29 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_2, all_38_2) % 40.67/7.29 | | | | | | | | | | | = v0)) % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | BETA: splitting (99) gives: % 40.67/7.29 | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | (108) all_57_0 = 0 % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | REDUCE: (89), (108) imply: % 40.67/7.29 | | | | | | | | | | | | (109) $false % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | CLOSE: (109) is inconsistent. % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | Case 2: % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | (110) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 40.67/7.29 | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 40.67/7.29 | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_3) = 0) % 40.67/7.29 | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_1, % 40.67/7.29 | | | | | | | | | | | | all_38_4) = 0) | ( ~ (v1 = 0) & % 40.67/7.29 | | | | | | | | | | | | distinct_lines(all_38_4, all_38_3) = v1) | ( ~ % 40.67/7.29 | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_1, all_38_2) % 40.67/7.29 | | | | | | | | | | | | = v0)) % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | DELTA: instantiating (110) with fresh symbols all_572_0, % 40.67/7.29 | | | | | | | | | | | | all_572_1, all_572_2, all_572_3 gives: % 40.67/7.29 | | | | | | | | | | | | (111) (all_572_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.29 | | | | | | | | | | | | all_38_3) = 0) | (all_572_1 = 0 & % 40.67/7.29 | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | % 40.67/7.29 | | | | | | | | | | | | ( ~ (all_572_2 = 0) & distinct_lines(all_38_4, % 40.67/7.29 | | | | | | | | | | | | all_38_3) = all_572_2) | ( ~ (all_572_3 = 0) & % 40.67/7.29 | | | | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_572_3) % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | BETA: splitting (104) gives: % 40.67/7.29 | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | Case 1: % 40.67/7.29 | | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | | (112) all_45_0 = 0 % 40.67/7.29 | | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | | REDUCE: (41), (112) imply: % 40.67/7.29 | | | | | | | | | | | | | (113) $false % 40.67/7.29 | | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 40.67/7.29 | | | | | | | | | | | | | % 40.67/7.29 | | | | | | | | | | | | Case 2: % 40.67/7.29 | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | (114) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 40.67/7.30 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 40.67/7.30 | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) % 40.67/7.30 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_1, % 40.67/7.30 | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (v1 = 0) & % 40.67/7.30 | | | | | | | | | | | | | distinct_lines(all_38_4, all_38_3) = v1) | ( ~ % 40.67/7.30 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_1, all_38_2) % 40.67/7.30 | | | | | | | | | | | | | = v0)) % 40.67/7.30 | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_632_0, % 40.67/7.30 | | | | | | | | | | | | | all_632_1, all_632_2, all_632_3 gives: % 40.67/7.30 | | | | | | | | | | | | | (115) (all_632_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.30 | | | | | | | | | | | | | all_38_4) = 0) | (all_632_1 = 0 & % 40.67/7.30 | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = 0) | % 40.67/7.30 | | | | | | | | | | | | | ( ~ (all_632_2 = 0) & distinct_lines(all_38_4, % 40.67/7.30 | | | | | | | | | | | | | all_38_3) = all_632_2) | ( ~ (all_632_3 = 0) & % 40.67/7.30 | | | | | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_632_3) % 40.67/7.30 | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | BETA: splitting (111) gives: % 40.67/7.30 | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | Case 1: % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | (116) (all_572_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.30 | | | | | | | | | | | | | | all_38_3) = 0) | (all_572_1 = 0 & % 40.67/7.30 | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | BETA: splitting (116) gives: % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | Case 1: % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | (117) all_572_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.30 | | | | | | | | | | | | | | | all_38_3) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | ALPHA: (117) implies: % 40.67/7.30 | | | | | | | | | | | | | | | (118) apart_point_and_line(all_38_2, all_38_3) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_45_0, 0, all_38_3, % 40.67/7.30 | | | | | | | | | | | | | | | all_38_2, simplifying with (42), (118) gives: % 40.67/7.30 | | | | | | | | | | | | | | | (119) all_45_0 = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | REDUCE: (41), (119) imply: % 40.67/7.30 | | | | | | | | | | | | | | | (120) $false % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | CLOSE: (120) is inconsistent. % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | Case 2: % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | (121) all_572_1 = 0 & apart_point_and_line(all_38_1, % 40.67/7.30 | | | | | | | | | | | | | | | all_38_4) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | ALPHA: (121) implies: % 40.67/7.30 | | | | | | | | | | | | | | | (122) apart_point_and_line(all_38_1, all_38_4) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_53_0, 0, all_38_4, % 40.67/7.30 | | | | | | | | | | | | | | | all_38_1, simplifying with (83), (122) gives: % 40.67/7.30 | | | | | | | | | | | | | | | (123) all_53_0 = 0 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | REDUCE: (91), (123) imply: % 40.67/7.30 | | | | | | | | | | | | | | | (124) $false % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | End of split % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | Case 2: % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | (125) ( ~ (all_572_2 = 0) & distinct_lines(all_38_4, % 40.67/7.30 | | | | | | | | | | | | | | all_38_3) = all_572_2) | ( ~ (all_572_3 = 0) & % 40.67/7.30 | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_572_3) % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | BETA: splitting (125) gives: % 40.67/7.30 | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | Case 1: % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | (126) ~ (all_572_2 = 0) & distinct_lines(all_38_4, % 40.67/7.30 | | | | | | | | | | | | | | | all_38_3) = all_572_2 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | ALPHA: (126) implies: % 40.67/7.30 | | | | | | | | | | | | | | | (127) distinct_lines(all_38_4, all_38_3) = all_572_2 % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 40.67/7.30 | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | Case 1: % 40.67/7.30 | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | (128) (all_632_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.30 | | | | | | | | | | | | | | | | all_38_4) = 0) | (all_632_1 = 0 & % 40.67/7.30 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = 0) % 40.67/7.30 | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 40.67/7.30 | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | Case 1: % 40.67/7.30 | | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | | (129) all_632_0 = 0 & apart_point_and_line(all_38_2, % 40.67/7.30 | | | | | | | | | | | | | | | | | all_38_4) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | | ALPHA: (129) implies: % 40.67/7.30 | | | | | | | | | | | | | | | | | (130) apart_point_and_line(all_38_2, all_38_4) = 0 % 40.67/7.30 | | | | | | | | | | | | | | | | | % 40.67/7.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (80), (88), (130) are inconsistent by % 41.29/7.30 | | | | | | | | | | | | | | | | | sub-proof #1. % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | Case 2: % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | | (131) all_632_1 = 0 & apart_point_and_line(all_38_1, % 41.29/7.30 | | | | | | | | | | | | | | | | | all_38_3) = 0 % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | | ALPHA: (131) implies: % 41.29/7.30 | | | | | | | | | | | | | | | | | (132) apart_point_and_line(all_38_1, all_38_3) = 0 % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_57_0, 0, all_38_3, % 41.29/7.30 | | | | | | | | | | | | | | | | | all_38_1, simplifying with (68), (132) gives: % 41.29/7.30 | | | | | | | | | | | | | | | | | (133) all_57_0 = 0 % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | | REDUCE: (89), (133) imply: % 41.29/7.30 | | | | | | | | | | | | | | | | | (134) $false % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 41.29/7.30 | | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | | End of split % 41.29/7.30 | | | | | | | | | | | | | | | | % 41.29/7.30 | | | | | | | | | | | | | | | Case 2: % 41.29/7.30 | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | (135) ( ~ (all_632_2 = 0) & distinct_lines(all_38_4, % 41.29/7.31 | | | | | | | | | | | | | | | | all_38_3) = all_632_2) | ( ~ (all_632_3 = 0) & % 41.29/7.31 | | | | | | | | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_632_3) % 41.29/7.31 | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | (136) ~ (all_632_2 = 0) & distinct_lines(all_38_4, % 41.29/7.31 | | | | | | | | | | | | | | | | | all_38_3) = all_632_2 % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | ALPHA: (136) implies: % 41.29/7.31 | | | | | | | | | | | | | | | | | (137) ~ (all_632_2 = 0) % 41.29/7.31 | | | | | | | | | | | | | | | | | (138) distinct_lines(all_38_4, all_38_3) = all_632_2 % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | (139) all_58_0 = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | REDUCE: (90), (139) imply: % 41.29/7.31 | | | | | | | | | | | | | | | | | | (140) $false % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | (141) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 41.29/7.31 | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 41.29/7.31 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | all_38_5) = 0) | ( ~ (v1 = 0) & % 41.29/7.31 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_5, all_38_4) = v1) | ( ~ % 41.29/7.31 | | | | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_2, all_38_2) % 41.29/7.31 | | | | | | | | | | | | | | | | | | = v0)) % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | DELTA: instantiating (141) with fresh symbols all_754_0, % 41.29/7.31 | | | | | | | | | | | | | | | | | | all_754_1, all_754_2, all_754_3 gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | (142) (all_754_0 = 0 & apart_point_and_line(all_38_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | all_38_4) = 0) | (all_754_1 = 0 & % 41.29/7.31 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | % 41.29/7.31 | | | | | | | | | | | | | | | | | | ( ~ (all_754_2 = 0) & distinct_lines(all_38_5, % 41.29/7.31 | | | | | | | | | | | | | | | | | | all_38_4) = all_754_2) | ( ~ (all_754_3 = 0) & % 41.29/7.31 | | | | | | | | | | | | | | | | | | distinct_points(all_38_2, all_38_2) = all_754_3) % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | (143) (all_754_0 = 0 & apart_point_and_line(all_38_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | all_38_4) = 0) | (all_754_1 = 0 & % 41.29/7.31 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (144) all_754_0 = 0 & apart_point_and_line(all_38_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_4) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (145) apart_point_and_line(all_38_2, all_38_4) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (80), (88), (145) are inconsistent by % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (146) all_754_1 = 0 & apart_point_and_line(all_38_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_5) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (147) apart_point_and_line(all_38_2, all_38_5) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_58_0, 0, all_38_5, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (73), (147) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (148) all_58_0 = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (148) imply: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (149) $false % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | End of split % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | (150) ( ~ (all_754_2 = 0) & distinct_lines(all_38_5, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | all_38_4) = all_754_2) | ( ~ (all_754_3 = 0) & % 41.29/7.31 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_2, all_38_2) = all_754_3) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (151) ~ (all_754_2 = 0) & distinct_lines(all_38_5, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_4) = all_754_2 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (152) ~ (all_754_2 = 0) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (153) distinct_lines(all_38_5, all_38_4) = all_754_2 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_754_2, all_38_4, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_5, simplifying with (100), (153) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (154) all_754_2 = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (154) imply: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (155) $false % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_572_2, all_632_2, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_4, simplifying with (127), (138) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (156) all_632_2 = all_572_2 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (156) imply: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (157) ~ (all_572_2 = 0) % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_38_3, all_38_4, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_3, all_572_2, simplifying with (20), (21), % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (25), (127) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | (158) all_572_2 = 0 | convergent_lines(all_38_3, % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | all_38_3) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | (159) convergent_lines(all_38_3, all_38_3) = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_3, simplifying % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | with (21), (159) gives: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | (160) $false % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | (161) all_572_2 = 0 % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (161) imply: % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | (162) $false % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | End of split % 41.29/7.31 | | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | | End of split % 41.29/7.31 | | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | | End of split % 41.29/7.31 | | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | | End of split % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.31 | | | | | | | | | | | | | | | | Case 2: % 41.29/7.31 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | | (163) ~ (all_632_3 = 0) & distinct_points(all_38_1, % 41.29/7.32 | | | | | | | | | | | | | | | | | all_38_2) = all_632_3 % 41.29/7.32 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 41.29/7.32 | | | | | | | | | | | | | | | | | (164) ~ (all_632_3 = 0) % 41.29/7.32 | | | | | | | | | | | | | | | | | (165) distinct_points(all_38_1, all_38_2) = all_632_3 % 41.29/7.32 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_632_3, all_38_2, % 41.29/7.32 | | | | | | | | | | | | | | | | | all_38_1, simplifying with (101), (165) gives: % 41.29/7.32 | | | | | | | | | | | | | | | | | (166) all_632_3 = 0 % 41.29/7.32 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | | REDUCE: (164), (166) imply: % 41.29/7.32 | | | | | | | | | | | | | | | | | (167) $false % 41.29/7.32 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 41.29/7.32 | | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | Case 2: % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | (168) ~ (all_572_3 = 0) & distinct_points(all_38_1, % 41.29/7.32 | | | | | | | | | | | | | | | all_38_2) = all_572_3 % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | ALPHA: (168) implies: % 41.29/7.32 | | | | | | | | | | | | | | | (169) ~ (all_572_3 = 0) % 41.29/7.32 | | | | | | | | | | | | | | | (170) distinct_points(all_38_1, all_38_2) = all_572_3 % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_572_3, all_38_2, % 41.29/7.32 | | | | | | | | | | | | | | | all_38_1, simplifying with (101), (170) gives: % 41.29/7.32 | | | | | | | | | | | | | | | (171) all_572_3 = 0 % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | REDUCE: (169), (171) imply: % 41.29/7.32 | | | | | | | | | | | | | | | (172) $false % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 41.29/7.32 | | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | | % 41.29/7.32 | | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | | % 41.29/7.32 | | | | | | | | | End of split % 41.29/7.32 | | | | | | | | | % 41.29/7.32 | | | | | | | | Case 2: % 41.29/7.32 | | | | | | | | | % 41.29/7.32 | | | | | | | | | (173) all_58_0 = 0 % 41.29/7.32 | | | | | | | | | % 41.29/7.32 | | | | | | | | | REDUCE: (90), (173) imply: % 41.29/7.32 | | | | | | | | | (174) $false % 41.29/7.32 | | | | | | | | | % 41.29/7.32 | | | | | | | | | CLOSE: (174) is inconsistent. % 41.29/7.32 | | | | | | | | | % 41.29/7.32 | | | | | | | | End of split % 41.29/7.32 | | | | | | | | % 41.29/7.32 | | | | | | | Case 2: % 41.29/7.32 | | | | | | | | % 41.29/7.32 | | | | | | | | (175) all_53_0 = 0 % 41.29/7.32 | | | | | | | | % 41.29/7.32 | | | | | | | | REDUCE: (91), (175) imply: % 41.29/7.32 | | | | | | | | (176) $false % 41.29/7.32 | | | | | | | | % 41.29/7.32 | | | | | | | | CLOSE: (176) is inconsistent. % 41.29/7.32 | | | | | | | | % 41.29/7.32 | | | | | | | End of split % 41.29/7.32 | | | | | | | % 41.29/7.32 | | | | | | End of split % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | Case 2: % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | | (177) ~ (all_58_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 41.29/7.32 | | | | | | all_58_1 % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | | ALPHA: (177) implies: % 41.29/7.32 | | | | | | (178) ~ (all_58_1 = 0) % 41.29/7.32 | | | | | | (179) convergent_lines(all_38_5, all_38_4) = all_58_1 % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | | GROUND_INST: instantiating (14) with 0, all_58_1, all_38_4, % 41.29/7.32 | | | | | | all_38_5, simplifying with (24), (179) gives: % 41.29/7.32 | | | | | | (180) all_58_1 = 0 % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | | REDUCE: (178), (180) imply: % 41.29/7.32 | | | | | | (181) $false % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | | CLOSE: (181) is inconsistent. % 41.29/7.32 | | | | | | % 41.29/7.32 | | | | | End of split % 41.29/7.32 | | | | | % 41.29/7.32 | | | | Case 2: % 41.29/7.32 | | | | | % 41.29/7.32 | | | | | (182) ~ (all_68_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 41.29/7.32 | | | | | all_68_1 % 41.29/7.32 | | | | | % 41.29/7.32 | | | | | ALPHA: (182) implies: % 41.29/7.32 | | | | | (183) ~ (all_68_1 = 0) % 41.29/7.32 | | | | | (184) convergent_lines(all_38_5, all_38_4) = all_68_1 % 41.29/7.32 | | | | | % 41.29/7.32 | | | | | GROUND_INST: instantiating (14) with 0, all_68_1, all_38_4, all_38_5, % 41.29/7.32 | | | | | simplifying with (24), (184) gives: % 41.29/7.32 | | | | | (185) all_68_1 = 0 % 41.29/7.32 | | | | | % 41.29/7.32 | | | | | REDUCE: (183), (185) imply: % 41.29/7.32 | | | | | (186) $false % 41.29/7.32 | | | | | % 41.29/7.32 | | | | | CLOSE: (186) is inconsistent. % 41.29/7.32 | | | | | % 41.29/7.32 | | | | End of split % 41.29/7.32 | | | | % 41.29/7.32 | | | Case 2: % 41.29/7.32 | | | | % 41.29/7.32 | | | | (187) ~ (all_57_1 = 0) & convergent_lines(all_38_3, all_38_4) = % 41.29/7.32 | | | | all_57_1 % 41.29/7.32 | | | | % 41.29/7.32 | | | | ALPHA: (187) implies: % 41.29/7.32 | | | | (188) ~ (all_57_1 = 0) % 41.29/7.32 | | | | (189) convergent_lines(all_38_3, all_38_4) = all_57_1 % 41.29/7.32 | | | | % 41.29/7.32 | | | | GROUND_INST: instantiating (14) with 0, all_57_1, all_38_4, all_38_3, % 41.29/7.32 | | | | simplifying with (25), (189) gives: % 41.29/7.32 | | | | (190) all_57_1 = 0 % 41.29/7.32 | | | | % 41.29/7.32 | | | | REDUCE: (188), (190) imply: % 41.29/7.32 | | | | (191) $false % 41.29/7.32 | | | | % 41.29/7.32 | | | | CLOSE: (191) is inconsistent. % 41.29/7.32 | | | | % 41.29/7.32 | | | End of split % 41.29/7.32 | | | % 41.29/7.32 | | Case 2: % 41.29/7.32 | | | % 41.29/7.32 | | | (192) all_38_0 = 0 % 41.29/7.32 | | | % 41.29/7.32 | | | REDUCE: (18), (192) imply: % 41.29/7.32 | | | (193) $false % 41.29/7.32 | | | % 41.29/7.32 | | | CLOSE: (193) is inconsistent. % 41.29/7.32 | | | % 41.29/7.32 | | End of split % 41.29/7.32 | | % 41.29/7.32 | Case 2: % 41.29/7.32 | | % 41.29/7.32 | | (194) ~ (all_59_1 = 0) & convergent_lines(all_38_3, all_38_4) = all_59_1 % 41.29/7.32 | | % 41.29/7.32 | | ALPHA: (194) implies: % 41.29/7.32 | | (195) ~ (all_59_1 = 0) % 41.29/7.32 | | (196) convergent_lines(all_38_3, all_38_4) = all_59_1 % 41.29/7.32 | | % 41.29/7.32 | | GROUND_INST: instantiating (14) with 0, all_59_1, all_38_4, all_38_3, % 41.29/7.32 | | simplifying with (25), (196) gives: % 41.29/7.32 | | (197) all_59_1 = 0 % 41.29/7.32 | | % 41.29/7.32 | | REDUCE: (195), (197) imply: % 41.29/7.32 | | (198) $false % 41.29/7.32 | | % 41.29/7.32 | | CLOSE: (198) is inconsistent. % 41.29/7.32 | | % 41.29/7.32 | End of split % 41.29/7.32 | % 41.29/7.32 End of proof % 41.29/7.32 % 41.29/7.32 Sub-proof #1 shows that the following formulas are inconsistent: % 41.29/7.32 ---------------------------------------------------------------- % 41.29/7.33 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 41.29/7.33 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 41.29/7.33 (apart_point_and_line(v3, v2) = v0)) % 41.29/7.33 (2) apart_point_and_line(all_38_2, all_38_4) = all_66_0 % 41.29/7.33 (3) apart_point_and_line(all_38_2, all_38_4) = 0 % 41.29/7.33 (4) ~ (all_66_0 = 0) % 41.29/7.33 % 41.29/7.33 Begin of proof % 41.29/7.33 | % 41.29/7.33 | GROUND_INST: instantiating (1) with all_66_0, 0, all_38_4, all_38_2, % 41.29/7.33 | simplifying with (2), (3) gives: % 41.29/7.33 | (5) all_66_0 = 0 % 41.29/7.33 | % 41.29/7.33 | REDUCE: (4), (5) imply: % 41.29/7.33 | (6) $false % 41.29/7.33 | % 41.29/7.33 | CLOSE: (6) is inconsistent. % 41.29/7.33 | % 41.29/7.33 End of proof % 41.29/7.33 % SZS output end Proof for theBenchmark % 41.29/7.33 % 41.29/7.33 6722ms %------------------------------------------------------------------------------