%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO213+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:23 EDT 2023 % Result : Theorem 12.89s 2.42s % Output : Proof 20.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO213+2 : TPTP v8.1.2. Released v3.3.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 23:10:53 EDT 2023 % 0.12/0.34 % CPUTime : % 0.66/0.63 ________ _____ % 0.66/0.63 ___ __ \_________(_)________________________________ % 0.66/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.63 (2023-06-19) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2023 % 0.66/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.63 Amanda Stjerna. % 0.66/0.63 Free software under BSD-3-Clause. % 0.66/0.63 % 0.66/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.63 % 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.64 Running up to 7 provers in parallel. % 0.76/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.76/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.76/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.76/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.76/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.76/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.76/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.61/1.06 Prover 4: Preprocessing ... % 2.61/1.06 Prover 1: Preprocessing ... % 3.00/1.10 Prover 6: Preprocessing ... % 3.00/1.10 Prover 0: Preprocessing ... % 3.00/1.10 Prover 5: Preprocessing ... % 3.00/1.10 Prover 3: Preprocessing ... % 3.00/1.10 Prover 2: Preprocessing ... % 5.08/1.37 Prover 5: Proving ... % 5.08/1.39 Prover 2: Proving ... % 5.08/1.43 Prover 1: Constructing countermodel ... % 5.08/1.43 Prover 6: Constructing countermodel ... % 5.08/1.45 Prover 3: Constructing countermodel ... % 6.41/1.56 Prover 3: gave up % 6.41/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.41/1.58 Prover 6: gave up % 6.41/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.41/1.60 Prover 1: gave up % 6.41/1.60 Prover 4: Constructing countermodel ... % 6.41/1.60 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.41/1.61 Prover 8: Preprocessing ... % 6.41/1.61 Prover 0: Proving ... % 6.41/1.61 Prover 7: Preprocessing ... % 6.94/1.63 Prover 9: Preprocessing ... % 7.27/1.68 Prover 7: Warning: ignoring some quantifiers % 7.27/1.70 Prover 7: Constructing countermodel ... % 7.92/1.76 Prover 7: gave up % 7.92/1.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.92/1.77 Prover 8: Warning: ignoring some quantifiers % 8.12/1.79 Prover 8: Constructing countermodel ... % 8.12/1.82 Prover 10: Preprocessing ... % 8.58/1.89 Prover 10: Warning: ignoring some quantifiers % 8.58/1.89 Prover 8: gave up % 8.58/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.58/1.90 Prover 10: Constructing countermodel ... % 9.11/1.91 Prover 11: Preprocessing ... % 9.11/1.92 Prover 9: Constructing countermodel ... % 9.11/1.94 Prover 10: gave up % 9.11/1.96 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.56/1.98 Prover 12: Preprocessing ... % 10.19/2.07 Prover 12: Proving ... % 10.72/2.13 Prover 11: Constructing countermodel ... % 12.89/2.41 Prover 0: proved (1767ms) % 12.89/2.42 % 12.89/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.89/2.42 % 12.89/2.42 Prover 9: stopped % 12.89/2.42 Prover 2: stopped % 12.89/2.42 Prover 12: stopped % 12.89/2.42 Prover 5: stopped % 12.89/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.89/2.42 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.89/2.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.14/2.45 Prover 13: Preprocessing ... % 13.14/2.45 Prover 16: Preprocessing ... % 13.14/2.46 Prover 19: Preprocessing ... % 13.14/2.47 Prover 16: Warning: ignoring some quantifiers % 13.14/2.48 Prover 13: Warning: ignoring some quantifiers % 13.14/2.48 Prover 16: Constructing countermodel ... % 13.14/2.48 Prover 13: Constructing countermodel ... % 13.14/2.51 Prover 13: gave up % 13.14/2.52 Prover 16: gave up % 13.76/2.53 Prover 19: Warning: ignoring some quantifiers % 13.76/2.54 Prover 19: Constructing countermodel ... % 13.76/2.58 Prover 19: gave up % 19.36/3.61 Prover 11: Found proof (size 662) % 19.36/3.61 Prover 11: proved (1718ms) % 19.36/3.61 Prover 4: stopped % 19.36/3.61 % 19.36/3.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.36/3.61 % 19.78/3.65 % SZS output start Proof for theBenchmark % 19.78/3.66 Assumptions after simplification: % 19.78/3.66 --------------------------------- % 19.78/3.66 % 19.78/3.66 (apart3) % 19.98/3.68 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 19.98/3.68 % 19.98/3.68 (apart6) % 19.98/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 19.98/3.69 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 19.98/3.69 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 19.98/3.69 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 19.98/3.69 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 19.98/3.69 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.69 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.98/3.69 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 19.98/3.69 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.69 convergent_lines(v1, v2) = 0) % 19.98/3.69 % 19.98/3.69 (ceq3) % 19.98/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0, % 19.98/3.69 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 19.98/3.69 convergent_lines(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 19.98/3.69 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, % 19.98/3.69 v1) = 0) % 19.98/3.69 % 19.98/3.69 (con) % 19.98/3.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 19.98/3.70 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & % 19.98/3.70 unorthogonal_lines(v0, v1) = 0 & distinct_lines(v0, v2) = v3 & $i(v2) & % 19.98/3.70 $i(v1) & $i(v0)) % 19.98/3.70 % 19.98/3.70 (oac1) % 19.98/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 19.98/3.72 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 19.98/3.72 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 19.98/3.72 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 19.98/3.72 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 19.98/3.72 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 19.98/3.72 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 19.98/3.72 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 19.98/3.72 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.98/3.72 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 19.98/3.72 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 19.98/3.72 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 19.98/3.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 19.98/3.72 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 19.98/3.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 19.98/3.72 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 19.98/3.72 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 19.98/3.72 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 19.98/3.72 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 19.98/3.72 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 19.98/3.72 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 19.98/3.72 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 19.98/3.72 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 19.98/3.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 19.98/3.72 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 19.98/3.72 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 19.98/3.72 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 19.98/3.72 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 19.98/3.72 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 19.98/3.72 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.98/3.72 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 19.98/3.72 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 19.98/3.72 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 19.98/3.72 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 19.98/3.72 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.98/3.72 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 19.98/3.72 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.72 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.98/3.72 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 19.98/3.72 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.98/3.72 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 19.98/3.72 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.72 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.98/3.72 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 19.98/3.72 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.98/3.72 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 19.98/3.72 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 19.98/3.72 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 19.98/3.72 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.98/3.72 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 19.98/3.72 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.72 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.98/3.72 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 19.98/3.72 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.98/3.72 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 19.98/3.72 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 19.98/3.72 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 19.98/3.72 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 19.98/3.72 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.98/3.72 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.72 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 19.98/3.72 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.72 unorthogonal_lines(v0, v1) = v4))) % 19.98/3.72 % 19.98/3.72 (occu1) % 19.98/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 19.98/3.72 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.72 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 19.98/3.72 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.72 unorthogonal_lines(v0, v1) = 0) % 19.98/3.72 % 19.98/3.72 (function-axioms) % 19.98/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.98/3.73 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 19.98/3.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 19.98/3.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 19.98/3.73 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.98/3.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 19.98/3.73 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.98/3.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 19.98/3.73 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 19.98/3.73 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 19.98/3.73 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.98/3.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.98/3.73 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 19.98/3.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.98/3.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 19.98/3.73 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.98/3.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.98/3.73 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 19.98/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.98/3.73 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 19.98/3.73 v0)) % 19.98/3.73 % 19.98/3.73 Further assumptions not needed in the proof: % 19.98/3.73 -------------------------------------------- % 19.98/3.73 apart1, apart2, apart4, apart5, ceq1, ceq2, con1, con2, cp1, cp2, cu1, cup1, % 19.98/3.73 ooc1, ooc2, ouo1 % 19.98/3.73 % 19.98/3.73 Those formulas are unsatisfiable: % 19.98/3.73 --------------------------------- % 19.98/3.73 % 19.98/3.73 Begin of proof % 19.98/3.73 | % 19.98/3.73 | ALPHA: (apart6) implies: % 19.98/3.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.98/3.73 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 19.98/3.73 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 19.98/3.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.98/3.73 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 19.98/3.73 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 19.98/3.73 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 19.98/3.73 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 19.98/3.73 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.73 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 19.98/3.73 | % 19.98/3.73 | ALPHA: (ceq3) implies: % 19.98/3.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 19.98/3.73 | (distinct_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 19.98/3.73 | : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 19.98/3.73 | % 19.98/3.73 | ALPHA: (occu1) implies: % 19.98/3.73 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 19.98/3.73 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.73 | unorthogonal_lines(v0, v1) = 0) % 19.98/3.73 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 19.98/3.73 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 19.98/3.73 | convergent_lines(v0, v1) = 0) % 19.98/3.73 | % 19.98/3.73 | ALPHA: (oac1) implies: % 19.98/3.74 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.98/3.74 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 19.98/3.74 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 19.98/3.74 | [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v1, % 19.98/3.74 | v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & % 19.98/3.74 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.74 | unorthogonal_lines(v0, v1) = v4))) % 19.98/3.74 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.98/3.74 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 19.98/3.74 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 19.98/3.74 | [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & unorthogonal_lines(v1, % 19.98/3.74 | v2) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v0, v2) = 0 & % 19.98/3.74 | convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.74 | unorthogonal_lines(v0, v1) = v4))) % 19.98/3.74 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.98/3.74 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) % 19.98/3.74 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 19.98/3.74 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.74 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 19.98/3.74 | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.74 | convergent_lines(v0, v1) = v4))) % 19.98/3.74 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.98/3.74 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = % 19.98/3.74 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 19.98/3.74 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.98/3.74 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 19.98/3.74 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.98/3.74 | unorthogonal_lines(v0, v1) = v4))) % 20.32/3.74 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 20.32/3.74 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 20.32/3.74 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 20.32/3.74 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 20.32/3.74 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 20.32/3.74 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 20.32/3.74 | convergent_lines(v0, v1) = v4))) % 20.32/3.75 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 20.32/3.75 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 20.32/3.75 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 20.32/3.75 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 20.32/3.75 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 20.32/3.75 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 20.32/3.75 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 20.32/3.75 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 20.32/3.75 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 20.32/3.75 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 20.32/3.75 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 20.32/3.75 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 20.32/3.75 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 20.32/3.75 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 20.32/3.75 | convergent_lines(v0, v1) = v5))) % 20.32/3.75 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 20.32/3.75 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) % 20.32/3.75 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 20.32/3.75 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 20.32/3.75 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 20.32/3.75 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 20.32/3.75 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 20.32/3.75 | convergent_lines(v0, v1) = v5))) % 20.32/3.75 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 20.32/3.75 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) % 20.32/3.75 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 20.32/3.75 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 20.32/3.75 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 20.32/3.75 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 20.32/3.75 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 20.32/3.75 | convergent_lines(v0, v1) = v5))) % 20.32/3.75 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 20.32/3.75 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, % 20.32/3.75 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 20.32/3.75 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 20.32/3.75 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 20.32/3.75 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 20.32/3.75 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 20.32/3.75 | convergent_lines(v0, v1) = v5))) % 20.32/3.75 | % 20.32/3.75 | ALPHA: (function-axioms) implies: % 20.32/3.75 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.32/3.75 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.32/3.75 | (convergent_lines(v3, v2) = v0)) % 20.32/3.75 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.32/3.75 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 20.32/3.75 | (unorthogonal_lines(v3, v2) = v0)) % 20.32/3.75 | % 20.32/3.75 | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2, % 20.32/3.75 | all_23_3, all_23_4 gives: % 20.32/3.76 | (19) ~ (all_23_0 = 0) & ~ (all_23_1 = 0) & unorthogonal_lines(all_23_3, % 20.32/3.76 | all_23_2) = all_23_0 & unorthogonal_lines(all_23_4, all_23_3) = 0 & % 20.32/3.76 | distinct_lines(all_23_4, all_23_2) = all_23_1 & $i(all_23_2) & % 20.32/3.76 | $i(all_23_3) & $i(all_23_4) % 20.32/3.76 | % 20.32/3.76 | ALPHA: (19) implies: % 20.32/3.76 | (20) ~ (all_23_1 = 0) % 20.32/3.76 | (21) ~ (all_23_0 = 0) % 20.32/3.76 | (22) $i(all_23_4) % 20.32/3.76 | (23) $i(all_23_3) % 20.32/3.76 | (24) $i(all_23_2) % 20.32/3.76 | (25) distinct_lines(all_23_4, all_23_2) = all_23_1 % 20.32/3.76 | (26) unorthogonal_lines(all_23_4, all_23_3) = 0 % 20.32/3.76 | (27) unorthogonal_lines(all_23_3, all_23_2) = all_23_0 % 20.32/3.76 | % 20.32/3.76 | GROUND_INST: instantiating (4) with all_23_4, all_23_2, all_23_1, simplifying % 20.32/3.76 | with (22), (24), (25) gives: % 20.32/3.76 | (28) all_23_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 20.32/3.76 | convergent_lines(all_23_4, all_23_2) = v0) % 20.32/3.76 | % 20.32/3.76 | GROUND_INST: instantiating (16) with all_23_4, all_23_4, all_23_3, 0, 0, % 20.32/3.76 | simplifying with (22), (23), (26) gives: % 20.32/3.76 | (29) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.32/3.76 | convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0 & % 20.32/3.76 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) & % 20.32/3.76 | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = 0) & % 20.32/3.76 | convergent_lines(all_23_4, all_23_4) = v0)) % 20.32/3.76 | % 20.32/3.76 | GROUND_INST: instantiating (11) with all_23_4, all_23_3, all_23_3, 0, % 20.32/3.76 | simplifying with (22), (23), (26) gives: % 20.32/3.76 | (30) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.32/3.76 | v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0 & % 20.32/3.76 | convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 & % 20.32/3.76 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v0 = 0) & % 20.32/3.76 | convergent_lines(all_23_4, all_23_3) = v0)) % 20.32/3.76 | % 20.32/3.76 | GROUND_INST: instantiating (16) with all_23_3, all_23_3, all_23_2, all_23_0, % 20.32/3.76 | all_23_0, simplifying with (23), (24), (27) gives: % 20.32/3.76 | (31) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.32/3.76 | all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0 % 20.32/3.76 | & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~ % 20.32/3.76 | (v1 = 0) & unorthogonal_lines(all_23_3, all_23_3) = v1) | ( ~ (v0 % 20.32/3.76 | = 0) & convergent_lines(all_23_3, all_23_3) = v0)) % 20.32/3.76 | % 20.32/3.76 | GROUND_INST: instantiating (12) with all_23_4, all_23_3, all_23_2, all_23_0, % 20.32/3.76 | simplifying with (22), (23), (24), (26), (27) gives: % 20.43/3.77 | (32) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.43/3.77 | all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0 % 20.43/3.77 | & v1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0 & % 20.43/3.77 | convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) & % 20.43/3.77 | convergent_lines(all_23_4, all_23_3) = v0)) % 20.43/3.77 | % 20.43/3.77 | GROUND_INST: instantiating (6) with all_23_3, all_23_2, all_23_0, simplifying % 20.43/3.77 | with (23), (24), (27) gives: % 20.43/3.77 | (33) all_23_0 = 0 | convergent_lines(all_23_3, all_23_2) = 0 % 20.43/3.77 | % 20.43/3.77 | DELTA: instantiating (30) with fresh symbols all_30_0, all_30_1, all_30_2, % 20.43/3.77 | all_30_3 gives: % 20.43/3.77 | (34) (all_30_0 = 0 & all_30_1 = 0 & unorthogonal_lines(all_23_3, all_23_3) % 20.43/3.77 | = 0 & convergent_lines(all_23_3, all_23_3) = 0) | (all_30_2 = 0 & % 20.43/3.77 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_30_3 = 0) & % 20.43/3.77 | convergent_lines(all_23_4, all_23_3) = all_30_3) % 20.43/3.77 | % 20.43/3.77 | DELTA: instantiating (29) with fresh symbols all_31_0, all_31_1, all_31_2, % 20.43/3.77 | all_31_3 gives: % 20.43/3.77 | (35) (all_31_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (all_31_1 % 20.43/3.77 | = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_31_2 = 0) % 20.43/3.77 | & unorthogonal_lines(all_23_4, all_23_4) = all_31_2) | ( ~ (all_31_3 % 20.43/3.77 | = 0) & convergent_lines(all_23_4, all_23_4) = all_31_3) % 20.43/3.77 | % 20.43/3.77 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2, % 20.43/3.77 | all_32_3 gives: % 20.43/3.77 | (36) (all_32_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = % 20.43/3.77 | 0) | (all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.77 | all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) | ( ~ % 20.43/3.77 | (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_32_3) % 20.43/3.77 | % 20.43/3.77 | DELTA: instantiating (31) with fresh symbols all_33_0, all_33_1, all_33_2, % 20.43/3.77 | all_33_3 gives: % 20.43/3.77 | (37) (all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = % 20.43/3.77 | 0) | (all_33_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, % 20.43/3.77 | all_23_2) = 0) | ( ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3, % 20.43/3.77 | all_23_3) = all_33_2) | ( ~ (all_33_3 = 0) & % 20.43/3.77 | convergent_lines(all_23_3, all_23_3) = all_33_3) % 20.43/3.77 | % 20.43/3.77 | BETA: splitting (33) gives: % 20.43/3.77 | % 20.43/3.77 | Case 1: % 20.43/3.77 | | % 20.43/3.77 | | (38) convergent_lines(all_23_3, all_23_2) = 0 % 20.43/3.77 | | % 20.43/3.77 | | BETA: splitting (28) gives: % 20.43/3.77 | | % 20.43/3.77 | | Case 1: % 20.43/3.77 | | | % 20.43/3.77 | | | (39) all_23_1 = 0 % 20.43/3.77 | | | % 20.43/3.77 | | | REDUCE: (20), (39) imply: % 20.43/3.77 | | | (40) $false % 20.43/3.77 | | | % 20.43/3.77 | | | CLOSE: (40) is inconsistent. % 20.43/3.77 | | | % 20.43/3.77 | | Case 2: % 20.43/3.77 | | | % 20.43/3.77 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4, all_23_2) % 20.43/3.77 | | | = v0) % 20.43/3.77 | | | % 20.43/3.77 | | | DELTA: instantiating (41) with fresh symbol all_40_0 gives: % 20.43/3.77 | | | (42) ~ (all_40_0 = 0) & convergent_lines(all_23_4, all_23_2) = % 20.43/3.77 | | | all_40_0 % 20.43/3.77 | | | % 20.43/3.77 | | | ALPHA: (42) implies: % 20.43/3.77 | | | (43) ~ (all_40_0 = 0) % 20.43/3.77 | | | (44) convergent_lines(all_23_4, all_23_2) = all_40_0 % 20.43/3.77 | | | % 20.43/3.77 | | | BETA: splitting (36) gives: % 20.43/3.77 | | | % 20.43/3.77 | | | Case 1: % 20.43/3.77 | | | | % 20.43/3.77 | | | | (45) all_32_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, % 20.43/3.77 | | | | all_23_2) = 0 % 20.43/3.77 | | | | % 20.43/3.77 | | | | ALPHA: (45) implies: % 20.43/3.77 | | | | (46) all_23_0 = 0 % 20.43/3.77 | | | | % 20.43/3.77 | | | | REDUCE: (21), (46) imply: % 20.43/3.77 | | | | (47) $false % 20.43/3.77 | | | | % 20.43/3.77 | | | | CLOSE: (47) is inconsistent. % 20.43/3.77 | | | | % 20.43/3.77 | | | Case 2: % 20.43/3.77 | | | | % 20.43/3.77 | | | | (48) (all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.77 | | | | all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) | % 20.43/3.77 | | | | ( ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = % 20.43/3.77 | | | | all_32_3) % 20.43/3.77 | | | | % 20.43/3.77 | | | | BETA: splitting (48) gives: % 20.43/3.77 | | | | % 20.43/3.77 | | | | Case 1: % 20.43/3.77 | | | | | % 20.43/3.77 | | | | | (49) all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.77 | | | | | all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0 % 20.43/3.77 | | | | | % 20.43/3.77 | | | | | ALPHA: (49) implies: % 20.43/3.77 | | | | | (50) convergent_lines(all_23_4, all_23_2) = 0 % 20.43/3.77 | | | | | % 20.43/3.77 | | | | | GROUND_INST: instantiating (17) with 0, all_40_0, all_23_2, all_23_4, % 20.43/3.77 | | | | | simplifying with (44), (50) gives: % 20.43/3.78 | | | | | (51) all_40_0 = 0 % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | REDUCE: (43), (51) imply: % 20.43/3.78 | | | | | (52) $false % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | CLOSE: (52) is inconsistent. % 20.43/3.78 | | | | | % 20.43/3.78 | | | | Case 2: % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | (53) ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = % 20.43/3.78 | | | | | all_32_3 % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | ALPHA: (53) implies: % 20.43/3.78 | | | | | (54) ~ (all_32_3 = 0) % 20.43/3.78 | | | | | (55) convergent_lines(all_23_4, all_23_3) = all_32_3 % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_3, % 20.43/3.78 | | | | | all_32_3, all_32_3, simplifying with (22), (23), (55) % 20.43/3.78 | | | | | gives: % 20.43/3.78 | | | | | (56) all_32_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 20.43/3.78 | | | | | convergent_lines(all_23_4, all_23_4) = v0) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4, all_23_3, % 20.43/3.78 | | | | | all_32_3, all_32_3, simplifying with (22), (23), (55) % 20.43/3.78 | | | | | gives: % 20.43/3.78 | | | | | (57) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & all_32_3 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.78 | | | | | all_23_3) = 0) | (v2 = 0 & all_32_3 = 0 & % 20.43/3.78 | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) % 20.43/3.78 | | | | | & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.78 | | | | | 0) & convergent_lines(all_23_4, all_23_4) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4, all_23_3, % 20.43/3.78 | | | | | all_32_3, 0, simplifying with (22), (23), (26), (55) % 20.43/3.78 | | | | | gives: % 20.43/3.78 | | | | | (58) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0 % 20.43/3.78 | | | | | & all_32_3 = 0) | ( ~ (v1 = 0) & % 20.43/3.78 | | | | | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.78 | | | | | 0) & convergent_lines(all_23_4, all_23_4) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4, all_23_3, 0, % 20.43/3.78 | | | | | all_32_3, simplifying with (22), (23), (26), (55) gives: % 20.43/3.78 | | | | | (59) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & all_32_3 = 0) | (v2 = 0 & % 20.43/3.78 | | | | | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) & % 20.43/3.78 | | | | | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.78 | | | | | 0) & convergent_lines(all_23_4, all_23_4) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3, all_23_3, % 20.43/3.78 | | | | | all_32_3, simplifying with (22), (23), (26), (55) gives: % 20.43/3.78 | | | | | (60) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0 % 20.43/3.78 | | | | | & convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 & % 20.43/3.78 | | | | | all_32_3 = 0) | ( ~ (v0 = 0) & convergent_lines(all_23_4, % 20.43/3.78 | | | | | all_23_3) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_2, % 20.43/3.78 | | | | | all_40_0, all_40_0, simplifying with (22), (24), (44) % 20.43/3.78 | | | | | gives: % 20.43/3.78 | | | | | (61) all_40_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 20.43/3.78 | | | | | convergent_lines(all_23_4, all_23_4) = v0) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4, all_23_2, % 20.43/3.78 | | | | | all_40_0, all_40_0, simplifying with (22), (24), (44) % 20.43/3.78 | | | | | gives: % 20.43/3.78 | | | | | (62) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.78 | | | | | all_23_2) = 0) | (v2 = 0 & all_40_0 = 0 & % 20.43/3.78 | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (v1 = 0) % 20.43/3.78 | | | | | & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.78 | | | | | 0) & convergent_lines(all_23_4, all_23_4) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (14) with all_23_3, all_23_4, all_23_2, % 20.43/3.78 | | | | | all_23_0, all_40_0, simplifying with (22), (23), (24), % 20.43/3.78 | | | | | (27), (44) gives: % 20.43/3.78 | | | | | (63) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.78 | | | | | ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.78 | | | | | all_23_2) = 0) | (v2 = 0 & all_23_0 = 0 & % 20.43/3.78 | | | | | convergent_lines(all_23_3, all_23_2) = 0) | ( ~ (v1 = 0) & % 20.43/3.78 | | | | | unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.78 | | | | | 0) & convergent_lines(all_23_3, all_23_4) = v0)) % 20.43/3.78 | | | | | % 20.43/3.78 | | | | | GROUND_INST: instantiating (5) with all_23_4, all_23_2, all_40_0, % 20.43/3.78 | | | | | simplifying with (22), (24), (44) gives: % 20.43/3.79 | | | | | (64) all_40_0 = 0 | unorthogonal_lines(all_23_4, all_23_2) = 0 % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | GROUND_INST: instantiating (7) with all_23_3, all_23_2, all_23_2, 0, % 20.43/3.79 | | | | | simplifying with (23), (24), (38) gives: % 20.43/3.79 | | | | | (65) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.79 | | | | | ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0 % 20.43/3.79 | | | | | & convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~ (v0 = 0) % 20.43/3.79 | | | | | & unorthogonal_lines(all_23_3, all_23_2) = v0)) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | GROUND_INST: instantiating (13) with all_23_3, all_23_4, all_23_2, 0, % 20.43/3.79 | | | | | all_40_0, simplifying with (22), (23), (24), (38), (44) % 20.43/3.79 | | | | | gives: % 20.43/3.79 | | | | | (66) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.79 | | | | | ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.79 | | | | | all_23_2) = 0) | (v2 = 0 & unorthogonal_lines(all_23_3, % 20.43/3.79 | | | | | all_23_2) = 0) | ( ~ (v1 = 0) & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0 = % 20.43/3.79 | | | | | 0) & convergent_lines(all_23_3, all_23_4) = v0)) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | GROUND_INST: instantiating (10) with all_23_3, all_23_2, all_23_2, % 20.43/3.79 | | | | | all_23_0, simplifying with (23), (24), (27), (38) gives: % 20.43/3.79 | | | | | (67) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 20.43/3.79 | | | | | ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0 % 20.43/3.79 | | | | | & convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 & % 20.43/3.79 | | | | | all_23_0 = 0) | ( ~ (v0 = 0) & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_3, all_23_2) = v0)) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (65) with fresh symbols all_57_0, all_57_1, % 20.43/3.79 | | | | | all_57_2, all_57_3 gives: % 20.43/3.79 | | | | | (68) (all_57_0 = 0 & all_57_1 = 0 & unorthogonal_lines(all_23_2, % 20.43/3.79 | | | | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) % 20.43/3.79 | | | | | | (all_57_2 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0) % 20.43/3.79 | | | | | | ( ~ (all_57_3 = 0) & unorthogonal_lines(all_23_3, all_23_2) % 20.43/3.79 | | | | | = all_57_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (58) with fresh symbols all_58_0, all_58_1, % 20.43/3.79 | | | | | all_58_2, all_58_3 gives: % 20.43/3.79 | | | | | (69) (all_58_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | % 20.43/3.79 | | | | | (all_58_1 = 0 & all_32_3 = 0) | ( ~ (all_58_2 = 0) & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_4, all_23_4) = all_58_2) | ( ~ % 20.43/3.79 | | | | | (all_58_3 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.79 | | | | | all_58_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (60) with fresh symbols all_60_0, all_60_1, % 20.43/3.79 | | | | | all_60_2, all_60_3 gives: % 20.43/3.79 | | | | | (70) (all_60_0 = 0 & all_60_1 = 0 & unorthogonal_lines(all_23_3, % 20.43/3.79 | | | | | all_23_3) = 0 & convergent_lines(all_23_3, all_23_3) = 0) % 20.43/3.79 | | | | | | (all_60_2 = 0 & all_32_3 = 0) | ( ~ (all_60_3 = 0) & % 20.43/3.79 | | | | | convergent_lines(all_23_4, all_23_3) = all_60_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (59) with fresh symbols all_61_0, all_61_1, % 20.43/3.79 | | | | | all_61_2, all_61_3 gives: % 20.43/3.79 | | | | | (71) (all_61_0 = 0 & all_32_3 = 0) | (all_61_1 = 0 & % 20.43/3.79 | | | | | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_61_2 = % 20.43/3.79 | | | | | 0) & unorthogonal_lines(all_23_4, all_23_4) = all_61_2) | % 20.43/3.79 | | | | | ( ~ (all_61_3 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.79 | | | | | all_61_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (67) with fresh symbols all_62_0, all_62_1, % 20.43/3.79 | | | | | all_62_2, all_62_3 gives: % 20.43/3.79 | | | | | (72) (all_62_0 = 0 & all_62_1 = 0 & unorthogonal_lines(all_23_2, % 20.43/3.79 | | | | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) % 20.43/3.79 | | | | | | (all_62_2 = 0 & all_23_0 = 0) | ( ~ (all_62_3 = 0) & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_3, all_23_2) = all_62_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (66) with fresh symbols all_65_0, all_65_1, % 20.43/3.79 | | | | | all_65_2, all_65_3 gives: % 20.43/3.79 | | | | | (73) (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.79 | | | | | all_23_2) = 0) | (all_65_1 = 0 & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~ (all_65_2 % 20.43/3.79 | | | | | = 0) & unorthogonal_lines(all_23_3, all_23_4) = all_65_2) % 20.43/3.79 | | | | | | ( ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) = % 20.43/3.79 | | | | | all_65_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (63) with fresh symbols all_66_0, all_66_1, % 20.43/3.79 | | | | | all_66_2, all_66_3 gives: % 20.43/3.79 | | | | | (74) (all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.79 | | | | | all_23_2) = 0) | (all_66_1 = 0 & all_23_0 = 0 & % 20.43/3.79 | | | | | convergent_lines(all_23_3, all_23_2) = 0) | ( ~ (all_66_2 = % 20.43/3.79 | | | | | 0) & unorthogonal_lines(all_23_3, all_23_4) = all_66_2) | % 20.43/3.79 | | | | | ( ~ (all_66_3 = 0) & convergent_lines(all_23_3, all_23_4) = % 20.43/3.79 | | | | | all_66_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (62) with fresh symbols all_67_0, all_67_1, % 20.43/3.79 | | | | | all_67_2, all_67_3 gives: % 20.43/3.79 | | | | | (75) (all_67_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.79 | | | | | all_23_2) = 0) | (all_67_1 = 0 & all_40_0 = 0 & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (all_67_2 % 20.43/3.79 | | | | | = 0) & unorthogonal_lines(all_23_4, all_23_4) = all_67_2) % 20.43/3.79 | | | | | | ( ~ (all_67_3 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.79 | | | | | all_67_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | DELTA: instantiating (57) with fresh symbols all_68_0, all_68_1, % 20.43/3.79 | | | | | all_68_2, all_68_3 gives: % 20.43/3.79 | | | | | (76) (all_68_0 = 0 & all_32_3 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.79 | | | | | all_23_3) = 0) | (all_68_1 = 0 & all_32_3 = 0 & % 20.43/3.79 | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~ (all_68_2 % 20.43/3.79 | | | | | = 0) & unorthogonal_lines(all_23_4, all_23_4) = all_68_2) % 20.43/3.79 | | | | | | ( ~ (all_68_3 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.79 | | | | | all_68_3) % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | BETA: splitting (64) gives: % 20.43/3.79 | | | | | % 20.43/3.79 | | | | | Case 1: % 20.43/3.79 | | | | | | % 20.43/3.79 | | | | | | (77) unorthogonal_lines(all_23_4, all_23_2) = 0 % 20.43/3.79 | | | | | | % 20.43/3.79 | | | | | | BETA: splitting (61) gives: % 20.43/3.79 | | | | | | % 20.43/3.79 | | | | | | Case 1: % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | (78) all_40_0 = 0 % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | REDUCE: (43), (78) imply: % 20.43/3.79 | | | | | | | (79) $false % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | CLOSE: (79) is inconsistent. % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | Case 2: % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4, % 20.43/3.79 | | | | | | | all_23_4) = v0) % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | DELTA: instantiating (80) with fresh symbol all_76_0 gives: % 20.43/3.79 | | | | | | | (81) ~ (all_76_0 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.79 | | | | | | | all_76_0 % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | ALPHA: (81) implies: % 20.43/3.79 | | | | | | | (82) convergent_lines(all_23_4, all_23_4) = all_76_0 % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | BETA: splitting (56) gives: % 20.43/3.79 | | | | | | | % 20.43/3.79 | | | | | | | Case 1: % 20.43/3.79 | | | | | | | | % 20.43/3.79 | | | | | | | | (83) all_32_3 = 0 % 20.43/3.79 | | | | | | | | % 20.43/3.79 | | | | | | | | REDUCE: (54), (83) imply: % 20.43/3.79 | | | | | | | | (84) $false % 20.43/3.79 | | | | | | | | % 20.43/3.79 | | | | | | | | CLOSE: (84) is inconsistent. % 20.43/3.79 | | | | | | | | % 20.43/3.79 | | | | | | | Case 2: % 20.43/3.79 | | | | | | | | % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | DELTA: instantiating (80) with fresh symbol all_81_0 gives: % 20.43/3.80 | | | | | | | | (85) ~ (all_81_0 = 0) & convergent_lines(all_23_4, all_23_4) % 20.43/3.80 | | | | | | | | = all_81_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | ALPHA: (85) implies: % 20.43/3.80 | | | | | | | | (86) ~ (all_81_0 = 0) % 20.43/3.80 | | | | | | | | (87) convergent_lines(all_23_4, all_23_4) = all_81_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | DELTA: instantiating (80) with fresh symbol all_86_0 gives: % 20.43/3.80 | | | | | | | | (88) ~ (all_86_0 = 0) & convergent_lines(all_23_4, all_23_4) % 20.43/3.80 | | | | | | | | = all_86_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | ALPHA: (88) implies: % 20.43/3.80 | | | | | | | | (89) convergent_lines(all_23_4, all_23_4) = all_86_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (17) with all_81_0, all_86_0, % 20.43/3.80 | | | | | | | | all_23_4, all_23_4, simplifying with (87), (89) % 20.43/3.80 | | | | | | | | gives: % 20.43/3.80 | | | | | | | | (90) all_86_0 = all_81_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (17) with all_76_0, all_86_0, % 20.43/3.80 | | | | | | | | all_23_4, all_23_4, simplifying with (82), (89) % 20.43/3.80 | | | | | | | | gives: % 20.43/3.80 | | | | | | | | (91) all_86_0 = all_76_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | COMBINE_EQS: (90), (91) imply: % 20.43/3.80 | | | | | | | | (92) all_81_0 = all_76_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | SIMP: (92) implies: % 20.43/3.80 | | | | | | | | (93) all_81_0 = all_76_0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | REDUCE: (86), (93) imply: % 20.43/3.80 | | | | | | | | (94) ~ (all_76_0 = 0) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4, % 20.43/3.80 | | | | | | | | all_23_4, all_76_0, all_76_0, simplifying with % 20.43/3.80 | | | | | | | | (22), (82) gives: % 20.43/3.80 | | | | | | | | (95) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & all_76_0 = 0 & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (v2 = % 20.43/3.80 | | | | | | | | 0 & all_76_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_4) = 0) | ( ~ (v1 = 0) & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ % 20.43/3.80 | | | | | | | | (v0 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.80 | | | | | | | | v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3, % 20.43/3.80 | | | | | | | | all_23_4, all_76_0, simplifying with (22), (23), % 20.43/3.80 | | | | | | | | (26), (82) gives: % 20.43/3.80 | | | | | | | | (96) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) | (v1 = 0 % 20.43/3.80 | | | | | | | | & all_76_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_4) = 0) | ( ~ (v0 = 0) & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_4, all_23_3) = v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (5) with all_23_4, all_23_4, % 20.43/3.80 | | | | | | | | all_76_0, simplifying with (22), (82) gives: % 20.43/3.80 | | | | | | | | (97) all_76_0 = 0 | unorthogonal_lines(all_23_4, all_23_4) = % 20.43/3.80 | | | | | | | | 0 % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (16) with all_23_4, all_23_4, % 20.43/3.80 | | | | | | | | all_23_2, 0, 0, simplifying with (22), (24), (77) % 20.43/3.80 | | | | | | | | gives: % 20.43/3.80 | | | | | | | | (98) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & convergent_lines(all_23_4, all_23_2) % 20.43/3.80 | | | | | | | | = 0) | (v2 = 0 & convergent_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_2) = 0) | ( ~ (v1 = 0) & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ % 20.43/3.80 | | | | | | | | (v0 = 0) & convergent_lines(all_23_4, all_23_4) = % 20.43/3.80 | | | | | | | | v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_2, % 20.43/3.80 | | | | | | | | all_23_2, 0, simplifying with (22), (24), (77) % 20.43/3.80 | | | | | | | | gives: % 20.43/3.80 | | | | | | | | (99) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 % 20.43/3.80 | | | | | | | | & convergent_lines(all_23_4, all_23_2) = 0) | ( ~ % 20.43/3.80 | | | | | | | | (v0 = 0) & convergent_lines(all_23_4, all_23_2) = % 20.43/3.80 | | | | | | | | v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4, % 20.43/3.80 | | | | | | | | all_23_2, all_40_0, 0, simplifying with (22), (24), % 20.43/3.80 | | | | | | | | (44), (77) gives: % 20.43/3.80 | | | | | | | | (100) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & convergent_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_2) = 0) | (v2 = 0 & all_40_0 = 0) | ( ~ % 20.43/3.80 | | | | | | | | (v1 = 0) & unorthogonal_lines(all_23_4, all_23_4) = % 20.43/3.80 | | | | | | | | v1) | ( ~ (v0 = 0) & convergent_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_4) = v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4, % 20.43/3.80 | | | | | | | | all_23_2, 0, all_40_0, simplifying with (22), (24), % 20.43/3.80 | | | | | | | | (44), (77) gives: % 20.43/3.80 | | | | | | | | (101) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & all_40_0 = 0) | (v2 = 0 & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v1 % 20.43/3.80 | | | | | | | | = 0) & unorthogonal_lines(all_23_4, all_23_4) = % 20.43/3.80 | | | | | | | | v1) | ( ~ (v0 = 0) & convergent_lines(all_23_4, % 20.43/3.80 | | | | | | | | all_23_4) = v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_2, % 20.43/3.80 | | | | | | | | all_23_3, 0, simplifying with (22), (23), (24), % 20.43/3.80 | | | | | | | | (26), (77) gives: % 20.43/3.80 | | | | | | | | (102) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | (v1 = 0 % 20.43/3.80 | | | | | | | | & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ % 20.43/3.80 | | | | | | | | (v0 = 0) & convergent_lines(all_23_4, all_23_2) = % 20.43/3.80 | | | | | | | | v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.80 | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2, % 20.43/3.80 | | | | | | | | all_23_2, all_40_0, simplifying with (22), (24), % 20.43/3.80 | | | | | | | | (44), (77) gives: % 20.43/3.80 | | | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.80 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.80 | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 % 20.43/3.80 | | | | | | | | & all_40_0 = 0) | ( ~ (v0 = 0) & % 20.43/3.80 | | | | | | | | convergent_lines(all_23_4, all_23_2) = v0)) % 20.43/3.80 | | | | | | | | % 20.43/3.81 | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2, % 20.43/3.81 | | | | | | | | all_23_3, all_32_3, simplifying with (22), (23), % 20.43/3.81 | | | | | | | | (24), (55), (77) gives: % 20.43/3.81 | | | | | | | | (104) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.81 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | (v1 = 0 % 20.43/3.81 | | | | | | | | & all_32_3 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_3) = 0) | ( ~ (v0 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_2) = v0)) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2, % 20.43/3.81 | | | | | | | | all_23_4, all_76_0, simplifying with (22), (24), % 20.43/3.81 | | | | | | | | (77), (82) gives: % 20.43/3.81 | | | | | | | | (105) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 20.43/3.81 | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0) | (v1 = 0 % 20.43/3.81 | | | | | | | | & all_76_0 = 0 & unorthogonal_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_4) = 0) | ( ~ (v0 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_2) = v0)) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (103) with fresh symbols all_97_0, % 20.43/3.81 | | | | | | | | all_97_1, all_97_2, all_97_3 gives: % 20.43/3.81 | | | | | | | | (106) (all_97_0 = 0 & all_97_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (all_97_2 % 20.43/3.81 | | | | | | | | = 0 & all_40_0 = 0) | ( ~ (all_97_3 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_97_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (102) with fresh symbols all_98_0, % 20.43/3.81 | | | | | | | | all_98_1, all_98_2, all_98_3 gives: % 20.43/3.81 | | | | | | | | (107) (all_98_0 = 0 & all_98_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | (all_98_2 % 20.43/3.81 | | | | | | | | = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_98_3 = 0) & convergent_lines(all_23_4, all_23_2) % 20.43/3.81 | | | | | | | | = all_98_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (101) with fresh symbols all_99_0, % 20.43/3.81 | | | | | | | | all_99_1, all_99_2, all_99_3 gives: % 20.43/3.81 | | | | | | | | (108) (all_99_0 = 0 & all_40_0 = 0) | (all_99_1 = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_99_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_4) = all_99_2) | ( ~ (all_99_3 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_99_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (100) with fresh symbols all_100_0, % 20.43/3.81 | | | | | | | | all_100_1, all_100_2, all_100_3 gives: % 20.43/3.81 | | | | | | | | (109) (all_100_0 = 0 & convergent_lines(all_23_4, all_23_2) = % 20.43/3.81 | | | | | | | | 0) | (all_100_1 = 0 & all_40_0 = 0) | ( ~ (all_100_2 % 20.43/3.81 | | | | | | | | = 0) & unorthogonal_lines(all_23_4, all_23_4) = % 20.43/3.81 | | | | | | | | all_100_2) | ( ~ (all_100_3 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_100_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (99) with fresh symbols all_102_0, % 20.43/3.81 | | | | | | | | all_102_1, all_102_2, all_102_3 gives: % 20.43/3.81 | | | | | | | | (110) (all_102_0 = 0 & all_102_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | % 20.43/3.81 | | | | | | | | (all_102_2 = 0 & convergent_lines(all_23_4, all_23_2) = % 20.43/3.81 | | | | | | | | 0) | ( ~ (all_102_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_2) = all_102_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (98) with fresh symbols all_103_0, % 20.43/3.81 | | | | | | | | all_103_1, all_103_2, all_103_3 gives: % 20.43/3.81 | | | | | | | | (111) (all_103_0 = 0 & convergent_lines(all_23_4, all_23_2) = % 20.43/3.81 | | | | | | | | 0) | (all_103_1 = 0 & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_2) = 0) | ( ~ (all_103_2 = 0) & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = all_103_2) | % 20.43/3.81 | | | | | | | | ( ~ (all_103_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_4) = all_103_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (105) with fresh symbols all_104_0, % 20.43/3.81 | | | | | | | | all_104_1, all_104_2, all_104_3 gives: % 20.43/3.81 | | | | | | | | (112) (all_104_0 = 0 & all_104_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0) | % 20.43/3.81 | | | | | | | | (all_104_2 = 0 & all_76_0 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_104_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_2) = all_104_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (104) with fresh symbols all_105_0, % 20.43/3.81 | | | | | | | | all_105_1, all_105_2, all_105_3 gives: % 20.43/3.81 | | | | | | | | (113) (all_105_0 = 0 & all_105_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | % 20.43/3.81 | | | | | | | | (all_105_2 = 0 & all_32_3 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_105_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_2) = all_105_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (96) with fresh symbols all_107_0, % 20.43/3.81 | | | | | | | | all_107_1, all_107_2, all_107_3 gives: % 20.43/3.81 | | | | | | | | (114) (all_107_0 = 0 & all_107_1 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) | % 20.43/3.81 | | | | | | | | (all_107_2 = 0 & all_76_0 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_107_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_3) = all_107_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | DELTA: instantiating (95) with fresh symbols all_108_0, % 20.43/3.81 | | | | | | | | all_108_1, all_108_2, all_108_3 gives: % 20.43/3.81 | | | | | | | | (115) (all_108_0 = 0 & all_76_0 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | % 20.43/3.81 | | | | | | | | (all_108_1 = 0 & all_76_0 = 0 & % 20.43/3.81 | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~ % 20.43/3.81 | | | | | | | | (all_108_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.81 | | | | | | | | all_23_4) = all_108_2) | ( ~ (all_108_3 = 0) & % 20.43/3.81 | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_108_3) % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | BETA: splitting (34) gives: % 20.43/3.81 | | | | | | | | % 20.43/3.81 | | | | | | | | Case 1: % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | (116) all_30_0 = 0 & all_30_1 = 0 & % 20.43/3.81 | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 & % 20.43/3.81 | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0 % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | ALPHA: (116) implies: % 20.43/3.81 | | | | | | | | | (117) convergent_lines(all_23_3, all_23_3) = 0 % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying % 20.43/3.81 | | | | | | | | | with (23), (117) gives: % 20.43/3.81 | | | | | | | | | (118) $false % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | CLOSE: (118) is inconsistent. % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | Case 2: % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | (119) (all_30_2 = 0 & convergent_lines(all_23_4, all_23_3) % 20.43/3.81 | | | | | | | | | = 0) | ( ~ (all_30_3 = 0) & % 20.43/3.81 | | | | | | | | | convergent_lines(all_23_4, all_23_3) = all_30_3) % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | BETA: splitting (119) gives: % 20.43/3.81 | | | | | | | | | % 20.43/3.81 | | | | | | | | | Case 1: % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | (120) all_30_2 = 0 & convergent_lines(all_23_4, all_23_3) % 20.43/3.81 | | | | | | | | | | = 0 % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | ALPHA: (120) implies: % 20.43/3.81 | | | | | | | | | | (121) convergent_lines(all_23_4, all_23_3) = 0 % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | GROUND_INST: instantiating (17) with all_32_3, 0, all_23_3, % 20.43/3.81 | | | | | | | | | | all_23_4, simplifying with (55), (121) gives: % 20.43/3.81 | | | | | | | | | | (122) all_32_3 = 0 % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | REDUCE: (54), (122) imply: % 20.43/3.81 | | | | | | | | | | (123) $false % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | CLOSE: (123) is inconsistent. % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | Case 2: % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | (124) ~ (all_30_3 = 0) & convergent_lines(all_23_4, % 20.43/3.81 | | | | | | | | | | all_23_3) = all_30_3 % 20.43/3.81 | | | | | | | | | | % 20.43/3.81 | | | | | | | | | | ALPHA: (124) implies: % 20.43/3.82 | | | | | | | | | | (125) ~ (all_30_3 = 0) % 20.43/3.82 | | | | | | | | | | (126) convergent_lines(all_23_4, all_23_3) = all_30_3 % 20.43/3.82 | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | BETA: splitting (97) gives: % 20.43/3.82 | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | (127) unorthogonal_lines(all_23_4, all_23_4) = 0 % 20.43/3.82 | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | BETA: splitting (69) gives: % 20.43/3.82 | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | (128) (all_58_0 = 0 & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | all_23_3) = 0) | (all_58_1 = 0 & all_32_3 = 0) % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | BETA: splitting (128) gives: % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | (129) all_58_0 = 0 & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | ALPHA: (129) implies: % 20.43/3.82 | | | | | | | | | | | | | (130) convergent_lines(all_23_4, all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (130) are inconsistent by % 20.43/3.82 | | | | | | | | | | | | | sub-proof #7. % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | (131) all_58_1 = 0 & all_32_3 = 0 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | ALPHA: (131) implies: % 20.43/3.82 | | | | | | | | | | | | | (132) all_32_3 = 0 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | REDUCE: (54), (132) imply: % 20.43/3.82 | | | | | | | | | | | | | (133) $false % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | CLOSE: (133) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | End of split % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | (134) ( ~ (all_58_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | all_23_4) = all_58_2) | ( ~ (all_58_3 = 0) & % 20.43/3.82 | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_58_3) % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | BETA: splitting (134) gives: % 20.43/3.82 | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | (135) ~ (all_58_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | all_23_4) = all_58_2 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | ALPHA: (135) implies: % 20.43/3.82 | | | | | | | | | | | | | (136) ~ (all_58_2 = 0) % 20.43/3.82 | | | | | | | | | | | | | (137) unorthogonal_lines(all_23_4, all_23_4) = all_58_2 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_58_2, all_23_4, % 20.43/3.82 | | | | | | | | | | | | | all_23_4, simplifying with (127), (137) gives: % 20.43/3.82 | | | | | | | | | | | | | (138) all_58_2 = 0 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | REDUCE: (136), (138) imply: % 20.43/3.82 | | | | | | | | | | | | | (139) $false % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | CLOSE: (139) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | (140) ~ (all_58_3 = 0) & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | all_23_4) = all_58_3 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | ALPHA: (140) implies: % 20.43/3.82 | | | | | | | | | | | | | (141) ~ (all_58_3 = 0) % 20.43/3.82 | | | | | | | | | | | | | (142) convergent_lines(all_23_4, all_23_4) = all_58_3 % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | BETA: splitting (76) gives: % 20.43/3.82 | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | (143) (all_68_0 = 0 & all_32_3 = 0 & % 20.43/3.82 | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | % 20.43/3.82 | | | | | | | | | | | | | | (all_68_1 = 0 & all_32_3 = 0 & % 20.43/3.82 | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | BETA: splitting (143) gives: % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | (144) all_68_0 = 0 & all_32_3 = 0 & % 20.43/3.82 | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | ALPHA: (144) implies: % 20.43/3.82 | | | | | | | | | | | | | | | (145) all_32_3 = 0 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | REDUCE: (54), (145) imply: % 20.43/3.82 | | | | | | | | | | | | | | | (146) $false % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | (147) all_68_1 = 0 & all_32_3 = 0 & % 20.43/3.82 | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | ALPHA: (147) implies: % 20.43/3.82 | | | | | | | | | | | | | | | (148) all_32_3 = 0 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | REDUCE: (54), (148) imply: % 20.43/3.82 | | | | | | | | | | | | | | | (149) $false % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | End of split % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | (150) ( ~ (all_68_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | all_23_4) = all_68_2) | ( ~ (all_68_3 = 0) & % 20.43/3.82 | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_68_3) % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | BETA: splitting (150) gives: % 20.43/3.82 | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | (151) ~ (all_68_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | all_23_4) = all_68_2 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | ALPHA: (151) implies: % 20.43/3.82 | | | | | | | | | | | | | | | (152) ~ (all_68_2 = 0) % 20.43/3.82 | | | | | | | | | | | | | | | (153) unorthogonal_lines(all_23_4, all_23_4) = all_68_2 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_68_2, all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (153) gives: % 20.43/3.82 | | | | | | | | | | | | | | | (154) all_68_2 = 0 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | REDUCE: (152), (154) imply: % 20.43/3.82 | | | | | | | | | | | | | | | (155) $false % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | (156) ~ (all_68_3 = 0) & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | all_23_4) = all_68_3 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | ALPHA: (156) implies: % 20.43/3.82 | | | | | | | | | | | | | | | (157) convergent_lines(all_23_4, all_23_4) = all_68_3 % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 20.43/3.82 | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | (158) (all_31_0 = 0 & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | all_23_3) = 0) | (all_31_1 = 0 & % 20.43/3.82 | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0) % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | (159) all_31_0 = 0 & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | ALPHA: (159) implies: % 20.43/3.82 | | | | | | | | | | | | | | | | | (160) convergent_lines(all_23_4, all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (160) are inconsistent by % 20.43/3.82 | | | | | | | | | | | | | | | | | sub-proof #7. % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | (161) all_31_1 = 0 & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | ALPHA: (161) implies: % 20.43/3.82 | | | | | | | | | | | | | | | | | (162) convergent_lines(all_23_4, all_23_3) = 0 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (162) are inconsistent by % 20.43/3.82 | | | | | | | | | | | | | | | | | sub-proof #7. % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | End of split % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | (163) ( ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | all_23_4) = all_31_2) | ( ~ (all_31_3 = 0) & % 20.43/3.82 | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_31_3) % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 20.43/3.82 | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | Case 1: % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | (164) ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | | all_23_4) = all_31_2 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | ALPHA: (164) implies: % 20.43/3.82 | | | | | | | | | | | | | | | | | (165) ~ (all_31_2 = 0) % 20.43/3.82 | | | | | | | | | | | | | | | | | (166) unorthogonal_lines(all_23_4, all_23_4) = all_31_2 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_31_2, all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (166) gives: % 20.43/3.82 | | | | | | | | | | | | | | | | | (167) all_31_2 = 0 % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | REDUCE: (165), (167) imply: % 20.43/3.82 | | | | | | | | | | | | | | | | | (168) $false % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | Case 2: % 20.43/3.82 | | | | | | | | | | | | | | | | | % 20.43/3.82 | | | | | | | | | | | | | | | | | (169) ~ (all_31_3 = 0) & convergent_lines(all_23_4, % 20.43/3.82 | | | | | | | | | | | | | | | | | all_23_4) = all_31_3 % 20.43/3.83 | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | (170) convergent_lines(all_23_4, all_23_4) = all_31_3 % 20.43/3.83 | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | Case 1: % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | (171) (all_100_0 = 0 & convergent_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_100_1 = 0 & all_40_0 = % 20.43/3.83 | | | | | | | | | | | | | | | | | | 0) % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | Case 1: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (172) all_100_0 = 0 & convergent_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (173) convergent_lines(all_23_4, all_23_2) = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (173) are inconsistent by % 20.43/3.83 | | | | | | | | | | | | | | | | | | | sub-proof #6. % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | Case 2: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (174) all_100_1 = 0 & all_40_0 = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (175) all_40_0 = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (43), (175) imply: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (176) $false % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | End of split % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | Case 2: % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | (177) ( ~ (all_100_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | all_23_4) = all_100_2) | ( ~ (all_100_3 = 0) & % 20.43/3.83 | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = % 20.43/3.83 | | | | | | | | | | | | | | | | | | all_100_3) % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | Case 1: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (178) ~ (all_100_2 = 0) & unorthogonal_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | | all_23_4) = all_100_2 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (179) ~ (all_100_2 = 0) % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (180) unorthogonal_lines(all_23_4, all_23_4) = all_100_2 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_100_2, all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (180) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (181) all_100_2 = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (179), (181) imply: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (182) $false % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | Case 2: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (183) ~ (all_100_3 = 0) & convergent_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | | all_23_4) = all_100_3 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | (184) convergent_lines(all_23_4, all_23_4) = all_100_3 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | Case 1: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | (185) (all_61_0 = 0 & all_32_3 = 0) | (all_61_1 = 0 & % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0) % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | (186) all_61_0 = 0 & all_32_3 = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | (187) all_32_3 = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (187) imply: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | (188) $false % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | Case 2: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | (189) all_61_1 = 0 & convergent_lines(all_23_4, % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | (190) convergent_lines(all_23_4, all_23_3) = 0 % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (190) are inconsistent by % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | End of split % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | % 20.43/3.83 | | | | | | | | | | | | | | | | | | | Case 2: % 20.43/3.83 | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | (191) ( ~ (all_61_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | all_23_4) = all_61_2) | ( ~ (all_61_3 = 0) & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_61_3) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_61_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_61_2 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (193) ~ (all_61_2 = 0) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (194) unorthogonal_lines(all_23_4, all_23_4) = all_61_2 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_61_2, all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (194) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (195) all_61_2 = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (195) imply: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (196) $false % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_61_3 = 0) & convergent_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_61_3 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | (198) convergent_lines(all_23_4, all_23_4) = all_61_3 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | (199) (all_103_0 = 0 & convergent_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_103_1 = 0 & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (200) all_103_0 = 0 & convergent_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (201) convergent_lines(all_23_4, all_23_2) = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (201) are inconsistent by % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (202) all_103_1 = 0 & convergent_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (203) convergent_lines(all_23_4, all_23_2) = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (203) are inconsistent by % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | (204) ( ~ (all_103_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_103_2) | ( ~ (all_103_3 = 0) & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | all_103_3) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (205) ~ (all_103_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_103_2 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_103_2 = 0) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (207) unorthogonal_lines(all_23_4, all_23_4) = all_103_2 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_103_2, all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (207) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (208) all_103_2 = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (208) imply: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (209) $false % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (210) ~ (all_103_3 = 0) & convergent_lines(all_23_4, % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_103_3 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | (211) convergent_lines(all_23_4, all_23_4) = all_103_3 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_67_0 = 0 & all_40_0 = 0 & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | (all_67_1 = 0 & all_40_0 = 0 & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_67_0 = 0 & all_40_0 = 0 & % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_40_0 = 0 % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (214) imply: % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | (215) $false % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.83 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_67_1 = 0 & all_40_0 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_40_0 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (217) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (218) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | (219) ( ~ (all_67_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_67_2) | ( ~ (all_67_3 = 0) & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_67_3) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_67_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_67_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_67_2 = 0) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (222) unorthogonal_lines(all_23_4, all_23_4) = all_67_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_67_2, all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (222) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_67_2 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (221), (223) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (225) ~ (all_67_3 = 0) & convergent_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_67_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | (226) convergent_lines(all_23_4, all_23_4) = all_67_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (227) (all_108_0 = 0 & all_76_0 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_108_1 = 0 & all_76_0 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_108_0 = 0 & all_76_0 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_76_0 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (229) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_108_1 = 0 & all_76_0 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_76_0 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (232) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ( ~ (all_108_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_108_2) | ( ~ (all_108_3 = 0) & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_3) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_108_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_108_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_108_2 = 0) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) unorthogonal_lines(all_23_4, all_23_4) = all_108_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_108_2, all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (237) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_108_2 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (238) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) ~ (all_108_3 = 0) & convergent_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_108_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) convergent_lines(all_23_4, all_23_4) = all_108_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) (all_99_0 = 0 & all_40_0 = 0) | (all_99_1 = 0 & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_99_0 = 0 & all_40_0 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_40_0 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (244) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_99_1 = 0 & convergent_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) convergent_lines(all_23_4, all_23_2) = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (247) are inconsistent by % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ( ~ (all_99_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_99_2) | ( ~ (all_99_3 = 0) & % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_99_3) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_99_2 = 0) & unorthogonal_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_99_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_99_2 = 0) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) unorthogonal_lines(all_23_4, all_23_4) = all_99_2 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_99_2, all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (127), (251) gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_99_2 = 0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_99_3 = 0) & convergent_lines(all_23_4, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_99_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) convergent_lines(all_23_4, all_23_4) = all_99_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_58_3, all_61_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (142), (198) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_61_3 = all_58_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_68_3, all_99_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (157), (255) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_99_3 = all_68_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_68_3, all_100_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (157), (184) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_100_3 = all_68_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_67_3, all_100_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (184), (226) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_100_3 = all_67_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_61_3, all_100_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (184), (198) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_100_3 = all_61_3 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_76_0, all_103_3, % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (82), (211) % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_103_3 = all_76_0 % 20.73/3.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_99_3, all_103_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (211), (255) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_103_3 = all_99_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_99_3, all_108_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (241), (255) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_108_3 = all_99_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_31_3, all_108_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (170), (241) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_108_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_32_3, all_30_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (55), (126) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_32_3 = all_30_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (264) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_99_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_99_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (262) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_99_3 = all_76_0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_99_3 = all_76_0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_68_3 = all_67_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (270) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_68_3 = all_67_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (260) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_67_3 = all_61_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (269) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_76_0 = all_68_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (269) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_76_0 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_68_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_68_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (276) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_67_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_67_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (278) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_61_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_61_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (280) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_3 = all_31_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (282) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_31_3 = 0) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, 0, simplifying with (22), (23), (26), % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & convergent_lines(all_23_4, all_23_4) = % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & convergent_lines(all_23_4, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = v0)) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbols all_160_0, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_160_1, all_160_2, all_160_3 gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) (all_160_0 = 0 & all_160_1 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_160_2 = 0 & convergent_lines(all_23_4, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0) | ( ~ (all_160_3 = 0) & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_160_3) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) (all_33_0 = 0 & all_23_0 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_33_1 = 0 & all_23_0 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_33_0 = 0 & all_23_0 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_23_0 = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (288) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) $false % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent. % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_33_1 = 0 & all_23_0 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_23_0 = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (291) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) $false % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) ( ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_33_2) | ( ~ (all_33_3 = 0) & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = all_33_3) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_33_2 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_33_2 = 0) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) unorthogonal_lines(all_23_3, all_23_3) = all_33_2 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_33_2, simplifying with (23), (296) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_33_2 = 0 | convergent_lines(all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) convergent_lines(all_23_3, all_23_3) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (298) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) $false % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent. % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_33_2 = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (300) imply: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) $false % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_33_3 = 0) & convergent_lines(all_23_3, % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_33_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_33_3 = 0) % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) convergent_lines(all_23_3, all_23_3) = all_33_3 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_60_0 = 0 & all_60_1 = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 & % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) convergent_lines(all_23_3, all_23_3) = 0 % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (306) gives: % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) $false % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 20.73/3.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) (all_60_2 = 0 & all_32_3 = 0) | ( ~ (all_60_3 = 0) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & convergent_lines(all_23_4, all_23_3) = % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_60_3) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_60_2 = 0 & all_32_3 = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_32_3 = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (310) imply: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_30_3 = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_30_3 = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (312) imply: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) $false % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent. % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_60_3 = 0) & convergent_lines(all_23_4, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_60_3 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_60_3 = 0) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) convergent_lines(all_23_4, all_23_3) = all_60_3 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_3, all_60_3, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (126), (316) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_60_3 = all_30_3 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_3, all_23_2, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_33_3, simplifying with (23), (24), % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (304) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_33_3 = 0 | convergent_lines(all_23_2, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_23_3, all_23_4, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_33_3, all_30_3, simplifying with % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (126), (304) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_33_3 = 0 | all_30_3 = 0 | ? [v0: int] : ( ~ % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_23_3, all_23_4) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_57_0 = 0 & all_57_1 = 0 & % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) convergent_lines(all_23_2, all_23_2) = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (321) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) $false % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) (all_57_2 = 0 & unorthogonal_lines(all_23_3, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (all_57_3 = 0) & % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_57_3) % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_57_2 = 0 & unorthogonal_lines(all_23_3, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, 0, all_23_2, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (27), (325) gives: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_23_0 = 0 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (326) imply: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) $false % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) ~ (all_57_3 = 0) & unorthogonal_lines(all_23_3, % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_57_3 % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies: % 20.73/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_57_3 = 0) % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) unorthogonal_lines(all_23_3, all_23_2) = all_57_3 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) convergent_lines(all_23_2, all_23_3) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_33_3 = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (332) imply: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) $false % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_30_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = v0) % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_30_3 = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (335) imply: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ? [v0: int] : ( ~ (v0 = 0) & % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = v0) % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (337) with fresh symbol all_214_0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (all_214_0 = 0) & convergent_lines(all_23_3, % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_214_0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_214_0 = 0) % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) convergent_lines(all_23_3, all_23_4) = all_214_0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_160_0 = 0 & all_160_1 = 0 & % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (21), (27), (43), (73), (330), (342), % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) are inconsistent by sub-proof #4. % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) (all_160_2 = 0 & convergent_lines(all_23_4, % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0) | ( ~ (all_160_3 = 0) & % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_160_3) % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_160_2 = 0 & convergent_lines(all_23_4, % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) convergent_lines(all_23_4, all_23_4) = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_31_3, 0, all_23_4, % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (170), (346) gives: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_31_3 = 0 % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (347) imply: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) $false % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent. % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_160_3 = 0) & convergent_lines(all_23_4, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_160_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) convergent_lines(all_23_4, all_23_3) = all_160_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_107_0 = 0 & all_107_1 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (21), (27), (43), (73), (330), (352), % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) are inconsistent by sub-proof #4. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) (all_107_2 = 0 & all_76_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_107_3 = 0) & convergent_lines(all_23_4, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_107_3) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_107_2 = 0 & all_76_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_76_0 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (356) imply: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_31_3 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (357) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_31_3 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (358) imply: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) $false % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (359) is inconsistent. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_107_3 = 0) & convergent_lines(all_23_4, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_107_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_107_3 = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) convergent_lines(all_23_4, all_23_3) = all_107_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_3, all_160_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (126), (350) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_160_3 = all_30_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_107_3, all_160_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (350), (362) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_160_3 = all_107_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, all_57_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_3, simplifying with (27), (330) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_57_3 = all_23_0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (363), (364) imply: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_107_3 = all_30_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (366) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_107_3 = all_30_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_62_0 = 0 & all_62_1 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (369) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) $false % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) (all_62_2 = 0 & all_23_0 = 0) | ( ~ (all_62_3 = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & unorthogonal_lines(all_23_3, all_23_2) = % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_62_3) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_62_2 = 0 & all_23_0 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_23_0 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (373) imply: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) $false % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_62_3 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_62_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_62_3 = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) unorthogonal_lines(all_23_3, all_23_2) = all_62_3 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, all_62_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_3, simplifying with (27), (377) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_62_3 = all_23_0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) (all_65_0 = 0 & all_40_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_65_1 = 0 & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_65_0 = 0 & all_40_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_40_0 = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (381) imply: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) $false % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (382) is inconsistent. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_65_1 = 0 & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (27), (330), (384) are inconsistent by % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) ( ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_65_2) | ( ~ (all_65_3 = 0) & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = all_65_3) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_65_2 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_65_2 = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) unorthogonal_lines(all_23_3, all_23_4) = all_65_2 % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) (all_66_0 = 0 & all_40_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_66_1 = 0 & all_23_0 = 0 & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (389) are inconsistent by sub-proof % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #3. % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) ( ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_2) | ( ~ (all_66_3 = 0) & % 20.89/3.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = all_66_3) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_2 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_66_2 = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) unorthogonal_lines(all_23_3, all_23_4) = all_66_2 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_65_2, all_66_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_3, simplifying with (388), (393) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_66_2 = all_65_2 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_4, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_214_0, simplifying with (22), (23), (340) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_214_0 = 0 | unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (387), (388), (396) are inconsistent by % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_214_0 = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (397) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) $false % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) ~ (all_66_3 = 0) & convergent_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) convergent_lines(all_23_3, all_23_4) = all_66_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_214_0, all_66_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_3, simplifying with (340), (400) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_214_0 = all_66_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (401) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_66_3 = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_4, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_66_3, simplifying with (22), (23), (400) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_66_3 = 0 | unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (387), (388), (404) are inconsistent by % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_66_3 = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (402), (405) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) $false % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ~ (all_65_3 = 0) & convergent_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_65_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) convergent_lines(all_23_3, all_23_4) = all_65_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_214_0, all_65_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_3, simplifying with (340), (408) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_214_0 = all_65_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (409) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (all_65_3 = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) (all_66_0 = 0 & all_40_0 = 0 & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_66_1 = 0 & all_23_0 = 0 & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (411) are inconsistent by sub-proof % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #3. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) ( ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_2) | ( ~ (all_66_3 = 0) & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = all_66_3) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_2 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_66_2 = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) unorthogonal_lines(all_23_3, all_23_4) = all_66_2 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_4, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_66_2, simplifying with (22), (23), (415) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_66_2 = 0 | convergent_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_65_3, all_23_4, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (408), (417) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_65_3 = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (410), (418) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) $false % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (419) is inconsistent. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_66_2 = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (414), (420) imply: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) $false % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent. % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) ~ (all_66_3 = 0) & convergent_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_66_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) ~ (all_66_3 = 0) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) convergent_lines(all_23_3, all_23_4) = all_66_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_65_3, all_66_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_3, simplifying with (408), (424) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_66_3 = all_65_3 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_23_4, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, 0, all_30_3, simplifying with (22), % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (126), (331) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_30_3 = 0 & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & unorthogonal_lines(all_23_2, all_23_3) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v1 = 0) & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = v1) | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v0 = 0) & convergent_lines(all_23_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = v0)) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_23_2, all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, 0, simplifying with (23), (24), (38), % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0) | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & v1 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 & convergent_lines(all_23_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (v0 = 0) & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = v0)) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_65_3, simplifying with (22), (23), % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (331), (408) gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_65_3 = 0 | convergent_lines(all_23_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0 % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (427) with fresh symbols all_269_0, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_269_1, all_269_2, all_269_3 gives: % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) (all_269_0 = 0 & unorthogonal_lines(all_23_3, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_269_1 = 0 & all_269_2 = % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | ( ~ % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_269_3 = 0) & unorthogonal_lines(all_23_2, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_269_3) % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (426) with fresh symbols all_278_0, % 20.89/3.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_278_1, all_278_2, all_278_3 gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) (all_278_0 = 0 & all_30_3 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_278_1 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | ( ~ (all_278_2 = 0) & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_278_2) | ( ~ (all_278_3 = 0) & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_278_3) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) convergent_lines(all_23_2, all_23_4) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_97_0 = 0 & all_97_1 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (433) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) $false % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_97_2 = 0 & all_40_0 = 0) | ( ~ (all_97_3 = 0) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & convergent_lines(all_23_4, all_23_2) = % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_97_3) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_97_2 = 0 & all_40_0 = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_40_0 = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (437) imply: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) $false % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_97_3 = 0) & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_97_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) convergent_lines(all_23_4, all_23_2) = all_97_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_97_3, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (44), (440) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_97_3 = all_40_0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_98_0 = 0 & all_98_1 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) unorthogonal_lines(all_23_2, all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (443), % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #1. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) (all_98_2 = 0 & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | ( ~ (all_98_3 = 0) & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_98_3) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_98_2 = 0 & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) convergent_lines(all_23_4, all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (446) are inconsistent by % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) ~ (all_98_3 = 0) & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_98_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ (all_98_3 = 0) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) convergent_lines(all_23_4, all_23_2) = all_98_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_98_3, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (44), (449) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_98_3 = all_40_0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_102_0 = 0 & all_102_1 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (452) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) $false % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (453) is inconsistent. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) (all_102_2 = 0 & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (all_102_3 = 0) & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_102_3) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_102_2 = 0 & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (455) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) convergent_lines(all_23_4, all_23_2) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (456) are inconsistent by % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) ~ (all_102_3 = 0) & convergent_lines(all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_102_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (457) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) convergent_lines(all_23_4, all_23_2) = all_102_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_102_3, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (44), (458) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_102_3 = all_40_0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_104_0 = 0 & all_104_1 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) unorthogonal_lines(all_23_2, all_23_4) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) (all_278_0 = 0 & all_30_3 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_278_1 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_278_0 = 0 & all_30_3 = 0 & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_30_3 = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (464) imply: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) $false % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_278_1 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) unorthogonal_lines(all_23_2, all_23_3) = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (467), % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #1. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) ( ~ (all_278_2 = 0) & unorthogonal_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_278_2) | ( ~ (all_278_3 = 0) & % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_278_3) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) ~ (all_278_2 = 0) & unorthogonal_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_278_2 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (all_278_2 = 0) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) unorthogonal_lines(all_23_2, all_23_4) = all_278_2 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_278_2, all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, simplifying with (461), (471) gives: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_278_2 = 0 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (472) imply: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) $false % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent. % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) ~ (all_278_3 = 0) & convergent_lines(all_23_2, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_278_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies: % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) ~ (all_278_3 = 0) % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) convergent_lines(all_23_2, all_23_4) = all_278_3 % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_278_3, all_23_4, % 20.89/3.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, simplifying with (431), (476) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_278_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (477) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) (all_104_2 = 0 & all_76_0 = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_104_3 = 0) & convergent_lines(all_23_4, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_104_3) % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_104_2 = 0 & all_76_0 = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_76_0 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (481) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_31_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (482) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_31_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (483) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (484) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) ~ (all_104_3 = 0) & convergent_lines(all_23_4, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_104_3 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) convergent_lines(all_23_4, all_23_2) = all_104_3 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_104_3, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (44), (486) % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_104_3 = all_40_0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_105_0 = 0 & all_105_1 = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) unorthogonal_lines(all_23_2, all_23_3) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (489), % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apart3) are inconsistent by sub-proof #1. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) (all_105_2 = 0 & all_32_3 = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_105_3 = 0) & convergent_lines(all_23_4, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_105_3) % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_105_2 = 0 & all_32_3 = 0 & % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_32_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (492) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_30_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_30_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (494) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (495) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_105_3 = 0) & convergent_lines(all_23_4, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_105_3 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) ~ (all_105_3 = 0) % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) convergent_lines(all_23_4, all_23_2) = all_105_3 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_105_3, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (44), (498) % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_105_3 = all_40_0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_4, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_40_0, simplifying with (22), (24), % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (431) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_40_0 = 0 | convergent_lines(all_23_2, % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (501) gives: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (502) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_40_0 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (503) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (504) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_65_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (410), (505) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_33_3 = 0 % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (507) imply: % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) $false % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent. % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | Case 2: % 20.89/3.90 | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | (509) all_76_0 = 0 % 20.89/3.90 | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | REDUCE: (94), (509) imply: % 20.89/3.90 | | | | | | | | | | | (510) $false % 20.89/3.90 | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | | CLOSE: (510) is inconsistent. % 20.89/3.90 | | | | | | | | | | | % 20.89/3.90 | | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | | % 20.89/3.90 | | | | | | | | | End of split % 20.89/3.90 | | | | | | | | | % 20.89/3.90 | | | | | | | | End of split % 20.89/3.90 | | | | | | | | % 20.89/3.90 | | | | | | | End of split % 20.89/3.90 | | | | | | | % 20.89/3.90 | | | | | | End of split % 20.89/3.90 | | | | | | % 20.89/3.90 | | | | | Case 2: % 20.89/3.90 | | | | | | % 20.89/3.90 | | | | | | (511) all_40_0 = 0 % 20.89/3.90 | | | | | | % 20.89/3.90 | | | | | | REDUCE: (43), (511) imply: % 20.89/3.90 | | | | | | (512) $false % 20.89/3.90 | | | | | | % 20.89/3.90 | | | | | | CLOSE: (512) is inconsistent. % 20.89/3.90 | | | | | | % 20.89/3.90 | | | | | End of split % 20.89/3.90 | | | | | % 20.89/3.90 | | | | End of split % 20.89/3.90 | | | | % 20.89/3.90 | | | End of split % 20.89/3.90 | | | % 20.89/3.90 | | End of split % 20.89/3.90 | | % 20.89/3.90 | Case 2: % 20.89/3.90 | | % 20.89/3.90 | | (513) all_23_0 = 0 % 20.89/3.90 | | % 20.89/3.90 | | REDUCE: (21), (513) imply: % 20.89/3.90 | | (514) $false % 20.89/3.90 | | % 20.89/3.90 | | CLOSE: (514) is inconsistent. % 20.89/3.90 | | % 20.89/3.90 | End of split % 20.89/3.90 | % 20.89/3.90 End of proof % 20.89/3.90 % 20.89/3.90 Sub-proof #1 shows that the following formulas are inconsistent: % 20.89/3.90 ---------------------------------------------------------------- % 20.89/3.90 (1) unorthogonal_lines(all_23_3, all_23_2) = all_57_3 % 20.89/3.90 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 20.89/3.90 (3) unorthogonal_lines(all_23_2, all_23_3) = 0 % 20.89/3.90 (4) ~ (all_23_0 = 0) % 20.89/3.90 (5) unorthogonal_lines(all_23_3, all_23_2) = all_23_0 % 20.89/3.90 (6) (all_269_0 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0) | (all_269_1 % 20.89/3.90 = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0 & % 20.89/3.90 convergent_lines(all_23_2, all_23_2) = 0) | ( ~ (all_269_3 = 0) & % 20.89/3.90 unorthogonal_lines(all_23_2, all_23_3) = all_269_3) % 20.89/3.90 (7) $i(all_23_2) % 20.89/3.91 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.91 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 20.89/3.91 (unorthogonal_lines(v3, v2) = v0)) % 20.89/3.91 % 20.89/3.91 Begin of proof % 20.89/3.91 | % 20.89/3.91 | BETA: splitting (6) gives: % 20.89/3.91 | % 20.89/3.91 | Case 1: % 20.89/3.91 | | % 20.89/3.91 | | (9) all_269_0 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.91 | | % 20.89/3.91 | | ALPHA: (9) implies: % 20.89/3.91 | | (10) unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.91 | | % 20.89/3.91 | | REF_CLOSE: (1), (4), (5), (8), (10) are inconsistent by sub-proof #5. % 20.89/3.91 | | % 20.89/3.91 | Case 2: % 20.89/3.91 | | % 20.89/3.91 | | (11) (all_269_1 = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.91 | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~ % 20.89/3.91 | | (all_269_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) = % 20.89/3.91 | | all_269_3) % 20.89/3.91 | | % 20.89/3.91 | | BETA: splitting (11) gives: % 20.89/3.91 | | % 20.89/3.91 | | Case 1: % 20.89/3.91 | | | % 20.89/3.91 | | | (12) all_269_1 = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2, % 20.89/3.91 | | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (12) implies: % 20.89/3.91 | | | (13) convergent_lines(all_23_2, all_23_2) = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | GROUND_INST: instantiating (2) with all_23_2, simplifying with (7), (13) % 20.89/3.91 | | | gives: % 20.89/3.91 | | | (14) $false % 20.89/3.91 | | | % 20.89/3.91 | | | CLOSE: (14) is inconsistent. % 20.89/3.91 | | | % 20.89/3.91 | | Case 2: % 20.89/3.91 | | | % 20.89/3.91 | | | (15) ~ (all_269_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) = % 20.89/3.91 | | | all_269_3 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (15) implies: % 20.89/3.91 | | | (16) ~ (all_269_3 = 0) % 20.89/3.91 | | | (17) unorthogonal_lines(all_23_2, all_23_3) = all_269_3 % 20.89/3.91 | | | % 20.89/3.91 | | | GROUND_INST: instantiating (8) with 0, all_269_3, all_23_3, all_23_2, % 20.89/3.91 | | | simplifying with (3), (17) gives: % 20.89/3.91 | | | (18) all_269_3 = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | REDUCE: (16), (18) imply: % 20.89/3.91 | | | (19) $false % 20.89/3.91 | | | % 20.89/3.91 | | | CLOSE: (19) is inconsistent. % 20.89/3.91 | | | % 20.89/3.91 | | End of split % 20.89/3.91 | | % 20.89/3.91 | End of split % 20.89/3.91 | % 20.89/3.91 End of proof % 20.89/3.91 % 20.89/3.91 Sub-proof #2 shows that the following formulas are inconsistent: % 20.89/3.91 ---------------------------------------------------------------- % 20.89/3.91 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.91 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 20.89/3.91 (unorthogonal_lines(v3, v2) = v0)) % 20.89/3.91 (2) unorthogonal_lines(all_23_3, all_23_4) = all_65_2 % 20.89/3.91 (3) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.91 (4) ~ (all_65_2 = 0) % 20.89/3.91 % 20.89/3.91 Begin of proof % 20.89/3.91 | % 20.89/3.91 | GROUND_INST: instantiating (1) with 0, all_65_2, all_23_4, all_23_3, % 20.89/3.91 | simplifying with (2), (3) gives: % 20.89/3.91 | (5) all_65_2 = 0 % 20.89/3.91 | % 20.89/3.91 | REDUCE: (4), (5) imply: % 20.89/3.91 | (6) $false % 20.89/3.91 | % 20.89/3.91 | CLOSE: (6) is inconsistent. % 20.89/3.91 | % 20.89/3.91 End of proof % 20.89/3.91 % 20.89/3.91 Sub-proof #3 shows that the following formulas are inconsistent: % 20.89/3.91 ---------------------------------------------------------------- % 20.89/3.91 (1) (all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2) = % 20.89/3.91 0) | (all_66_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, % 20.89/3.91 all_23_2) = 0) % 20.89/3.91 (2) ~ (all_40_0 = 0) % 20.89/3.91 (3) ~ (all_23_0 = 0) % 20.89/3.91 % 20.89/3.91 Begin of proof % 20.89/3.91 | % 20.89/3.91 | BETA: splitting (1) gives: % 20.89/3.91 | % 20.89/3.91 | Case 1: % 20.89/3.91 | | % 20.89/3.91 | | (4) all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2) % 20.89/3.91 | | = 0 % 20.89/3.91 | | % 20.89/3.91 | | ALPHA: (4) implies: % 20.89/3.91 | | (5) all_40_0 = 0 % 20.89/3.91 | | % 20.89/3.91 | | REDUCE: (2), (5) imply: % 20.89/3.91 | | (6) $false % 20.89/3.91 | | % 20.89/3.91 | | CLOSE: (6) is inconsistent. % 20.89/3.91 | | % 20.89/3.91 | Case 2: % 20.89/3.91 | | % 20.89/3.91 | | (7) all_66_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = % 20.89/3.91 | | 0 % 20.89/3.91 | | % 20.89/3.91 | | ALPHA: (7) implies: % 20.89/3.91 | | (8) all_23_0 = 0 % 20.89/3.91 | | % 20.89/3.91 | | REDUCE: (3), (8) imply: % 20.89/3.91 | | (9) $false % 20.89/3.91 | | % 20.89/3.91 | | CLOSE: (9) is inconsistent. % 20.89/3.91 | | % 20.89/3.91 | End of split % 20.89/3.91 | % 20.89/3.91 End of proof % 20.89/3.91 % 20.89/3.91 Sub-proof #4 shows that the following formulas are inconsistent: % 20.89/3.91 ---------------------------------------------------------------- % 20.89/3.91 (1) unorthogonal_lines(all_23_3, all_23_2) = all_57_3 % 20.89/3.91 (2) ~ (all_23_0 = 0) % 20.89/3.91 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.91 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.89/3.91 (convergent_lines(v3, v2) = v0)) % 20.89/3.91 (4) unorthogonal_lines(all_23_3, all_23_2) = all_23_0 % 20.89/3.91 (5) (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2) = % 20.89/3.91 0) | (all_65_1 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~ % 20.89/3.91 (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) = all_65_2) | ( % 20.89/3.91 ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) = all_65_3) % 20.89/3.91 (6) ~ (all_40_0 = 0) % 20.89/3.91 (7) unorthogonal_lines(all_23_3, all_23_4) = 0 % 20.89/3.91 (8) convergent_lines(all_23_3, all_23_4) = 0 % 20.89/3.91 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.91 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 20.89/3.91 (unorthogonal_lines(v3, v2) = v0)) % 20.89/3.91 % 20.89/3.91 Begin of proof % 20.89/3.91 | % 20.89/3.91 | BETA: splitting (5) gives: % 20.89/3.91 | % 20.89/3.91 | Case 1: % 20.89/3.91 | | % 20.89/3.91 | | (10) (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.89/3.91 | | all_23_2) = 0) | (all_65_1 = 0 & unorthogonal_lines(all_23_3, % 20.89/3.91 | | all_23_2) = 0) % 20.89/3.91 | | % 20.89/3.91 | | BETA: splitting (10) gives: % 20.89/3.91 | | % 20.89/3.91 | | Case 1: % 20.89/3.91 | | | % 20.89/3.91 | | | (11) all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, % 20.89/3.91 | | | all_23_2) = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (11) implies: % 20.89/3.91 | | | (12) all_40_0 = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | REDUCE: (6), (12) imply: % 20.89/3.91 | | | (13) $false % 20.89/3.91 | | | % 20.89/3.91 | | | CLOSE: (13) is inconsistent. % 20.89/3.91 | | | % 20.89/3.91 | | Case 2: % 20.89/3.91 | | | % 20.89/3.91 | | | (14) all_65_1 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (14) implies: % 20.89/3.91 | | | (15) unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | REF_CLOSE: (1), (2), (4), (9), (15) are inconsistent by sub-proof #5. % 20.89/3.91 | | | % 20.89/3.91 | | End of split % 20.89/3.91 | | % 20.89/3.91 | Case 2: % 20.89/3.91 | | % 20.89/3.91 | | (16) ( ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) = % 20.89/3.91 | | all_65_2) | ( ~ (all_65_3 = 0) & convergent_lines(all_23_3, % 20.89/3.91 | | all_23_4) = all_65_3) % 20.89/3.91 | | % 20.89/3.91 | | BETA: splitting (16) gives: % 20.89/3.91 | | % 20.89/3.91 | | Case 1: % 20.89/3.91 | | | % 20.89/3.91 | | | (17) ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) = % 20.89/3.91 | | | all_65_2 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (17) implies: % 20.89/3.91 | | | (18) ~ (all_65_2 = 0) % 20.89/3.91 | | | (19) unorthogonal_lines(all_23_3, all_23_4) = all_65_2 % 20.89/3.91 | | | % 20.89/3.91 | | | GROUND_INST: instantiating (9) with 0, all_65_2, all_23_4, all_23_3, % 20.89/3.91 | | | simplifying with (7), (19) gives: % 20.89/3.91 | | | (20) all_65_2 = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | REDUCE: (18), (20) imply: % 20.89/3.91 | | | (21) $false % 20.89/3.91 | | | % 20.89/3.91 | | | CLOSE: (21) is inconsistent. % 20.89/3.91 | | | % 20.89/3.91 | | Case 2: % 20.89/3.91 | | | % 20.89/3.91 | | | (22) ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) = % 20.89/3.91 | | | all_65_3 % 20.89/3.91 | | | % 20.89/3.91 | | | ALPHA: (22) implies: % 20.89/3.91 | | | (23) ~ (all_65_3 = 0) % 20.89/3.91 | | | (24) convergent_lines(all_23_3, all_23_4) = all_65_3 % 20.89/3.91 | | | % 20.89/3.91 | | | GROUND_INST: instantiating (3) with 0, all_65_3, all_23_4, all_23_3, % 20.89/3.91 | | | simplifying with (8), (24) gives: % 20.89/3.91 | | | (25) all_65_3 = 0 % 20.89/3.91 | | | % 20.89/3.91 | | | REDUCE: (23), (25) imply: % 20.89/3.91 | | | (26) $false % 20.89/3.91 | | | % 20.89/3.91 | | | CLOSE: (26) is inconsistent. % 20.89/3.91 | | | % 20.89/3.91 | | End of split % 20.89/3.91 | | % 20.89/3.91 | End of split % 20.89/3.91 | % 20.89/3.91 End of proof % 20.89/3.91 % 20.89/3.91 Sub-proof #5 shows that the following formulas are inconsistent: % 20.89/3.91 ---------------------------------------------------------------- % 20.89/3.91 (1) unorthogonal_lines(all_23_3, all_23_2) = all_57_3 % 20.89/3.91 (2) ~ (all_23_0 = 0) % 20.89/3.91 (3) unorthogonal_lines(all_23_3, all_23_2) = 0 % 20.89/3.91 (4) unorthogonal_lines(all_23_3, all_23_2) = all_23_0 % 20.89/3.92 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.92 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 20.89/3.92 (unorthogonal_lines(v3, v2) = v0)) % 20.89/3.92 % 20.89/3.92 Begin of proof % 20.89/3.92 | % 20.89/3.92 | GROUND_INST: instantiating (5) with all_23_0, all_57_3, all_23_2, all_23_3, % 20.89/3.92 | simplifying with (1), (4) gives: % 20.89/3.92 | (6) all_57_3 = all_23_0 % 20.89/3.92 | % 20.89/3.92 | GROUND_INST: instantiating (5) with 0, all_57_3, all_23_2, all_23_3, % 20.89/3.92 | simplifying with (1), (3) gives: % 20.89/3.92 | (7) all_57_3 = 0 % 20.89/3.92 | % 20.89/3.92 | COMBINE_EQS: (6), (7) imply: % 20.89/3.92 | (8) all_23_0 = 0 % 20.89/3.92 | % 20.89/3.92 | REDUCE: (2), (8) imply: % 20.89/3.92 | (9) $false % 20.89/3.92 | % 20.89/3.92 | CLOSE: (9) is inconsistent. % 20.89/3.92 | % 20.89/3.92 End of proof % 20.89/3.92 % 20.89/3.92 Sub-proof #6 shows that the following formulas are inconsistent: % 20.89/3.92 ---------------------------------------------------------------- % 20.89/3.92 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.92 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.89/3.92 (convergent_lines(v3, v2) = v0)) % 20.89/3.92 (2) convergent_lines(all_23_4, all_23_2) = all_40_0 % 20.89/3.92 (3) convergent_lines(all_23_4, all_23_2) = 0 % 20.89/3.92 (4) ~ (all_40_0 = 0) % 20.89/3.92 % 20.89/3.92 Begin of proof % 20.89/3.92 | % 20.89/3.92 | GROUND_INST: instantiating (1) with 0, all_40_0, all_23_2, all_23_4, % 20.89/3.92 | simplifying with (2), (3) gives: % 20.89/3.92 | (5) all_40_0 = 0 % 20.89/3.92 | % 20.89/3.92 | REDUCE: (4), (5) imply: % 20.89/3.92 | (6) $false % 20.89/3.92 | % 20.89/3.92 | CLOSE: (6) is inconsistent. % 20.89/3.92 | % 20.89/3.92 End of proof % 20.89/3.92 % 20.89/3.92 Sub-proof #7 shows that the following formulas are inconsistent: % 20.89/3.92 ---------------------------------------------------------------- % 20.89/3.92 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.89/3.92 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.89/3.92 (convergent_lines(v3, v2) = v0)) % 20.89/3.92 (2) convergent_lines(all_23_4, all_23_3) = all_30_3 % 20.89/3.92 (3) convergent_lines(all_23_4, all_23_3) = 0 % 20.89/3.92 (4) ~ (all_30_3 = 0) % 20.89/3.92 % 20.89/3.92 Begin of proof % 20.89/3.92 | % 20.89/3.92 | GROUND_INST: instantiating (1) with all_30_3, 0, all_23_3, all_23_4, % 20.89/3.92 | simplifying with (2), (3) gives: % 20.89/3.92 | (5) all_30_3 = 0 % 20.89/3.92 | % 20.89/3.92 | REDUCE: (4), (5) imply: % 20.89/3.92 | (6) $false % 20.89/3.92 | % 20.89/3.92 | CLOSE: (6) is inconsistent. % 20.89/3.92 | % 20.89/3.92 End of proof % 20.89/3.92 % SZS output end Proof for theBenchmark % 20.89/3.92 % 20.89/3.92 3289ms %------------------------------------------------------------------------------