%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO180+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 : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:21:55 EDT 2023 % Result : Theorem 17.43s 3.08s % Output : Proof 27.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO180+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n024.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Tue Aug 29 22:47:23 EDT 2023 % 0.11/0.31 % CPUTime : % 0.16/0.57 ________ _____ % 0.16/0.57 ___ __ \_________(_)________________________________ % 0.16/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.57 % 0.16/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.57 (2023-06-19) % 0.16/0.57 % 0.16/0.57 (c) Philipp Rümmer, 2009-2023 % 0.16/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.57 Amanda Stjerna. % 0.16/0.57 Free software under BSD-3-Clause. % 0.16/0.57 % 0.16/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.57 % 0.16/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.58 Running up to 7 provers in parallel. % 0.16/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.53/1.13 Prover 4: Preprocessing ... % 3.54/1.13 Prover 1: Preprocessing ... % 3.54/1.17 Prover 5: Preprocessing ... % 3.54/1.17 Prover 3: Preprocessing ... % 3.54/1.17 Prover 0: Preprocessing ... % 3.54/1.17 Prover 2: Preprocessing ... % 3.54/1.19 Prover 6: Preprocessing ... % 7.84/1.77 Prover 2: Proving ... % 7.84/1.77 Prover 5: Proving ... % 8.29/1.82 Prover 6: Constructing countermodel ... % 8.73/1.86 Prover 3: Constructing countermodel ... % 8.73/1.86 Prover 1: Constructing countermodel ... % 9.91/2.11 Prover 3: gave up % 9.91/2.12 Prover 6: gave up % 9.91/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.91/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.02/2.23 Prover 8: Preprocessing ... % 11.02/2.24 Prover 7: Preprocessing ... % 11.47/2.32 Prover 4: Constructing countermodel ... % 11.47/2.32 Prover 7: Warning: ignoring some quantifiers % 11.47/2.33 Prover 1: gave up % 11.47/2.33 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.47/2.36 Prover 7: Constructing countermodel ... % 12.26/2.38 Prover 9: Preprocessing ... % 12.52/2.40 Prover 0: Proving ... % 13.52/2.56 Prover 8: Warning: ignoring some quantifiers % 13.52/2.59 Prover 8: Constructing countermodel ... % 15.67/2.87 Prover 9: Constructing countermodel ... % 16.40/2.96 Prover 8: gave up % 16.40/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.91/3.01 Prover 10: Preprocessing ... % 16.91/3.06 Prover 7: gave up % 16.91/3.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.43/3.07 Prover 10: Warning: ignoring some quantifiers % 17.43/3.08 Prover 0: proved (2490ms) % 17.43/3.08 % 17.43/3.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.43/3.08 % 17.43/3.08 Prover 9: stopped % 17.43/3.08 Prover 2: stopped % 17.43/3.08 Prover 5: stopped % 17.43/3.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.43/3.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.43/3.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.43/3.12 Prover 10: Constructing countermodel ... % 17.43/3.14 Prover 11: Preprocessing ... % 17.43/3.14 Prover 16: Preprocessing ... % 17.43/3.16 Prover 13: Preprocessing ... % 18.11/3.17 Prover 19: Preprocessing ... % 18.37/3.21 Prover 16: Warning: ignoring some quantifiers % 18.62/3.23 Prover 16: Constructing countermodel ... % 18.62/3.24 Prover 13: Warning: ignoring some quantifiers % 18.62/3.26 Prover 13: Constructing countermodel ... % 18.62/3.28 Prover 10: gave up % 19.37/3.35 Prover 19: Warning: ignoring some quantifiers % 19.37/3.36 Prover 19: Constructing countermodel ... % 19.37/3.48 Prover 11: Constructing countermodel ... % 21.05/3.64 Prover 19: gave up % 21.85/3.67 Prover 13: gave up % 25.67/4.29 Prover 4: Found proof (size 282) % 25.67/4.29 Prover 4: proved (3704ms) % 25.67/4.30 Prover 11: stopped % 25.67/4.30 Prover 16: stopped % 25.67/4.30 % 25.67/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.67/4.30 % 25.67/4.34 % SZS output start Proof for theBenchmark % 25.67/4.35 Assumptions after simplification: % 25.67/4.35 --------------------------------- % 25.67/4.35 % 25.67/4.35 (ceq1) % 25.97/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 25.97/4.39 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 25.97/4.39 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 25.97/4.39 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 25.97/4.39 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 25.97/4.39 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 25.97/4.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 25.97/4.39 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 25.97/4.39 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 25.97/4.39 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 25.97/4.39 % 25.97/4.39 (ceq2) % 25.97/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 25.97/4.39 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 25.97/4.39 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 25.97/4.39 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 25.97/4.39 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 25.97/4.39 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 25.97/4.39 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 25.97/4.39 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 25.97/4.39 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 25.97/4.39 apart_point_and_line(v0, v2) = 0) % 25.97/4.39 % 25.97/4.40 (ci1) % 25.97/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 25.97/4.40 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.97/4.40 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 25.97/4.40 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.97/4.40 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.97/4.40 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 25.97/4.40 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 25.97/4.40 % 25.97/4.40 (ci2) % 25.97/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 25.97/4.40 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.97/4.40 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 25.97/4.40 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.97/4.40 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.97/4.40 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 25.97/4.40 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 25.97/4.40 % 25.97/4.40 (con) % 26.19/4.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 26.19/4.41 int] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) % 26.19/4.41 = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 % 26.19/4.41 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.19/4.41 % 26.19/4.41 (con1) % 26.19/4.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 26.19/4.41 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 26.19/4.41 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 26.19/4.41 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 26.19/4.41 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 26.19/4.41 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 26.19/4.41 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 26.19/4.41 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 26.19/4.41 0))) % 26.19/4.41 % 26.19/4.41 (cu1) % 26.19/4.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 26.19/4.42 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 26.19/4.42 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.19/4.42 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.19/4.42 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 26.19/4.42 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.19/4.42 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.19/4.42 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 26.19/4.42 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 26.19/4.43 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 26.19/4.43 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 26.19/4.43 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 26.19/4.43 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.19/4.43 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.19/4.43 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.19/4.43 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 26.19/4.43 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.19/4.43 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.19/4.43 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 26.19/4.43 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 26.19/4.43 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 26.19/4.43 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.19/4.43 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 26.19/4.43 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 26.19/4.43 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 26.19/4.43 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 26.19/4.43 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 26.19/4.43 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 26.19/4.43 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.19/4.43 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.19/4.43 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 26.19/4.43 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 26.19/4.43 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 26.19/4.43 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 26.19/4.43 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 26.19/4.43 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.19/4.43 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 26.19/4.43 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 26.19/4.43 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.19/4.43 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 26.19/4.43 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 26.19/4.43 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 26.19/4.43 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 26.19/4.43 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 26.19/4.43 % 26.19/4.43 (function-axioms) % 26.19/4.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.19/4.44 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 26.19/4.44 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.19/4.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.19/4.44 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 26.19/4.44 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.19/4.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 26.19/4.44 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.19/4.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.19/4.44 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 26.19/4.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.19/4.44 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 26.19/4.44 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.19/4.44 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 26.19/4.44 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 26.19/4.44 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 26.19/4.44 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.19/4.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 26.19/4.44 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.19/4.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 26.19/4.44 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.19/4.44 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 26.19/4.44 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.19/4.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.19/4.44 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 26.19/4.44 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.19/4.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 26.19/4.44 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.19/4.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.19/4.44 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 26.19/4.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.19/4.44 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 26.19/4.44 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.19/4.44 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 26.19/4.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.19/4.44 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 26.19/4.44 % 26.19/4.44 Further assumptions not needed in the proof: % 26.19/4.44 -------------------------------------------- % 26.19/4.44 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq3, ci3, % 26.19/4.44 ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, % 26.19/4.44 orth1, ouo1, p1, par1 % 26.19/4.44 % 26.19/4.44 Those formulas are unsatisfiable: % 26.19/4.44 --------------------------------- % 26.19/4.44 % 26.19/4.44 Begin of proof % 26.19/4.44 | % 26.19/4.44 | ALPHA: (ci1) implies: % 26.19/4.44 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.19/4.44 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.19/4.44 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 26.19/4.44 | $i(v2))) % 26.40/4.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.40/4.45 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.40/4.45 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.40/4.45 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.40/4.45 | % 26.40/4.45 | ALPHA: (ci2) implies: % 26.40/4.45 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.40/4.45 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 26.40/4.45 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 26.40/4.45 | $i(v2))) % 26.40/4.45 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.40/4.45 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.40/4.45 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 26.40/4.45 | ~ (v4 = 0) | ~ (v3 = 0)))) % 26.40/4.45 | % 26.40/4.45 | ALPHA: (cu1) implies: % 26.40/4.45 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.40/4.45 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 26.40/4.45 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 26.40/4.45 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.40/4.45 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 26.40/4.45 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 26.40/4.45 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.40/4.46 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.40/4.46 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 26.40/4.46 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.40/4.46 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.40/4.46 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 26.40/4.46 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 26.40/4.46 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.40/4.46 | | v8 = 0))) % 26.40/4.46 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.40/4.46 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.40/4.46 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.40/4.46 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 26.40/4.46 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 26.40/4.46 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 26.40/4.46 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 26.40/4.46 | | v8 = 0))) % 26.40/4.46 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.40/4.46 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 26.40/4.46 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 26.40/4.46 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.40/4.46 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 26.40/4.46 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 26.40/4.46 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 26.40/4.46 | % 26.40/4.46 | ALPHA: (ceq1) implies: % 26.40/4.46 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.40/4.46 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = % 26.40/4.47 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, % 26.40/4.47 | v1) = 0) % 26.40/4.47 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 26.40/4.47 | : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 26.40/4.47 | (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.40/4.47 | ? [v5: int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 26.40/4.47 | % 26.40/4.47 | ALPHA: (ceq2) implies: % 26.40/4.47 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.40/4.47 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 26.40/4.47 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.40/4.47 | distinct_lines(v1, v2) = 0) % 26.40/4.47 | % 26.40/4.47 | ALPHA: (con1) implies: % 26.40/4.47 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 26.40/4.47 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 26.40/4.47 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 26.40/4.47 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 26.40/4.47 | | v5 = 0))) % 26.40/4.47 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 26.40/4.47 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 26.40/4.47 | [v5: any] : ? [v6: any] : (point(v1) = v4 & point(v0) = v3 & % 26.40/4.47 | line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ % 26.40/4.47 | (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 26.40/4.47 | % 26.40/4.47 | ALPHA: (function-axioms) implies: % 26.40/4.47 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.40/4.47 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 26.40/4.47 | (distinct_points(v3, v2) = v0)) % 26.40/4.48 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.40/4.48 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 26.40/4.48 | (distinct_lines(v3, v2) = v0)) % 26.40/4.48 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.40/4.48 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 26.40/4.48 | (apart_point_and_line(v3, v2) = v0)) % 26.40/4.48 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.40/4.48 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 26.40/4.48 | % 26.40/4.48 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 26.40/4.48 | all_38_3, all_38_4, all_38_5 gives: % 26.40/4.48 | (18) ~ (all_38_0 = 0) & line_connecting(all_38_3, all_38_4) = all_38_1 & % 26.40/4.48 | line_connecting(all_38_5, all_38_4) = all_38_2 & % 26.40/4.48 | apart_point_and_line(all_38_3, all_38_2) = 0 & % 26.40/4.48 | apart_point_and_line(all_38_5, all_38_1) = all_38_0 & % 26.40/4.48 | distinct_points(all_38_5, all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) % 26.40/4.48 | & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) % 26.40/4.48 | % 26.40/4.48 | ALPHA: (18) implies: % 26.40/4.48 | (19) ~ (all_38_0 = 0) % 26.40/4.48 | (20) $i(all_38_5) % 26.40/4.48 | (21) $i(all_38_4) % 26.40/4.48 | (22) $i(all_38_3) % 26.40/4.48 | (23) $i(all_38_1) % 26.40/4.48 | (24) distinct_points(all_38_5, all_38_4) = 0 % 26.40/4.48 | (25) apart_point_and_line(all_38_5, all_38_1) = all_38_0 % 26.40/4.48 | (26) apart_point_and_line(all_38_3, all_38_2) = 0 % 26.40/4.49 | (27) line_connecting(all_38_5, all_38_4) = all_38_2 % 26.40/4.49 | (28) line_connecting(all_38_3, all_38_4) = all_38_1 % 26.40/4.49 | % 26.40/4.49 | GROUND_INST: instantiating (12) with all_38_5, all_38_4, simplifying with % 26.40/4.49 | (20), (21), (24) gives: % 26.40/4.49 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 26.40/4.49 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(v2) = v3 & % 26.40/4.49 | line_connecting(all_38_5, all_38_4) = v2 & $i(v2) & ( ~ (v1 = 0) | % 26.40/4.49 | ~ (v0 = 0) | v3 = 0)) % 26.40/4.49 | % 26.40/4.49 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (20), % 26.40/4.49 | (21), (24) gives: % 26.40/4.49 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 26.40/4.49 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 26.40/4.49 | % 26.40/4.49 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (20), % 26.40/4.49 | (21), (24) gives: % 26.40/4.49 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5, % 26.40/4.49 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0)) % 26.40/4.49 | % 26.40/4.49 | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_1, all_38_1, % 26.40/4.49 | all_38_0, all_38_0, simplifying with (20), (21), (23), (24), (25) % 26.40/4.49 | gives: % 26.40/4.49 | (32) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.40/4.49 | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.40/4.49 | apart_point_and_line(all_38_4, all_38_1) = v1 & % 26.40/4.49 | distinct_lines(all_38_1, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 26.40/4.49 | = 0)) % 26.40/4.49 | % 26.40/4.50 | GROUND_INST: instantiating (7) with all_38_5, all_38_5, all_38_1, all_38_1, % 26.40/4.50 | all_38_0, all_38_0, simplifying with (20), (23), (25) gives: % 26.40/4.50 | (33) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 26.40/4.50 | any] : (apart_point_and_line(all_38_5, all_38_1) = v3 & % 26.40/4.50 | apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.40/4.50 | distinct_lines(all_38_1, all_38_1) = v1 & distinct_points(all_38_5, % 26.40/4.50 | all_38_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.40/4.50 | % 26.40/4.50 | GROUND_INST: instantiating (13) with all_38_5, all_38_4, all_38_2, simplifying % 26.40/4.50 | with (20), (21), (27) gives: % 26.40/4.50 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.40/4.50 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_2) = v3 & % 26.40/4.50 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 26.40/4.50 | 0) | ~ (v0 = 0) | v3 = 0)) % 26.40/4.50 | % 26.40/4.50 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 26.40/4.50 | with (20), (21), (27) gives: % 26.40/4.50 | (35) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 26.40/4.50 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.40/4.50 | (v1 = 0) | ~ (v0 = 0))) % 26.40/4.50 | % 26.40/4.50 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 26.40/4.50 | with (20), (21), (27) gives: % 26.40/4.50 | (36) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5, % 26.40/4.50 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.40/4.50 | (v1 = 0) | ~ (v0 = 0))) % 26.40/4.50 | % 26.40/4.50 | GROUND_INST: instantiating (13) with all_38_3, all_38_4, all_38_1, simplifying % 26.40/4.50 | with (21), (22), (28) gives: % 26.40/4.50 | (37) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.40/4.50 | (point(all_38_3) = v0 & point(all_38_4) = v1 & line(all_38_1) = v3 & % 26.40/4.50 | distinct_points(all_38_3, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 26.40/4.50 | 0) | ~ (v0 = 0) | v3 = 0)) % 26.40/4.50 | % 26.40/4.50 | GROUND_INST: instantiating (4) with all_38_3, all_38_4, all_38_1, simplifying % 26.40/4.50 | with (21), (22), (28) gives: % 26.40/4.51 | (38) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 26.40/4.51 | all_38_1) = v1 & distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 26.40/4.51 | (v1 = 0) | ~ (v0 = 0))) % 26.40/4.51 | % 26.40/4.51 | GROUND_INST: instantiating (2) with all_38_3, all_38_4, all_38_1, simplifying % 26.40/4.51 | with (21), (22), (28) gives: % 26.40/4.51 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 26.40/4.51 | all_38_1) = v1 & distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 26.40/4.51 | (v1 = 0) | ~ (v0 = 0))) % 26.40/4.51 | % 26.40/4.51 | DELTA: instantiating (31) with fresh symbols all_49_0, all_49_1 gives: % 26.40/4.51 | (40) ~ (all_49_0 = 0) & line_connecting(all_38_5, all_38_4) = all_49_1 & % 26.40/4.51 | apart_point_and_line(all_38_5, all_49_1) = all_49_0 & $i(all_49_1) % 26.40/4.51 | % 26.40/4.51 | ALPHA: (40) implies: % 26.40/4.51 | (41) $i(all_49_1) % 26.40/4.51 | (42) apart_point_and_line(all_38_5, all_49_1) = all_49_0 % 26.40/4.51 | (43) line_connecting(all_38_5, all_38_4) = all_49_1 % 26.40/4.51 | % 26.40/4.51 | DELTA: instantiating (36) with fresh symbols all_51_0, all_51_1 gives: % 26.40/4.51 | (44) apart_point_and_line(all_38_5, all_38_2) = all_51_0 & % 26.40/4.51 | distinct_points(all_38_5, all_38_4) = all_51_1 & ( ~ (all_51_0 = 0) | % 26.40/4.51 | ~ (all_51_1 = 0)) % 26.40/4.51 | % 26.40/4.51 | ALPHA: (44) implies: % 26.40/4.51 | (45) distinct_points(all_38_5, all_38_4) = all_51_1 % 26.40/4.51 | (46) apart_point_and_line(all_38_5, all_38_2) = all_51_0 % 26.40/4.51 | (47) ~ (all_51_0 = 0) | ~ (all_51_1 = 0) % 26.40/4.51 | % 26.40/4.51 | DELTA: instantiating (35) with fresh symbols all_53_0, all_53_1 gives: % 26.40/4.51 | (48) apart_point_and_line(all_38_4, all_38_2) = all_53_0 & % 26.40/4.51 | distinct_points(all_38_5, all_38_4) = all_53_1 & ( ~ (all_53_0 = 0) | % 26.40/4.51 | ~ (all_53_1 = 0)) % 26.40/4.51 | % 26.40/4.51 | ALPHA: (48) implies: % 26.40/4.51 | (49) distinct_points(all_38_5, all_38_4) = all_53_1 % 26.40/4.51 | (50) apart_point_and_line(all_38_4, all_38_2) = all_53_0 % 26.40/4.51 | % 26.40/4.51 | DELTA: instantiating (39) with fresh symbols all_55_0, all_55_1 gives: % 26.40/4.51 | (51) apart_point_and_line(all_38_3, all_38_1) = all_55_0 & % 26.40/4.51 | distinct_points(all_38_3, all_38_4) = all_55_1 & ( ~ (all_55_0 = 0) | % 26.40/4.51 | ~ (all_55_1 = 0)) % 26.40/4.51 | % 26.40/4.51 | ALPHA: (51) implies: % 26.40/4.51 | (52) distinct_points(all_38_3, all_38_4) = all_55_1 % 26.40/4.51 | (53) apart_point_and_line(all_38_3, all_38_1) = all_55_0 % 26.40/4.51 | (54) ~ (all_55_0 = 0) | ~ (all_55_1 = 0) % 26.40/4.51 | % 26.40/4.51 | DELTA: instantiating (38) with fresh symbols all_57_0, all_57_1 gives: % 26.40/4.52 | (55) apart_point_and_line(all_38_4, all_38_1) = all_57_0 & % 26.40/4.52 | distinct_points(all_38_3, all_38_4) = all_57_1 & ( ~ (all_57_0 = 0) | % 26.40/4.52 | ~ (all_57_1 = 0)) % 26.40/4.52 | % 26.40/4.52 | ALPHA: (55) implies: % 26.40/4.52 | (56) distinct_points(all_38_3, all_38_4) = all_57_1 % 26.40/4.52 | (57) apart_point_and_line(all_38_4, all_38_1) = all_57_0 % 26.40/4.52 | (58) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) % 26.40/4.52 | % 26.40/4.52 | DELTA: instantiating (30) with fresh symbols all_59_0, all_59_1 gives: % 26.40/4.52 | (59) ~ (all_59_0 = 0) & line_connecting(all_38_5, all_38_4) = all_59_1 & % 26.40/4.52 | apart_point_and_line(all_38_4, all_59_1) = all_59_0 & $i(all_59_1) % 26.40/4.52 | % 26.40/4.52 | ALPHA: (59) implies: % 26.40/4.52 | (60) ~ (all_59_0 = 0) % 26.40/4.52 | (61) apart_point_and_line(all_38_4, all_59_1) = all_59_0 % 26.40/4.52 | (62) line_connecting(all_38_5, all_38_4) = all_59_1 % 26.40/4.52 | % 26.40/4.52 | DELTA: instantiating (34) with fresh symbols all_61_0, all_61_1, all_61_2, % 26.40/4.52 | all_61_3 gives: % 26.40/4.52 | (63) point(all_38_4) = all_61_2 & point(all_38_5) = all_61_3 & % 26.40/4.52 | line(all_38_2) = all_61_0 & distinct_points(all_38_5, all_38_4) = % 26.40/4.52 | all_61_1 & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | ~ (all_61_3 = 0) % 26.40/4.52 | | all_61_0 = 0) % 26.40/4.52 | % 26.40/4.52 | ALPHA: (63) implies: % 26.40/4.52 | (64) distinct_points(all_38_5, all_38_4) = all_61_1 % 26.40/4.52 | % 26.40/4.52 | DELTA: instantiating (37) with fresh symbols all_63_0, all_63_1, all_63_2, % 26.40/4.52 | all_63_3 gives: % 26.40/4.52 | (65) point(all_38_3) = all_63_3 & point(all_38_4) = all_63_2 & % 26.40/4.52 | line(all_38_1) = all_63_0 & distinct_points(all_38_3, all_38_4) = % 26.40/4.52 | all_63_1 & ( ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | ~ (all_63_3 = 0) % 26.40/4.52 | | all_63_0 = 0) % 26.40/4.52 | % 26.40/4.52 | ALPHA: (65) implies: % 26.40/4.52 | (66) distinct_points(all_38_3, all_38_4) = all_63_1 % 26.40/4.52 | % 26.40/4.52 | DELTA: instantiating (29) with fresh symbols all_65_0, all_65_1, all_65_2, % 26.40/4.52 | all_65_3 gives: % 26.40/4.52 | (67) point(all_38_4) = all_65_2 & point(all_38_5) = all_65_3 & % 26.40/4.52 | line(all_65_1) = all_65_0 & line_connecting(all_38_5, all_38_4) = % 26.40/4.52 | all_65_1 & $i(all_65_1) & ( ~ (all_65_2 = 0) | ~ (all_65_3 = 0) | % 26.40/4.52 | all_65_0 = 0) % 26.40/4.52 | % 26.40/4.52 | ALPHA: (67) implies: % 26.40/4.52 | (68) line_connecting(all_38_5, all_38_4) = all_65_1 % 26.40/4.52 | % 26.40/4.52 | BETA: splitting (32) gives: % 26.40/4.52 | % 26.40/4.52 | Case 1: % 26.40/4.52 | | % 26.40/4.52 | | (69) all_38_0 = 0 % 26.40/4.52 | | % 26.40/4.52 | | REDUCE: (19), (69) imply: % 26.40/4.52 | | (70) $false % 26.40/4.53 | | % 26.40/4.53 | | CLOSE: (70) is inconsistent. % 26.40/4.53 | | % 26.40/4.53 | Case 2: % 26.40/4.53 | | % 26.40/4.53 | | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.40/4.53 | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.40/4.53 | | apart_point_and_line(all_38_4, all_38_1) = v1 & % 26.40/4.53 | | distinct_lines(all_38_1, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 26.40/4.53 | | v1 = 0)) % 26.40/4.53 | | % 26.40/4.53 | | DELTA: instantiating (71) with fresh symbols all_75_0, all_75_1, all_75_2 % 26.40/4.53 | | gives: % 26.40/4.53 | | (72) apart_point_and_line(all_38_4, all_38_1) = all_75_0 & % 26.40/4.53 | | apart_point_and_line(all_38_4, all_38_1) = all_75_1 & % 26.40/4.53 | | distinct_lines(all_38_1, all_38_1) = all_75_2 & ( ~ (all_75_2 = 0) | % 26.40/4.53 | | all_75_0 = 0 | all_75_1 = 0) % 26.40/4.53 | | % 26.40/4.53 | | ALPHA: (72) implies: % 26.40/4.53 | | (73) apart_point_and_line(all_38_4, all_38_1) = all_75_1 % 26.40/4.53 | | (74) apart_point_and_line(all_38_4, all_38_1) = all_75_0 % 26.40/4.53 | | % 26.40/4.53 | | BETA: splitting (33) gives: % 26.40/4.53 | | % 26.40/4.53 | | Case 1: % 26.40/4.53 | | | % 26.40/4.53 | | | (75) all_38_0 = 0 % 26.40/4.53 | | | % 26.40/4.53 | | | REDUCE: (19), (75) imply: % 26.40/4.53 | | | (76) $false % 26.40/4.53 | | | % 26.40/4.53 | | | CLOSE: (76) is inconsistent. % 26.40/4.53 | | | % 26.40/4.53 | | Case 2: % 26.40/4.53 | | | % 26.40/4.53 | | | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.40/4.53 | | | (apart_point_and_line(all_38_5, all_38_1) = v3 & % 26.40/4.53 | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.40/4.53 | | | distinct_lines(all_38_1, all_38_1) = v1 & % 26.40/4.53 | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.40/4.53 | | | = 0) | v3 = 0 | v2 = 0)) % 26.40/4.53 | | | % 26.40/4.53 | | | DELTA: instantiating (77) with fresh symbols all_85_0, all_85_1, all_85_2, % 26.40/4.53 | | | all_85_3 gives: % 26.40/4.53 | | | (78) apart_point_and_line(all_38_5, all_38_1) = all_85_0 & % 26.40/4.53 | | | apart_point_and_line(all_38_5, all_38_1) = all_85_1 & % 26.40/4.53 | | | distinct_lines(all_38_1, all_38_1) = all_85_2 & % 26.40/4.53 | | | distinct_points(all_38_5, all_38_5) = all_85_3 & ( ~ (all_85_2 = % 26.40/4.53 | | | 0) | ~ (all_85_3 = 0) | all_85_0 = 0 | all_85_1 = 0) % 26.40/4.53 | | | % 26.40/4.53 | | | ALPHA: (78) implies: % 26.40/4.53 | | | (79) apart_point_and_line(all_38_5, all_38_1) = all_85_1 % 26.40/4.53 | | | (80) apart_point_and_line(all_38_5, all_38_1) = all_85_0 % 26.40/4.53 | | | % 26.40/4.53 | | | GROUND_INST: instantiating (14) with 0, all_53_1, all_38_4, all_38_5, % 26.40/4.53 | | | simplifying with (24), (49) gives: % 26.40/4.53 | | | (81) all_53_1 = 0 % 26.40/4.53 | | | % 26.40/4.53 | | | GROUND_INST: instantiating (14) with all_53_1, all_61_1, all_38_4, % 26.40/4.53 | | | all_38_5, simplifying with (49), (64) gives: % 26.40/4.53 | | | (82) all_61_1 = all_53_1 % 26.40/4.53 | | | % 26.40/4.53 | | | GROUND_INST: instantiating (14) with all_51_1, all_61_1, all_38_4, % 26.40/4.53 | | | all_38_5, simplifying with (45), (64) gives: % 26.40/4.53 | | | (83) all_61_1 = all_51_1 % 26.40/4.53 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (14) with all_57_1, all_63_1, all_38_4, % 26.40/4.54 | | | all_38_3, simplifying with (56), (66) gives: % 26.40/4.54 | | | (84) all_63_1 = all_57_1 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (14) with all_55_1, all_63_1, all_38_4, % 26.40/4.54 | | | all_38_3, simplifying with (52), (66) gives: % 26.40/4.54 | | | (85) all_63_1 = all_55_1 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (16) with all_38_0, all_85_0, all_38_1, % 26.40/4.54 | | | all_38_5, simplifying with (25), (80) gives: % 26.40/4.54 | | | (86) all_85_0 = all_38_0 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (16) with all_85_1, all_85_0, all_38_1, % 26.40/4.54 | | | all_38_5, simplifying with (79), (80) gives: % 26.40/4.54 | | | (87) all_85_0 = all_85_1 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (16) with all_75_1, all_75_0, all_38_1, % 26.40/4.54 | | | all_38_4, simplifying with (73), (74) gives: % 26.40/4.54 | | | (88) all_75_0 = all_75_1 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (16) with all_57_0, all_75_0, all_38_1, % 26.40/4.54 | | | all_38_4, simplifying with (57), (74) gives: % 26.40/4.54 | | | (89) all_75_0 = all_57_0 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (17) with all_49_1, all_59_1, all_38_4, % 26.40/4.54 | | | all_38_5, simplifying with (43), (62) gives: % 26.40/4.54 | | | (90) all_59_1 = all_49_1 % 26.40/4.54 | | | % 26.40/4.54 | | | GROUND_INST: instantiating (17) with all_38_2, all_65_1, all_38_4, % 26.40/4.54 | | | all_38_5, simplifying with (27), (68) gives: % 26.40/4.54 | | | (91) all_65_1 = all_38_2 % 26.40/4.54 | | | % 26.83/4.54 | | | GROUND_INST: instantiating (17) with all_59_1, all_65_1, all_38_4, % 26.83/4.54 | | | all_38_5, simplifying with (62), (68) gives: % 26.83/4.54 | | | (92) all_65_1 = all_59_1 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (86), (87) imply: % 26.83/4.54 | | | (93) all_85_1 = all_38_0 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (88), (89) imply: % 26.83/4.54 | | | (94) all_75_1 = all_57_0 % 26.83/4.54 | | | % 26.83/4.54 | | | SIMP: (94) implies: % 26.83/4.54 | | | (95) all_75_1 = all_57_0 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (91), (92) imply: % 26.83/4.54 | | | (96) all_59_1 = all_38_2 % 26.83/4.54 | | | % 26.83/4.54 | | | SIMP: (96) implies: % 26.83/4.54 | | | (97) all_59_1 = all_38_2 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (84), (85) imply: % 26.83/4.54 | | | (98) all_57_1 = all_55_1 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (82), (83) imply: % 26.83/4.54 | | | (99) all_53_1 = all_51_1 % 26.83/4.54 | | | % 26.83/4.54 | | | SIMP: (99) implies: % 26.83/4.54 | | | (100) all_53_1 = all_51_1 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (90), (97) imply: % 26.83/4.54 | | | (101) all_49_1 = all_38_2 % 26.83/4.54 | | | % 26.83/4.54 | | | SIMP: (101) implies: % 26.83/4.54 | | | (102) all_49_1 = all_38_2 % 26.83/4.54 | | | % 26.83/4.54 | | | COMBINE_EQS: (81), (100) imply: % 26.83/4.54 | | | (103) all_51_1 = 0 % 26.83/4.54 | | | % 26.83/4.54 | | | SIMP: (103) implies: % 26.83/4.54 | | | (104) all_51_1 = 0 % 26.83/4.54 | | | % 26.83/4.54 | | | REDUCE: (61), (97) imply: % 26.83/4.54 | | | (105) apart_point_and_line(all_38_4, all_38_2) = all_59_0 % 26.83/4.54 | | | % 26.83/4.54 | | | REDUCE: (42), (102) imply: % 26.83/4.54 | | | (106) apart_point_and_line(all_38_5, all_38_2) = all_49_0 % 26.83/4.54 | | | % 26.83/4.54 | | | REDUCE: (41), (102) imply: % 26.83/4.54 | | | (107) $i(all_38_2) % 26.83/4.54 | | | % 26.83/4.54 | | | BETA: splitting (47) gives: % 26.83/4.54 | | | % 26.83/4.54 | | | Case 1: % 26.83/4.54 | | | | % 26.83/4.54 | | | | (108) ~ (all_51_0 = 0) % 26.83/4.54 | | | | % 26.83/4.54 | | | | GROUND_INST: instantiating (16) with all_51_0, all_49_0, all_38_2, % 26.83/4.54 | | | | all_38_5, simplifying with (46), (106) gives: % 26.83/4.54 | | | | (109) all_51_0 = all_49_0 % 26.83/4.54 | | | | % 26.83/4.54 | | | | GROUND_INST: instantiating (16) with all_53_0, all_59_0, all_38_2, % 26.83/4.54 | | | | all_38_4, simplifying with (50), (105) gives: % 26.83/4.54 | | | | (110) all_59_0 = all_53_0 % 26.83/4.54 | | | | % 26.83/4.54 | | | | REDUCE: (60), (110) imply: % 26.83/4.54 | | | | (111) ~ (all_53_0 = 0) % 26.83/4.54 | | | | % 26.83/4.54 | | | | REDUCE: (108), (109) imply: % 26.83/4.54 | | | | (112) ~ (all_49_0 = 0) % 26.83/4.54 | | | | % 26.83/4.54 | | | | GROUND_INST: instantiating (9) with all_38_3, all_38_2, all_38_4, % 26.83/4.54 | | | | all_55_1, simplifying with (21), (22), (26), (52), (107) % 26.83/4.54 | | | | gives: % 26.83/4.54 | | | | (113) all_55_1 = 0 | apart_point_and_line(all_38_4, all_38_2) = 0 % 26.83/4.54 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_1, all_49_0, all_38_0, simplifying with (20), (21), % 26.83/4.55 | | | | (23), (24), (25), (106), (107) gives: % 26.83/4.55 | | | | (114) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.83/4.55 | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 26.83/4.55 | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = % 26.83/4.55 | | | | 0 | v1 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_5, all_38_2, % 26.83/4.55 | | | | all_38_1, all_49_0, all_38_0, simplifying with (20), (23), % 26.83/4.55 | | | | (25), (106), (107) gives: % 26.83/4.55 | | | | (115) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_5, % 26.83/4.55 | | | | all_38_1) = v2 & apart_point_and_line(all_38_5, all_38_2) = % 26.83/4.55 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.55 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_5, all_38_2, % 26.83/4.55 | | | | all_38_1, all_38_0, all_49_0, simplifying with (20), (23), % 26.83/4.55 | | | | (25), (106), (107) gives: % 26.83/4.55 | | | | (116) all_49_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_5, % 26.83/4.55 | | | | all_38_1) = v3 & apart_point_and_line(all_38_5, all_38_2) = % 26.83/4.55 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.55 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_1, all_38_0, all_53_0, simplifying with (20), (21), % 26.83/4.55 | | | | (23), (25), (50), (107) gives: % 26.83/4.55 | | | | (117) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.55 | | | | all_38_1) = v3 & apart_point_and_line(all_38_5, all_38_2) = % 26.83/4.55 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.55 | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (7) with all_38_4, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_2, all_53_0, all_53_0, simplifying with (21), (50), % 26.83/4.55 | | | | (107) gives: % 26.83/4.55 | | | | (118) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.55 | | | | [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v3 & % 26.83/4.55 | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 26.83/4.55 | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 26.83/4.55 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (10) with all_38_3, all_38_2, all_38_4, % 26.83/4.55 | | | | all_55_1, all_53_0, simplifying with (21), (22), (50), % 26.83/4.55 | | | | (52), (107) gives: % 26.83/4.55 | | | | (119) all_55_1 = 0 | all_53_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.55 | | | | apart_point_and_line(all_38_3, all_38_2) = v0) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_1, all_53_0, all_57_0, simplifying with (20), (21), % 26.83/4.55 | | | | (23), (24), (50), (57), (107) gives: % 26.83/4.55 | | | | (120) all_57_0 = 0 | all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.83/4.55 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 26.83/4.55 | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ (v0 = 0) | v2 = % 26.83/4.55 | | | | 0 | v1 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (7) with all_38_4, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_1, all_53_0, all_57_0, simplifying with (21), (23), % 26.83/4.55 | | | | (50), (57), (107) gives: % 26.83/4.55 | | | | (121) all_57_0 = 0 | all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.55 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.55 | | | | all_38_1) = v2 & apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.55 | | | | v3 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.55 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.55 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.55 | | | | % 26.83/4.55 | | | | GROUND_INST: instantiating (6) with all_38_4, all_38_4, all_38_2, % 26.83/4.55 | | | | all_38_1, all_57_0, all_53_0, simplifying with (21), (23), % 26.83/4.55 | | | | (50), (57), (107) gives: % 26.83/4.56 | | | | (122) all_57_0 = 0 | all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.56 | | | | all_38_1) = v3 & apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.56 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.56 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.56 | | | | % 26.83/4.56 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_4, all_38_2, % 26.83/4.56 | | | | all_38_1, all_49_0, all_57_0, simplifying with (20), (21), % 26.83/4.56 | | | | (23), (57), (106), (107) gives: % 26.83/4.56 | | | | (123) all_57_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.56 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.56 | | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_1) = % 26.83/4.56 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.56 | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 26.83/4.56 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.56 | | | | % 26.83/4.56 | | | | GROUND_INST: instantiating (11) with all_38_3, all_38_2, all_38_1, % 26.83/4.56 | | | | all_55_0, simplifying with (22), (23), (26), (53), (107) % 26.83/4.56 | | | | gives: % 26.83/4.56 | | | | (124) all_55_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0 % 26.83/4.56 | | | | % 26.83/4.56 | | | | BETA: splitting (119) gives: % 26.83/4.56 | | | | % 26.83/4.56 | | | | Case 1: % 26.83/4.56 | | | | | % 26.83/4.56 | | | | | (125) all_55_1 = 0 % 26.83/4.56 | | | | | % 26.83/4.56 | | | | | COMBINE_EQS: (98), (125) imply: % 26.83/4.56 | | | | | (126) all_57_1 = 0 % 26.83/4.56 | | | | | % 26.83/4.56 | | | | | BETA: splitting (54) gives: % 26.83/4.56 | | | | | % 26.83/4.56 | | | | | Case 1: % 26.83/4.56 | | | | | | % 26.83/4.56 | | | | | | (127) ~ (all_55_0 = 0) % 26.83/4.56 | | | | | | % 26.83/4.56 | | | | | | BETA: splitting (58) gives: % 26.83/4.56 | | | | | | % 26.83/4.56 | | | | | | Case 1: % 26.83/4.56 | | | | | | | % 26.83/4.56 | | | | | | | (128) ~ (all_57_0 = 0) % 26.83/4.56 | | | | | | | % 26.83/4.56 | | | | | | | BETA: splitting (120) gives: % 26.83/4.56 | | | | | | | % 26.83/4.56 | | | | | | | Case 1: % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | (129) all_57_0 = 0 % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | REDUCE: (128), (129) imply: % 26.83/4.56 | | | | | | | | (130) $false % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | CLOSE: (130) is inconsistent. % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | Case 2: % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | (131) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 26.83/4.56 | | | | | | | | any] : (apart_point_and_line(all_38_5, all_38_1) = v2 % 26.83/4.56 | | | | | | | | & apart_point_and_line(all_38_5, all_38_2) = v1 & % 26.83/4.56 | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ (v0 = % 26.83/4.56 | | | | | | | | 0) | v2 = 0 | v1 = 0)) % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | BETA: splitting (117) gives: % 26.83/4.56 | | | | | | | | % 26.83/4.56 | | | | | | | | Case 1: % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | (132) all_53_0 = 0 % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | REDUCE: (111), (132) imply: % 26.83/4.56 | | | | | | | | | (133) $false % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | CLOSE: (133) is inconsistent. % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | Case 2: % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | (134) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 26.83/4.56 | | | | | | | | | any] : ? [v3: any] : % 26.83/4.56 | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v3 & % 26.83/4.56 | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.83/4.56 | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.56 | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 % 26.83/4.56 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | BETA: splitting (121) gives: % 26.83/4.56 | | | | | | | | | % 26.83/4.56 | | | | | | | | | Case 1: % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | (135) all_57_0 = 0 % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | REDUCE: (128), (135) imply: % 26.83/4.56 | | | | | | | | | | (136) $false % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | CLOSE: (136) is inconsistent. % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | Case 2: % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | (137) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.56 | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.83/4.56 | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.83/4.56 | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 26.83/4.56 | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.56 | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 26.83/4.56 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | BETA: splitting (122) gives: % 26.83/4.56 | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | Case 1: % 26.83/4.56 | | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | | (138) all_57_0 = 0 % 26.83/4.56 | | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | | REDUCE: (128), (138) imply: % 26.83/4.56 | | | | | | | | | | | (139) $false % 26.83/4.56 | | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | | CLOSE: (139) is inconsistent. % 26.83/4.56 | | | | | | | | | | | % 26.83/4.56 | | | | | | | | | | Case 2: % 26.83/4.56 | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | (140) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.57 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.83/4.57 | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v3 & % 26.83/4.57 | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 26.83/4.57 | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.57 | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.57 | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | BETA: splitting (116) gives: % 26.83/4.57 | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | (141) all_49_0 = 0 % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | REDUCE: (112), (141) imply: % 26.83/4.57 | | | | | | | | | | | | (142) $false % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | CLOSE: (142) is inconsistent. % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | Case 2: % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | (143) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.57 | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.83/4.57 | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v3 & % 26.83/4.57 | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.83/4.57 | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.57 | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | BETA: splitting (114) gives: % 26.83/4.57 | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | (144) all_49_0 = 0 % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | REDUCE: (112), (144) imply: % 26.83/4.57 | | | | | | | | | | | | | (145) $false % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | Case 2: % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | (146) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.57 | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_38_4, % 26.83/4.57 | | | | | | | | | | | | | all_38_1) = v2 & % 26.83/4.57 | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 26.83/4.57 | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | BETA: splitting (115) gives: % 26.83/4.57 | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | (147) all_49_0 = 0 % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | REDUCE: (112), (147) imply: % 26.83/4.57 | | | | | | | | | | | | | | (148) $false % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | Case 2: % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | (149) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.57 | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.83/4.57 | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.83/4.57 | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 26.83/4.57 | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.57 | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 26.83/4.57 | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | (150) all_57_0 = 0 % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | REDUCE: (128), (150) imply: % 26.83/4.57 | | | | | | | | | | | | | | | (151) $false % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | Case 2: % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | (152) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 26.83/4.57 | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 26.83/4.57 | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v3 & % 26.83/4.57 | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.83/4.57 | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.57 | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 26.83/4.57 | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | (153) distinct_lines(all_38_2, all_38_1) = 0 % 26.83/4.57 | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 26.83/4.57 | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | Case 1: % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | (154) all_38_0 = 0 % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | REDUCE: (19), (154) imply: % 26.83/4.57 | | | | | | | | | | | | | | | | | (155) $false % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | Case 2: % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | (156) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.83/4.57 | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.83/4.57 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 26.83/4.57 | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 26.83/4.57 | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_362_0, % 26.83/4.57 | | | | | | | | | | | | | | | | | all_362_1, all_362_2 gives: % 26.83/4.57 | | | | | | | | | | | | | | | | | (157) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.57 | | | | | | | | | | | | | | | | | all_362_0 & apart_point_and_line(all_38_4, % 26.83/4.57 | | | | | | | | | | | | | | | | | all_38_2) = all_362_1 & distinct_lines(all_38_2, % 26.83/4.57 | | | | | | | | | | | | | | | | | all_38_1) = all_362_2 & ( ~ (all_362_2 = 0) | % 26.83/4.57 | | | | | | | | | | | | | | | | | all_362_0 = 0 | all_362_1 = 0) % 26.83/4.57 | | | | | | | | | | | | | | | | | % 26.83/4.57 | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 26.83/4.57 | | | | | | | | | | | | | | | | | (158) distinct_lines(all_38_2, all_38_1) = all_362_2 % 26.83/4.57 | | | | | | | | | | | | | | | | | (159) apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.57 | | | | | | | | | | | | | | | | | all_362_1 % 26.83/4.57 | | | | | | | | | | | | | | | | | (160) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.57 | | | | | | | | | | | | | | | | | all_362_0 % 26.83/4.58 | | | | | | | | | | | | | | | | | (161) ~ (all_362_2 = 0) | all_362_0 = 0 | all_362_1 = 0 % 26.83/4.58 | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | BETA: splitting (143) gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | (162) all_38_0 = 0 % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | REDUCE: (19), (162) imply: % 26.83/4.58 | | | | | | | | | | | | | | | | | | (163) $false % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent. % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | (164) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.58 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_5, % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 26.83/4.58 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | DELTA: instantiating (164) with fresh symbols all_372_0, % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_372_1, all_372_2, all_372_3 gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | (165) apart_point_and_line(all_38_5, all_38_1) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_372_0 & apart_point_and_line(all_38_5, % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_38_2) = all_372_1 & distinct_lines(all_38_2, % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_38_1) = all_372_2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_372_3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | ( ~ (all_372_2 = 0) | ~ (all_372_3 = 0) | % 26.83/4.58 | | | | | | | | | | | | | | | | | | all_372_0 = 0 | all_372_1 = 0) % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 26.83/4.58 | | | | | | | | | | | | | | | | | | (166) distinct_lines(all_38_2, all_38_1) = all_372_2 % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (167) all_53_0 = 0 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | REDUCE: (111), (167) imply: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (168) $false % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (169) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v0 & ( ~ % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_378_0, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | all_378_1, all_378_2 gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (170) apart_point_and_line(all_38_5, all_38_1) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | | all_378_0 & apart_point_and_line(all_38_5, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | all_38_2) = all_378_1 & distinct_lines(all_38_2, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | all_38_1) = all_378_2 & ( ~ (all_378_2 = 0) | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | all_378_0 = 0 | all_378_1 = 0) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | (171) distinct_lines(all_38_2, all_38_1) = all_378_2 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (172) all_53_0 = 0 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (172) imply: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (173) $false % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_388_0, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_388_1, all_388_2, all_388_3 gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (175) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_388_0 & apart_point_and_line(all_38_4, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_38_2) = all_388_1 & distinct_lines(all_38_2, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_38_1) = all_388_2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_388_3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | ( ~ (all_388_2 = 0) | ~ (all_388_3 = 0) | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_388_0 = 0 | all_388_1 = 0) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (176) distinct_lines(all_38_2, all_38_1) = all_388_2 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (177) apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_388_1 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | (178) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | all_388_0 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (179) all_49_0 = 0 % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (179) imply: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (180) $false % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (181) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (181) with fresh symbols all_394_0, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_394_1, all_394_2, all_394_3 gives: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (182) apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_394_0 & apart_point_and_line(all_38_5, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_394_1 & distinct_lines(all_38_2, % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_394_2 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = all_394_3 & % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_394_2 = 0) | ~ (all_394_3 = 0) | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | all_394_0 = 0 | all_394_1 = 0) % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies: % 26.83/4.58 | | | | | | | | | | | | | | | | | | | | | (183) distinct_lines(all_38_2, all_38_1) = all_394_2 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | (184) apart_point_and_line(all_38_4, all_38_2) = % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | all_394_0 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (185) all_38_0 = 0 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (185) imply: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (186) $false % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent. % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (187) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v3 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (187) with fresh symbols all_400_0, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_400_1, all_400_2, all_400_3 gives: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (188) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_400_0 & apart_point_and_line(all_38_5, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_400_1 & distinct_lines(all_38_2, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_400_2 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_4) = all_400_3 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_400_2 = 0) | ~ (all_400_3 = 0) | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_400_0 = 0 | all_400_1 = 0) % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (189) distinct_lines(all_38_2, all_38_1) = all_400_2 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | (190) apart_point_and_line(all_38_4, all_38_1) = % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | all_400_0 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | (191) all_38_0 = 0 % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (191) imply: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | (192) $false % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | (193) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_5, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v3 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (193) with fresh symbols all_410_0, % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_410_1, all_410_2, all_410_3 gives: % 26.83/4.59 | | | | | | | | | | | | | | | | | | | | | | | (194) apart_point_and_line(all_38_5, all_38_1) = % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_410_1 & apart_point_and_line(all_38_5, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_410_0 & distinct_lines(all_38_2, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_410_2 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_410_3 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_410_2 = 0) | ~ (all_410_3 = 0) | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | all_410_0 = 0 | all_410_1 = 0) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | (195) distinct_lines(all_38_2, all_38_1) = all_410_2 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (196) all_53_0 = 0 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (196) imply: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (197) $false % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (198) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = v2 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (198) with fresh symbols all_416_0, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_416_1, all_416_2, all_416_3 gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (199) apart_point_and_line(all_38_4, all_38_1) = % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_416_1 & apart_point_and_line(all_38_4, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_416_0 & distinct_lines(all_38_2, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_416_2 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_4) = all_416_3 & % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_416_2 = 0) | ~ (all_416_3 = 0) | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_416_0 = 0 | all_416_1 = 0) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (200) distinct_lines(all_38_2, all_38_1) = all_416_2 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (201) apart_point_and_line(all_38_4, all_38_2) = % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_416_0 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (202) apart_point_and_line(all_38_4, all_38_1) = % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_416_1 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_378_2, all_394_2, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (171), (183) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (203) all_394_2 = all_378_2 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_362_2, all_394_2, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (158), (183) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (204) all_394_2 = all_362_2 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_400_2, all_38_1, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (153), (189) gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (205) all_400_2 = 0 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_388_2, all_400_2, % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (176), (189) % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | (206) all_400_2 = all_388_2 % 27.06/4.59 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_378_2, all_400_2, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (171), (189) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (207) all_400_2 = all_378_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_410_2, all_416_2, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (195), (200) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (208) all_416_2 = all_410_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_378_2, all_416_2, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (171), (200) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (209) all_416_2 = all_378_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_372_2, all_416_2, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_2, simplifying with (166), (200) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (210) all_416_2 = all_372_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_362_1, all_394_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (159), (184) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (211) all_394_0 = all_362_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_53_0, all_416_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (50), (201) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (212) all_416_0 = all_53_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_394_0, all_416_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (184), (201) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (213) all_416_0 = all_394_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_388_1, all_416_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (177), (201) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (214) all_416_0 = all_388_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_57_0, all_400_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (57), (190) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (215) all_400_0 = all_57_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_388_0, all_400_0, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (178), (190) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (216) all_400_0 = all_388_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_388_0, all_416_1, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (178), (202) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (217) all_416_1 = all_388_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_362_0, all_416_1, % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (160), (202) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (218) all_416_1 = all_362_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (214) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (219) all_394_0 = all_388_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (220) all_394_0 = all_388_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (214) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (221) all_388_1 = all_53_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (218) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (222) all_388_0 = all_362_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (223) all_388_0 = all_362_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (210) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (224) all_410_2 = all_372_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (209) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (225) all_410_2 = all_378_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (225) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (226) all_378_2 = all_372_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (227) all_378_2 = all_372_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (216) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (228) all_388_0 = all_57_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (229) all_388_0 = all_57_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (206) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_388_2 = 0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (207) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (231) all_388_2 = all_378_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (220) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (232) all_388_1 = all_362_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (233) all_388_1 = all_362_1 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (204) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (234) all_378_2 = all_362_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (235) all_378_2 = all_362_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (229) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (236) all_362_0 = all_57_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (237) all_362_0 = all_57_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (233) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (238) all_362_1 = all_53_0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (231) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (239) all_378_2 = 0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (240) all_378_2 = 0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (235) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (241) all_372_2 = all_362_2 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (240) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (242) all_372_2 = 0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (241), (242) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | (243) all_362_2 = 0 % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_362_2 = 0) % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (243), (244) imply: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (245) $false % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.60 | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_362_0 = 0 | all_362_1 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_362_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (247) imply: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_57_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_57_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (249) imply: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (250) $false % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_362_1 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (251) imply: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_53_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_53_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (253) imply: % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (254) $false % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | Case 2: % 27.06/4.61 | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | (255) all_55_0 = 0 % 27.06/4.61 | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | REDUCE: (127), (255) imply: % 27.06/4.61 | | | | | | | | | | | | | | | | (256) $false % 27.06/4.61 | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 27.06/4.61 | | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | | % 27.06/4.61 | | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | | % 27.06/4.61 | | | | | | | | | End of split % 27.06/4.61 | | | | | | | | | % 27.06/4.61 | | | | | | | | End of split % 27.06/4.61 | | | | | | | | % 27.06/4.61 | | | | | | | End of split % 27.06/4.61 | | | | | | | % 27.06/4.61 | | | | | | Case 2: % 27.06/4.61 | | | | | | | % 27.06/4.61 | | | | | | | (257) ~ (all_57_1 = 0) % 27.06/4.61 | | | | | | | % 27.06/4.61 | | | | | | | REDUCE: (126), (257) imply: % 27.06/4.61 | | | | | | | (258) $false % 27.06/4.61 | | | | | | | % 27.06/4.61 | | | | | | | CLOSE: (258) is inconsistent. % 27.06/4.61 | | | | | | | % 27.06/4.61 | | | | | | End of split % 27.06/4.61 | | | | | | % 27.06/4.61 | | | | | Case 2: % 27.06/4.61 | | | | | | % 27.06/4.61 | | | | | | (259) ~ (all_55_1 = 0) % 27.06/4.61 | | | | | | % 27.06/4.61 | | | | | | REF_CLOSE: (16), (50), (111), (113), (118), (259) are inconsistent % 27.06/4.61 | | | | | | by sub-proof #1. % 27.06/4.61 | | | | | | % 27.06/4.61 | | | | | End of split % 27.06/4.61 | | | | | % 27.06/4.61 | | | | Case 2: % 27.06/4.61 | | | | | % 27.06/4.61 | | | | | (260) ~ (all_55_1 = 0) % 27.06/4.61 | | | | | % 27.06/4.61 | | | | | REF_CLOSE: (16), (50), (111), (113), (118), (260) are inconsistent by % 27.06/4.61 | | | | | sub-proof #1. % 27.06/4.61 | | | | | % 27.06/4.61 | | | | End of split % 27.06/4.61 | | | | % 27.06/4.61 | | | Case 2: % 27.06/4.61 | | | | % 27.06/4.61 | | | | (261) ~ (all_51_1 = 0) % 27.06/4.61 | | | | % 27.06/4.61 | | | | REDUCE: (104), (261) imply: % 27.06/4.61 | | | | (262) $false % 27.06/4.61 | | | | % 27.06/4.61 | | | | CLOSE: (262) is inconsistent. % 27.06/4.61 | | | | % 27.06/4.61 | | | End of split % 27.06/4.61 | | | % 27.06/4.61 | | End of split % 27.06/4.61 | | % 27.06/4.61 | End of split % 27.06/4.61 | % 27.06/4.61 End of proof % 27.06/4.61 % 27.06/4.61 Sub-proof #1 shows that the following formulas are inconsistent: % 27.06/4.61 ---------------------------------------------------------------- % 27.06/4.61 (1) apart_point_and_line(all_38_4, all_38_2) = all_53_0 % 27.06/4.61 (2) ~ (all_55_1 = 0) % 27.06/4.61 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 27.06/4.61 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 27.06/4.61 (apart_point_and_line(v3, v2) = v0)) % 27.06/4.61 (4) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] % 27.06/4.61 : (apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.06/4.61 apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.06/4.61 distinct_lines(all_38_2, all_38_2) = v1 & distinct_points(all_38_4, % 27.06/4.61 all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.06/4.61 (5) ~ (all_53_0 = 0) % 27.06/4.61 (6) all_55_1 = 0 | apart_point_and_line(all_38_4, all_38_2) = 0 % 27.06/4.61 % 27.06/4.61 Begin of proof % 27.06/4.61 | % 27.06/4.61 | BETA: splitting (4) gives: % 27.06/4.61 | % 27.06/4.61 | Case 1: % 27.06/4.61 | | % 27.06/4.61 | | (7) all_53_0 = 0 % 27.06/4.61 | | % 27.06/4.61 | | REDUCE: (5), (7) imply: % 27.06/4.61 | | (8) $false % 27.06/4.61 | | % 27.06/4.61 | | CLOSE: (8) is inconsistent. % 27.06/4.61 | | % 27.06/4.61 | Case 2: % 27.06/4.61 | | % 27.06/4.61 | | (9) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 27.06/4.61 | | (apart_point_and_line(all_38_4, all_38_2) = v3 & % 27.06/4.61 | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 27.06/4.61 | | distinct_lines(all_38_2, all_38_2) = v1 & distinct_points(all_38_4, % 27.06/4.61 | | all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 27.06/4.61 | | % 27.06/4.61 | | DELTA: instantiating (9) with fresh symbols all_131_0, all_131_1, all_131_2, % 27.06/4.61 | | all_131_3 gives: % 27.06/4.61 | | (10) apart_point_and_line(all_38_4, all_38_2) = all_131_0 & % 27.06/4.61 | | apart_point_and_line(all_38_4, all_38_2) = all_131_1 & % 27.06/4.61 | | distinct_lines(all_38_2, all_38_2) = all_131_2 & % 27.06/4.61 | | distinct_points(all_38_4, all_38_4) = all_131_3 & ( ~ (all_131_2 = % 27.06/4.61 | | 0) | ~ (all_131_3 = 0) | all_131_0 = 0 | all_131_1 = 0) % 27.06/4.61 | | % 27.06/4.61 | | ALPHA: (10) implies: % 27.06/4.61 | | (11) apart_point_and_line(all_38_4, all_38_2) = all_131_1 % 27.06/4.61 | | (12) apart_point_and_line(all_38_4, all_38_2) = all_131_0 % 27.06/4.61 | | % 27.06/4.61 | | BETA: splitting (6) gives: % 27.06/4.61 | | % 27.06/4.61 | | Case 1: % 27.06/4.61 | | | % 27.06/4.61 | | | (13) apart_point_and_line(all_38_4, all_38_2) = 0 % 27.06/4.61 | | | % 27.06/4.61 | | | GROUND_INST: instantiating (3) with all_53_0, all_131_0, all_38_2, % 27.06/4.61 | | | all_38_4, simplifying with (1), (12) gives: % 27.06/4.61 | | | (14) all_131_0 = all_53_0 % 27.06/4.61 | | | % 27.06/4.62 | | | GROUND_INST: instantiating (3) with all_131_1, all_131_0, all_38_2, % 27.06/4.62 | | | all_38_4, simplifying with (11), (12) gives: % 27.06/4.62 | | | (15) all_131_0 = all_131_1 % 27.06/4.62 | | | % 27.06/4.62 | | | GROUND_INST: instantiating (3) with 0, all_131_0, all_38_2, all_38_4, % 27.06/4.62 | | | simplifying with (12), (13) gives: % 27.06/4.62 | | | (16) all_131_0 = 0 % 27.06/4.62 | | | % 27.06/4.62 | | | COMBINE_EQS: (15), (16) imply: % 27.06/4.62 | | | (17) all_131_1 = 0 % 27.06/4.62 | | | % 27.06/4.62 | | | COMBINE_EQS: (14), (15) imply: % 27.06/4.62 | | | (18) all_131_1 = all_53_0 % 27.06/4.62 | | | % 27.06/4.62 | | | COMBINE_EQS: (17), (18) imply: % 27.06/4.62 | | | (19) all_53_0 = 0 % 27.06/4.62 | | | % 27.06/4.62 | | | SIMP: (19) implies: % 27.06/4.62 | | | (20) all_53_0 = 0 % 27.06/4.62 | | | % 27.06/4.62 | | | REDUCE: (5), (20) imply: % 27.06/4.62 | | | (21) $false % 27.06/4.62 | | | % 27.06/4.62 | | | CLOSE: (21) is inconsistent. % 27.06/4.62 | | | % 27.06/4.62 | | Case 2: % 27.06/4.62 | | | % 27.06/4.62 | | | (22) all_55_1 = 0 % 27.06/4.62 | | | % 27.06/4.62 | | | REDUCE: (2), (22) imply: % 27.06/4.62 | | | (23) $false % 27.06/4.62 | | | % 27.06/4.62 | | | CLOSE: (23) is inconsistent. % 27.06/4.62 | | | % 27.06/4.62 | | End of split % 27.06/4.62 | | % 27.06/4.62 | End of split % 27.06/4.62 | % 27.06/4.62 End of proof % 27.06/4.62 % SZS output end Proof for theBenchmark % 27.06/4.62 % 27.06/4.62 4047ms %------------------------------------------------------------------------------