%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO182+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 23:21:57 EDT 2023 % Result : Theorem 14.05s 2.89s % Output : Proof 19.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : GEO182+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 21:06:42 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.69/1.13 Prover 4: Preprocessing ... % 2.69/1.13 Prover 1: Preprocessing ... % 3.35/1.19 Prover 5: Preprocessing ... % 3.35/1.19 Prover 3: Preprocessing ... % 3.35/1.19 Prover 0: Preprocessing ... % 3.35/1.19 Prover 2: Preprocessing ... % 3.48/1.20 Prover 6: Preprocessing ... % 4.88/1.51 Prover 5: Proving ... % 4.88/1.51 Prover 2: Proving ... % 4.88/1.51 Prover 6: Constructing countermodel ... % 4.88/1.54 Prover 3: Constructing countermodel ... % 4.88/1.56 Prover 1: Constructing countermodel ... % 6.85/1.68 Prover 3: gave up % 6.85/1.68 Prover 1: gave up % 6.85/1.70 Prover 6: gave up % 6.85/1.70 Prover 0: Proving ... % 6.85/1.70 Prover 4: Constructing countermodel ... % 6.99/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.99/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.99/1.71 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.07/1.76 Prover 8: Preprocessing ... % 7.07/1.77 Prover 7: Preprocessing ... % 7.07/1.78 Prover 9: Preprocessing ... % 7.66/1.85 Prover 7: Warning: ignoring some quantifiers % 7.66/1.87 Prover 7: Constructing countermodel ... % 8.20/1.90 Prover 8: Warning: ignoring some quantifiers % 8.20/1.93 Prover 8: Constructing countermodel ... % 9.04/2.00 Prover 8: gave up % 9.16/2.02 Prover 9: Constructing countermodel ... % 9.16/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.16/2.05 Prover 7: gave up % 9.16/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.16/2.07 Prover 10: Preprocessing ... % 9.78/2.11 Prover 11: Preprocessing ... % 9.78/2.11 Prover 10: Warning: ignoring some quantifiers % 9.78/2.12 Prover 10: Constructing countermodel ... % 9.78/2.17 Prover 10: gave up % 9.78/2.19 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.78/2.22 Prover 12: Preprocessing ... % 10.70/2.34 Prover 11: Constructing countermodel ... % 11.68/2.40 Prover 12: Proving ... % 14.05/2.89 Prover 0: proved (2254ms) % 14.05/2.89 % 14.05/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.05/2.89 % 14.05/2.89 Prover 9: stopped % 14.05/2.90 Prover 12: stopped % 14.05/2.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.05/2.90 Prover 2: stopped % 14.05/2.90 Prover 5: stopped % 14.05/2.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.05/2.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.34/2.91 Prover 13: Preprocessing ... % 15.34/2.92 Prover 19: Preprocessing ... % 15.34/2.92 Prover 16: Preprocessing ... % 15.34/2.94 Prover 13: Warning: ignoring some quantifiers % 15.34/2.94 Prover 16: Warning: ignoring some quantifiers % 15.34/2.94 Prover 16: Constructing countermodel ... % 15.34/2.94 Prover 13: Constructing countermodel ... % 15.34/2.96 Prover 19: Warning: ignoring some quantifiers % 15.34/2.97 Prover 19: Constructing countermodel ... % 15.98/2.99 Prover 19: gave up % 15.98/3.03 Prover 13: gave up % 15.98/3.03 Prover 16: gave up % 18.27/3.39 Prover 4: Found proof (size 223) % 18.27/3.39 Prover 4: proved (2751ms) % 18.27/3.39 Prover 11: stopped % 18.27/3.39 % 18.27/3.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.27/3.39 % 18.47/3.42 % SZS output start Proof for theBenchmark % 18.47/3.43 Assumptions after simplification: % 18.47/3.43 --------------------------------- % 18.47/3.43 % 18.47/3.43 (apart1) % 18.47/3.47 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 18.47/3.47 % 18.47/3.47 (apart4) % 18.47/3.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 18.47/3.48 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 18.47/3.48 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 18.47/3.48 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.47/3.48 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 18.47/3.48 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.47/3.48 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.47/3.48 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 18.47/3.48 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.47/3.48 distinct_points(v1, v2) = 0) % 18.47/3.48 % 18.47/3.48 (ceq2) % 18.47/3.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 18.47/3.48 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 18.47/3.48 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 18.47/3.48 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 18.47/3.48 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 18.47/3.48 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.47/3.48 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.47/3.48 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 18.47/3.48 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.47/3.48 apart_point_and_line(v0, v2) = 0) % 18.47/3.48 % 18.47/3.48 (ci1) % 18.47/3.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 18.47/3.49 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 18.47/3.49 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 18.47/3.49 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.47/3.49 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 18.47/3.49 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 18.47/3.49 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 18.47/3.49 % 18.47/3.49 (ci2) % 18.47/3.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 18.47/3.49 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 18.47/3.49 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 18.47/3.49 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.47/3.49 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 18.47/3.49 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 18.47/3.49 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 18.47/3.49 % 18.47/3.49 (con) % 18.47/3.49 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 18.47/3.49 int] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) % 18.47/3.49 = v3 & apart_point_and_line(v2, v4) = v5 & apart_point_and_line(v2, v3) = 0 % 18.47/3.49 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.47/3.49 % 18.47/3.49 (cu1) % 18.47/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 18.47/3.50 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 18.47/3.50 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 18.47/3.50 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 18.47/3.50 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 18.47/3.50 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 18.47/3.50 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.47/3.50 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 18.47/3.50 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 18.47/3.50 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 18.47/3.50 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 18.47/3.50 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 18.47/3.50 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.47/3.50 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 18.47/3.50 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 18.47/3.50 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 18.47/3.50 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 18.47/3.50 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 18.47/3.50 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 18.47/3.50 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.47/3.50 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 18.47/3.50 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 18.47/3.50 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 18.47/3.50 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 18.47/3.50 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 18.47/3.50 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 18.47/3.50 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 18.47/3.50 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 18.47/3.50 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.47/3.50 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 18.47/3.50 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 18.47/3.50 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 18.47/3.50 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 18.47/3.50 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 18.47/3.50 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 18.47/3.50 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 18.47/3.50 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 18.47/3.50 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 18.47/3.50 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.47/3.50 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 18.47/3.50 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 18.47/3.50 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 18.47/3.50 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 18.47/3.50 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 18.47/3.50 % 18.47/3.50 (function-axioms) % 18.80/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.80/3.50 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 18.80/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.80/3.50 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 18.80/3.50 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.80/3.50 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 18.80/3.50 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.80/3.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.80/3.50 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 18.80/3.50 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.80/3.50 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 18.80/3.50 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.80/3.50 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 18.80/3.50 (distinct_points(v3, v2) = v0)) % 18.80/3.50 % 18.80/3.50 Further assumptions not needed in the proof: % 18.80/3.50 -------------------------------------------- % 18.80/3.50 apart2, apart3, apart5, ax6, ceq1, ceq3, ci3, ci4 % 18.80/3.50 % 18.80/3.50 Those formulas are unsatisfiable: % 18.80/3.50 --------------------------------- % 18.80/3.50 % 18.80/3.50 Begin of proof % 18.80/3.50 | % 18.80/3.50 | ALPHA: (apart4) implies: % 18.80/3.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.80/3.51 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 18.80/3.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 18.80/3.51 | % 18.80/3.51 | ALPHA: (ci1) implies: % 18.80/3.51 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 18.80/3.51 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 18.80/3.51 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 18.80/3.51 | $i(v2))) % 18.80/3.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 18.80/3.51 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 18.80/3.51 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 18.80/3.51 | ~ (v4 = 0) | ~ (v3 = 0)))) % 18.80/3.51 | % 18.80/3.51 | ALPHA: (ci2) implies: % 18.80/3.51 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 18.80/3.51 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 18.80/3.51 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 18.80/3.51 | $i(v2))) % 18.80/3.51 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 18.80/3.51 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 18.80/3.51 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 18.80/3.51 | ~ (v4 = 0) | ~ (v3 = 0)))) % 18.80/3.51 | % 18.80/3.51 | ALPHA: (cu1) implies: % 18.80/3.51 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.80/3.51 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ % 18.80/3.51 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 18.80/3.51 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3) % 18.80/3.51 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, % 18.80/3.51 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | % 18.80/3.51 | v5 = 0 | v4 = 0))) % 18.80/3.51 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.80/3.51 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 18.80/3.51 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 18.80/3.51 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.80/3.51 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 18.80/3.51 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 18.80/3.51 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 18.80/3.51 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.80/3.51 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 18.80/3.51 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) % 18.80/3.51 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 18.80/3.51 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & % 18.80/3.51 | apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & % 18.80/3.51 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 18.80/3.51 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.80/3.51 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 18.80/3.51 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 18.80/3.51 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 18.80/3.51 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 18.80/3.51 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 18.80/3.51 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 18.80/3.51 | | v8 = 0))) % 18.80/3.52 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 18.80/3.52 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 18.80/3.52 | v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ % 18.80/3.52 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? % 18.80/3.52 | [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 18.80/3.52 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 18.80/3.52 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 18.80/3.52 | | v8 = 0))) % 18.80/3.52 | % 18.80/3.52 | ALPHA: (ceq2) implies: % 18.80/3.52 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.80/3.52 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 18.80/3.52 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.80/3.52 | distinct_lines(v1, v2) = 0) % 18.80/3.52 | % 18.80/3.52 | ALPHA: (function-axioms) implies: % 18.80/3.52 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.80/3.52 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 18.80/3.52 | (distinct_points(v3, v2) = v0)) % 18.80/3.52 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.80/3.52 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 18.80/3.52 | (apart_point_and_line(v3, v2) = v0)) % 18.80/3.52 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.80/3.52 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 18.80/3.52 | % 18.80/3.52 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 18.80/3.52 | all_17_3, all_17_4, all_17_5 gives: % 18.80/3.52 | (15) ~ (all_17_0 = 0) & line_connecting(all_17_4, all_17_5) = all_17_1 & % 18.80/3.52 | line_connecting(all_17_5, all_17_4) = all_17_2 & % 18.80/3.52 | apart_point_and_line(all_17_3, all_17_1) = all_17_0 & % 18.80/3.52 | apart_point_and_line(all_17_3, all_17_2) = 0 & % 18.80/3.52 | distinct_points(all_17_5, all_17_4) = 0 & $i(all_17_1) & $i(all_17_2) % 18.80/3.52 | & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) % 18.80/3.52 | % 18.80/3.52 | ALPHA: (15) implies: % 18.80/3.52 | (16) ~ (all_17_0 = 0) % 18.80/3.52 | (17) $i(all_17_5) % 18.80/3.52 | (18) $i(all_17_4) % 18.80/3.52 | (19) $i(all_17_3) % 18.80/3.52 | (20) $i(all_17_2) % 18.80/3.52 | (21) $i(all_17_1) % 18.80/3.52 | (22) distinct_points(all_17_5, all_17_4) = 0 % 18.80/3.52 | (23) apart_point_and_line(all_17_3, all_17_2) = 0 % 18.80/3.52 | (24) apart_point_and_line(all_17_3, all_17_1) = all_17_0 % 18.80/3.52 | (25) line_connecting(all_17_5, all_17_4) = all_17_2 % 18.80/3.52 | (26) line_connecting(all_17_4, all_17_5) = all_17_1 % 18.80/3.52 | % 18.80/3.52 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (17), % 18.80/3.52 | (18), (22) gives: % 18.80/3.52 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 18.80/3.52 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 18.80/3.52 | % 18.80/3.52 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (17), % 18.80/3.52 | (18), (22) gives: % 18.80/3.52 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 18.80/3.52 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 18.80/3.52 | % 18.80/3.52 | GROUND_INST: instantiating (10) with all_17_3, all_17_3, all_17_1, all_17_1, % 18.80/3.52 | all_17_0, all_17_0, simplifying with (19), (21), (24) gives: % 18.80/3.52 | (29) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 18.80/3.52 | any] : (apart_point_and_line(all_17_3, all_17_1) = v3 & % 18.80/3.52 | apart_point_and_line(all_17_3, all_17_1) = v2 & % 18.80/3.52 | distinct_lines(all_17_1, all_17_1) = v1 & distinct_points(all_17_3, % 18.80/3.52 | all_17_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.52 | % 18.80/3.53 | GROUND_INST: instantiating (11) with all_17_3, all_17_2, all_17_1, all_17_0, % 18.80/3.53 | simplifying with (19), (20), (21), (23), (24) gives: % 18.80/3.53 | (30) all_17_0 = 0 | distinct_lines(all_17_2, all_17_1) = 0 % 18.80/3.53 | % 18.80/3.53 | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying % 18.80/3.53 | with (17), (18), (25) gives: % 18.80/3.53 | (31) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4, % 18.80/3.53 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 18.80/3.53 | (v1 = 0) | ~ (v0 = 0))) % 18.80/3.53 | % 18.80/3.53 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying % 18.80/3.53 | with (17), (18), (25) gives: % 18.80/3.53 | (32) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5, % 18.80/3.53 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~ % 18.80/3.53 | (v1 = 0) | ~ (v0 = 0))) % 18.80/3.53 | % 18.80/3.53 | GROUND_INST: instantiating (5) with all_17_4, all_17_5, all_17_1, simplifying % 18.80/3.53 | with (17), (18), (26) gives: % 18.80/3.53 | (33) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5, % 18.80/3.53 | all_17_1) = v1 & distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 18.80/3.53 | (v1 = 0) | ~ (v0 = 0))) % 18.80/3.53 | % 18.80/3.53 | GROUND_INST: instantiating (3) with all_17_4, all_17_5, all_17_1, simplifying % 18.80/3.53 | with (17), (18), (26) gives: % 18.80/3.53 | (34) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4, % 18.80/3.53 | all_17_1) = v1 & distinct_points(all_17_4, all_17_5) = v0 & ( ~ % 18.80/3.53 | (v1 = 0) | ~ (v0 = 0))) % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (34) with fresh symbols all_24_0, all_24_1 gives: % 18.80/3.53 | (35) apart_point_and_line(all_17_4, all_17_1) = all_24_0 & % 18.80/3.53 | distinct_points(all_17_4, all_17_5) = all_24_1 & ( ~ (all_24_0 = 0) | % 18.80/3.53 | ~ (all_24_1 = 0)) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (35) implies: % 18.80/3.53 | (36) distinct_points(all_17_4, all_17_5) = all_24_1 % 18.80/3.53 | (37) apart_point_and_line(all_17_4, all_17_1) = all_24_0 % 18.80/3.53 | (38) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (33) with fresh symbols all_26_0, all_26_1 gives: % 18.80/3.53 | (39) apart_point_and_line(all_17_5, all_17_1) = all_26_0 & % 18.80/3.53 | distinct_points(all_17_4, all_17_5) = all_26_1 & ( ~ (all_26_0 = 0) | % 18.80/3.53 | ~ (all_26_1 = 0)) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (39) implies: % 18.80/3.53 | (40) distinct_points(all_17_4, all_17_5) = all_26_1 % 18.80/3.53 | (41) apart_point_and_line(all_17_5, all_17_1) = all_26_0 % 18.80/3.53 | (42) ~ (all_26_0 = 0) | ~ (all_26_1 = 0) % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (28) with fresh symbols all_28_0, all_28_1 gives: % 18.80/3.53 | (43) ~ (all_28_0 = 0) & line_connecting(all_17_5, all_17_4) = all_28_1 & % 18.80/3.53 | apart_point_and_line(all_17_5, all_28_1) = all_28_0 & $i(all_28_1) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (43) implies: % 18.80/3.53 | (44) $i(all_28_1) % 18.80/3.53 | (45) apart_point_and_line(all_17_5, all_28_1) = all_28_0 % 18.80/3.53 | (46) line_connecting(all_17_5, all_17_4) = all_28_1 % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (27) with fresh symbols all_30_0, all_30_1 gives: % 18.80/3.53 | (47) ~ (all_30_0 = 0) & line_connecting(all_17_5, all_17_4) = all_30_1 & % 18.80/3.53 | apart_point_and_line(all_17_4, all_30_1) = all_30_0 & $i(all_30_1) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (47) implies: % 18.80/3.53 | (48) apart_point_and_line(all_17_4, all_30_1) = all_30_0 % 18.80/3.53 | (49) line_connecting(all_17_5, all_17_4) = all_30_1 % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1 gives: % 18.80/3.53 | (50) apart_point_and_line(all_17_5, all_17_2) = all_32_0 & % 18.80/3.53 | distinct_points(all_17_5, all_17_4) = all_32_1 & ( ~ (all_32_0 = 0) | % 18.80/3.53 | ~ (all_32_1 = 0)) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (50) implies: % 18.80/3.53 | (51) distinct_points(all_17_5, all_17_4) = all_32_1 % 18.80/3.53 | (52) apart_point_and_line(all_17_5, all_17_2) = all_32_0 % 18.80/3.53 | (53) ~ (all_32_0 = 0) | ~ (all_32_1 = 0) % 18.80/3.53 | % 18.80/3.53 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives: % 18.80/3.53 | (54) apart_point_and_line(all_17_4, all_17_2) = all_34_0 & % 18.80/3.53 | distinct_points(all_17_5, all_17_4) = all_34_1 & ( ~ (all_34_0 = 0) | % 18.80/3.53 | ~ (all_34_1 = 0)) % 18.80/3.53 | % 18.80/3.53 | ALPHA: (54) implies: % 18.80/3.54 | (55) distinct_points(all_17_5, all_17_4) = all_34_1 % 18.80/3.54 | (56) apart_point_and_line(all_17_4, all_17_2) = all_34_0 % 18.80/3.54 | (57) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 18.80/3.54 | % 18.80/3.54 | BETA: splitting (30) gives: % 18.80/3.54 | % 18.80/3.54 | Case 1: % 18.80/3.54 | | % 18.80/3.54 | | (58) distinct_lines(all_17_2, all_17_1) = 0 % 18.80/3.54 | | % 18.80/3.54 | | BETA: splitting (29) gives: % 18.80/3.54 | | % 18.80/3.54 | | Case 1: % 18.80/3.54 | | | % 18.80/3.54 | | | (59) all_17_0 = 0 % 18.80/3.54 | | | % 18.80/3.54 | | | REDUCE: (16), (59) imply: % 18.80/3.54 | | | (60) $false % 18.80/3.54 | | | % 18.80/3.54 | | | CLOSE: (60) is inconsistent. % 18.80/3.54 | | | % 18.80/3.54 | | Case 2: % 18.80/3.54 | | | % 18.80/3.54 | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 18.80/3.54 | | | (apart_point_and_line(all_17_3, all_17_1) = v3 & % 18.80/3.54 | | | apart_point_and_line(all_17_3, all_17_1) = v2 & % 18.80/3.54 | | | distinct_lines(all_17_1, all_17_1) = v1 & % 18.80/3.54 | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 18.80/3.54 | | | = 0) | v3 = 0 | v2 = 0)) % 18.80/3.54 | | | % 18.80/3.54 | | | DELTA: instantiating (61) with fresh symbols all_44_0, all_44_1, all_44_2, % 18.80/3.54 | | | all_44_3 gives: % 18.80/3.54 | | | (62) apart_point_and_line(all_17_3, all_17_1) = all_44_0 & % 18.80/3.54 | | | apart_point_and_line(all_17_3, all_17_1) = all_44_1 & % 18.80/3.54 | | | distinct_lines(all_17_1, all_17_1) = all_44_2 & % 18.80/3.54 | | | distinct_points(all_17_3, all_17_3) = all_44_3 & ( ~ (all_44_2 = % 18.80/3.54 | | | 0) | ~ (all_44_3 = 0) | all_44_0 = 0 | all_44_1 = 0) % 18.80/3.54 | | | % 18.80/3.54 | | | ALPHA: (62) implies: % 18.80/3.54 | | | (63) apart_point_and_line(all_17_3, all_17_1) = all_44_1 % 18.80/3.54 | | | (64) apart_point_and_line(all_17_3, all_17_1) = all_44_0 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (12) with 0, all_34_1, all_17_4, all_17_5, % 18.80/3.54 | | | simplifying with (22), (55) gives: % 18.80/3.54 | | | (65) all_34_1 = 0 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (12) with all_32_1, all_34_1, all_17_4, % 18.80/3.54 | | | all_17_5, simplifying with (51), (55) gives: % 18.80/3.54 | | | (66) all_34_1 = all_32_1 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (12) with all_24_1, all_26_1, all_17_5, % 18.80/3.54 | | | all_17_4, simplifying with (36), (40) gives: % 18.80/3.54 | | | (67) all_26_1 = all_24_1 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (13) with all_17_0, all_44_0, all_17_1, % 18.80/3.54 | | | all_17_3, simplifying with (24), (64) gives: % 18.80/3.54 | | | (68) all_44_0 = all_17_0 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (13) with all_44_1, all_44_0, all_17_1, % 18.80/3.54 | | | all_17_3, simplifying with (63), (64) gives: % 18.80/3.54 | | | (69) all_44_0 = all_44_1 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (14) with all_17_2, all_30_1, all_17_4, % 18.80/3.54 | | | all_17_5, simplifying with (25), (49) gives: % 18.80/3.54 | | | (70) all_30_1 = all_17_2 % 18.80/3.54 | | | % 18.80/3.54 | | | GROUND_INST: instantiating (14) with all_28_1, all_30_1, all_17_4, % 18.80/3.54 | | | all_17_5, simplifying with (46), (49) gives: % 18.80/3.54 | | | (71) all_30_1 = all_28_1 % 18.80/3.54 | | | % 18.80/3.54 | | | COMBINE_EQS: (68), (69) imply: % 18.80/3.54 | | | (72) all_44_1 = all_17_0 % 18.80/3.54 | | | % 18.80/3.54 | | | COMBINE_EQS: (65), (66) imply: % 18.80/3.54 | | | (73) all_32_1 = 0 % 18.80/3.54 | | | % 18.80/3.54 | | | COMBINE_EQS: (70), (71) imply: % 18.80/3.54 | | | (74) all_28_1 = all_17_2 % 18.80/3.54 | | | % 18.80/3.54 | | | REDUCE: (48), (70) imply: % 18.80/3.54 | | | (75) apart_point_and_line(all_17_4, all_17_2) = all_30_0 % 18.80/3.54 | | | % 18.80/3.54 | | | REDUCE: (45), (74) imply: % 18.80/3.54 | | | (76) apart_point_and_line(all_17_5, all_17_2) = all_28_0 % 18.80/3.54 | | | % 18.80/3.54 | | | BETA: splitting (53) gives: % 18.80/3.54 | | | % 18.80/3.54 | | | Case 1: % 18.80/3.54 | | | | % 18.80/3.54 | | | | (77) ~ (all_32_0 = 0) % 18.80/3.54 | | | | % 18.80/3.54 | | | | BETA: splitting (57) gives: % 18.80/3.54 | | | | % 18.80/3.54 | | | | Case 1: % 18.80/3.54 | | | | | % 18.80/3.54 | | | | | (78) ~ (all_34_0 = 0) % 18.80/3.54 | | | | | % 18.80/3.54 | | | | | GROUND_INST: instantiating (13) with all_32_0, all_28_0, all_17_2, % 18.80/3.54 | | | | | all_17_5, simplifying with (52), (76) gives: % 18.80/3.54 | | | | | (79) all_32_0 = all_28_0 % 18.80/3.54 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (13) with all_34_0, all_30_0, all_17_2, % 18.80/3.55 | | | | | all_17_4, simplifying with (56), (75) gives: % 18.80/3.55 | | | | | (80) all_34_0 = all_30_0 % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | REDUCE: (78), (80) imply: % 18.80/3.55 | | | | | (81) ~ (all_30_0 = 0) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | REDUCE: (77), (79) imply: % 18.80/3.55 | | | | | (82) ~ (all_28_0 = 0) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (1) with all_17_5, all_17_4, all_17_5, % 18.80/3.55 | | | | | all_24_1, simplifying with (17), (18), (22), (36) gives: % 18.80/3.55 | | | | | (83) all_24_1 = 0 | distinct_points(all_17_5, all_17_5) = 0 % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (6) with all_17_5, all_17_4, all_17_2, % 18.80/3.55 | | | | | all_17_1, simplifying with (17), (18), (20), (21), (22), % 18.80/3.55 | | | | | (58) gives: % 18.80/3.55 | | | | | (84) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 18.80/3.55 | | | | | (apart_point_and_line(all_17_4, all_17_1) = v3 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_5, all_17_1) = v1 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_5, all_17_2) = v0 & (v3 = 0 | v2 % 18.80/3.55 | | | | | = 0 | v1 = 0 | v0 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (10) with all_17_3, all_17_5, all_17_1, % 18.80/3.55 | | | | | all_17_2, all_17_0, all_28_0, simplifying with (17), % 18.80/3.55 | | | | | (19), (20), (21), (24), (76) gives: % 18.80/3.55 | | | | | (85) all_28_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.55 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.55 | | | | | all_17_2) = v2 & apart_point_and_line(all_17_5, all_17_1) % 18.80/3.55 | | | | | = v3 & distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.55 | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.55 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (9) with all_17_5, all_17_3, all_17_1, % 18.80/3.55 | | | | | all_17_2, all_28_0, all_17_0, simplifying with (17), % 18.80/3.55 | | | | | (19), (20), (21), (24), (76) gives: % 18.80/3.55 | | | | | (86) all_28_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.55 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.55 | | | | | all_17_2) = v3 & apart_point_and_line(all_17_5, all_17_1) % 18.80/3.55 | | | | | = v2 & distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.55 | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.55 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (7) with all_17_5, all_17_4, all_17_2, % 18.80/3.55 | | | | | all_17_2, all_28_0, all_28_0, simplifying with (17), % 18.80/3.55 | | | | | (18), (20), (22), (76) gives: % 18.80/3.55 | | | | | (87) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.55 | | | | | (apart_point_and_line(all_17_4, all_17_2) = v2 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 18.80/3.55 | | | | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 % 18.80/3.55 | | | | | = 0 | v1 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (8) with all_17_5, all_17_5, all_17_2, % 18.80/3.55 | | | | | all_17_1, all_28_0, all_28_0, simplifying with (17), % 18.80/3.55 | | | | | (20), (21), (58), (76) gives: % 18.80/3.55 | | | | | (88) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.55 | | | | | (apart_point_and_line(all_17_5, all_17_1) = v2 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_5, all_17_1) = v1 & % 18.80/3.55 | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v0 = 0) | v2 % 18.80/3.55 | | | | | = 0 | v1 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (10) with all_17_5, all_17_5, all_17_2, % 18.80/3.55 | | | | | all_17_2, all_28_0, all_28_0, simplifying with (17), % 18.80/3.55 | | | | | (20), (76) gives: % 18.80/3.55 | | | | | (89) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.55 | | | | | [v3: any] : (apart_point_and_line(all_17_5, all_17_2) = v3 & % 18.80/3.55 | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 18.80/3.55 | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 18.80/3.55 | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.55 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (10) with all_17_3, all_17_4, all_17_1, % 18.80/3.55 | | | | | all_17_2, all_17_0, all_30_0, simplifying with (18), % 18.80/3.55 | | | | | (19), (20), (21), (24), (75) gives: % 18.80/3.55 | | | | | (90) all_30_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.55 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.55 | | | | | all_17_2) = v2 & apart_point_and_line(all_17_4, all_17_1) % 18.80/3.55 | | | | | = v3 & distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.55 | | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.55 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.55 | | | | | % 18.80/3.55 | | | | | GROUND_INST: instantiating (10) with all_17_4, all_17_3, all_17_2, % 18.80/3.55 | | | | | all_17_1, all_30_0, all_17_0, simplifying with (18), % 18.80/3.55 | | | | | (19), (20), (21), (24), (75) gives: % 18.80/3.56 | | | | | (91) all_30_0 = 0 | all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.56 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.56 | | | | | all_17_2) = v3 & apart_point_and_line(all_17_4, all_17_1) % 18.80/3.56 | | | | | = v2 & distinct_lines(all_17_2, all_17_1) = v1 & % 18.80/3.56 | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.56 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_17_2, % 18.80/3.56 | | | | | all_17_1, all_30_0, all_30_0, simplifying with (18), % 18.80/3.56 | | | | | (20), (21), (58), (75) gives: % 18.80/3.56 | | | | | (92) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.56 | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 18.80/3.56 | | | | | apart_point_and_line(all_17_4, all_17_1) = v1 & % 18.80/3.56 | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v0 = 0) | v2 % 18.80/3.56 | | | | | = 0 | v1 = 0)) % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | GROUND_INST: instantiating (10) with all_17_4, all_17_4, all_17_2, % 18.80/3.56 | | | | | all_17_2, all_30_0, all_30_0, simplifying with (18), % 18.80/3.56 | | | | | (20), (75) gives: % 18.80/3.56 | | | | | (93) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.56 | | | | | [v3: any] : (apart_point_and_line(all_17_4, all_17_2) = v3 & % 18.80/3.56 | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 18.80/3.56 | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 18.80/3.56 | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | ~ % 18.80/3.56 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | DELTA: instantiating (84) with fresh symbols all_67_0, all_67_1, % 18.80/3.56 | | | | | all_67_2, all_67_3 gives: % 18.80/3.56 | | | | | (94) apart_point_and_line(all_17_4, all_17_1) = all_67_0 & % 18.80/3.56 | | | | | apart_point_and_line(all_17_4, all_17_2) = all_67_1 & % 18.80/3.56 | | | | | apart_point_and_line(all_17_5, all_17_1) = all_67_2 & % 18.80/3.56 | | | | | apart_point_and_line(all_17_5, all_17_2) = all_67_3 & % 18.80/3.56 | | | | | (all_67_0 = 0 | all_67_1 = 0 | all_67_2 = 0 | all_67_3 = 0) % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | ALPHA: (94) implies: % 18.80/3.56 | | | | | (95) apart_point_and_line(all_17_5, all_17_2) = all_67_3 % 18.80/3.56 | | | | | (96) apart_point_and_line(all_17_5, all_17_1) = all_67_2 % 18.80/3.56 | | | | | (97) apart_point_and_line(all_17_4, all_17_2) = all_67_1 % 18.80/3.56 | | | | | (98) apart_point_and_line(all_17_4, all_17_1) = all_67_0 % 18.80/3.56 | | | | | (99) all_67_0 = 0 | all_67_1 = 0 | all_67_2 = 0 | all_67_3 = 0 % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | BETA: splitting (88) gives: % 18.80/3.56 | | | | | % 18.80/3.56 | | | | | Case 1: % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | (100) all_28_0 = 0 % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | REDUCE: (82), (100) imply: % 18.80/3.56 | | | | | | (101) $false % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | CLOSE: (101) is inconsistent. % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | Case 2: % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | (102) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.56 | | | | | | (apart_point_and_line(all_17_5, all_17_1) = v2 & % 18.80/3.56 | | | | | | apart_point_and_line(all_17_5, all_17_1) = v1 & % 18.80/3.56 | | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v0 = 0) | % 18.80/3.56 | | | | | | v2 = 0 | v1 = 0)) % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | DELTA: instantiating (102) with fresh symbols all_80_0, all_80_1, % 18.80/3.56 | | | | | | all_80_2 gives: % 18.80/3.56 | | | | | | (103) apart_point_and_line(all_17_5, all_17_1) = all_80_0 & % 18.80/3.56 | | | | | | apart_point_and_line(all_17_5, all_17_1) = all_80_1 & % 18.80/3.56 | | | | | | distinct_points(all_17_5, all_17_5) = all_80_2 & ( ~ % 18.80/3.56 | | | | | | (all_80_2 = 0) | all_80_0 = 0 | all_80_1 = 0) % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | ALPHA: (103) implies: % 18.80/3.56 | | | | | | (104) apart_point_and_line(all_17_5, all_17_1) = all_80_1 % 18.80/3.56 | | | | | | (105) apart_point_and_line(all_17_5, all_17_1) = all_80_0 % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | BETA: splitting (87) gives: % 18.80/3.56 | | | | | | % 18.80/3.56 | | | | | | Case 1: % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | (106) all_28_0 = 0 % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | REDUCE: (82), (106) imply: % 18.80/3.56 | | | | | | | (107) $false % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | CLOSE: (107) is inconsistent. % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | Case 2: % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | (108) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.56 | | | | | | | (apart_point_and_line(all_17_4, all_17_2) = v2 & % 18.80/3.56 | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v1 & % 18.80/3.56 | | | | | | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) % 18.80/3.56 | | | | | | | | v2 = 0 | v1 = 0)) % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | DELTA: instantiating (108) with fresh symbols all_85_0, all_85_1, % 18.80/3.56 | | | | | | | all_85_2 gives: % 18.80/3.56 | | | | | | | (109) apart_point_and_line(all_17_4, all_17_2) = all_85_0 & % 18.80/3.56 | | | | | | | apart_point_and_line(all_17_4, all_17_2) = all_85_1 & % 18.80/3.56 | | | | | | | distinct_lines(all_17_2, all_17_2) = all_85_2 & ( ~ % 18.80/3.56 | | | | | | | (all_85_2 = 0) | all_85_0 = 0 | all_85_1 = 0) % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | ALPHA: (109) implies: % 18.80/3.56 | | | | | | | (110) apart_point_and_line(all_17_4, all_17_2) = all_85_1 % 18.80/3.56 | | | | | | | (111) apart_point_and_line(all_17_4, all_17_2) = all_85_0 % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | BETA: splitting (89) gives: % 18.80/3.56 | | | | | | | % 18.80/3.56 | | | | | | | Case 1: % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | (112) all_28_0 = 0 % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | REDUCE: (82), (112) imply: % 18.80/3.56 | | | | | | | | (113) $false % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | CLOSE: (113) is inconsistent. % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | Case 2: % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 18.80/3.56 | | | | | | | | any] : (apart_point_and_line(all_17_5, all_17_2) = v3 % 18.80/3.56 | | | | | | | | & apart_point_and_line(all_17_5, all_17_2) = v2 & % 18.80/3.56 | | | | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 18.80/3.56 | | | | | | | | distinct_points(all_17_5, all_17_5) = v0 & ( ~ (v1 = % 18.80/3.56 | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | DELTA: instantiating (114) with fresh symbols all_90_0, % 18.80/3.56 | | | | | | | | all_90_1, all_90_2, all_90_3 gives: % 18.80/3.56 | | | | | | | | (115) apart_point_and_line(all_17_5, all_17_2) = all_90_0 & % 18.80/3.56 | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = all_90_1 & % 18.80/3.56 | | | | | | | | distinct_lines(all_17_2, all_17_2) = all_90_2 & % 18.80/3.56 | | | | | | | | distinct_points(all_17_5, all_17_5) = all_90_3 & ( ~ % 18.80/3.56 | | | | | | | | (all_90_2 = 0) | ~ (all_90_3 = 0) | all_90_0 = 0 | % 18.80/3.56 | | | | | | | | all_90_1 = 0) % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | ALPHA: (115) implies: % 18.80/3.56 | | | | | | | | (116) apart_point_and_line(all_17_5, all_17_2) = all_90_1 % 18.80/3.56 | | | | | | | | (117) apart_point_and_line(all_17_5, all_17_2) = all_90_0 % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | BETA: splitting (90) gives: % 18.80/3.56 | | | | | | | | % 18.80/3.56 | | | | | | | | Case 1: % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | (118) all_30_0 = 0 % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | REDUCE: (81), (118) imply: % 18.80/3.56 | | | | | | | | | (119) $false % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | CLOSE: (119) is inconsistent. % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | Case 2: % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | (120) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 18.80/3.56 | | | | | | | | | any] : ? [v3: any] : % 18.80/3.56 | | | | | | | | | (apart_point_and_line(all_17_3, all_17_2) = v2 & % 18.80/3.56 | | | | | | | | | apart_point_and_line(all_17_4, all_17_1) = v3 & % 18.80/3.56 | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.56 | | | | | | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ (v1 % 18.80/3.56 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | BETA: splitting (91) gives: % 18.80/3.56 | | | | | | | | | % 18.80/3.56 | | | | | | | | | Case 1: % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | (121) all_30_0 = 0 % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | REDUCE: (81), (121) imply: % 18.80/3.56 | | | | | | | | | | (122) $false % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | CLOSE: (122) is inconsistent. % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | Case 2: % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | (123) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.56 | | | | | | | | | | [v2: any] : ? [v3: any] : % 18.80/3.56 | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_2) = v3 & % 18.80/3.56 | | | | | | | | | | apart_point_and_line(all_17_4, all_17_1) = v2 & % 18.80/3.56 | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 18.80/3.56 | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 18.80/3.56 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | BETA: splitting (86) gives: % 18.80/3.56 | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | Case 1: % 18.80/3.56 | | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | | (124) all_28_0 = 0 % 18.80/3.56 | | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | | REDUCE: (82), (124) imply: % 18.80/3.56 | | | | | | | | | | | (125) $false % 18.80/3.56 | | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | | CLOSE: (125) is inconsistent. % 18.80/3.56 | | | | | | | | | | | % 18.80/3.56 | | | | | | | | | | Case 2: % 18.80/3.56 | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | (126) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.57 | | | | | | | | | | | [v2: any] : ? [v3: any] : % 18.80/3.57 | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_2) = v3 & % 18.80/3.57 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 18.80/3.57 | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | BETA: splitting (85) gives: % 18.80/3.57 | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | (127) all_28_0 = 0 % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | REDUCE: (82), (127) imply: % 18.80/3.57 | | | | | | | | | | | | (128) $false % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | CLOSE: (128) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | (129) all_17_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 18.80/3.57 | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 18.80/3.57 | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_2) = v2 & % 18.80/3.57 | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v3 & % 18.80/3.57 | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | BETA: splitting (92) gives: % 18.80/3.57 | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | (130) all_30_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | REDUCE: (81), (130) imply: % 18.80/3.57 | | | | | | | | | | | | | (131) $false % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | (132) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.80/3.57 | | | | | | | | | | | | | (apart_point_and_line(all_17_4, all_17_1) = v2 & % 18.80/3.57 | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_1) = v1 & % 18.80/3.57 | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_111_0, % 18.80/3.57 | | | | | | | | | | | | | all_111_1, all_111_2 gives: % 18.80/3.57 | | | | | | | | | | | | | (133) apart_point_and_line(all_17_4, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | all_111_0 & apart_point_and_line(all_17_4, % 18.80/3.57 | | | | | | | | | | | | | all_17_1) = all_111_1 & % 18.80/3.57 | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = all_111_2 & % 18.80/3.57 | | | | | | | | | | | | | ( ~ (all_111_2 = 0) | all_111_0 = 0 | all_111_1 = % 18.80/3.57 | | | | | | | | | | | | | 0) % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | ALPHA: (133) implies: % 18.80/3.57 | | | | | | | | | | | | | (134) apart_point_and_line(all_17_4, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | all_111_1 % 18.80/3.57 | | | | | | | | | | | | | (135) apart_point_and_line(all_17_4, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | all_111_0 % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | BETA: splitting (93) gives: % 18.80/3.57 | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | (136) all_30_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | REDUCE: (81), (136) imply: % 18.80/3.57 | | | | | | | | | | | | | | (137) $false % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | CLOSE: (137) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | (138) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.57 | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_4, % 18.80/3.57 | | | | | | | | | | | | | | all_17_2) = v3 & % 18.80/3.57 | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = v2 & % 18.80/3.57 | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | DELTA: instantiating (138) with fresh symbols all_116_0, % 18.80/3.57 | | | | | | | | | | | | | | all_116_1, all_116_2, all_116_3 gives: % 18.80/3.57 | | | | | | | | | | | | | | (139) apart_point_and_line(all_17_4, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | all_116_0 & apart_point_and_line(all_17_4, % 18.80/3.57 | | | | | | | | | | | | | | all_17_2) = all_116_1 & distinct_lines(all_17_2, % 18.80/3.57 | | | | | | | | | | | | | | all_17_2) = all_116_2 & % 18.80/3.57 | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_4) = all_116_3 & % 18.80/3.57 | | | | | | | | | | | | | | ( ~ (all_116_2 = 0) | ~ (all_116_3 = 0) | % 18.80/3.57 | | | | | | | | | | | | | | all_116_0 = 0 | all_116_1 = 0) % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | ALPHA: (139) implies: % 18.80/3.57 | | | | | | | | | | | | | | (140) apart_point_and_line(all_17_4, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | all_116_1 % 18.80/3.57 | | | | | | | | | | | | | | (141) apart_point_and_line(all_17_4, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | all_116_0 % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | BETA: splitting (120) gives: % 18.80/3.57 | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | (142) all_17_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | REDUCE: (16), (142) imply: % 18.80/3.57 | | | | | | | | | | | | | | | (143) $false % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | CLOSE: (143) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.57 | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.57 | | | | | | | | | | | | | | | all_17_2) = v2 & % 18.80/3.57 | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_1) = v3 & % 18.80/3.57 | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_4) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_127_0, % 18.80/3.57 | | | | | | | | | | | | | | | all_127_1, all_127_2, all_127_3 gives: % 18.80/3.57 | | | | | | | | | | | | | | | (145) apart_point_and_line(all_17_3, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | | all_127_1 & apart_point_and_line(all_17_4, % 18.80/3.57 | | | | | | | | | | | | | | | all_17_1) = all_127_0 & distinct_lines(all_17_1, % 18.80/3.57 | | | | | | | | | | | | | | | all_17_2) = all_127_2 & % 18.80/3.57 | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_4) = all_127_3 & % 18.80/3.57 | | | | | | | | | | | | | | | ( ~ (all_127_2 = 0) | ~ (all_127_3 = 0) | % 18.80/3.57 | | | | | | | | | | | | | | | all_127_0 = 0 | all_127_1 = 0) % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | ALPHA: (145) implies: % 18.80/3.57 | | | | | | | | | | | | | | | (146) apart_point_and_line(all_17_4, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | | | all_127_0 % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 18.80/3.57 | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | (147) all_17_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | REDUCE: (16), (147) imply: % 18.80/3.57 | | | | | | | | | | | | | | | | (148) $false % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | (149) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.57 | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.57 | | | | | | | | | | | | | | | | all_17_2) = v3 & % 18.80/3.57 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_4, all_17_1) = v2 & % 18.80/3.57 | | | | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1 & % 18.80/3.57 | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | DELTA: instantiating (149) with fresh symbols all_132_0, % 18.80/3.57 | | | | | | | | | | | | | | | | all_132_1, all_132_2, all_132_3 gives: % 18.80/3.57 | | | | | | | | | | | | | | | | (150) apart_point_and_line(all_17_3, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | | | all_132_0 & apart_point_and_line(all_17_4, % 18.80/3.57 | | | | | | | | | | | | | | | | all_17_1) = all_132_1 & distinct_lines(all_17_2, % 18.80/3.57 | | | | | | | | | | | | | | | | all_17_1) = all_132_2 & % 18.80/3.57 | | | | | | | | | | | | | | | | distinct_points(all_17_4, all_17_3) = all_132_3 & % 18.80/3.57 | | | | | | | | | | | | | | | | ( ~ (all_132_2 = 0) | ~ (all_132_3 = 0) | % 18.80/3.57 | | | | | | | | | | | | | | | | all_132_0 = 0 | all_132_1 = 0) % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 18.80/3.57 | | | | | | | | | | | | | | | | (151) apart_point_and_line(all_17_4, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | | | | all_132_1 % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 18.80/3.57 | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | (152) all_17_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | REDUCE: (16), (152) imply: % 18.80/3.57 | | | | | | | | | | | | | | | | | (153) $false % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.57 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.57 | | | | | | | | | | | | | | | | | all_17_2) = v3 & % 18.80/3.57 | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v2 & % 18.80/3.57 | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_137_0, % 18.80/3.57 | | | | | | | | | | | | | | | | | all_137_1, all_137_2, all_137_3 gives: % 18.80/3.57 | | | | | | | | | | | | | | | | | (155) apart_point_and_line(all_17_3, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | | | | all_137_0 & apart_point_and_line(all_17_5, % 18.80/3.57 | | | | | | | | | | | | | | | | | all_17_1) = all_137_1 & distinct_lines(all_17_1, % 18.80/3.57 | | | | | | | | | | | | | | | | | all_17_2) = all_137_2 & % 18.80/3.57 | | | | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_3) = all_137_3 & % 18.80/3.57 | | | | | | | | | | | | | | | | | ( ~ (all_137_2 = 0) | ~ (all_137_3 = 0) | % 18.80/3.57 | | | | | | | | | | | | | | | | | all_137_0 = 0 | all_137_1 = 0) % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | ALPHA: (155) implies: % 18.80/3.57 | | | | | | | | | | | | | | | | | (156) apart_point_and_line(all_17_5, all_17_1) = % 18.80/3.57 | | | | | | | | | | | | | | | | | all_137_1 % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 18.80/3.57 | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | (157) all_17_0 = 0 % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | REDUCE: (16), (157) imply: % 18.80/3.57 | | | | | | | | | | | | | | | | | | (158) $false % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | (159) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 18.80/3.57 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3, % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_17_2) = v2 & % 18.80/3.57 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = v3 & % 18.80/3.57 | | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 18.80/3.57 | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~ % 18.80/3.57 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_142_0, % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_142_1, all_142_2, all_142_3 gives: % 18.80/3.57 | | | | | | | | | | | | | | | | | | (160) apart_point_and_line(all_17_3, all_17_2) = % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_142_1 & apart_point_and_line(all_17_5, % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_17_1) = all_142_0 & distinct_lines(all_17_1, % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_17_2) = all_142_2 & % 18.80/3.57 | | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = all_142_3 & % 18.80/3.57 | | | | | | | | | | | | | | | | | | ( ~ (all_142_2 = 0) | ~ (all_142_3 = 0) | % 18.80/3.57 | | | | | | | | | | | | | | | | | | all_142_0 = 0 | all_142_1 = 0) % 18.80/3.57 | | | | | | | | | | | | | | | | | | % 18.80/3.57 | | | | | | | | | | | | | | | | | | ALPHA: (160) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (161) apart_point_and_line(all_17_5, all_17_1) = % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_142_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_28_0, all_90_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (76), (117) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (162) all_90_0 = all_28_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_90_1, all_90_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (116), (117) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (163) all_90_0 = all_90_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_67_3, all_90_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (95), (117) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (164) all_90_0 = all_67_3 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_26_0, all_137_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_5, simplifying with (41), (156) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (165) all_137_1 = all_26_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_80_0, all_137_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_5, simplifying with (105), (156) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (166) all_137_1 = all_80_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_80_1, all_137_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_5, simplifying with (104), (156) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (167) all_137_1 = all_80_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_80_0, all_142_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_5, simplifying with (105), (161) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (168) all_142_0 = all_80_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_67_2, all_142_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_5, simplifying with (96), (161) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (169) all_142_0 = all_67_2 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_85_1, all_85_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (110), (111) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (170) all_85_0 = all_85_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_30_0, all_116_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (75), (140) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (171) all_116_1 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_85_0, all_116_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (111), (140) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (172) all_116_1 = all_85_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_85_1, all_116_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (110), (141) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (173) all_116_0 = all_85_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_67_1, all_116_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_2, all_17_4, simplifying with (97), (141) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (174) all_116_0 = all_67_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_24_0, all_111_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (37), (135) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (175) all_111_0 = all_24_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_111_1, all_111_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (134), (135) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (176) all_111_0 = all_111_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_111_0, all_127_0, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (135), (146) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (177) all_127_0 = all_111_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_127_0, all_132_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (146), (151) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (178) all_132_1 = all_127_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_67_0, all_132_1, % 18.80/3.58 | | | | | | | | | | | | | | | | | | all_17_1, all_17_4, simplifying with (98), (151) % 18.80/3.58 | | | | | | | | | | | | | | | | | | gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (179) all_132_1 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (169) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (180) all_80_0 = all_67_2 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (180) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (181) all_80_0 = all_67_2 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (167) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (182) all_80_0 = all_80_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (182) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (183) all_80_0 = all_80_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (167) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (184) all_80_1 = all_26_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (179) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (185) all_127_0 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (185) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (186) all_127_0 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (186) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (187) all_111_0 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (187) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (188) all_111_0 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (174) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (189) all_85_1 = all_67_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (189) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (190) all_85_1 = all_67_1 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (172) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (191) all_85_0 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (191) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (192) all_85_0 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (176) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (193) all_111_1 = all_24_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (188) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (194) all_111_1 = all_67_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (195) all_67_0 = all_24_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (196) all_90_1 = all_28_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (164) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (197) all_90_1 = all_67_3 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (197) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (198) all_67_3 = all_28_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (198) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (199) all_67_3 = all_28_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (192) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (200) all_85_1 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (200) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (201) all_85_1 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (201) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (202) all_67_1 = all_30_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (183) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (203) all_80_1 = all_67_2 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (203) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (204) all_80_1 = all_67_2 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (204) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (205) all_67_2 = all_26_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | (206) all_67_2 = all_26_0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | (207) ~ (all_24_0 = 0) % 18.80/3.58 | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | (208) ~ (all_26_0 = 0) % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | (209) all_67_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (209) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | (210) all_24_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (210) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | (211) $false % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | (212) all_67_1 = 0 | all_67_2 = 0 | all_67_3 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | (213) all_67_1 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (213) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | (214) all_30_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | (215) all_30_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (215) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | (216) $false % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent. % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | (217) all_67_2 = 0 | all_67_3 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (218) all_67_2 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (218) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (219) all_26_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (220) all_26_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (220) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (221) $false % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (222) all_67_3 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (222) imply: % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | (223) all_28_0 = 0 % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (223) implies: % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | (224) all_28_0 = 0 % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (224) imply: % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | (225) $false % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | End of split % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | End of split % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | (226) ~ (all_26_1 = 0) % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (226) imply: % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | (227) ~ (all_24_1 = 0) % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (83), (227), (apart1) are inconsistent by % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 18.80/3.59 | | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | End of split % 18.80/3.59 | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | Case 2: % 18.80/3.59 | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | (228) ~ (all_24_1 = 0) % 18.80/3.59 | | | | | | | | | | | | | | | | | | | % 18.80/3.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (83), (228), (apart1) are inconsistent by % 18.80/3.59 | | | | | | | | | | | | | | | | | | | sub-proof #1. % 18.80/3.59 | | | | | | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | | % 19.29/3.59 | | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | | % 19.29/3.59 | | | | | | | | | End of split % 19.29/3.59 | | | | | | | | | % 19.29/3.59 | | | | | | | | End of split % 19.29/3.59 | | | | | | | | % 19.29/3.59 | | | | | | | End of split % 19.29/3.59 | | | | | | | % 19.29/3.59 | | | | | | End of split % 19.29/3.59 | | | | | | % 19.29/3.59 | | | | | End of split % 19.29/3.59 | | | | | % 19.29/3.59 | | | | Case 2: % 19.29/3.59 | | | | | % 19.29/3.59 | | | | | (229) ~ (all_34_1 = 0) % 19.29/3.59 | | | | | % 19.29/3.59 | | | | | REDUCE: (65), (229) imply: % 19.29/3.59 | | | | | (230) $false % 19.29/3.59 | | | | | % 19.29/3.59 | | | | | CLOSE: (230) is inconsistent. % 19.29/3.59 | | | | | % 19.29/3.59 | | | | End of split % 19.29/3.59 | | | | % 19.29/3.59 | | | Case 2: % 19.29/3.59 | | | | % 19.29/3.59 | | | | (231) ~ (all_32_1 = 0) % 19.29/3.59 | | | | % 19.29/3.59 | | | | REDUCE: (73), (231) imply: % 19.29/3.59 | | | | (232) $false % 19.29/3.59 | | | | % 19.29/3.59 | | | | CLOSE: (232) is inconsistent. % 19.29/3.59 | | | | % 19.29/3.59 | | | End of split % 19.29/3.59 | | | % 19.29/3.59 | | End of split % 19.29/3.59 | | % 19.29/3.59 | Case 2: % 19.29/3.59 | | % 19.29/3.59 | | (233) all_17_0 = 0 % 19.29/3.59 | | % 19.29/3.59 | | REDUCE: (16), (233) imply: % 19.29/3.59 | | (234) $false % 19.29/3.59 | | % 19.29/3.59 | | CLOSE: (234) is inconsistent. % 19.29/3.59 | | % 19.29/3.59 | End of split % 19.29/3.59 | % 19.29/3.59 End of proof % 19.29/3.59 % 19.29/3.59 Sub-proof #1 shows that the following formulas are inconsistent: % 19.29/3.59 ---------------------------------------------------------------- % 19.29/3.59 (1) all_24_1 = 0 | distinct_points(all_17_5, all_17_5) = 0 % 19.29/3.59 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 19.29/3.59 (3) $i(all_17_5) % 19.29/3.59 (4) ~ (all_24_1 = 0) % 19.29/3.59 % 19.29/3.59 Begin of proof % 19.29/3.59 | % 19.29/3.59 | BETA: splitting (1) gives: % 19.29/3.59 | % 19.29/3.59 | Case 1: % 19.29/3.59 | | % 19.29/3.59 | | (5) distinct_points(all_17_5, all_17_5) = 0 % 19.29/3.59 | | % 19.29/3.59 | | GROUND_INST: instantiating (2) with all_17_5, simplifying with (3), (5) % 19.29/3.59 | | gives: % 19.29/3.59 | | (6) $false % 19.29/3.59 | | % 19.29/3.59 | | CLOSE: (6) is inconsistent. % 19.29/3.59 | | % 19.29/3.59 | Case 2: % 19.29/3.59 | | % 19.29/3.59 | | (7) all_24_1 = 0 % 19.29/3.59 | | % 19.29/3.59 | | REDUCE: (4), (7) imply: % 19.29/3.59 | | (8) $false % 19.29/3.59 | | % 19.29/3.59 | | CLOSE: (8) is inconsistent. % 19.29/3.59 | | % 19.29/3.59 | End of split % 19.29/3.59 | % 19.29/3.59 End of proof % 19.29/3.59 % SZS output end Proof for theBenchmark % 19.29/3.59 % 19.29/3.59 2973ms %------------------------------------------------------------------------------