%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO212+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 23:22:22 EDT 2023 % Result : Theorem 16.61s 3.03s % Output : Proof 29.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : GEO212+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 20:58:38 EDT 2023 % 0.14/0.36 % CPUTime : % 0.61/0.69 ________ _____ % 0.61/0.69 ___ __ \_________(_)________________________________ % 0.61/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.69 % 0.61/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.69 (2023-06-19) % 0.61/0.69 % 0.61/0.69 (c) Philipp Rümmer, 2009-2023 % 0.61/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.69 Amanda Stjerna. % 0.61/0.69 Free software under BSD-3-Clause. % 0.61/0.69 % 0.61/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.69 % 0.61/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.70 Running up to 7 provers in parallel. % 0.61/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.61/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.65/1.15 Prover 1: Preprocessing ... % 2.65/1.15 Prover 4: Preprocessing ... % 3.16/1.19 Prover 2: Preprocessing ... % 3.16/1.19 Prover 5: Preprocessing ... % 3.16/1.19 Prover 6: Preprocessing ... % 3.16/1.19 Prover 0: Preprocessing ... % 3.16/1.19 Prover 3: Preprocessing ... % 5.08/1.46 Prover 5: Proving ... % 5.08/1.47 Prover 2: Proving ... % 5.60/1.51 Prover 3: Constructing countermodel ... % 5.60/1.52 Prover 6: Constructing countermodel ... % 5.60/1.55 Prover 1: Constructing countermodel ... % 6.07/1.64 Prover 3: gave up % 6.07/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.07/1.66 Prover 6: gave up % 6.07/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.79/1.68 Prover 1: gave up % 7.01/1.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.01/1.72 Prover 7: Preprocessing ... % 7.01/1.72 Prover 8: Preprocessing ... % 7.24/1.74 Prover 9: Preprocessing ... % 7.24/1.77 Prover 7: Warning: ignoring some quantifiers % 7.24/1.77 Prover 0: Proving ... % 7.24/1.78 Prover 4: Constructing countermodel ... % 7.24/1.81 Prover 7: Constructing countermodel ... % 7.24/1.86 Prover 7: gave up % 8.17/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.17/1.89 Prover 8: Warning: ignoring some quantifiers % 8.17/1.90 Prover 8: Constructing countermodel ... % 8.17/1.93 Prover 10: Preprocessing ... % 8.86/1.99 Prover 10: Warning: ignoring some quantifiers % 8.86/1.99 Prover 8: gave up % 8.86/2.00 Prover 10: Constructing countermodel ... % 8.86/2.01 Prover 9: Constructing countermodel ... % 8.86/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.86/2.03 Prover 10: gave up % 8.86/2.03 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.59/2.05 Prover 12: Preprocessing ... % 9.59/2.06 Prover 11: Preprocessing ... % 9.94/2.13 Prover 12: Proving ... % 11.05/2.27 Prover 11: Constructing countermodel ... % 16.61/3.03 Prover 0: proved (2318ms) % 16.61/3.03 % 16.61/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.61/3.03 % 16.61/3.03 Prover 9: stopped % 16.61/3.03 Prover 2: stopped % 16.61/3.04 Prover 5: stopped % 16.61/3.04 Prover 12: stopped % 16.61/3.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.61/3.04 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.13/3.05 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.13/3.05 Prover 13: Preprocessing ... % 17.13/3.05 Prover 16: Preprocessing ... % 17.28/3.07 Prover 19: Preprocessing ... % 17.28/3.08 Prover 13: Warning: ignoring some quantifiers % 17.28/3.09 Prover 13: Constructing countermodel ... % 17.28/3.09 Prover 16: Warning: ignoring some quantifiers % 17.28/3.10 Prover 16: Constructing countermodel ... % 17.66/3.12 Prover 13: gave up % 17.66/3.13 Prover 19: Warning: ignoring some quantifiers % 17.66/3.14 Prover 19: Constructing countermodel ... % 17.66/3.15 Prover 16: gave up % 17.90/3.17 Prover 19: gave up % 28.20/5.13 Prover 11: Found proof (size 560) % 28.20/5.13 Prover 11: proved (3110ms) % 28.20/5.13 Prover 4: stopped % 28.20/5.13 % 28.20/5.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 28.20/5.13 % 28.41/5.17 % SZS output start Proof for theBenchmark % 28.41/5.17 Assumptions after simplification: % 28.41/5.17 --------------------------------- % 28.41/5.17 % 28.41/5.17 (apart3) % 28.41/5.20 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 28.41/5.20 % 28.41/5.20 (ax6) % 28.41/5.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 28.41/5.21 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 28.41/5.21 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 28.41/5.21 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 28.41/5.21 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 28.41/5.21 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.21 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.41/5.21 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 28.41/5.21 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.21 convergent_lines(v1, v2) = 0) % 28.41/5.21 % 28.41/5.21 (ci3) % 28.41/5.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 28.41/5.21 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 28.41/5.21 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 28.41/5.21 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 28.41/5.21 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 28.41/5.21 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 28.41/5.21 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 28.41/5.21 % 28.41/5.21 (ci4) % 28.41/5.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 28.41/5.21 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 28.41/5.21 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 28.41/5.21 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 28.41/5.21 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 28.41/5.21 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 28.41/5.21 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 28.41/5.21 % 28.41/5.21 (con) % 28.41/5.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 28.41/5.21 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & % 28.41/5.21 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v2) = v3 & $i(v2) & % 28.41/5.21 $i(v1) & $i(v0)) % 28.41/5.21 % 28.41/5.21 (cup1) % 28.41/5.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 28.41/5.22 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 28.41/5.22 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.22 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~ % 28.41/5.22 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 28.41/5.22 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 28.41/5.22 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 28.41/5.22 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 28.41/5.22 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 28.41/5.22 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 28.41/5.22 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ % 28.41/5.22 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.22 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( % 28.41/5.22 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] % 28.41/5.22 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = % 28.41/5.22 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 28.41/5.22 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 28.41/5.22 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] % 28.41/5.22 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 28.41/5.22 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 28.41/5.22 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 28.41/5.22 (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 28.41/5.22 % 28.41/5.22 (oac1) % 28.41/5.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 28.41/5.25 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 28.41/5.25 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 28.41/5.25 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 28.41/5.25 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.25 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 28.41/5.25 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 28.41/5.25 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 28.41/5.25 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.25 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.25 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 28.41/5.25 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 28.41/5.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 28.41/5.25 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 28.41/5.25 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 28.41/5.25 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 28.41/5.25 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.25 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 28.41/5.25 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 28.41/5.25 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 28.41/5.25 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 28.41/5.25 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 28.41/5.25 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 28.41/5.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 28.41/5.25 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 28.41/5.25 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 28.41/5.25 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 28.41/5.25 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 28.41/5.25 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 28.41/5.25 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 28.41/5.25 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 28.41/5.25 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 28.41/5.25 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 28.41/5.25 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 28.41/5.25 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.25 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 28.41/5.25 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.25 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.41/5.25 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 28.41/5.25 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 28.41/5.25 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 28.41/5.25 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.25 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.41/5.25 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 28.41/5.25 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.25 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 28.41/5.25 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 28.41/5.25 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 28.41/5.25 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 28.41/5.25 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 28.41/5.25 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.25 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.41/5.25 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 28.41/5.25 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 28.41/5.25 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 28.41/5.25 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 28.41/5.25 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 28.41/5.25 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 28.41/5.25 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 28.41/5.25 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.25 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 28.41/5.25 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.25 unorthogonal_lines(v0, v1) = v4))) % 28.41/5.25 % 28.41/5.25 (occu1) % 28.41/5.25 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.41/5.25 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.25 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 28.41/5.25 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.25 unorthogonal_lines(v0, v1) = 0) % 28.41/5.25 % 28.41/5.25 (function-axioms) % 28.41/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.41/5.26 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 28.41/5.26 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 28.41/5.26 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 28.41/5.26 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.41/5.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 28.41/5.26 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.41/5.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 28.41/5.26 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 28.41/5.26 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 28.41/5.26 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.41/5.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.41/5.26 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 28.41/5.26 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.41/5.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 28.41/5.26 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.41/5.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.41/5.26 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 28.41/5.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.41/5.26 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 28.41/5.26 v0)) % 28.41/5.26 % 28.41/5.26 Further assumptions not needed in the proof: % 28.41/5.26 -------------------------------------------- % 28.41/5.26 apart1, apart2, apart4, apart5, ceq1, ceq2, ceq3, ci1, ci2, cp1, cp2, cu1, ooc1, % 28.41/5.26 ooc2, ouo1 % 28.41/5.26 % 28.41/5.26 Those formulas are unsatisfiable: % 28.41/5.26 --------------------------------- % 28.41/5.26 % 28.41/5.26 Begin of proof % 28.41/5.26 | % 28.41/5.26 | ALPHA: (ax6) implies: % 28.41/5.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 28.41/5.26 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 28.41/5.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 28.41/5.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 28.41/5.26 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 28.41/5.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 28.41/5.26 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 28.41/5.26 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 28.41/5.26 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.26 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 28.41/5.26 | % 28.41/5.26 | ALPHA: (ci3) implies: % 28.41/5.26 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 28.41/5.26 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.41/5.26 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 28.41/5.26 | & $i(v2))) % 28.41/5.26 | % 28.41/5.26 | ALPHA: (ci4) implies: % 28.41/5.26 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 28.41/5.26 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 28.41/5.26 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 28.41/5.26 | & $i(v2))) % 28.41/5.26 | % 28.41/5.26 | ALPHA: (cup1) implies: % 28.41/5.26 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 28.41/5.26 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 28.41/5.26 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 28.41/5.26 | $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 28.41/5.26 | convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 28.41/5.26 | v2) = v5))) % 28.41/5.26 | % 28.41/5.26 | ALPHA: (occu1) implies: % 28.41/5.27 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.41/5.27 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.27 | unorthogonal_lines(v0, v1) = 0) % 28.41/5.27 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.41/5.27 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 28.41/5.27 | convergent_lines(v0, v1) = 0) % 28.41/5.27 | % 28.41/5.27 | ALPHA: (oac1) implies: % 28.41/5.27 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 28.41/5.27 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) % 28.41/5.27 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 28.41/5.27 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.27 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 28.41/5.27 | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.27 | convergent_lines(v0, v1) = v4))) % 28.41/5.27 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 28.41/5.27 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 28.41/5.27 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 28.41/5.27 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 28.41/5.27 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 28.41/5.27 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 28.41/5.27 | convergent_lines(v0, v1) = v4))) % 28.41/5.27 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 28.41/5.27 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 28.41/5.27 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 28.41/5.27 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 28.41/5.27 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 28.41/5.27 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 28.41/5.27 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 28.41/5.27 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 28.41/5.27 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 28.41/5.27 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 28.41/5.27 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.27 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.27 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.27 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 28.41/5.27 | convergent_lines(v0, v1) = v5))) % 28.41/5.27 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 28.41/5.27 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) % 28.41/5.27 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 28.41/5.27 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.27 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.27 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.27 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 28.41/5.27 | convergent_lines(v0, v1) = v5))) % 28.41/5.27 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 28.41/5.27 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) % 28.41/5.27 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 28.41/5.27 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.27 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.27 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.27 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 28.41/5.27 | convergent_lines(v0, v1) = v5))) % 28.41/5.27 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 28.41/5.28 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, % 28.41/5.28 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 28.41/5.28 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 28.41/5.28 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 28.41/5.28 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 28.41/5.28 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 28.41/5.28 | convergent_lines(v0, v1) = v5))) % 28.41/5.28 | % 28.41/5.28 | ALPHA: (function-axioms) implies: % 28.41/5.28 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.41/5.28 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 28.41/5.28 | (convergent_lines(v3, v2) = v0)) % 28.41/5.28 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.41/5.28 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 28.41/5.28 | v0)) % 28.41/5.28 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.41/5.28 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 28.41/5.28 | (unorthogonal_lines(v3, v2) = v0)) % 28.41/5.28 | % 28.41/5.28 | DELTA: instantiating (con) with fresh symbols all_25_0, all_25_1, all_25_2, % 28.41/5.28 | all_25_3, all_25_4 gives: % 28.41/5.28 | (19) ~ (all_25_0 = 0) & ~ (all_25_1 = 0) & unorthogonal_lines(all_25_3, % 28.41/5.28 | all_25_2) = all_25_0 & unorthogonal_lines(all_25_4, all_25_3) = 0 & % 28.41/5.28 | convergent_lines(all_25_4, all_25_2) = all_25_1 & $i(all_25_2) & % 28.41/5.28 | $i(all_25_3) & $i(all_25_4) % 28.41/5.28 | % 28.41/5.28 | ALPHA: (19) implies: % 28.41/5.28 | (20) ~ (all_25_1 = 0) % 28.41/5.28 | (21) ~ (all_25_0 = 0) % 28.41/5.28 | (22) $i(all_25_4) % 28.41/5.28 | (23) $i(all_25_3) % 28.41/5.28 | (24) $i(all_25_2) % 28.41/5.28 | (25) convergent_lines(all_25_4, all_25_2) = all_25_1 % 28.41/5.28 | (26) unorthogonal_lines(all_25_4, all_25_3) = 0 % 28.41/5.28 | (27) unorthogonal_lines(all_25_3, all_25_2) = all_25_0 % 28.41/5.28 | % 28.41/5.28 | GROUND_INST: instantiating (3) with all_25_4, all_25_4, all_25_2, all_25_1, % 28.41/5.28 | all_25_1, simplifying with (22), (24), (25) gives: % 28.41/5.28 | (28) all_25_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 28.41/5.28 | convergent_lines(all_25_4, all_25_4) = v0) % 28.41/5.28 | % 28.41/5.28 | GROUND_INST: instantiating (12) with all_25_4, all_25_4, all_25_2, all_25_1, % 28.41/5.28 | all_25_1, simplifying with (22), (24), (25) gives: % 28.41/5.28 | (29) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.28 | all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0) | (v2 = % 28.41/5.28 | 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0) | ( % 28.41/5.28 | ~ (v1 = 0) & unorthogonal_lines(all_25_4, all_25_4) = v1) | ( ~ % 28.41/5.28 | (v0 = 0) & convergent_lines(all_25_4, all_25_4) = v0)) % 28.41/5.28 | % 28.41/5.28 | GROUND_INST: instantiating (7) with all_25_4, all_25_2, all_25_1, simplifying % 28.41/5.28 | with (22), (24), (25) gives: % 28.41/5.28 | (30) all_25_1 = 0 | unorthogonal_lines(all_25_4, all_25_2) = 0 % 28.41/5.28 | % 28.41/5.28 | GROUND_INST: instantiating (15) with all_25_4, all_25_4, all_25_3, 0, 0, % 28.41/5.28 | simplifying with (22), (23), (26) gives: % 28.41/5.28 | (31) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.28 | convergent_lines(all_25_4, all_25_3) = 0) | (v2 = 0 & % 28.41/5.28 | convergent_lines(all_25_4, all_25_3) = 0) | ( ~ (v1 = 0) & % 28.41/5.28 | unorthogonal_lines(all_25_4, all_25_4) = v1) | ( ~ (v0 = 0) & % 28.41/5.28 | convergent_lines(all_25_4, all_25_4) = v0)) % 28.41/5.28 | % 28.41/5.28 | GROUND_INST: instantiating (10) with all_25_4, all_25_3, all_25_3, 0, % 28.41/5.28 | simplifying with (22), (23), (26) gives: % 28.41/5.29 | (32) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | v2 = 0 & unorthogonal_lines(all_25_3, all_25_3) = 0 & % 28.41/5.29 | convergent_lines(all_25_3, all_25_3) = 0) | (v1 = 0 & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = 0) | ( ~ (v0 = 0) & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (9) with all_25_4, all_25_3, all_25_2, all_25_1, % 28.41/5.29 | simplifying with (22), (23), (24), (25), (26) gives: % 28.41/5.29 | (33) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | v2 = 0 & unorthogonal_lines(all_25_3, all_25_2) = 0 & % 28.41/5.29 | convergent_lines(all_25_3, all_25_2) = 0) | (v1 = 0 & all_25_1 = 0 % 28.41/5.29 | & unorthogonal_lines(all_25_4, all_25_2) = 0) | ( ~ (v0 = 0) & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (15) with all_25_3, all_25_3, all_25_2, all_25_0, % 28.41/5.29 | all_25_0, simplifying with (23), (24), (27) gives: % 28.41/5.29 | (34) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) | (v2 = 0 % 28.41/5.29 | & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) | ( ~ % 28.41/5.29 | (v1 = 0) & unorthogonal_lines(all_25_3, all_25_3) = v1) | ( ~ (v0 % 28.41/5.29 | = 0) & convergent_lines(all_25_3, all_25_3) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (11) with all_25_4, all_25_3, all_25_2, all_25_0, % 28.41/5.29 | simplifying with (22), (23), (24), (26), (27) gives: % 28.41/5.29 | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) | (v2 = 0 % 28.41/5.29 | & v1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0 & % 28.41/5.29 | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ (v0 = 0) & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (14) with all_25_4, all_25_3, all_25_2, all_25_1, % 28.41/5.29 | all_25_0, simplifying with (22), (23), (24), (25), (27) gives: % 28.41/5.29 | (36) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) | (v2 = 0 % 28.41/5.29 | & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0) | ( ~ % 28.41/5.29 | (v1 = 0) & unorthogonal_lines(all_25_4, all_25_3) = v1) | ( ~ (v0 % 28.41/5.29 | = 0) & convergent_lines(all_25_4, all_25_3) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (13) with all_25_3, all_25_4, all_25_2, all_25_0, % 28.41/5.29 | all_25_1, simplifying with (22), (23), (24), (25), (27) gives: % 28.41/5.29 | (37) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 28.41/5.29 | all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0) | (v2 = % 28.41/5.29 | 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) | ( ~ % 28.41/5.29 | (v1 = 0) & unorthogonal_lines(all_25_3, all_25_4) = v1) | ( ~ (v0 % 28.41/5.29 | = 0) & convergent_lines(all_25_3, all_25_4) = v0)) % 28.41/5.29 | % 28.41/5.29 | GROUND_INST: instantiating (8) with all_25_3, all_25_2, all_25_0, simplifying % 28.41/5.29 | with (23), (24), (27) gives: % 28.41/5.29 | (38) all_25_0 = 0 | convergent_lines(all_25_3, all_25_2) = 0 % 28.41/5.29 | % 28.41/5.29 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2, % 28.41/5.29 | all_32_3 gives: % 28.41/5.29 | (39) (all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_25_3, all_25_3) % 28.41/5.29 | = 0 & convergent_lines(all_25_3, all_25_3) = 0) | (all_32_2 = 0 & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = 0) | ( ~ (all_32_3 = 0) & % 28.41/5.29 | convergent_lines(all_25_4, all_25_3) = all_32_3) % 28.41/5.29 | % 28.41/5.29 | DELTA: instantiating (31) with fresh symbols all_33_0, all_33_1, all_33_2, % 28.41/5.29 | all_33_3 gives: % 28.41/5.29 | (40) (all_33_0 = 0 & convergent_lines(all_25_4, all_25_3) = 0) | (all_33_1 % 28.41/5.29 | = 0 & convergent_lines(all_25_4, all_25_3) = 0) | ( ~ (all_33_2 = 0) % 28.41/5.29 | & unorthogonal_lines(all_25_4, all_25_4) = all_33_2) | ( ~ (all_33_3 % 28.41/5.29 | = 0) & convergent_lines(all_25_4, all_25_4) = all_33_3) % 28.41/5.29 | % 28.41/5.29 | DELTA: instantiating (33) with fresh symbols all_34_0, all_34_1, all_34_2, % 28.41/5.29 | all_34_3 gives: % 28.41/5.30 | (41) (all_34_0 = 0 & all_34_1 = 0 & unorthogonal_lines(all_25_3, all_25_2) % 28.41/5.30 | = 0 & convergent_lines(all_25_3, all_25_2) = 0) | (all_34_2 = 0 & % 28.41/5.30 | all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = 0) | ( ~ % 28.41/5.30 | (all_34_3 = 0) & convergent_lines(all_25_4, all_25_3) = all_34_3) % 28.41/5.30 | % 28.41/5.30 | DELTA: instantiating (35) with fresh symbols all_35_0, all_35_1, all_35_2, % 28.41/5.30 | all_35_3 gives: % 28.41/5.30 | (42) (all_35_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = % 28.41/5.30 | 0) | (all_35_1 = 0 & all_35_2 = 0 & unorthogonal_lines(all_25_4, % 28.41/5.30 | all_25_2) = 0 & convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 28.41/5.30 | (all_35_3 = 0) & convergent_lines(all_25_4, all_25_3) = all_35_3) % 28.41/5.30 | % 28.41/5.30 | DELTA: instantiating (34) with fresh symbols all_36_0, all_36_1, all_36_2, % 28.41/5.30 | all_36_3 gives: % 28.41/5.30 | (43) (all_36_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = % 28.41/5.30 | 0) | (all_36_1 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, % 28.41/5.30 | all_25_2) = 0) | ( ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, % 28.41/5.30 | all_25_3) = all_36_2) | ( ~ (all_36_3 = 0) & % 28.41/5.30 | convergent_lines(all_25_3, all_25_3) = all_36_3) % 28.41/5.30 | % 28.41/5.30 | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1, all_37_2, % 28.41/5.30 | all_37_3 gives: % 28.41/5.30 | (44) (all_37_0 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) % 28.41/5.30 | = 0) | (all_37_1 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, % 28.41/5.30 | all_25_2) = 0) | ( ~ (all_37_2 = 0) & unorthogonal_lines(all_25_4, % 28.41/5.30 | all_25_4) = all_37_2) | ( ~ (all_37_3 = 0) & % 28.41/5.30 | convergent_lines(all_25_4, all_25_4) = all_37_3) % 28.41/5.30 | % 28.41/5.30 | DELTA: instantiating (37) with fresh symbols all_38_0, all_38_1, all_38_2, % 28.41/5.30 | all_38_3 gives: % 28.99/5.30 | (45) (all_38_0 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) % 28.99/5.30 | = 0) | (all_38_1 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, % 28.99/5.30 | all_25_2) = 0) | ( ~ (all_38_2 = 0) & unorthogonal_lines(all_25_3, % 28.99/5.30 | all_25_4) = all_38_2) | ( ~ (all_38_3 = 0) & % 28.99/5.30 | convergent_lines(all_25_3, all_25_4) = all_38_3) % 28.99/5.30 | % 28.99/5.30 | DELTA: instantiating (36) with fresh symbols all_39_0, all_39_1, all_39_2, % 28.99/5.30 | all_39_3 gives: % 28.99/5.30 | (46) (all_39_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = % 28.99/5.30 | 0) | (all_39_1 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, % 28.99/5.30 | all_25_2) = 0) | ( ~ (all_39_2 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.30 | all_25_3) = all_39_2) | ( ~ (all_39_3 = 0) & % 28.99/5.30 | convergent_lines(all_25_4, all_25_3) = all_39_3) % 28.99/5.30 | % 28.99/5.30 | BETA: splitting (30) gives: % 28.99/5.30 | % 28.99/5.30 | Case 1: % 28.99/5.30 | | % 28.99/5.30 | | (47) unorthogonal_lines(all_25_4, all_25_2) = 0 % 28.99/5.30 | | % 28.99/5.30 | | BETA: splitting (38) gives: % 28.99/5.30 | | % 28.99/5.30 | | Case 1: % 28.99/5.30 | | | % 28.99/5.30 | | | (48) convergent_lines(all_25_3, all_25_2) = 0 % 28.99/5.30 | | | % 28.99/5.30 | | | BETA: splitting (41) gives: % 28.99/5.30 | | | % 28.99/5.30 | | | Case 1: % 28.99/5.30 | | | | % 28.99/5.30 | | | | (49) all_34_0 = 0 & all_34_1 = 0 & unorthogonal_lines(all_25_3, % 28.99/5.30 | | | | all_25_2) = 0 & convergent_lines(all_25_3, all_25_2) = 0 % 28.99/5.30 | | | | % 28.99/5.30 | | | | ALPHA: (49) implies: % 28.99/5.30 | | | | (50) unorthogonal_lines(all_25_3, all_25_2) = 0 % 28.99/5.30 | | | | % 28.99/5.30 | | | | REF_CLOSE: (18), (21), (27), (50) are inconsistent by sub-proof #8. % 28.99/5.30 | | | | % 28.99/5.30 | | | Case 2: % 28.99/5.30 | | | | % 28.99/5.30 | | | | (51) (all_34_2 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, % 28.99/5.30 | | | | all_25_2) = 0) | ( ~ (all_34_3 = 0) & % 28.99/5.30 | | | | convergent_lines(all_25_4, all_25_3) = all_34_3) % 28.99/5.30 | | | | % 28.99/5.30 | | | | BETA: splitting (51) gives: % 28.99/5.30 | | | | % 28.99/5.30 | | | | Case 1: % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | (52) all_34_2 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, % 28.99/5.30 | | | | | all_25_2) = 0 % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | ALPHA: (52) implies: % 28.99/5.30 | | | | | (53) all_25_1 = 0 % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | REDUCE: (20), (53) imply: % 28.99/5.30 | | | | | (54) $false % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | CLOSE: (54) is inconsistent. % 28.99/5.30 | | | | | % 28.99/5.30 | | | | Case 2: % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | (55) ~ (all_34_3 = 0) & convergent_lines(all_25_4, all_25_3) = % 28.99/5.30 | | | | | all_34_3 % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | ALPHA: (55) implies: % 28.99/5.30 | | | | | (56) convergent_lines(all_25_4, all_25_3) = all_34_3 % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | BETA: splitting (28) gives: % 28.99/5.30 | | | | | % 28.99/5.30 | | | | | Case 1: % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | (57) all_25_1 = 0 % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | REDUCE: (20), (57) imply: % 28.99/5.30 | | | | | | (58) $false % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | CLOSE: (58) is inconsistent. % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | Case 2: % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_25_4, % 28.99/5.30 | | | | | | all_25_4) = v0) % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | DELTA: instantiating (59) with fresh symbol all_53_0 gives: % 28.99/5.30 | | | | | | (60) ~ (all_53_0 = 0) & convergent_lines(all_25_4, all_25_4) = % 28.99/5.30 | | | | | | all_53_0 % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | ALPHA: (60) implies: % 28.99/5.30 | | | | | | (61) ~ (all_53_0 = 0) % 28.99/5.30 | | | | | | (62) convergent_lines(all_25_4, all_25_4) = all_53_0 % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | BETA: splitting (42) gives: % 28.99/5.30 | | | | | | % 28.99/5.30 | | | | | | Case 1: % 28.99/5.30 | | | | | | | % 28.99/5.30 | | | | | | | (63) all_35_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, % 28.99/5.30 | | | | | | | all_25_2) = 0 % 28.99/5.30 | | | | | | | % 28.99/5.30 | | | | | | | ALPHA: (63) implies: % 28.99/5.31 | | | | | | | (64) all_25_0 = 0 % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | | REDUCE: (21), (64) imply: % 28.99/5.31 | | | | | | | (65) $false % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | | CLOSE: (65) is inconsistent. % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | Case 2: % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | | (66) (all_35_1 = 0 & all_35_2 = 0 & % 28.99/5.31 | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 & % 28.99/5.31 | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 28.99/5.31 | | | | | | | (all_35_3 = 0) & convergent_lines(all_25_4, all_25_3) = % 28.99/5.31 | | | | | | | all_35_3) % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | | BETA: splitting (66) gives: % 28.99/5.31 | | | | | | | % 28.99/5.31 | | | | | | | Case 1: % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | (67) all_35_1 = 0 & all_35_2 = 0 & % 28.99/5.31 | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 & % 28.99/5.31 | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0 % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | ALPHA: (67) implies: % 28.99/5.31 | | | | | | | | (68) convergent_lines(all_25_4, all_25_2) = 0 % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | REF_CLOSE: (16), (20), (25), (68) are inconsistent by sub-proof % 28.99/5.31 | | | | | | | | #7. % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | Case 2: % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | (69) ~ (all_35_3 = 0) & convergent_lines(all_25_4, all_25_3) % 28.99/5.31 | | | | | | | | = all_35_3 % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | ALPHA: (69) implies: % 28.99/5.31 | | | | | | | | (70) ~ (all_35_3 = 0) % 28.99/5.31 | | | | | | | | (71) convergent_lines(all_25_4, all_25_3) = all_35_3 % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | BETA: splitting (46) gives: % 28.99/5.31 | | | | | | | | % 28.99/5.31 | | | | | | | | Case 1: % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | (72) (all_39_0 = 0 & all_25_0 = 0 & % 28.99/5.31 | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0) | % 28.99/5.31 | | | | | | | | | (all_39_1 = 0 & all_25_1 = 0 & % 28.99/5.31 | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | BETA: splitting (72) gives: % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | Case 1: % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | (73) all_39_0 = 0 & all_25_0 = 0 & % 28.99/5.31 | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | ALPHA: (73) implies: % 28.99/5.31 | | | | | | | | | | (74) all_25_0 = 0 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | REDUCE: (21), (74) imply: % 28.99/5.31 | | | | | | | | | | (75) $false % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | CLOSE: (75) is inconsistent. % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | Case 2: % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | (76) all_39_1 = 0 & all_25_1 = 0 & % 28.99/5.31 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | ALPHA: (76) implies: % 28.99/5.31 | | | | | | | | | | (77) all_25_1 = 0 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | REDUCE: (20), (77) imply: % 28.99/5.31 | | | | | | | | | | (78) $false % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | CLOSE: (78) is inconsistent. % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | End of split % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | Case 2: % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | (79) ( ~ (all_39_2 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.31 | | | | | | | | | all_25_3) = all_39_2) | ( ~ (all_39_3 = 0) & % 28.99/5.31 | | | | | | | | | convergent_lines(all_25_4, all_25_3) = all_39_3) % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | BETA: splitting (79) gives: % 28.99/5.31 | | | | | | | | | % 28.99/5.31 | | | | | | | | | Case 1: % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | (80) ~ (all_39_2 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.31 | | | | | | | | | | all_25_3) = all_39_2 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | ALPHA: (80) implies: % 28.99/5.31 | | | | | | | | | | (81) ~ (all_39_2 = 0) % 28.99/5.31 | | | | | | | | | | (82) unorthogonal_lines(all_25_4, all_25_3) = all_39_2 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_39_2, all_25_3, % 28.99/5.31 | | | | | | | | | | all_25_4, simplifying with (26), (82) gives: % 28.99/5.31 | | | | | | | | | | (83) all_39_2 = 0 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | REDUCE: (81), (83) imply: % 28.99/5.31 | | | | | | | | | | (84) $false % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | CLOSE: (84) is inconsistent. % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | Case 2: % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | (85) ~ (all_39_3 = 0) & convergent_lines(all_25_4, % 28.99/5.31 | | | | | | | | | | all_25_3) = all_39_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | ALPHA: (85) implies: % 28.99/5.31 | | | | | | | | | | (86) convergent_lines(all_25_4, all_25_3) = all_39_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | GROUND_INST: instantiating (16) with all_35_3, all_39_3, % 28.99/5.31 | | | | | | | | | | all_25_3, all_25_4, simplifying with (71), (86) % 28.99/5.31 | | | | | | | | | | gives: % 28.99/5.31 | | | | | | | | | | (87) all_39_3 = all_35_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | GROUND_INST: instantiating (16) with all_34_3, all_39_3, % 28.99/5.31 | | | | | | | | | | all_25_3, all_25_4, simplifying with (56), (86) % 28.99/5.31 | | | | | | | | | | gives: % 28.99/5.31 | | | | | | | | | | (88) all_39_3 = all_34_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | COMBINE_EQS: (87), (88) imply: % 28.99/5.31 | | | | | | | | | | (89) all_35_3 = all_34_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | SIMP: (89) implies: % 28.99/5.31 | | | | | | | | | | (90) all_35_3 = all_34_3 % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | REDUCE: (70), (90) imply: % 28.99/5.31 | | | | | | | | | | (91) ~ (all_34_3 = 0) % 28.99/5.31 | | | | | | | | | | % 28.99/5.31 | | | | | | | | | | GROUND_INST: instantiating (12) with all_25_4, all_25_4, % 28.99/5.31 | | | | | | | | | | all_25_4, all_53_0, all_53_0, simplifying with % 28.99/5.31 | | | | | | | | | | (22), (62) gives: % 28.99/5.32 | | | | | | | | | | (92) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.32 | | | | | | | | | | int] : ((v3 = 0 & all_53_0 = 0 & % 28.99/5.32 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | % 28.99/5.32 | | | | | | | | | | (v2 = 0 & all_53_0 = 0 & % 28.99/5.32 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( % 28.99/5.32 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.32 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 28.99/5.32 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 28.99/5.32 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (9) with all_25_4, all_25_3, % 28.99/5.33 | | | | | | | | | | all_25_4, all_53_0, simplifying with (22), (23), % 28.99/5.33 | | | | | | | | | | (26), (62) gives: % 28.99/5.33 | | | | | | | | | | (93) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0) | (v1 % 28.99/5.33 | | | | | | | | | | = 0 & all_53_0 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( % 28.99/5.33 | | | | | | | | | | ~ (v0 = 0) & convergent_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_3) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (7) with all_25_4, all_25_4, % 28.99/5.33 | | | | | | | | | | all_53_0, simplifying with (22), (62) gives: % 28.99/5.33 | | | | | | | | | | (94) all_53_0 = 0 | unorthogonal_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_4) = 0 % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (12) with all_25_4, all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_3, all_34_3, all_34_3, simplifying with % 28.99/5.33 | | | | | | | | | | (22), (23), (56) gives: % 28.99/5.33 | | | | | | | | | | (95) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & all_34_3 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) | % 28.99/5.33 | | | | | | | | | | (v2 = 0 & all_34_3 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) | ( % 28.99/5.33 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (14) with all_25_4, all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_3, all_34_3, 0, simplifying with (22), % 28.99/5.33 | | | | | | | | | | (23), (26), (56) gives: % 28.99/5.33 | | | | | | | | | | (96) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & convergent_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_3) = 0) | (v2 = 0 & all_34_3 = 0) | ( ~ % 28.99/5.33 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (13) with all_25_4, all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_3, 0, all_34_3, simplifying with (22), % 28.99/5.33 | | | | | | | | | | (23), (26), (56) gives: % 28.99/5.33 | | | | | | | | | | (97) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & all_34_3 = 0) | (v2 = 0 & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = 0) | ( ~ % 28.99/5.33 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (9) with all_25_4, all_25_3, % 28.99/5.33 | | | | | | | | | | all_25_3, all_34_3, simplifying with (22), (23), % 28.99/5.33 | | | | | | | | | | (26), (56) gives: % 28.99/5.33 | | | | | | | | | | (98) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_3) = 0 & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_3, all_25_3) = 0) | (v1 % 28.99/5.33 | | | | | | | | | | = 0 & all_34_3 = 0) | ( ~ (v0 = 0) & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (12) with all_25_3, all_25_4, % 28.99/5.33 | | | | | | | | | | all_25_2, 0, all_25_1, simplifying with (22), % 28.99/5.33 | | | | | | | | | | (23), (24), (25), (48) gives: % 28.99/5.33 | | | | | | | | | | (99) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 28.99/5.33 | | | | | | | | | | int] : ((v3 = 0 & all_25_1 = 0 & % 28.99/5.33 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) | % 28.99/5.33 | | | | | | | | | | (v2 = 0 & unorthogonal_lines(all_25_3, all_25_2) = % 28.99/5.33 | | | | | | | | | | 0) | ( ~ (v1 = 0) & unorthogonal_lines(all_25_3, % 28.99/5.33 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 28.99/5.33 | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = v0)) % 28.99/5.33 | | | | | | | | | | % 28.99/5.33 | | | | | | | | | | GROUND_INST: instantiating (5) with all_25_3, all_25_2, % 28.99/5.33 | | | | | | | | | | simplifying with (23), (24), (48) gives: % 28.99/5.34 | | | | | | | | | | (100) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 28.99/5.34 | | | | | | | | | | intersection_point(all_25_3, all_25_2) = v0 & % 28.99/5.34 | | | | | | | | | | apart_point_and_line(v0, all_25_2) = v1 & $i(v0)) % 28.99/5.34 | | | | | | | | | | % 28.99/5.34 | | | | | | | | | | GROUND_INST: instantiating (4) with all_25_3, all_25_2, % 28.99/5.34 | | | | | | | | | | simplifying with (23), (24), (48) gives: % 28.99/5.34 | | | | | | | | | | (101) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 28.99/5.34 | | | | | | | | | | intersection_point(all_25_3, all_25_2) = v0 & % 28.99/5.34 | | | | | | | | | | apart_point_and_line(v0, all_25_3) = v1 & $i(v0)) % 28.99/5.34 | | | | | | | | | | % 28.99/5.34 | | | | | | | | | | GROUND_INST: instantiating (15) with all_25_4, all_25_4, % 28.99/5.34 | | | | | | | | | | all_25_2, 0, 0, simplifying with (22), (24), (47) % 28.99/5.34 | | | | | | | | | | gives: % 29.29/5.34 | | | | | | | | | | (102) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.29/5.34 | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_2) = 0) | (v2 = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 29.29/5.34 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | GROUND_INST: instantiating (14) with all_25_4, all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_2, all_25_1, 0, simplifying with (22), % 29.29/5.34 | | | | | | | | | | (24), (25), (47) gives: % 29.29/5.34 | | | | | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.29/5.34 | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_2) = 0) | (v2 = 0 & all_25_1 = 0) | ( % 29.29/5.34 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | GROUND_INST: instantiating (13) with all_25_4, all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_2, 0, all_25_1, simplifying with (22), % 29.29/5.34 | | | | | | | | | | (24), (25), (47) gives: % 29.29/5.34 | | | | | | | | | | (104) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.29/5.34 | | | | | | | | | | [v3: int] : ((v3 = 0 & all_25_1 = 0) | (v2 = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 29.29/5.34 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = v1) | ( ~ (v0 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = v0)) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_72_0, % 29.29/5.34 | | | | | | | | | | all_72_1 gives: % 29.29/5.34 | | | | | | | | | | (105) ~ (all_72_0 = 0) & intersection_point(all_25_3, % 29.29/5.34 | | | | | | | | | | all_25_2) = all_72_1 & % 29.29/5.34 | | | | | | | | | | apart_point_and_line(all_72_1, all_25_3) = all_72_0 % 29.29/5.34 | | | | | | | | | | & $i(all_72_1) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | ALPHA: (105) implies: % 29.29/5.34 | | | | | | | | | | (106) intersection_point(all_25_3, all_25_2) = all_72_1 % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (100) with fresh symbols all_74_0, % 29.29/5.34 | | | | | | | | | | all_74_1 gives: % 29.29/5.34 | | | | | | | | | | (107) ~ (all_74_0 = 0) & intersection_point(all_25_3, % 29.29/5.34 | | | | | | | | | | all_25_2) = all_74_1 & % 29.29/5.34 | | | | | | | | | | apart_point_and_line(all_74_1, all_25_2) = all_74_0 % 29.29/5.34 | | | | | | | | | | & $i(all_74_1) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | ALPHA: (107) implies: % 29.29/5.34 | | | | | | | | | | (108) ~ (all_74_0 = 0) % 29.29/5.34 | | | | | | | | | | (109) $i(all_74_1) % 29.29/5.34 | | | | | | | | | | (110) apart_point_and_line(all_74_1, all_25_2) = all_74_0 % 29.29/5.34 | | | | | | | | | | (111) intersection_point(all_25_3, all_25_2) = all_74_1 % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_77_0, % 29.29/5.34 | | | | | | | | | | all_77_1, all_77_2, all_77_3 gives: % 29.29/5.34 | | | | | | | | | | (112) (all_77_0 = 0 & all_25_1 = 0) | (all_77_1 = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 29.29/5.34 | | | | | | | | | | (all_77_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = all_77_2) | ( ~ (all_77_3 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_77_3) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_83_0, % 29.29/5.34 | | | | | | | | | | all_83_1, all_83_2, all_83_3 gives: % 29.29/5.34 | | | | | | | | | | (113) (all_83_0 = 0 & all_83_1 = 0 & % 29.29/5.34 | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_3) = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_3, all_25_3) = 0) | % 29.29/5.34 | | | | | | | | | | (all_83_2 = 0 & all_34_3 = 0) | ( ~ (all_83_3 = 0) % 29.29/5.34 | | | | | | | | | | & convergent_lines(all_25_4, all_25_3) = % 29.29/5.34 | | | | | | | | | | all_83_3) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_84_0, % 29.29/5.34 | | | | | | | | | | all_84_1, all_84_2, all_84_3 gives: % 29.29/5.34 | | | | | | | | | | (114) (all_84_0 = 0 & all_34_3 = 0) | (all_84_1 = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = 0) | ( ~ % 29.29/5.34 | | | | | | | | | | (all_84_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = all_84_2) | ( ~ (all_84_3 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_84_3) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (96) with fresh symbols all_85_0, % 29.29/5.34 | | | | | | | | | | all_85_1, all_85_2, all_85_3 gives: % 29.29/5.34 | | | | | | | | | | (115) (all_85_0 = 0 & convergent_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_3) = 0) | (all_85_1 = 0 & all_34_3 = 0) % 29.29/5.34 | | | | | | | | | | | ( ~ (all_85_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = all_85_2) | ( ~ (all_85_3 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_85_3) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_87_0, % 29.29/5.34 | | | | | | | | | | all_87_1, all_87_2, all_87_3 gives: % 29.29/5.34 | | | | | | | | | | (116) (all_87_0 = 0 & convergent_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_2) = 0) | (all_87_1 = 0 & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) | ( ~ % 29.29/5.34 | | | | | | | | | | (all_87_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.34 | | | | | | | | | | all_25_4) = all_87_2) | ( ~ (all_87_3 = 0) & % 29.29/5.34 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_87_3) % 29.29/5.34 | | | | | | | | | | % 29.29/5.34 | | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_88_0, % 29.29/5.35 | | | | | | | | | | all_88_1, all_88_2, all_88_3 gives: % 29.29/5.35 | | | | | | | | | | (117) (all_88_0 = 0 & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | all_25_2) = 0) | (all_88_1 = 0 & all_25_1 = 0) % 29.29/5.35 | | | | | | | | | | | ( ~ (all_88_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | all_25_4) = all_88_2) | ( ~ (all_88_3 = 0) & % 29.29/5.35 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_88_3) % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | DELTA: instantiating (99) with fresh symbols all_92_0, % 29.29/5.35 | | | | | | | | | | all_92_1, all_92_2, all_92_3 gives: % 29.29/5.35 | | | | | | | | | | (118) (all_92_0 = 0 & all_25_1 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) | % 29.29/5.35 | | | | | | | | | | (all_92_1 = 0 & unorthogonal_lines(all_25_3, % 29.29/5.35 | | | | | | | | | | all_25_2) = 0) | ( ~ (all_92_2 = 0) & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = % 29.29/5.35 | | | | | | | | | | all_92_2) | ( ~ (all_92_3 = 0) & % 29.29/5.35 | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = all_92_3) % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | DELTA: instantiating (93) with fresh symbols all_95_0, % 29.29/5.35 | | | | | | | | | | all_95_1, all_95_2, all_95_3 gives: % 29.29/5.35 | | | | | | | | | | (119) (all_95_0 = 0 & all_95_1 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.29/5.35 | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0) | % 29.29/5.35 | | | | | | | | | | (all_95_2 = 0 & all_53_0 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( ~ % 29.29/5.35 | | | | | | | | | | (all_95_3 = 0) & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | all_25_3) = all_95_3) % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | DELTA: instantiating (92) with fresh symbols all_96_0, % 29.29/5.35 | | | | | | | | | | all_96_1, all_96_2, all_96_3 gives: % 29.29/5.35 | | | | | | | | | | (120) (all_96_0 = 0 & all_53_0 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | % 29.29/5.35 | | | | | | | | | | (all_96_1 = 0 & all_53_0 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( ~ % 29.29/5.35 | | | | | | | | | | (all_96_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | all_25_4) = all_96_2) | ( ~ (all_96_3 = 0) & % 29.29/5.35 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_96_3) % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | DELTA: instantiating (95) with fresh symbols all_97_0, % 29.29/5.35 | | | | | | | | | | all_97_1, all_97_2, all_97_3 gives: % 29.29/5.35 | | | | | | | | | | (121) (all_97_0 = 0 & all_34_3 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) | % 29.29/5.35 | | | | | | | | | | (all_97_1 = 0 & all_34_3 = 0 & % 29.29/5.35 | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) | ( ~ % 29.29/5.35 | | | | | | | | | | (all_97_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | all_25_4) = all_97_2) | ( ~ (all_97_3 = 0) & % 29.29/5.35 | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_97_3) % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | BETA: splitting (94) gives: % 29.29/5.35 | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | (122) unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.29/5.35 | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | BETA: splitting (115) gives: % 29.29/5.35 | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | (123) (all_85_0 = 0 & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | all_25_3) = 0) | (all_85_1 = 0 & all_34_3 = 0) % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | BETA: splitting (123) gives: % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | (124) all_85_0 = 0 & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | | all_25_3) = 0 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | ALPHA: (124) implies: % 29.29/5.35 | | | | | | | | | | | | | (125) convergent_lines(all_25_4, all_25_3) = 0 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | REF_CLOSE: (16), (56), (91), (125) are inconsistent by % 29.29/5.35 | | | | | | | | | | | | | sub-proof #6. % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | Case 2: % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | (126) all_85_1 = 0 & all_34_3 = 0 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | ALPHA: (126) implies: % 29.29/5.35 | | | | | | | | | | | | | (127) all_34_3 = 0 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | REDUCE: (91), (127) imply: % 29.29/5.35 | | | | | | | | | | | | | (128) $false % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | CLOSE: (128) is inconsistent. % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | End of split % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | Case 2: % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | (129) ( ~ (all_85_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | all_25_4) = all_85_2) | ( ~ (all_85_3 = 0) & % 29.29/5.35 | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_85_3) % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | BETA: splitting (129) gives: % 29.29/5.35 | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | (130) ~ (all_85_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | | all_25_4) = all_85_2 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | ALPHA: (130) implies: % 29.29/5.35 | | | | | | | | | | | | | (131) ~ (all_85_2 = 0) % 29.29/5.35 | | | | | | | | | | | | | (132) unorthogonal_lines(all_25_4, all_25_4) = all_85_2 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_85_2, all_25_4, % 29.29/5.35 | | | | | | | | | | | | | all_25_4, simplifying with (122), (132) gives: % 29.29/5.35 | | | | | | | | | | | | | (133) all_85_2 = 0 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | REDUCE: (131), (133) imply: % 29.29/5.35 | | | | | | | | | | | | | (134) $false % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | Case 2: % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | (135) ~ (all_85_3 = 0) & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | | all_25_4) = all_85_3 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | ALPHA: (135) implies: % 29.29/5.35 | | | | | | | | | | | | | (136) convergent_lines(all_25_4, all_25_4) = all_85_3 % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | BETA: splitting (40) gives: % 29.29/5.35 | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | (137) (all_33_0 = 0 & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | | | all_25_3) = 0) | (all_33_1 = 0 & % 29.29/5.35 | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = 0) % 29.29/5.35 | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | BETA: splitting (137) gives: % 29.29/5.35 | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | Case 1: % 29.29/5.35 | | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | | (138) all_33_0 = 0 & convergent_lines(all_25_4, % 29.29/5.35 | | | | | | | | | | | | | | | all_25_3) = 0 % 29.29/5.35 | | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | | ALPHA: (138) implies: % 29.29/5.35 | | | | | | | | | | | | | | | (139) convergent_lines(all_25_4, all_25_3) = 0 % 29.29/5.35 | | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (91), (139) are inconsistent by % 29.29/5.35 | | | | | | | | | | | | | | | sub-proof #6. % 29.29/5.35 | | | | | | | | | | | | | | | % 29.29/5.35 | | | | | | | | | | | | | | Case 2: % 29.29/5.35 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | (140) all_33_1 = 0 & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | all_25_3) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | ALPHA: (140) implies: % 29.29/5.36 | | | | | | | | | | | | | | | (141) convergent_lines(all_25_4, all_25_3) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (91), (141) are inconsistent by % 29.29/5.36 | | | | | | | | | | | | | | | sub-proof #6. % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | End of split % 29.29/5.36 | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | (142) ( ~ (all_33_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | all_25_4) = all_33_2) | ( ~ (all_33_3 = 0) & % 29.29/5.36 | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_33_3) % 29.29/5.36 | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | BETA: splitting (142) gives: % 29.29/5.36 | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | (143) ~ (all_33_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | all_25_4) = all_33_2 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | ALPHA: (143) implies: % 29.29/5.36 | | | | | | | | | | | | | | | (144) ~ (all_33_2 = 0) % 29.29/5.36 | | | | | | | | | | | | | | | (145) unorthogonal_lines(all_25_4, all_25_4) = all_33_2 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_33_2, all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (145) gives: % 29.29/5.36 | | | | | | | | | | | | | | | (146) all_33_2 = 0 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | REDUCE: (144), (146) imply: % 29.29/5.36 | | | | | | | | | | | | | | | (147) $false % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | (148) ~ (all_33_3 = 0) & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | all_25_4) = all_33_3 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | ALPHA: (148) implies: % 29.29/5.36 | | | | | | | | | | | | | | | (149) convergent_lines(all_25_4, all_25_4) = all_33_3 % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 29.29/5.36 | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | (150) (all_77_0 = 0 & all_25_1 = 0) | (all_77_1 = 0 & % 29.29/5.36 | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | (151) all_77_0 = 0 & all_25_1 = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | (152) all_25_1 = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | REDUCE: (20), (152) imply: % 29.29/5.36 | | | | | | | | | | | | | | | | | (153) $false % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | (154) all_77_1 = 0 & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | ALPHA: (154) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | (155) convergent_lines(all_25_4, all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (25), (155) are inconsistent by % 29.29/5.36 | | | | | | | | | | | | | | | | | sub-proof #7. % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | End of split % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | (156) ( ~ (all_77_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | all_25_4) = all_77_2) | ( ~ (all_77_3 = 0) & % 29.29/5.36 | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_77_3) % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 29.29/5.36 | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | (157) ~ (all_77_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | all_25_4) = all_77_2 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | (158) ~ (all_77_2 = 0) % 29.29/5.36 | | | | | | | | | | | | | | | | | (159) unorthogonal_lines(all_25_4, all_25_4) = all_77_2 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_77_2, all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (159) gives: % 29.29/5.36 | | | | | | | | | | | | | | | | | (160) all_77_2 = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | REDUCE: (158), (160) imply: % 29.29/5.36 | | | | | | | | | | | | | | | | | (161) $false % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | (162) ~ (all_77_3 = 0) & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | all_25_4) = all_77_3 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | (163) convergent_lines(all_25_4, all_25_4) = all_77_3 % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 29.29/5.36 | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | (164) (all_87_0 = 0 & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | | all_25_2) = 0) | (all_87_1 = 0 & % 29.29/5.36 | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = 0) % 29.29/5.36 | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 29.29/5.36 | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | (165) all_87_0 = 0 & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | | | (166) convergent_lines(all_25_4, all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (25), (166) are inconsistent by % 29.29/5.36 | | | | | | | | | | | | | | | | | | | sub-proof #7. % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | (167) all_87_1 = 0 & convergent_lines(all_25_4, % 29.29/5.36 | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 29.29/5.36 | | | | | | | | | | | | | | | | | | | (168) convergent_lines(all_25_4, all_25_2) = 0 % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (25), (168) are inconsistent by % 29.29/5.36 | | | | | | | | | | | | | | | | | | | sub-proof #7. % 29.29/5.36 | | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | | End of split % 29.29/5.36 | | | | | | | | | | | | | | | | | | % 29.29/5.36 | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.36 | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | (169) ( ~ (all_87_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | all_25_4) = all_87_2) | ( ~ (all_87_3 = 0) & % 29.29/5.37 | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_87_3) % 29.29/5.37 | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (170) ~ (all_87_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | all_25_4) = all_87_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (171) ~ (all_87_2 = 0) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (172) unorthogonal_lines(all_25_4, all_25_4) = all_87_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_87_2, all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (172) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (173) all_87_2 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | REDUCE: (171), (173) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (174) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (175) ~ (all_87_3 = 0) & convergent_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | all_25_4) = all_87_3 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | (176) convergent_lines(all_25_4, all_25_4) = all_87_3 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | (177) (all_84_0 = 0 & all_34_3 = 0) | (all_84_1 = 0 & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = 0) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (178) all_84_0 = 0 & all_34_3 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (179) all_34_3 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (179) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (180) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (181) all_84_1 = 0 & convergent_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | all_25_3) = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (182) convergent_lines(all_25_4, all_25_3) = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (91), (182) are inconsistent by % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | End of split % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | (183) ( ~ (all_84_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | all_25_4) = all_84_2) | ( ~ (all_84_3 = 0) & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_84_3) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_84_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_84_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_84_2 = 0) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (186) unorthogonal_lines(all_25_4, all_25_4) = all_84_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_84_2, all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (186) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (187) all_84_2 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (187) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (188) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (189) ~ (all_84_3 = 0) & convergent_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_84_3 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | (190) convergent_lines(all_25_4, all_25_4) = all_84_3 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | (191) (all_96_0 = 0 & all_53_0 = 0 & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | (all_96_1 = 0 & all_53_0 = 0 & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (192) all_96_0 = 0 & all_53_0 = 0 & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (193) all_53_0 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (193) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (194) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (195) all_96_1 = 0 & all_53_0 = 0 & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (196) all_53_0 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (196) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (197) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | End of split % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | (198) ( ~ (all_96_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_96_2) | ( ~ (all_96_3 = 0) & % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_96_3) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_96_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_96_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (all_96_2 = 0) % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (201) unorthogonal_lines(all_25_4, all_25_4) = all_96_2 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_96_2, all_25_4, % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (201) gives: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (202) all_96_2 = 0 % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (202) imply: % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | (203) $false % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 29.29/5.37 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_96_3 = 0) & convergent_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_96_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | (205) convergent_lines(all_25_4, all_25_4) = all_96_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | (206) (all_97_0 = 0 & all_34_3 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | (all_97_1 = 0 & all_34_3 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_97_0 = 0 & all_34_3 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_34_3 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (208) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (209) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_97_1 = 0 & all_34_3 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_3) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_34_3 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (211) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (212) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | (213) ( ~ (all_97_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_97_2) | ( ~ (all_97_3 = 0) & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_97_3) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (214) ~ (all_97_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_97_2 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_97_2 = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (216) unorthogonal_lines(all_25_4, all_25_4) = all_97_2 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_97_2, all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (216) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_97_2 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (217) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (218) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_97_3 = 0) & convergent_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_97_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | (220) convergent_lines(all_25_4, all_25_4) = all_97_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) (all_37_0 = 0 & all_25_1 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_37_1 = 0 & all_25_1 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_37_0 = 0 & all_25_1 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_25_1 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (223) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_37_1 = 0 & all_25_1 = 0 & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_25_1 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (226) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (228) ( ~ (all_37_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_37_2) | ( ~ (all_37_3 = 0) & % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_37_3) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_37_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_37_2 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_37_2 = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) unorthogonal_lines(all_25_4, all_25_4) = all_37_2 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_37_2, all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (231) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_37_2 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (230), (232) imply: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) $false % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_37_3 = 0) & convergent_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_37_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_37_3 = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) convergent_lines(all_25_4, all_25_4) = all_37_3 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) (all_88_0 = 0 & convergent_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0) | (all_88_1 = 0 & all_25_1 = 0) % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_88_0 = 0 & convergent_lines(all_25_4, % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) convergent_lines(all_25_4, all_25_2) = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (25), (239) are inconsistent by % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_88_1 = 0 & all_25_1 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_25_1 = 0 % 29.29/5.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (241) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) $false % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) ( ~ (all_88_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_88_2) | ( ~ (all_88_3 = 0) & % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_4) = all_88_3) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_88_2 = 0) & unorthogonal_lines(all_25_4, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_88_2 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_88_2 = 0) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) unorthogonal_lines(all_25_4, all_25_4) = all_88_2 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_88_2, all_25_4, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, simplifying with (122), (246) gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_88_2 = 0 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (247) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_88_3 = 0) & convergent_lines(all_25_4, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_88_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) convergent_lines(all_25_4, all_25_4) = all_88_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_77_3, all_85_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (136), (163) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_85_3 = all_77_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_87_3, all_88_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (176), (250) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_88_3 = all_87_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_85_3, all_88_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (136), (250) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_88_3 = all_85_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_84_3, all_88_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (190), (250) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_88_3 = all_84_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_37_3, all_88_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (236), (250) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_88_3 = all_37_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_53_0, all_96_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (62), (205) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_96_3 = all_53_0 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_87_3, all_96_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (176), (205) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_96_3 = all_87_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_85_3, all_97_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (136), (220) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_97_3 = all_85_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_33_3, all_97_3, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (149), (220) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_97_3 = all_33_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_72_1, all_74_1, % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (106), (111) % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_74_1 = all_72_1 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_85_3 = all_33_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (261) implies: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_85_3 = all_33_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_87_3 = all_53_0 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_87_3 = all_53_0 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (255) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_84_3 = all_37_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (254) imply: % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_85_3 = all_84_3 % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.29/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_85_3 = all_84_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (254) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_87_3 = all_84_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_87_3 = all_84_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (269) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_84_3 = all_53_0 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (270) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_84_3 = all_53_0 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (262) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_77_3 = all_33_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (267) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_84_3 = all_77_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_84_3 = all_77_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (274) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_77_3 = all_53_0 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_77_3 = all_53_0 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (271) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_53_0 = all_37_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (276) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_53_0 = all_33_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (278) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_53_0 = all_33_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (279) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_37_3 = all_33_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (280) implies: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_37_3 = all_33_3 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (235), (281) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_33_3 = 0) % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (260) imply: % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) apart_point_and_line(all_72_1, all_25_2) = % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_0 % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (260) imply: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) $i(all_72_1) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_72_1, all_25_2, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_74_0, all_74_0, simplifying with % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (283), (284) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_74_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & convergent_lines(all_25_2, all_25_2) = % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & distinct_lines(all_25_2, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = v0)) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_25_4, all_25_2, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, 0, simplifying with (22), (24), (47), % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_2, all_25_4) = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_2, all_25_4) = 0) | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & convergent_lines(all_25_4, all_25_4) = % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = v0)) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_25_4, all_25_3, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, 0, simplifying with (22), (23), (26), % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0) | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & convergent_lines(all_25_4, all_25_4) = % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = v0)) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (287) with fresh symbols all_147_0, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_147_1, all_147_2, all_147_3 gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) (all_147_0 = 0 & all_147_1 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0) | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_147_2 = 0 & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0) | ( ~ (all_147_3 = 0) & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_147_3) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (286) with fresh symbols all_148_0, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_148_1, all_148_2, all_148_3 gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_148_0 = 0 & all_148_1 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_2, all_25_4) = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_2, all_25_4) = 0) | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_148_2 = 0 & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0) | ( ~ (all_148_3 = 0) & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_148_3) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_32_0 = 0 & all_32_1 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_3) = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) unorthogonal_lines(all_25_3, all_25_3) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (21), (43), (291), (292) are % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) (all_32_2 = 0 & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = 0) | ( ~ (all_32_3 = 0) & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = all_32_3) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_32_2 = 0 & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) convergent_lines(all_25_4, all_25_3) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (91), (295) are inconsistent by % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_32_3 = 0) & convergent_lines(all_25_4, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_32_3 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) convergent_lines(all_25_4, all_25_3) = all_32_3 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_74_0 = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (298) imply: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) $false % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent. % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_2, all_25_2) = 0) | ( % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0) & distinct_lines(all_25_2, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = v0)) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (300) with fresh symbols all_159_0, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_159_1 gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) (all_159_0 = 0 & convergent_lines(all_25_2, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0) | ( ~ (all_159_1 = 0) & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_2, all_25_2) = all_159_1) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_34_3, all_32_3, % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, all_25_4, simplifying with (56), (297) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_34_3 = all_32_3 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (302) imply: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_32_3 = 0) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) (all_36_0 = 0 & all_25_0 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0) | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_36_1 = 0 & all_25_0 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0) % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_36_0 = 0 & all_25_0 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_25_0 = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (306) imply: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) $false % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_36_1 = 0 & all_25_0 = 0 & % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_25_0 = 0 % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (309) imply: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) $false % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) ( ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_36_2) | ( ~ (all_36_3 = 0) & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_3) = all_36_3) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_36_2 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_36_2 = 0) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) unorthogonal_lines(all_25_3, all_25_3) = all_36_2 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_95_0 = 0 & all_95_1 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) unorthogonal_lines(all_25_3, all_25_4) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (20), (21), (27), (118), (316), (317) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #4. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) (all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_95_3 = 0) & convergent_lines(all_25_4, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_95_3) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (319) are inconsistent by sub-proof % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #3. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_25_3, all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_36_2, simplifying with (23), (314) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_36_2 = 0 | convergent_lines(all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_25_3, simplifying % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (321) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) $false % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_36_2 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (313), (323) imply: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) $false % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) ~ (all_36_3 = 0) & convergent_lines(all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_36_3 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_36_3 = 0) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) convergent_lines(all_25_3, all_25_3) = all_36_3 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_83_0 = 0 & all_83_1 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_3) = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) unorthogonal_lines(all_25_3, all_25_3) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (21), (43), (329), (330) are % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) (all_83_2 = 0 & all_34_3 = 0) | ( ~ (all_83_3 = 0) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & convergent_lines(all_25_4, all_25_3) = % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_83_3) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_83_2 = 0 & all_34_3 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_34_3 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (333) imply: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_32_3 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_32_3 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (335) imply: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_83_3 = 0) & convergent_lines(all_25_4, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_83_3 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) convergent_lines(all_25_4, all_25_3) = all_83_3 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_83_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, all_25_4, simplifying with (297), (338) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_83_3 = all_32_3 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) (all_38_0 = 0 & all_25_1 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0) | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_38_1 = 0 & all_25_0 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_38_0 = 0 & all_25_1 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_2) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_25_1 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (342) imply: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) $false % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_38_1 = 0 & all_25_0 = 0 & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_2) = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_25_0 = 0 % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (345) imply: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) $false % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (346) is inconsistent. % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) ( ~ (all_38_2 = 0) & unorthogonal_lines(all_25_3, % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_38_2) | ( ~ (all_38_3 = 0) & % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = all_38_3) % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives: % 29.55/5.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_38_2 = 0) & unorthogonal_lines(all_25_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_38_2 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_38_2 = 0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) unorthogonal_lines(all_25_3, all_25_4) = all_38_2 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_147_0 = 0 & all_147_1 = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) unorthogonal_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (20), (21), (27), (118), (352), (353) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #4. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) (all_147_2 = 0 & convergent_lines(all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0) | ( ~ (all_147_3 = 0) & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_3) = % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_147_3) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_147_2 = 0 & convergent_lines(all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) convergent_lines(all_25_4, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (149), (282), (356) are inconsistent by % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) ~ (all_147_3 = 0) & convergent_lines(all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_147_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) convergent_lines(all_25_4, all_25_3) = all_147_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_95_0 = 0 & all_95_1 = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) unorthogonal_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (20), (21), (27), (118), (360), (361) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #4. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_95_3 = 0) & convergent_lines(all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_95_3) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (363) are inconsistent by sub-proof % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #3. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_95_3 = 0) & convergent_lines(all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_95_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_95_3 = 0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) convergent_lines(all_25_4, all_25_3) = all_95_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_147_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, all_25_4, simplifying with (297), (358) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_147_3 = all_32_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_95_3, all_147_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, all_25_4, simplifying with (358), (366) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_147_3 = all_95_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (368) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_95_3 = all_32_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_25_3, all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, all_36_3, all_32_3, simplifying with % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (297), (327) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_36_3 = 0 | all_32_3 = 0 | ? [v0: int] : ( ~ % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_25_3, all_25_4) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_25_3, all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2, simplifying with (22), (23), (350) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_38_2 = 0 | convergent_lines(all_25_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_36_3 = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (373) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) $false % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_32_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = v0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (375) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_32_3 = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (376) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) ? [v0: int] : ( ~ (v0 = 0) & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = v0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (378) with fresh symbol all_332_0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) ~ (all_332_0 = 0) & convergent_lines(all_25_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_332_0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_332_0 = 0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) convergent_lines(all_25_3, all_25_4) = all_332_0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_332_0, all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, simplifying with (372), (381) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_332_0 = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (382) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) $false % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_38_2 = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (384) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) $false % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_38_3 = 0) & convergent_lines(all_25_3, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_38_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_38_3 = 0) % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) convergent_lines(all_25_3, all_25_4) = all_38_3 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_95_0 = 0 & all_95_1 = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_3, all_25_4) = 0 & % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_38_3, all_25_4, % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, simplifying with (388), (390) gives: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_38_3 = 0 % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (391) imply: % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) $false % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (392) is inconsistent. % 29.55/5.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) (all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0) | ( % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_95_3 = 0) & convergent_lines(all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_95_3) % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_95_2 = 0 & all_53_0 = 0 & % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (394) are inconsistent by sub-proof % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #3. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_25_3, all_25_2, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_38_3, simplifying with (22), (23), % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (48), (388) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_38_3 = 0 | convergent_lines(all_25_2, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) convergent_lines(all_25_2, all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_148_0 = 0 & all_148_1 = 0 & % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_25_2, all_25_4) = 0 & % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_2, all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_25_2, all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_1, simplifying with (22), (24), % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (396) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_25_1 = 0 | convergent_lines(all_25_2, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (24), (398), (apart3) are inconsistent by % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_148_2 = 0 & convergent_lines(all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0) | ( ~ (all_148_3 = 0) & % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_25_4, all_25_2) = % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_148_3) % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_148_2 = 0 & convergent_lines(all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) convergent_lines(all_25_4, all_25_4) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (149), (282), (401) are inconsistent by % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_148_3 = 0) & convergent_lines(all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = all_148_3 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (402) implies: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) ~ (all_148_3 = 0) % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) convergent_lines(all_25_4, all_25_2) = all_148_3 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_25_1, all_148_3, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_4, simplifying with (25), (404) % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_148_3 = all_25_1 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_159_0 = 0 & convergent_lines(all_25_2, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (406) implies: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) convergent_lines(all_25_2, all_25_2) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_25_2, simplifying % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (24), (407) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) $false % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (408) is inconsistent. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_25_2, all_25_4, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_1, simplifying with (22), (24), % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (396) gives: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_25_1 = 0 | convergent_lines(all_25_2, % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2) = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (24), (409), (apart3) are inconsistent by % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_38_3 = 0 % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (410) imply: % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) $false % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | Case 2: % 29.55/5.43 | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | (412) all_53_0 = 0 % 29.55/5.43 | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | REDUCE: (61), (412) imply: % 29.55/5.43 | | | | | | | | | | | (413) $false % 29.55/5.43 | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | | CLOSE: (413) is inconsistent. % 29.55/5.43 | | | | | | | | | | | % 29.55/5.43 | | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | | % 29.55/5.43 | | | | | | | | | End of split % 29.55/5.43 | | | | | | | | | % 29.55/5.43 | | | | | | | | End of split % 29.55/5.43 | | | | | | | | % 29.55/5.43 | | | | | | | End of split % 29.55/5.43 | | | | | | | % 29.55/5.43 | | | | | | End of split % 29.55/5.43 | | | | | | % 29.55/5.43 | | | | | End of split % 29.55/5.43 | | | | | % 29.55/5.43 | | | | End of split % 29.55/5.43 | | | | % 29.55/5.43 | | | End of split % 29.55/5.43 | | | % 29.55/5.43 | | Case 2: % 29.55/5.43 | | | % 29.55/5.43 | | | (414) all_25_0 = 0 % 29.55/5.43 | | | % 29.55/5.43 | | | REDUCE: (21), (414) imply: % 29.55/5.43 | | | (415) $false % 29.55/5.43 | | | % 29.55/5.43 | | | CLOSE: (415) is inconsistent. % 29.55/5.43 | | | % 29.55/5.43 | | End of split % 29.55/5.43 | | % 29.55/5.43 | Case 2: % 29.55/5.43 | | % 29.55/5.43 | | (416) all_25_1 = 0 % 29.55/5.43 | | % 29.55/5.43 | | REDUCE: (20), (416) imply: % 29.55/5.43 | | (417) $false % 29.55/5.43 | | % 29.55/5.43 | | CLOSE: (417) is inconsistent. % 29.55/5.43 | | % 29.55/5.43 | End of split % 29.55/5.43 | % 29.55/5.43 End of proof % 29.55/5.43 % 29.55/5.43 Sub-proof #1 shows that the following formulas are inconsistent: % 29.55/5.43 ---------------------------------------------------------------- % 29.55/5.43 (1) all_25_1 = 0 | convergent_lines(all_25_2, all_25_2) = 0 % 29.55/5.43 (2) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 29.55/5.43 (3) $i(all_25_2) % 29.55/5.43 (4) ~ (all_25_1 = 0) % 29.55/5.43 % 29.55/5.43 Begin of proof % 29.55/5.43 | % 29.55/5.43 | BETA: splitting (1) gives: % 29.55/5.43 | % 29.55/5.43 | Case 1: % 29.55/5.43 | | % 29.55/5.43 | | (5) convergent_lines(all_25_2, all_25_2) = 0 % 29.55/5.43 | | % 29.55/5.43 | | GROUND_INST: instantiating (2) with all_25_2, simplifying with (3), (5) % 29.55/5.43 | | gives: % 29.55/5.43 | | (6) $false % 29.55/5.43 | | % 29.55/5.43 | | CLOSE: (6) is inconsistent. % 29.55/5.43 | | % 29.55/5.43 | Case 2: % 29.55/5.43 | | % 29.55/5.43 | | (7) all_25_1 = 0 % 29.55/5.43 | | % 29.55/5.43 | | REDUCE: (4), (7) imply: % 29.55/5.43 | | (8) $false % 29.55/5.43 | | % 29.55/5.43 | | CLOSE: (8) is inconsistent. % 29.55/5.43 | | % 29.55/5.43 | End of split % 29.55/5.43 | % 29.55/5.43 End of proof % 29.55/5.43 % 29.55/5.43 Sub-proof #2 shows that the following formulas are inconsistent: % 29.55/5.43 ---------------------------------------------------------------- % 29.55/5.43 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.43 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.55/5.43 (convergent_lines(v3, v2) = v0)) % 29.55/5.43 (2) convergent_lines(all_25_4, all_25_4) = all_33_3 % 29.55/5.43 (3) convergent_lines(all_25_4, all_25_4) = 0 % 29.55/5.43 (4) ~ (all_33_3 = 0) % 29.55/5.43 % 29.55/5.43 Begin of proof % 29.55/5.43 | % 29.55/5.43 | GROUND_INST: instantiating (1) with all_33_3, 0, all_25_4, all_25_4, % 29.55/5.43 | simplifying with (2), (3) gives: % 29.55/5.43 | (5) all_33_3 = 0 % 29.55/5.43 | % 29.55/5.43 | REDUCE: (4), (5) imply: % 29.55/5.43 | (6) $false % 29.55/5.43 | % 29.55/5.43 | CLOSE: (6) is inconsistent. % 29.55/5.43 | % 29.55/5.43 End of proof % 29.55/5.43 % 29.55/5.43 Sub-proof #3 shows that the following formulas are inconsistent: % 29.55/5.43 ---------------------------------------------------------------- % 29.55/5.43 (1) all_95_2 = 0 & all_53_0 = 0 & unorthogonal_lines(all_25_4, all_25_4) = 0 % 29.55/5.43 (2) all_53_0 = all_33_3 % 29.55/5.43 (3) ~ (all_33_3 = 0) % 29.55/5.43 % 29.55/5.43 Begin of proof % 29.55/5.43 | % 29.55/5.43 | ALPHA: (1) implies: % 29.55/5.43 | (4) all_53_0 = 0 % 29.55/5.43 | % 29.55/5.43 | COMBINE_EQS: (2), (4) imply: % 29.55/5.43 | (5) all_33_3 = 0 % 29.55/5.43 | % 29.55/5.43 | SIMP: (5) implies: % 29.55/5.43 | (6) all_33_3 = 0 % 29.55/5.43 | % 29.55/5.43 | REDUCE: (3), (6) imply: % 29.55/5.43 | (7) $false % 29.55/5.43 | % 29.55/5.43 | CLOSE: (7) is inconsistent. % 29.55/5.43 | % 29.55/5.43 End of proof % 29.55/5.43 % 29.55/5.43 Sub-proof #4 shows that the following formulas are inconsistent: % 29.55/5.43 ---------------------------------------------------------------- % 29.55/5.43 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.43 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 29.55/5.43 (unorthogonal_lines(v3, v2) = v0)) % 29.55/5.43 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.43 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.55/5.43 (convergent_lines(v3, v2) = v0)) % 29.55/5.43 (3) convergent_lines(all_25_3, all_25_4) = 0 % 29.55/5.43 (4) unorthogonal_lines(all_25_3, all_25_4) = 0 % 29.55/5.43 (5) ~ (all_25_0 = 0) % 29.55/5.43 (6) (all_92_0 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) = % 29.55/5.43 0) | (all_92_1 = 0 & unorthogonal_lines(all_25_3, all_25_2) = 0) | ( ~ % 29.55/5.43 (all_92_2 = 0) & unorthogonal_lines(all_25_3, all_25_4) = all_92_2) | ( % 29.55/5.43 ~ (all_92_3 = 0) & convergent_lines(all_25_3, all_25_4) = all_92_3) % 29.55/5.43 (7) unorthogonal_lines(all_25_3, all_25_2) = all_25_0 % 29.55/5.43 (8) ~ (all_25_1 = 0) % 29.55/5.43 % 29.55/5.43 Begin of proof % 29.55/5.43 | % 29.55/5.43 | BETA: splitting (6) gives: % 29.55/5.43 | % 29.55/5.43 | Case 1: % 29.55/5.43 | | % 29.55/5.43 | | (9) (all_92_0 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, all_25_2) % 29.55/5.43 | | = 0) | (all_92_1 = 0 & unorthogonal_lines(all_25_3, all_25_2) = 0) % 29.55/5.43 | | % 29.55/5.43 | | BETA: splitting (9) gives: % 29.55/5.43 | | % 29.55/5.43 | | Case 1: % 29.55/5.43 | | | % 29.55/5.43 | | | (10) all_92_0 = 0 & all_25_1 = 0 & unorthogonal_lines(all_25_4, % 29.55/5.43 | | | all_25_2) = 0 % 29.55/5.43 | | | % 29.55/5.43 | | | ALPHA: (10) implies: % 29.55/5.43 | | | (11) all_25_1 = 0 % 29.55/5.43 | | | % 29.55/5.43 | | | REDUCE: (8), (11) imply: % 29.55/5.43 | | | (12) $false % 29.55/5.43 | | | % 29.55/5.43 | | | CLOSE: (12) is inconsistent. % 29.55/5.43 | | | % 29.55/5.43 | | Case 2: % 29.55/5.43 | | | % 29.55/5.43 | | | (13) all_92_1 = 0 & unorthogonal_lines(all_25_3, all_25_2) = 0 % 29.55/5.43 | | | % 29.55/5.43 | | | ALPHA: (13) implies: % 29.55/5.43 | | | (14) unorthogonal_lines(all_25_3, all_25_2) = 0 % 29.55/5.43 | | | % 29.55/5.43 | | | REF_CLOSE: (1), (5), (7), (14) are inconsistent by sub-proof #8. % 29.55/5.43 | | | % 29.55/5.43 | | End of split % 29.55/5.43 | | % 29.55/5.43 | Case 2: % 29.55/5.43 | | % 29.55/5.43 | | (15) ( ~ (all_92_2 = 0) & unorthogonal_lines(all_25_3, all_25_4) = % 29.55/5.43 | | all_92_2) | ( ~ (all_92_3 = 0) & convergent_lines(all_25_3, % 29.55/5.43 | | all_25_4) = all_92_3) % 29.55/5.43 | | % 29.55/5.43 | | BETA: splitting (15) gives: % 29.55/5.43 | | % 29.55/5.43 | | Case 1: % 29.55/5.43 | | | % 29.55/5.43 | | | (16) ~ (all_92_2 = 0) & unorthogonal_lines(all_25_3, all_25_4) = % 29.55/5.43 | | | all_92_2 % 29.55/5.43 | | | % 29.55/5.43 | | | ALPHA: (16) implies: % 29.55/5.43 | | | (17) ~ (all_92_2 = 0) % 29.55/5.44 | | | (18) unorthogonal_lines(all_25_3, all_25_4) = all_92_2 % 29.55/5.44 | | | % 29.55/5.44 | | | GROUND_INST: instantiating (1) with 0, all_92_2, all_25_4, all_25_3, % 29.55/5.44 | | | simplifying with (4), (18) gives: % 29.55/5.44 | | | (19) all_92_2 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (17), (19) imply: % 29.55/5.44 | | | (20) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (20) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | Case 2: % 29.55/5.44 | | | % 29.55/5.44 | | | (21) ~ (all_92_3 = 0) & convergent_lines(all_25_3, all_25_4) = % 29.55/5.44 | | | all_92_3 % 29.55/5.44 | | | % 29.55/5.44 | | | ALPHA: (21) implies: % 29.55/5.44 | | | (22) ~ (all_92_3 = 0) % 29.55/5.44 | | | (23) convergent_lines(all_25_3, all_25_4) = all_92_3 % 29.55/5.44 | | | % 29.55/5.44 | | | GROUND_INST: instantiating (2) with 0, all_92_3, all_25_4, all_25_3, % 29.55/5.44 | | | simplifying with (3), (23) gives: % 29.55/5.44 | | | (24) all_92_3 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (22), (24) imply: % 29.55/5.44 | | | (25) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (25) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | End of split % 29.55/5.44 | | % 29.55/5.44 | End of split % 29.55/5.44 | % 29.55/5.44 End of proof % 29.55/5.44 % 29.55/5.44 Sub-proof #5 shows that the following formulas are inconsistent: % 29.55/5.44 ---------------------------------------------------------------- % 29.55/5.44 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.44 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 29.55/5.44 (unorthogonal_lines(v3, v2) = v0)) % 29.55/5.44 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.44 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.55/5.44 (convergent_lines(v3, v2) = v0)) % 29.55/5.44 (3) unorthogonal_lines(all_25_3, all_25_3) = 0 % 29.55/5.44 (4) (all_36_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = 0) % 29.55/5.44 | (all_36_1 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = % 29.55/5.44 0) | ( ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, all_25_3) = % 29.55/5.44 all_36_2) | ( ~ (all_36_3 = 0) & convergent_lines(all_25_3, all_25_3) = % 29.55/5.44 all_36_3) % 29.55/5.44 (5) ~ (all_25_0 = 0) % 29.55/5.44 (6) convergent_lines(all_25_3, all_25_3) = 0 % 29.55/5.44 % 29.55/5.44 Begin of proof % 29.55/5.44 | % 29.55/5.44 | BETA: splitting (4) gives: % 29.55/5.44 | % 29.55/5.44 | Case 1: % 29.55/5.44 | | % 29.55/5.44 | | (7) (all_36_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) = % 29.55/5.44 | | 0) | (all_36_1 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, % 29.55/5.44 | | all_25_2) = 0) % 29.55/5.44 | | % 29.55/5.44 | | BETA: splitting (7) gives: % 29.55/5.44 | | % 29.55/5.44 | | Case 1: % 29.55/5.44 | | | % 29.55/5.44 | | | (8) all_36_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) % 29.55/5.44 | | | = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | ALPHA: (8) implies: % 29.55/5.44 | | | (9) all_25_0 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (5), (9) imply: % 29.55/5.44 | | | (10) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (10) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | Case 2: % 29.55/5.44 | | | % 29.55/5.44 | | | (11) all_36_1 = 0 & all_25_0 = 0 & convergent_lines(all_25_3, all_25_2) % 29.55/5.44 | | | = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | ALPHA: (11) implies: % 29.55/5.44 | | | (12) all_25_0 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (5), (12) imply: % 29.55/5.44 | | | (13) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (13) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | End of split % 29.55/5.44 | | % 29.55/5.44 | Case 2: % 29.55/5.44 | | % 29.55/5.44 | | (14) ( ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, all_25_3) = % 29.55/5.44 | | all_36_2) | ( ~ (all_36_3 = 0) & convergent_lines(all_25_3, % 29.55/5.44 | | all_25_3) = all_36_3) % 29.55/5.44 | | % 29.55/5.44 | | BETA: splitting (14) gives: % 29.55/5.44 | | % 29.55/5.44 | | Case 1: % 29.55/5.44 | | | % 29.55/5.44 | | | (15) ~ (all_36_2 = 0) & unorthogonal_lines(all_25_3, all_25_3) = % 29.55/5.44 | | | all_36_2 % 29.55/5.44 | | | % 29.55/5.44 | | | ALPHA: (15) implies: % 29.55/5.44 | | | (16) ~ (all_36_2 = 0) % 29.55/5.44 | | | (17) unorthogonal_lines(all_25_3, all_25_3) = all_36_2 % 29.55/5.44 | | | % 29.55/5.44 | | | GROUND_INST: instantiating (1) with 0, all_36_2, all_25_3, all_25_3, % 29.55/5.44 | | | simplifying with (3), (17) gives: % 29.55/5.44 | | | (18) all_36_2 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (16), (18) imply: % 29.55/5.44 | | | (19) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (19) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | Case 2: % 29.55/5.44 | | | % 29.55/5.44 | | | (20) ~ (all_36_3 = 0) & convergent_lines(all_25_3, all_25_3) = % 29.55/5.44 | | | all_36_3 % 29.55/5.44 | | | % 29.55/5.44 | | | ALPHA: (20) implies: % 29.55/5.44 | | | (21) ~ (all_36_3 = 0) % 29.55/5.44 | | | (22) convergent_lines(all_25_3, all_25_3) = all_36_3 % 29.55/5.44 | | | % 29.55/5.44 | | | GROUND_INST: instantiating (2) with 0, all_36_3, all_25_3, all_25_3, % 29.55/5.44 | | | simplifying with (6), (22) gives: % 29.55/5.44 | | | (23) all_36_3 = 0 % 29.55/5.44 | | | % 29.55/5.44 | | | REDUCE: (21), (23) imply: % 29.55/5.44 | | | (24) $false % 29.55/5.44 | | | % 29.55/5.44 | | | CLOSE: (24) is inconsistent. % 29.55/5.44 | | | % 29.55/5.44 | | End of split % 29.55/5.44 | | % 29.55/5.44 | End of split % 29.55/5.44 | % 29.55/5.44 End of proof % 29.55/5.44 % 29.55/5.44 Sub-proof #6 shows that the following formulas are inconsistent: % 29.55/5.44 ---------------------------------------------------------------- % 29.55/5.44 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.44 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.55/5.44 (convergent_lines(v3, v2) = v0)) % 29.55/5.44 (2) convergent_lines(all_25_4, all_25_3) = all_34_3 % 29.55/5.44 (3) convergent_lines(all_25_4, all_25_3) = 0 % 29.55/5.44 (4) ~ (all_34_3 = 0) % 29.55/5.44 % 29.55/5.44 Begin of proof % 29.55/5.44 | % 29.55/5.44 | GROUND_INST: instantiating (1) with all_34_3, 0, all_25_3, all_25_4, % 29.55/5.44 | simplifying with (2), (3) gives: % 29.55/5.44 | (5) all_34_3 = 0 % 29.55/5.44 | % 29.55/5.44 | REDUCE: (4), (5) imply: % 29.55/5.44 | (6) $false % 29.55/5.44 | % 29.55/5.44 | CLOSE: (6) is inconsistent. % 29.55/5.44 | % 29.55/5.44 End of proof % 29.55/5.44 % 29.55/5.44 Sub-proof #7 shows that the following formulas are inconsistent: % 29.55/5.44 ---------------------------------------------------------------- % 29.55/5.44 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.44 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 29.55/5.44 (convergent_lines(v3, v2) = v0)) % 29.55/5.44 (2) convergent_lines(all_25_4, all_25_2) = all_25_1 % 29.55/5.44 (3) convergent_lines(all_25_4, all_25_2) = 0 % 29.55/5.44 (4) ~ (all_25_1 = 0) % 29.55/5.44 % 29.55/5.44 Begin of proof % 29.55/5.44 | % 29.55/5.44 | GROUND_INST: instantiating (1) with all_25_1, 0, all_25_2, all_25_4, % 29.55/5.44 | simplifying with (2), (3) gives: % 29.55/5.44 | (5) all_25_1 = 0 % 29.55/5.44 | % 29.55/5.44 | REDUCE: (4), (5) imply: % 29.55/5.44 | (6) $false % 29.55/5.44 | % 29.55/5.44 | CLOSE: (6) is inconsistent. % 29.55/5.44 | % 29.55/5.44 End of proof % 29.55/5.44 % 29.55/5.44 Sub-proof #8 shows that the following formulas are inconsistent: % 29.55/5.44 ---------------------------------------------------------------- % 29.55/5.44 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.55/5.44 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 29.55/5.44 (unorthogonal_lines(v3, v2) = v0)) % 29.55/5.44 (2) unorthogonal_lines(all_25_3, all_25_2) = all_25_0 % 29.55/5.44 (3) unorthogonal_lines(all_25_3, all_25_2) = 0 % 29.55/5.44 (4) ~ (all_25_0 = 0) % 29.55/5.44 % 29.55/5.44 Begin of proof % 29.55/5.44 | % 29.55/5.44 | GROUND_INST: instantiating (1) with all_25_0, 0, all_25_2, all_25_3, % 29.55/5.44 | simplifying with (2), (3) gives: % 29.55/5.44 | (5) all_25_0 = 0 % 29.55/5.44 | % 29.55/5.44 | REDUCE: (4), (5) imply: % 29.55/5.44 | (6) $false % 29.55/5.44 | % 29.55/5.44 | CLOSE: (6) is inconsistent. % 29.55/5.44 | % 29.55/5.44 End of proof % 29.55/5.44 % SZS output end Proof for theBenchmark % 29.55/5.44 % 29.55/5.44 4748ms %------------------------------------------------------------------------------