%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO215+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 : n011.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 23:22:25 EDT 2023 % Result : Theorem 16.09s 2.88s % Output : Proof 23.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO215+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 20:44:26 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.65/1.07 Prover 1: Preprocessing ... % 2.65/1.08 Prover 4: Preprocessing ... % 3.06/1.12 Prover 3: Preprocessing ... % 3.06/1.12 Prover 6: Preprocessing ... % 3.06/1.12 Prover 0: Preprocessing ... % 3.06/1.12 Prover 2: Preprocessing ... % 3.06/1.12 Prover 5: Preprocessing ... % 5.09/1.42 Prover 2: Proving ... % 5.09/1.42 Prover 5: Proving ... % 5.09/1.44 Prover 1: Constructing countermodel ... % 5.09/1.46 Prover 3: Constructing countermodel ... % 5.82/1.48 Prover 6: Constructing countermodel ... % 6.46/1.58 Prover 3: gave up % 6.46/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.46/1.59 Prover 6: gave up % 6.46/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.46/1.62 Prover 1: gave up % 6.46/1.62 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.86/1.63 Prover 8: Preprocessing ... % 6.86/1.63 Prover 7: Preprocessing ... % 7.12/1.67 Prover 9: Preprocessing ... % 7.12/1.68 Prover 4: Constructing countermodel ... % 7.12/1.69 Prover 0: Proving ... % 7.12/1.70 Prover 7: Warning: ignoring some quantifiers % 7.12/1.72 Prover 7: Constructing countermodel ... % 7.12/1.73 Prover 8: Warning: ignoring some quantifiers % 7.69/1.74 Prover 8: Constructing countermodel ... % 8.01/1.82 Prover 7: gave up % 8.01/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.50/1.84 Prover 8: gave up % 8.50/1.85 Prover 10: Preprocessing ... % 8.50/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.67/1.90 Prover 11: Preprocessing ... % 8.67/1.90 Prover 10: Warning: ignoring some quantifiers % 9.06/1.93 Prover 10: Constructing countermodel ... % 9.06/1.96 Prover 10: gave up % 9.06/1.98 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.06/2.01 Prover 9: Constructing countermodel ... % 9.06/2.01 Prover 12: Preprocessing ... % 10.58/2.14 Prover 11: Constructing countermodel ... % 10.58/2.16 Prover 12: Proving ... % 16.09/2.88 Prover 0: proved (2259ms) % 16.09/2.88 % 16.09/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.09/2.88 % 16.09/2.88 Prover 9: stopped % 16.09/2.88 Prover 2: stopped % 16.09/2.88 Prover 5: stopped % 16.09/2.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.09/2.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 16.09/2.89 Prover 12: stopped % 16.09/2.90 Prover 13: Preprocessing ... % 16.09/2.90 Prover 16: Preprocessing ... % 16.09/2.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.09/2.92 Prover 19: Preprocessing ... % 16.09/2.93 Prover 16: Warning: ignoring some quantifiers % 16.09/2.93 Prover 16: Constructing countermodel ... % 16.09/2.94 Prover 13: Warning: ignoring some quantifiers % 16.09/2.95 Prover 13: Constructing countermodel ... % 16.88/2.98 Prover 19: Warning: ignoring some quantifiers % 16.88/3.00 Prover 19: Constructing countermodel ... % 17.32/3.05 Prover 13: gave up % 17.32/3.06 Prover 19: gave up % 18.26/3.18 Prover 16: gave up % 21.67/3.82 Prover 4: Found proof (size 427) % 21.67/3.82 Prover 4: proved (3193ms) % 21.67/3.82 Prover 11: stopped % 21.67/3.82 % 21.67/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.67/3.82 % 21.67/3.93 % SZS output start Proof for theBenchmark % 21.67/3.93 Assumptions after simplification: % 21.67/3.93 --------------------------------- % 21.67/3.93 % 21.67/3.93 (apart3) % 21.67/3.97 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 21.67/3.97 % 21.67/3.97 (ceq3) % 21.67/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.67/3.97 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 21.67/3.97 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 21.67/3.97 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.67/3.97 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 21.67/3.97 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.67/3.97 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.67/3.97 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 21.67/3.97 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.67/3.97 convergent_lines(v0, v2) = 0) % 21.67/3.97 % 21.67/3.97 (ci3) % 21.67/3.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 21.67/3.98 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.67/3.98 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 21.67/3.98 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.67/3.98 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.67/3.98 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 21.67/3.98 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 21.67/3.98 % 21.67/3.98 (ci4) % 21.67/3.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 21.67/3.98 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.67/3.98 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 21.67/3.98 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.67/3.98 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.67/3.98 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 21.67/3.98 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 21.67/3.98 % 21.67/3.98 (con) % 21.67/3.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 21.67/3.98 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & % 21.67/3.98 unorthogonal_lines(v0, v2) = v3 & convergent_lines(v0, v1) = 0 & $i(v2) & % 21.67/3.98 $i(v1) & $i(v0)) % 21.67/3.98 % 21.67/3.98 (cu1) % 21.67/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 21.67/4.00 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 21.67/4.00 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.67/4.00 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.67/4.00 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 21.67/4.00 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.67/4.00 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.67/4.00 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 21.67/4.00 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 21.67/4.00 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 21.67/4.00 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 21.67/4.00 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 21.67/4.00 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.67/4.00 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.67/4.00 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.67/4.00 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 21.67/4.00 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 21.67/4.00 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 21.67/4.00 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 21.67/4.00 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.67/4.00 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 21.67/4.00 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.67/4.00 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 21.67/4.00 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 21.67/4.00 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 21.67/4.00 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 21.67/4.00 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.67/4.00 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.67/4.00 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.67/4.00 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.67/4.00 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 21.67/4.00 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 21.67/4.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 21.67/4.00 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 21.67/4.00 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.67/4.00 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.67/4.00 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 21.67/4.00 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.67/4.00 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 21.67/4.00 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 21.67/4.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 21.67/4.00 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 21.67/4.00 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 21.67/4.00 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 21.67/4.00 % 21.67/4.00 (cup1) % 21.67/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.67/4.00 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 21.67/4.01 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.67/4.01 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 & % 21.67/4.01 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 21.67/4.01 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 21.67/4.01 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 21.67/4.01 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 21.67/4.01 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = % 21.67/4.01 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.67/4.01 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 21.67/4.01 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 21.67/4.01 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 & % 21.67/4.01 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! % 21.67/4.01 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 21.67/4.01 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 21.67/4.01 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 & % 21.67/4.01 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! % 21.67/4.01 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, % 22.35/4.01 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 22.35/4.01 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 & % 22.35/4.01 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) % 22.35/4.01 % 22.35/4.01 (oac1) % 22.35/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 22.35/4.02 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 22.35/4.02 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 22.35/4.02 any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = v6 & % 22.35/4.02 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & % 22.35/4.02 convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 % 22.35/4.02 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.35/4.02 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 22.35/4.02 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 22.35/4.02 (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & % 22.35/4.02 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = % 22.35/4.02 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: % 22.35/4.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 22.35/4.02 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 22.35/4.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 22.35/4.02 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 22.35/4.02 v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 % 22.35/4.02 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & % 22.35/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 22.35/4.02 (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ~ % 22.35/4.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 22.35/4.02 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, % 22.35/4.02 v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = % 22.35/4.02 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 22.35/4.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.35/4.02 (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 22.35/4.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 22.35/4.02 : ? [v7: any] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) % 22.35/4.02 = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ % 22.35/4.02 (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 22.35/4.02 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) % 22.35/4.02 | ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & % 22.35/4.02 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 22.35/4.02 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 22.35/4.02 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 22.35/4.02 ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & % 22.35/4.02 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 22.35/4.02 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 22.35/4.02 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | % 22.35/4.02 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & % 22.35/4.02 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = % 22.35/4.02 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 22.35/4.02 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 22.35/4.02 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 22.35/4.02 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 22.35/4.02 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: % 22.35/4.02 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 22.35/4.02 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 22.35/4.02 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = % 22.35/4.02 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 22.35/4.02 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 22.35/4.02 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 22.35/4.02 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & % 22.35/4.02 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 % 22.35/4.02 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 22.35/4.02 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | % 22.35/4.02 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 22.35/4.02 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 22.35/4.02 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & % 22.35/4.02 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 % 22.35/4.02 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) % 22.35/4.02 % 22.35/4.02 (occu1) % 22.35/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 22.35/4.02 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 22.35/4.02 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 22.35/4.02 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 22.35/4.02 unorthogonal_lines(v0, v1) = 0) % 22.35/4.02 % 22.35/4.02 (ouo1) % 22.35/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 22.35/4.03 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ % 22.35/4.03 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 22.35/4.03 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 22.35/4.03 (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = % 22.35/4.03 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 22.35/4.03 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) % 22.35/4.03 = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 22.35/4.03 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 22.35/4.03 (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & % 22.35/4.03 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 22.35/4.03 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 22.35/4.03 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 22.35/4.03 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 22.35/4.03 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 22.35/4.03 (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & % 22.35/4.03 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 22.35/4.03 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 22.35/4.03 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 22.35/4.03 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 22.35/4.03 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 22.35/4.03 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = % 22.35/4.03 0 | v6 = 0))) % 22.35/4.03 % 22.35/4.03 (function-axioms) % 22.35/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.35/4.03 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 22.35/4.03 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 22.35/4.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 22.35/4.03 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.35/4.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 22.35/4.03 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.35/4.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 22.35/4.03 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.35/4.03 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 22.35/4.03 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.35/4.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.35/4.03 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 22.35/4.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 22.35/4.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.35/4.03 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.35/4.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.35/4.03 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 22.35/4.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.35/4.03 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 22.35/4.03 v0)) % 22.35/4.03 % 22.35/4.03 Further assumptions not needed in the proof: % 22.35/4.03 -------------------------------------------- % 22.35/4.03 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2, ci1, ci2, cp1, cp2, ooc1, ooc2 % 22.35/4.03 % 22.35/4.03 Those formulas are unsatisfiable: % 22.35/4.03 --------------------------------- % 22.35/4.03 % 22.35/4.03 Begin of proof % 22.35/4.03 | % 22.35/4.03 | ALPHA: (ci3) implies: % 22.35/4.04 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 22.35/4.04 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.35/4.04 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 22.35/4.04 | & $i(v2))) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (ci4) implies: % 22.35/4.04 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 22.35/4.04 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 22.35/4.04 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 22.35/4.04 | & $i(v2))) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (cu1) implies: % 22.35/4.04 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 22.35/4.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 22.35/4.04 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 22.35/4.04 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 22.35/4.04 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 22.35/4.04 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 22.35/4.04 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 22.35/4.04 | | v8 = 0))) % 22.35/4.04 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 22.35/4.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 22.35/4.04 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 22.35/4.04 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 22.35/4.04 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 22.35/4.04 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 22.35/4.04 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 22.35/4.04 | | v8 = 0))) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (ceq3) implies: % 22.35/4.04 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.35/4.04 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 22.35/4.04 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, v2) = 0) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (cup1) implies: % 22.35/4.04 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 22.35/4.04 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 22.35/4.04 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 22.35/4.04 | $i(v0) | ? [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 % 22.35/4.04 | & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (occu1) implies: % 22.35/4.04 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 22.35/4.04 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 22.35/4.04 | convergent_lines(v0, v1) = 0) % 22.35/4.04 | % 22.35/4.04 | ALPHA: (oac1) implies: % 22.35/4.05 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.35/4.05 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 22.35/4.05 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 22.35/4.05 | [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 & % 22.35/4.05 | unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & % 22.35/4.05 | convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | % 22.35/4.05 | (v5 = 0 & v3 = 0)))) % 22.35/4.05 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.35/4.05 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) % 22.35/4.05 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 22.35/4.05 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 & % 22.35/4.05 | unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & % 22.35/4.05 | convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | % 22.35/4.05 | (v5 = 0 & v3 = 0)))) % 22.35/4.05 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.35/4.05 | (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = % 22.35/4.05 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 22.35/4.05 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v0, v2) = % 22.35/4.05 | v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = % 22.35/4.05 | v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = % 22.35/4.05 | 0) | (v6 = 0 & v5 = 0)))) % 22.35/4.05 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.35/4.05 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 22.35/4.05 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 22.35/4.05 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 22.35/4.05 | v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) % 22.35/4.05 | = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) % 22.35/4.05 | | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 22.35/4.05 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.35/4.05 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) % 22.35/4.05 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 22.35/4.05 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = % 22.35/4.05 | v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = % 22.35/4.05 | v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 22.35/4.05 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 22.35/4.05 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.35/4.05 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) % 22.35/4.05 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 22.35/4.05 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, v2) = % 22.35/4.05 | v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = % 22.35/4.05 | v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | % 22.35/4.05 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 22.35/4.06 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.35/4.06 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, % 22.35/4.06 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 22.35/4.06 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, % 22.35/4.06 | v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, % 22.35/4.06 | v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 % 22.35/4.06 | = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) % 22.35/4.06 | % 22.35/4.06 | ALPHA: (ouo1) implies: % 22.35/4.06 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 22.35/4.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) % 22.35/4.06 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | % 22.35/4.06 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 22.35/4.06 | (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 % 22.35/4.06 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 22.35/4.06 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 22.35/4.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) % 22.35/4.06 | | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 22.35/4.06 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 22.35/4.06 | (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 % 22.35/4.06 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 22.35/4.06 | % 22.35/4.06 | ALPHA: (function-axioms) implies: % 22.35/4.06 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.35/4.06 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 22.35/4.06 | (distinct_lines(v3, v2) = v0)) % 22.35/4.06 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.35/4.06 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.35/4.06 | (convergent_lines(v3, v2) = v0)) % 22.35/4.06 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.35/4.06 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 22.35/4.06 | (apart_point_and_line(v3, v2) = v0)) % 22.35/4.06 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.35/4.06 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 22.35/4.06 | v0)) % 22.35/4.06 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.35/4.06 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.35/4.06 | (unorthogonal_lines(v3, v2) = v0)) % 22.35/4.06 | % 22.35/4.06 | DELTA: instantiating (con) with fresh symbols all_25_0, all_25_1, all_25_2, % 22.35/4.06 | all_25_3, all_25_4 gives: % 22.35/4.06 | (22) ~ (all_25_0 = 0) & ~ (all_25_1 = 0) & unorthogonal_lines(all_25_3, % 22.35/4.06 | all_25_2) = all_25_0 & unorthogonal_lines(all_25_4, all_25_2) = % 22.35/4.06 | all_25_1 & convergent_lines(all_25_4, all_25_3) = 0 & $i(all_25_2) & % 22.35/4.06 | $i(all_25_3) & $i(all_25_4) % 22.35/4.06 | % 22.35/4.06 | ALPHA: (22) implies: % 22.35/4.06 | (23) ~ (all_25_1 = 0) % 22.35/4.06 | (24) ~ (all_25_0 = 0) % 22.35/4.06 | (25) $i(all_25_4) % 22.35/4.06 | (26) $i(all_25_3) % 22.35/4.06 | (27) $i(all_25_2) % 22.35/4.06 | (28) convergent_lines(all_25_4, all_25_3) = 0 % 22.35/4.06 | (29) unorthogonal_lines(all_25_4, all_25_2) = all_25_1 % 22.35/4.06 | (30) unorthogonal_lines(all_25_3, all_25_2) = all_25_0 % 22.35/4.06 | % 22.35/4.06 | GROUND_INST: instantiating (8) with all_25_4, all_25_3, all_25_3, 0, % 22.35/4.06 | simplifying with (25), (26), (28) gives: % 22.35/4.07 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_3, all_25_3) = v3 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_3) = v1 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_3) = v0 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_3) = v2 & ( ~ (v0 = 0) | v1 = 0 | % 22.35/4.07 | (v3 = 0 & v2 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (11) with all_25_4, all_25_4, all_25_3, 0, 0, % 22.35/4.07 | simplifying with (25), (26), (28) gives: % 22.35/4.07 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_4, all_25_3) = v3 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_3) = v2 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 22.35/4.07 | 0) | v3 = 0 | v2 = 0)) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (2) with all_25_4, all_25_3, simplifying with (25), % 22.35/4.07 | (26), (28) gives: % 22.35/4.07 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.35/4.07 | intersection_point(all_25_4, all_25_3) = v0 & % 22.35/4.07 | apart_point_and_line(v0, all_25_3) = v1 & $i(v0)) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (1) with all_25_4, all_25_3, simplifying with (25), % 22.35/4.07 | (26), (28) gives: % 22.35/4.07 | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.35/4.07 | intersection_point(all_25_4, all_25_3) = v0 & % 22.35/4.07 | apart_point_and_line(v0, all_25_4) = v1 & $i(v0)) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (14) with all_25_4, all_25_4, all_25_2, all_25_1, % 22.35/4.07 | all_25_1, simplifying with (25), (27), (29) gives: % 22.35/4.07 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_4, all_25_4) = v1 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v3 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v2 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 22.35/4.07 | 0) | (v3 = 0 & all_25_1 = 0) | (v2 = 0 & all_25_1 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (9) with all_25_4, all_25_3, all_25_2, all_25_1, % 22.35/4.07 | simplifying with (25), (26), (27), (28), (29) gives: % 22.35/4.07 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_3, all_25_2) = v3 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_3) = v0 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v2 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v1 & ( ~ (v0 = 0) | (v3 = 0 & % 22.35/4.07 | v2 = 0) | (v1 = 0 & all_25_1 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (7) with all_25_4, all_25_2, all_25_1, simplifying % 22.35/4.07 | with (25), (27), (29) gives: % 22.35/4.07 | (37) all_25_1 = 0 | convergent_lines(all_25_4, all_25_2) = 0 % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (14) with all_25_3, all_25_3, all_25_2, all_25_0, % 22.35/4.07 | all_25_0, simplifying with (26), (27), (30) gives: % 22.35/4.07 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_3, all_25_3) = v1 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v3 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v2 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 22.35/4.07 | 0) | (v3 = 0 & all_25_0 = 0) | (v2 = 0 & all_25_0 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (14) with all_25_4, all_25_3, all_25_2, all_25_1, % 22.35/4.07 | all_25_0, simplifying with (25), (26), (27), (29), (30) gives: % 22.35/4.07 | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_4, all_25_3) = v1 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v3 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v2 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 22.35/4.07 | 0) | (v3 = 0 & all_25_0 = 0) | (v2 = 0 & all_25_1 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (14) with all_25_3, all_25_4, all_25_2, all_25_0, % 22.35/4.07 | all_25_1, simplifying with (25), (26), (27), (29), (30) gives: % 22.35/4.07 | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_3, all_25_4) = v1 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v2 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_4) = v0 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v3 & ( ~ (v1 = 0) | ~ (v0 = % 22.35/4.07 | 0) | (v3 = 0 & all_25_1 = 0) | (v2 = 0 & all_25_0 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (10) with all_25_4, all_25_3, all_25_2, all_25_0, % 22.35/4.07 | simplifying with (25), (26), (27), (28), (30) gives: % 22.35/4.07 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.35/4.07 | (unorthogonal_lines(all_25_4, all_25_2) = v2 & % 22.35/4.07 | unorthogonal_lines(all_25_4, all_25_3) = v0 & % 22.35/4.07 | convergent_lines(all_25_3, all_25_2) = v3 & % 22.35/4.07 | convergent_lines(all_25_4, all_25_2) = v1 & ( ~ (v0 = 0) | (v3 = 0 & % 22.35/4.07 | all_25_0 = 0) | (v2 = 0 & v1 = 0))) % 22.35/4.07 | % 22.35/4.07 | GROUND_INST: instantiating (7) with all_25_3, all_25_2, all_25_0, simplifying % 22.35/4.07 | with (26), (27), (30) gives: % 22.35/4.07 | (42) all_25_0 = 0 | convergent_lines(all_25_3, all_25_2) = 0 % 22.35/4.07 | % 22.35/4.07 | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1 gives: % 22.35/4.07 | (43) ~ (all_32_0 = 0) & intersection_point(all_25_4, all_25_3) = all_32_1 % 22.35/4.07 | & apart_point_and_line(all_32_1, all_25_4) = all_32_0 & $i(all_32_1) % 22.35/4.07 | % 22.35/4.07 | ALPHA: (43) implies: % 22.35/4.07 | (44) ~ (all_32_0 = 0) % 22.35/4.07 | (45) apart_point_and_line(all_32_1, all_25_4) = all_32_0 % 22.35/4.08 | (46) intersection_point(all_25_4, all_25_3) = all_32_1 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (33) with fresh symbols all_34_0, all_34_1 gives: % 22.35/4.08 | (47) ~ (all_34_0 = 0) & intersection_point(all_25_4, all_25_3) = all_34_1 % 22.35/4.08 | & apart_point_and_line(all_34_1, all_25_3) = all_34_0 & $i(all_34_1) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (47) implies: % 22.35/4.08 | (48) ~ (all_34_0 = 0) % 22.35/4.08 | (49) $i(all_34_1) % 22.35/4.08 | (50) apart_point_and_line(all_34_1, all_25_3) = all_34_0 % 22.35/4.08 | (51) intersection_point(all_25_4, all_25_3) = all_34_1 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (32) with fresh symbols all_36_0, all_36_1, all_36_2, % 22.35/4.08 | all_36_3 gives: % 22.35/4.08 | (52) unorthogonal_lines(all_25_4, all_25_3) = all_36_0 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_3) = all_36_1 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_4) = all_36_2 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_4) = all_36_3 & ( ~ (all_36_2 = 0) | % 22.35/4.08 | ~ (all_36_3 = 0) | all_36_0 = 0 | all_36_1 = 0) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (52) implies: % 22.35/4.08 | (53) convergent_lines(all_25_4, all_25_4) = all_36_3 % 22.35/4.08 | (54) unorthogonal_lines(all_25_4, all_25_4) = all_36_2 % 22.35/4.08 | (55) unorthogonal_lines(all_25_4, all_25_3) = all_36_1 % 22.35/4.08 | (56) unorthogonal_lines(all_25_4, all_25_3) = all_36_0 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (31) with fresh symbols all_38_0, all_38_1, all_38_2, % 22.35/4.08 | all_38_3 gives: % 22.35/4.08 | (57) unorthogonal_lines(all_25_3, all_25_3) = all_38_0 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_3) = all_38_2 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_3) = all_38_3 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_3) = all_38_1 & ( ~ (all_38_3 = 0) | % 22.35/4.08 | all_38_2 = 0 | (all_38_0 = 0 & all_38_1 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (57) implies: % 22.35/4.08 | (58) convergent_lines(all_25_3, all_25_3) = all_38_1 % 22.35/4.08 | (59) unorthogonal_lines(all_25_4, all_25_3) = all_38_3 % 22.35/4.08 | (60) unorthogonal_lines(all_25_4, all_25_3) = all_38_2 % 22.35/4.08 | (61) unorthogonal_lines(all_25_3, all_25_3) = all_38_0 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (36) with fresh symbols all_40_0, all_40_1, all_40_2, % 22.35/4.08 | all_40_3 gives: % 22.35/4.08 | (62) unorthogonal_lines(all_25_3, all_25_2) = all_40_0 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_3) = all_40_3 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_40_1 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_40_2 & ( ~ (all_40_3 = 0) | % 22.35/4.08 | (all_40_0 = 0 & all_40_1 = 0) | (all_40_2 = 0 & all_25_1 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (62) implies: % 22.35/4.08 | (63) convergent_lines(all_25_4, all_25_2) = all_40_2 % 22.35/4.08 | (64) convergent_lines(all_25_3, all_25_2) = all_40_1 % 22.35/4.08 | (65) unorthogonal_lines(all_25_4, all_25_3) = all_40_3 % 22.35/4.08 | (66) unorthogonal_lines(all_25_3, all_25_2) = all_40_0 % 22.35/4.08 | (67) ~ (all_40_3 = 0) | (all_40_0 = 0 & all_40_1 = 0) | (all_40_2 = 0 & % 22.35/4.08 | all_25_1 = 0) % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (41) with fresh symbols all_42_0, all_42_1, all_42_2, % 22.35/4.08 | all_42_3 gives: % 22.35/4.08 | (68) unorthogonal_lines(all_25_4, all_25_2) = all_42_1 & % 22.35/4.08 | unorthogonal_lines(all_25_4, all_25_3) = all_42_3 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_42_0 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_42_2 & ( ~ (all_42_3 = 0) | % 22.35/4.08 | (all_42_0 = 0 & all_25_0 = 0) | (all_42_1 = 0 & all_42_2 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (68) implies: % 22.35/4.08 | (69) convergent_lines(all_25_4, all_25_2) = all_42_2 % 22.35/4.08 | (70) convergent_lines(all_25_3, all_25_2) = all_42_0 % 22.35/4.08 | (71) unorthogonal_lines(all_25_4, all_25_3) = all_42_3 % 22.35/4.08 | (72) unorthogonal_lines(all_25_4, all_25_2) = all_42_1 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (35) with fresh symbols all_44_0, all_44_1, all_44_2, % 22.35/4.08 | all_44_3 gives: % 22.35/4.08 | (73) unorthogonal_lines(all_25_4, all_25_4) = all_44_2 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_44_0 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_44_1 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_4) = all_44_3 & ( ~ (all_44_2 = 0) | % 22.35/4.08 | ~ (all_44_3 = 0) | (all_44_0 = 0 & all_25_1 = 0) | (all_44_1 = 0 & % 22.35/4.08 | all_25_1 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (73) implies: % 22.35/4.08 | (74) convergent_lines(all_25_4, all_25_4) = all_44_3 % 22.35/4.08 | (75) convergent_lines(all_25_4, all_25_2) = all_44_1 % 22.35/4.08 | (76) convergent_lines(all_25_4, all_25_2) = all_44_0 % 22.35/4.08 | (77) unorthogonal_lines(all_25_4, all_25_4) = all_44_2 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (38) with fresh symbols all_46_0, all_46_1, all_46_2, % 22.35/4.08 | all_46_3 gives: % 22.35/4.08 | (78) unorthogonal_lines(all_25_3, all_25_3) = all_46_2 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_46_0 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_46_1 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_3) = all_46_3 & ( ~ (all_46_2 = 0) | % 22.35/4.08 | ~ (all_46_3 = 0) | (all_46_0 = 0 & all_25_0 = 0) | (all_46_1 = 0 & % 22.35/4.08 | all_25_0 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (78) implies: % 22.35/4.08 | (79) convergent_lines(all_25_3, all_25_3) = all_46_3 % 22.35/4.08 | (80) convergent_lines(all_25_3, all_25_2) = all_46_1 % 22.35/4.08 | (81) convergent_lines(all_25_3, all_25_2) = all_46_0 % 22.35/4.08 | (82) unorthogonal_lines(all_25_3, all_25_3) = all_46_2 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (40) with fresh symbols all_48_0, all_48_1, all_48_2, % 22.35/4.08 | all_48_3 gives: % 22.35/4.08 | (83) unorthogonal_lines(all_25_3, all_25_4) = all_48_2 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_48_1 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_4) = all_48_3 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_48_0 & ( ~ (all_48_2 = 0) | % 22.35/4.08 | ~ (all_48_3 = 0) | (all_48_0 = 0 & all_25_1 = 0) | (all_48_1 = 0 & % 22.35/4.08 | all_25_0 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (83) implies: % 22.35/4.08 | (84) convergent_lines(all_25_4, all_25_2) = all_48_0 % 22.35/4.08 | (85) convergent_lines(all_25_3, all_25_4) = all_48_3 % 22.35/4.08 | (86) convergent_lines(all_25_3, all_25_2) = all_48_1 % 22.35/4.08 | (87) unorthogonal_lines(all_25_3, all_25_4) = all_48_2 % 22.35/4.08 | % 22.35/4.08 | DELTA: instantiating (39) with fresh symbols all_50_0, all_50_1, all_50_2, % 22.35/4.08 | all_50_3 gives: % 22.35/4.08 | (88) unorthogonal_lines(all_25_4, all_25_3) = all_50_2 & % 22.35/4.08 | convergent_lines(all_25_3, all_25_2) = all_50_0 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_2) = all_50_1 & % 22.35/4.08 | convergent_lines(all_25_4, all_25_3) = all_50_3 & ( ~ (all_50_2 = 0) | % 22.35/4.08 | ~ (all_50_3 = 0) | (all_50_0 = 0 & all_25_0 = 0) | (all_50_1 = 0 & % 22.35/4.08 | all_25_1 = 0)) % 22.35/4.08 | % 22.35/4.08 | ALPHA: (88) implies: % 22.35/4.08 | (89) convergent_lines(all_25_4, all_25_3) = all_50_3 % 22.35/4.08 | (90) convergent_lines(all_25_4, all_25_2) = all_50_1 % 22.35/4.08 | (91) convergent_lines(all_25_3, all_25_2) = all_50_0 % 22.35/4.08 | (92) unorthogonal_lines(all_25_4, all_25_3) = all_50_2 % 22.35/4.08 | % 22.35/4.09 | BETA: splitting (42) gives: % 22.35/4.09 | % 22.35/4.09 | Case 1: % 22.35/4.09 | | % 22.35/4.09 | | (93) convergent_lines(all_25_3, all_25_2) = 0 % 22.35/4.09 | | % 22.35/4.09 | | BETA: splitting (37) gives: % 22.35/4.09 | | % 22.35/4.09 | | Case 1: % 22.35/4.09 | | | % 22.35/4.09 | | | (94) convergent_lines(all_25_4, all_25_2) = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_36_3, all_44_3, all_25_4, % 22.35/4.09 | | | all_25_4, simplifying with (53), (74) gives: % 22.35/4.09 | | | (95) all_44_3 = all_36_3 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with 0, all_50_3, all_25_3, all_25_4, % 22.35/4.09 | | | simplifying with (28), (89) gives: % 22.35/4.09 | | | (96) all_50_3 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_40_2, all_42_2, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (63), (69) gives: % 22.35/4.09 | | | (97) all_42_2 = all_40_2 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_42_2, all_44_0, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (69), (76) gives: % 22.35/4.09 | | | (98) all_44_0 = all_42_2 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_44_0, all_48_0, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (76), (84) gives: % 22.35/4.09 | | | (99) all_48_0 = all_44_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with 0, all_48_0, all_25_2, all_25_4, % 22.35/4.09 | | | simplifying with (84), (94) gives: % 22.35/4.09 | | | (100) all_48_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_44_0, all_50_1, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (76), (90) gives: % 22.35/4.09 | | | (101) all_50_1 = all_44_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_44_1, all_50_1, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (75), (90) gives: % 22.35/4.09 | | | (102) all_50_1 = all_44_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_38_1, all_46_3, all_25_3, % 22.35/4.09 | | | all_25_3, simplifying with (58), (79) gives: % 22.35/4.09 | | | (103) all_46_3 = all_38_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_46_1, all_46_0, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (80), (81) gives: % 22.35/4.09 | | | (104) all_46_0 = all_46_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_46_1, all_48_1, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (80), (86) gives: % 22.35/4.09 | | | (105) all_48_1 = all_46_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_42_0, all_48_1, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (70), (86) gives: % 22.35/4.09 | | | (106) all_48_1 = all_42_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_40_1, all_48_1, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (64), (86) gives: % 22.35/4.09 | | | (107) all_48_1 = all_40_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with all_46_0, all_50_0, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (81), (91) gives: % 22.35/4.09 | | | (108) all_50_0 = all_46_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (18) with 0, all_50_0, all_25_2, all_25_3, % 22.35/4.09 | | | simplifying with (91), (93) gives: % 22.35/4.09 | | | (109) all_50_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (20) with all_32_1, all_34_1, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (46), (51) gives: % 22.35/4.09 | | | (110) all_34_1 = all_32_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_36_2, all_44_2, all_25_4, % 22.35/4.09 | | | all_25_4, simplifying with (54), (77) gives: % 22.35/4.09 | | | (111) all_44_2 = all_36_2 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_38_3, all_38_2, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (59), (60) gives: % 22.35/4.09 | | | (112) all_38_2 = all_38_3 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_36_1, all_38_2, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (55), (60) gives: % 22.35/4.09 | | | (113) all_38_2 = all_36_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_38_2, all_42_3, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (60), (71) gives: % 22.35/4.09 | | | (114) all_42_3 = all_38_2 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_36_0, all_42_3, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (56), (71) gives: % 22.35/4.09 | | | (115) all_42_3 = all_36_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_42_3, all_50_2, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (71), (92) gives: % 22.35/4.09 | | | (116) all_50_2 = all_42_3 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_40_3, all_50_2, all_25_3, % 22.35/4.09 | | | all_25_4, simplifying with (65), (92) gives: % 22.35/4.09 | | | (117) all_50_2 = all_40_3 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_25_1, all_42_1, all_25_2, % 22.35/4.09 | | | all_25_4, simplifying with (29), (72) gives: % 22.35/4.09 | | | (118) all_42_1 = all_25_1 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_38_0, all_46_2, all_25_3, % 22.35/4.09 | | | all_25_3, simplifying with (61), (82) gives: % 22.35/4.09 | | | (119) all_46_2 = all_38_0 % 22.35/4.09 | | | % 22.35/4.09 | | | GROUND_INST: instantiating (21) with all_25_0, all_40_0, all_25_2, % 22.35/4.09 | | | all_25_3, simplifying with (30), (66) gives: % 22.35/4.09 | | | (120) all_40_0 = all_25_0 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (108), (109) imply: % 22.35/4.09 | | | (121) all_46_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (121) implies: % 22.35/4.09 | | | (122) all_46_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (101), (102) imply: % 22.35/4.09 | | | (123) all_44_0 = all_44_1 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (123) implies: % 22.35/4.09 | | | (124) all_44_0 = all_44_1 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (116), (117) imply: % 22.35/4.09 | | | (125) all_42_3 = all_40_3 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (125) implies: % 22.35/4.09 | | | (126) all_42_3 = all_40_3 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (99), (100) imply: % 22.35/4.09 | | | (127) all_44_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (127) implies: % 22.35/4.09 | | | (128) all_44_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (105), (106) imply: % 22.35/4.09 | | | (129) all_46_1 = all_42_0 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (129) implies: % 22.35/4.09 | | | (130) all_46_1 = all_42_0 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (106), (107) imply: % 22.35/4.09 | | | (131) all_42_0 = all_40_1 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (104), (122) imply: % 22.35/4.09 | | | (132) all_46_1 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (132) implies: % 22.35/4.09 | | | (133) all_46_1 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | COMBINE_EQS: (130), (133) imply: % 22.35/4.09 | | | (134) all_42_0 = 0 % 22.35/4.09 | | | % 22.35/4.09 | | | SIMP: (134) implies: % 22.35/4.09 | | | (135) all_42_0 = 0 % 22.35/4.09 | | | % 22.35/4.10 | | | COMBINE_EQS: (124), (128) imply: % 22.35/4.10 | | | (136) all_44_1 = 0 % 22.35/4.10 | | | % 22.35/4.10 | | | COMBINE_EQS: (98), (124) imply: % 22.35/4.10 | | | (137) all_44_1 = all_42_2 % 22.35/4.10 | | | % 22.35/4.10 | | | COMBINE_EQS: (136), (137) imply: % 22.35/4.10 | | | (138) all_42_2 = 0 % 22.35/4.10 | | | % 22.35/4.10 | | | SIMP: (138) implies: % 22.35/4.10 | | | (139) all_42_2 = 0 % 22.35/4.10 | | | % 22.35/4.10 | | | COMBINE_EQS: (131), (135) imply: % 22.35/4.10 | | | (140) all_40_1 = 0 % 22.35/4.10 | | | % 22.35/4.10 | | | SIMP: (140) implies: % 23.02/4.10 | | | (141) all_40_1 = 0 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (97), (139) imply: % 23.02/4.10 | | | (142) all_40_2 = 0 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (114), (126) imply: % 23.02/4.10 | | | (143) all_40_3 = all_38_2 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (115), (126) imply: % 23.02/4.10 | | | (144) all_40_3 = all_36_0 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (143), (144) imply: % 23.02/4.10 | | | (145) all_38_2 = all_36_0 % 23.02/4.10 | | | % 23.02/4.10 | | | SIMP: (145) implies: % 23.02/4.10 | | | (146) all_38_2 = all_36_0 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (112), (113) imply: % 23.02/4.10 | | | (147) all_38_3 = all_36_1 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (112), (146) imply: % 23.02/4.10 | | | (148) all_38_3 = all_36_0 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (147), (148) imply: % 23.02/4.10 | | | (149) all_36_0 = all_36_1 % 23.02/4.10 | | | % 23.02/4.10 | | | COMBINE_EQS: (144), (149) imply: % 23.02/4.10 | | | (150) all_40_3 = all_36_1 % 23.02/4.10 | | | % 23.02/4.10 | | | REDUCE: (50), (110) imply: % 23.02/4.10 | | | (151) apart_point_and_line(all_32_1, all_25_3) = all_34_0 % 23.02/4.10 | | | % 23.02/4.10 | | | REDUCE: (49), (110) imply: % 23.02/4.10 | | | (152) $i(all_32_1) % 23.02/4.10 | | | % 23.02/4.10 | | | BETA: splitting (67) gives: % 23.02/4.10 | | | % 23.02/4.10 | | | Case 1: % 23.02/4.10 | | | | % 23.02/4.10 | | | | (153) ~ (all_40_3 = 0) % 23.02/4.10 | | | | % 23.02/4.10 | | | | REDUCE: (150), (153) imply: % 23.02/4.10 | | | | (154) ~ (all_36_1 = 0) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (5) with all_25_4, all_25_3, all_25_4, % 23.02/4.10 | | | | all_36_3, simplifying with (25), (26), (28), (53) gives: % 23.02/4.10 | | | | (155) all_36_3 = 0 | distinct_lines(all_25_3, all_25_4) = 0 % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (11) with all_25_4, all_25_4, all_25_2, 0, 0, % 23.02/4.10 | | | | simplifying with (25), (27), (94) gives: % 23.02/4.10 | | | | (156) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_4, all_25_2) = v3 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_4, all_25_2) = v2 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (13) with all_25_4, all_25_4, all_25_2, 0, % 23.02/4.10 | | | | all_25_1, simplifying with (25), (27), (29), (94) gives: % 23.02/4.10 | | | | (157) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_4, all_25_2) = v2 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_4, all_25_2) = v3 & % 23.02/4.10 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v2 = 0 | (v3 = 0 & all_25_1 = 0))) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (12) with all_25_4, all_25_4, all_25_2, % 23.02/4.10 | | | | all_25_1, 0, simplifying with (25), (27), (29), (94) gives: % 23.02/4.10 | | | | (158) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_4, all_25_2) = v3 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_4, all_25_2) = v2 & % 23.02/4.10 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v3 = 0 | (v2 = 0 & all_25_1 = 0))) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (8) with all_25_3, all_25_2, all_25_2, 0, % 23.02/4.10 | | | | simplifying with (26), (27), (93) gives: % 23.02/4.10 | | | | (159) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_2, all_25_2) = v3 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_2) = v1 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.02/4.10 | | | | convergent_lines(all_25_2, all_25_2) = v2 & ( ~ (v0 = 0) | v1 % 23.02/4.10 | | | | = 0 | (v3 = 0 & v2 = 0))) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (11) with all_25_3, all_25_3, all_25_2, 0, 0, % 23.02/4.10 | | | | simplifying with (26), (27), (93) gives: % 23.02/4.10 | | | | (160) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_3, all_25_2) = v3 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_3) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_3) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (11) with all_25_3, all_25_4, all_25_2, 0, 0, % 23.02/4.10 | | | | simplifying with (25), (26), (27), (93), (94) gives: % 23.02/4.10 | | | | (161) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_4) = v1 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_4, all_25_2) = v3 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (13) with all_25_3, all_25_3, all_25_2, 0, % 23.02/4.10 | | | | all_25_0, simplifying with (26), (27), (30), (93) gives: % 23.02/4.10 | | | | (162) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_3) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_2) = v3 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_3) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v2 = 0 | (v3 = 0 & all_25_0 = 0))) % 23.02/4.10 | | | | % 23.02/4.10 | | | | GROUND_INST: instantiating (12) with all_25_3, all_25_3, all_25_2, % 23.02/4.10 | | | | all_25_0, 0, simplifying with (26), (27), (30), (93) gives: % 23.02/4.10 | | | | (163) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.10 | | | | (unorthogonal_lines(all_25_3, all_25_2) = v3 & % 23.02/4.10 | | | | unorthogonal_lines(all_25_3, all_25_3) = v1 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_2) = v2 & % 23.02/4.10 | | | | convergent_lines(all_25_3, all_25_3) = v0 & ( ~ (v1 = 0) | ~ % 23.02/4.10 | | | | (v0 = 0) | v3 = 0 | (v2 = 0 & all_25_0 = 0))) % 23.02/4.10 | | | | % 23.02/4.11 | | | | GROUND_INST: instantiating (13) with all_25_3, all_25_4, all_25_2, 0, % 23.02/4.11 | | | | all_25_1, simplifying with (25), (26), (27), (29), (93) % 23.02/4.11 | | | | gives: % 23.02/4.11 | | | | (164) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.11 | | | | (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.02/4.11 | | | | unorthogonal_lines(all_25_3, all_25_4) = v1 & % 23.02/4.11 | | | | convergent_lines(all_25_3, all_25_4) = v0 & % 23.02/4.11 | | | | convergent_lines(all_25_4, all_25_2) = v3 & ( ~ (v1 = 0) | ~ % 23.02/4.11 | | | | (v0 = 0) | v2 = 0 | (v3 = 0 & all_25_1 = 0))) % 23.02/4.11 | | | | % 23.02/4.11 | | | | GROUND_INST: instantiating (8) with all_25_3, all_25_2, all_25_3, % 23.02/4.11 | | | | all_38_1, simplifying with (26), (27), (58), (93) gives: % 23.02/4.11 | | | | (165) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.11 | | | | (unorthogonal_lines(all_25_2, all_25_3) = v3 & % 23.02/4.11 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.02/4.11 | | | | unorthogonal_lines(all_25_3, all_25_3) = v1 & % 23.02/4.11 | | | | convergent_lines(all_25_2, all_25_3) = v2 & ( ~ (v0 = 0) | % 23.02/4.11 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_38_1 = 0))) % 23.02/4.11 | | | | % 23.02/4.11 | | | | GROUND_INST: instantiating (8) with all_25_3, all_25_2, all_25_4, % 23.02/4.11 | | | | all_48_3, simplifying with (25), (26), (27), (85), (93) % 23.02/4.11 | | | | gives: % 23.02/4.11 | | | | (166) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.02/4.11 | | | | (unorthogonal_lines(all_25_2, all_25_4) = v3 & % 23.02/4.11 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.02/4.11 | | | | unorthogonal_lines(all_25_3, all_25_4) = v1 & % 23.02/4.11 | | | | convergent_lines(all_25_2, all_25_4) = v2 & ( ~ (v0 = 0) | % 23.02/4.11 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_48_3 = 0))) % 23.07/4.11 | | | | % 23.07/4.11 | | | | GROUND_INST: instantiating (9) with all_25_3, all_25_2, all_25_2, % 23.07/4.11 | | | | all_25_0, simplifying with (26), (27), (30), (93) gives: % 23.07/4.11 | | | | (167) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.07/4.11 | | | | (unorthogonal_lines(all_25_2, all_25_2) = v3 & % 23.07/4.11 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.07/4.11 | | | | convergent_lines(all_25_2, all_25_2) = v2 & % 23.07/4.11 | | | | convergent_lines(all_25_3, all_25_2) = v1 & ( ~ (v0 = 0) | % 23.07/4.11 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_25_0 = 0))) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (15) with all_32_1, all_25_3, all_25_4, % 23.08/4.11 | | | | all_25_2, all_32_0, all_25_0, simplifying with (25), (26), % 23.08/4.11 | | | | (27), (30), (45), (152) gives: % 23.08/4.11 | | | | (168) all_32_0 = 0 | all_25_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.11 | | | | [v2: any] : (unorthogonal_lines(all_25_4, all_25_2) = v2 & % 23.08/4.11 | | | | apart_point_and_line(all_32_1, all_25_3) = v1 & % 23.08/4.11 | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = 0) | v2 = % 23.08/4.11 | | | | 0 | v1 = 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (6) with all_32_1, all_25_4, all_25_4, % 23.08/4.11 | | | | all_32_0, all_32_0, simplifying with (25), (45), (152) % 23.08/4.11 | | | | gives: % 23.08/4.11 | | | | (169) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : % 23.08/4.11 | | | | (convergent_lines(all_25_4, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_lines(all_25_4, all_25_4) = v0 & ( ~ (v0 = 0) | v1 = % 23.08/4.11 | | | | 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (4) with all_32_1, all_32_1, all_25_4, % 23.08/4.11 | | | | all_25_4, all_32_0, all_32_0, simplifying with (25), (45), % 23.08/4.11 | | | | (152) gives: % 23.08/4.11 | | | | (170) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 23.08/4.11 | | | | [v3: any] : (apart_point_and_line(all_32_1, all_25_4) = v3 & % 23.08/4.11 | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.11 | | | | distinct_lines(all_25_4, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.11 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (16) with all_32_1, all_25_3, all_25_4, % 23.08/4.11 | | | | all_25_2, all_34_0, all_25_1, simplifying with (25), (26), % 23.08/4.11 | | | | (27), (29), (151), (152) gives: % 23.08/4.11 | | | | (171) all_34_0 = 0 | all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.11 | | | | [v2: any] : (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.08/4.11 | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = 0) | v2 = % 23.08/4.11 | | | | 0 | v1 = 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (15) with all_32_1, all_25_4, all_25_3, % 23.08/4.11 | | | | all_25_2, all_34_0, all_25_1, simplifying with (25), (26), % 23.08/4.11 | | | | (27), (29), (151), (152) gives: % 23.08/4.11 | | | | (172) all_34_0 = 0 | all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.11 | | | | [v2: any] : (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.08/4.11 | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_lines(all_25_4, all_25_3) = v0 & ( ~ (v0 = 0) | v2 = % 23.08/4.11 | | | | 0 | v1 = 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (6) with all_32_1, all_25_3, all_25_4, % 23.08/4.11 | | | | all_34_0, all_32_0, simplifying with (25), (26), (45), % 23.08/4.11 | | | | (151), (152) gives: % 23.08/4.11 | | | | (173) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : % 23.08/4.11 | | | | (convergent_lines(all_25_3, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = 0) | v1 = % 23.08/4.11 | | | | 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (4) with all_32_1, all_32_1, all_25_4, % 23.08/4.11 | | | | all_25_3, all_32_0, all_34_0, simplifying with (25), (26), % 23.08/4.11 | | | | (45), (151), (152) gives: % 23.08/4.11 | | | | (174) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.11 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.11 | | | | all_25_3) = v2 & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.11 | | | | v3 & distinct_lines(all_25_4, all_25_3) = v1 & % 23.08/4.11 | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.11 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.11 | | | | % 23.08/4.11 | | | | GROUND_INST: instantiating (4) with all_32_1, all_32_1, all_25_3, % 23.08/4.11 | | | | all_25_4, all_34_0, all_32_0, simplifying with (25), (26), % 23.08/4.11 | | | | (45), (151), (152) gives: % 23.08/4.11 | | | | (175) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.11 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.11 | | | | all_25_3) = v3 & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.11 | | | | v2 & distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.11 | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.11 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.11 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (3) with all_32_1, all_32_1, all_25_3, % 23.08/4.12 | | | | all_25_4, all_32_0, all_34_0, simplifying with (25), (26), % 23.08/4.12 | | | | (45), (151), (152) gives: % 23.08/4.12 | | | | (176) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.12 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.12 | | | | all_25_3) = v2 & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.12 | | | | v3 & distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.12 | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.12 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (3) with all_32_1, all_32_1, all_25_4, % 23.08/4.12 | | | | all_25_3, all_34_0, all_32_0, simplifying with (25), (26), % 23.08/4.12 | | | | (45), (151), (152) gives: % 23.08/4.12 | | | | (177) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.12 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.12 | | | | all_25_3) = v3 & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.12 | | | | v2 & distinct_lines(all_25_4, all_25_3) = v1 & % 23.08/4.12 | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.12 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (9) with all_25_4, all_25_2, all_25_4, % 23.08/4.12 | | | | all_36_2, simplifying with (25), (27), (54), (94) gives: % 23.08/4.12 | | | | (178) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_2, all_25_4) = v3 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_2) = v0 & % 23.08/4.12 | | | | convergent_lines(all_25_2, all_25_4) = v2 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_4) = v1 & ( ~ (v0 = 0) | % 23.08/4.12 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_36_2 = 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (16) with all_32_1, all_25_3, all_25_4, % 23.08/4.12 | | | | all_25_3, all_34_0, all_36_1, simplifying with (25), (26), % 23.08/4.12 | | | | (55), (151), (152) gives: % 23.08/4.12 | | | | (179) all_36_1 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.12 | | | | [v2: any] : (unorthogonal_lines(all_25_3, all_25_3) = v2 & % 23.08/4.12 | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.12 | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = 0) | v2 = % 23.08/4.12 | | | | 0 | v1 = 0)) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (15) with all_32_1, all_25_4, all_25_3, % 23.08/4.12 | | | | all_25_3, all_34_0, all_36_1, simplifying with (25), (26), % 23.08/4.12 | | | | (55), (151), (152) gives: % 23.08/4.12 | | | | (180) all_36_1 = 0 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.12 | | | | [v2: any] : (unorthogonal_lines(all_25_3, all_25_3) = v2 & % 23.08/4.12 | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.12 | | | | distinct_lines(all_25_4, all_25_3) = v0 & ( ~ (v0 = 0) | v2 = % 23.08/4.12 | | | | 0 | v1 = 0)) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (14) with all_25_4, all_25_4, all_25_3, % 23.08/4.12 | | | | all_36_1, all_36_1, simplifying with (25), (26), (55) % 23.08/4.12 | | | | gives: % 23.08/4.12 | | | | (181) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_3) = v3 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_3) = v2 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.12 | | | | (v0 = 0) | (v3 = 0 & all_36_1 = 0) | (v2 = 0 & all_36_1 = % 23.08/4.12 | | | | 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (13) with all_25_4, all_25_4, all_25_3, 0, % 23.08/4.12 | | | | all_36_1, simplifying with (25), (26), (28), (55) gives: % 23.08/4.12 | | | | (182) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_4, all_25_3) = v2 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_3) = v3 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.12 | | | | (v0 = 0) | v2 = 0 | (v3 = 0 & all_36_1 = 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (12) with all_25_4, all_25_4, all_25_3, % 23.08/4.12 | | | | all_36_1, 0, simplifying with (25), (26), (28), (55) gives: % 23.08/4.12 | | | | (183) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_4, all_25_3) = v3 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_4) = v1 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_3) = v2 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_4) = v0 & ( ~ (v1 = 0) | ~ % 23.08/4.12 | | | | (v0 = 0) | v3 = 0 | (v2 = 0 & all_36_1 = 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (9) with all_25_3, all_25_2, all_25_4, % 23.08/4.12 | | | | all_48_2, simplifying with (25), (26), (27), (87), (93) % 23.08/4.12 | | | | gives: % 23.08/4.12 | | | | (184) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_2, all_25_4) = v3 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.08/4.12 | | | | convergent_lines(all_25_2, all_25_4) = v2 & % 23.08/4.12 | | | | convergent_lines(all_25_3, all_25_4) = v1 & ( ~ (v0 = 0) | % 23.08/4.12 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_48_2 = 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | GROUND_INST: instantiating (9) with all_25_3, all_25_2, all_25_3, % 23.08/4.12 | | | | all_38_0, simplifying with (26), (27), (61), (93) gives: % 23.08/4.12 | | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.12 | | | | (unorthogonal_lines(all_25_2, all_25_3) = v3 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_2) = v0 & % 23.08/4.12 | | | | convergent_lines(all_25_2, all_25_3) = v2 & % 23.08/4.12 | | | | convergent_lines(all_25_3, all_25_3) = v1 & ( ~ (v0 = 0) | % 23.08/4.12 | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_38_0 = 0))) % 23.08/4.12 | | | | % 23.08/4.12 | | | | DELTA: instantiating (156) with fresh symbols all_83_0, all_83_1, % 23.08/4.12 | | | | all_83_2, all_83_3 gives: % 23.08/4.12 | | | | (186) unorthogonal_lines(all_25_4, all_25_2) = all_83_0 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_2) = all_83_1 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_4) = all_83_2 & % 23.08/4.12 | | | | convergent_lines(all_25_4, all_25_4) = all_83_3 & ( ~ (all_83_2 % 23.08/4.12 | | | | = 0) | ~ (all_83_3 = 0) | all_83_0 = 0 | all_83_1 = 0) % 23.08/4.12 | | | | % 23.08/4.12 | | | | ALPHA: (186) implies: % 23.08/4.12 | | | | (187) convergent_lines(all_25_4, all_25_4) = all_83_3 % 23.08/4.12 | | | | % 23.08/4.12 | | | | DELTA: instantiating (161) with fresh symbols all_87_0, all_87_1, % 23.08/4.12 | | | | all_87_2, all_87_3 gives: % 23.08/4.12 | | | | (188) unorthogonal_lines(all_25_3, all_25_2) = all_87_1 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_4) = all_87_2 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_4, all_25_2) = all_87_0 & % 23.08/4.12 | | | | convergent_lines(all_25_3, all_25_4) = all_87_3 & ( ~ (all_87_2 % 23.08/4.12 | | | | = 0) | ~ (all_87_3 = 0) | all_87_0 = 0 | all_87_1 = 0) % 23.08/4.12 | | | | % 23.08/4.12 | | | | ALPHA: (188) implies: % 23.08/4.12 | | | | (189) unorthogonal_lines(all_25_3, all_25_2) = all_87_1 % 23.08/4.12 | | | | % 23.08/4.12 | | | | DELTA: instantiating (160) with fresh symbols all_89_0, all_89_1, % 23.08/4.12 | | | | all_89_2, all_89_3 gives: % 23.08/4.12 | | | | (190) unorthogonal_lines(all_25_3, all_25_2) = all_89_0 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_89_1 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_3) = all_89_2 & % 23.08/4.12 | | | | convergent_lines(all_25_3, all_25_3) = all_89_3 & ( ~ (all_89_2 % 23.08/4.12 | | | | = 0) | ~ (all_89_3 = 0) | all_89_0 = 0 | all_89_1 = 0) % 23.08/4.12 | | | | % 23.08/4.12 | | | | ALPHA: (190) implies: % 23.08/4.12 | | | | (191) unorthogonal_lines(all_25_3, all_25_2) = all_89_1 % 23.08/4.12 | | | | (192) unorthogonal_lines(all_25_3, all_25_2) = all_89_0 % 23.08/4.12 | | | | % 23.08/4.12 | | | | DELTA: instantiating (159) with fresh symbols all_91_0, all_91_1, % 23.08/4.12 | | | | all_91_2, all_91_3 gives: % 23.08/4.12 | | | | (193) unorthogonal_lines(all_25_2, all_25_2) = all_91_0 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_91_2 & % 23.08/4.12 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_91_3 & % 23.08/4.12 | | | | convergent_lines(all_25_2, all_25_2) = all_91_1 & ( ~ (all_91_3 % 23.08/4.12 | | | | = 0) | all_91_2 = 0 | (all_91_0 = 0 & all_91_1 = 0)) % 23.08/4.12 | | | | % 23.08/4.12 | | | | ALPHA: (193) implies: % 23.08/4.12 | | | | (194) unorthogonal_lines(all_25_3, all_25_2) = all_91_3 % 23.08/4.13 | | | | (195) unorthogonal_lines(all_25_3, all_25_2) = all_91_2 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (185) with fresh symbols all_95_0, all_95_1, % 23.08/4.13 | | | | all_95_2, all_95_3 gives: % 23.08/4.13 | | | | (196) unorthogonal_lines(all_25_2, all_25_3) = all_95_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_95_3 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_3) = all_95_1 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_3) = all_95_2 & ( ~ (all_95_3 % 23.08/4.13 | | | | = 0) | (all_95_0 = 0 & all_95_1 = 0) | (all_95_2 = 0 & % 23.08/4.13 | | | | all_38_0 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (196) implies: % 23.08/4.13 | | | | (197) unorthogonal_lines(all_25_3, all_25_2) = all_95_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (166) with fresh symbols all_97_0, all_97_1, % 23.08/4.13 | | | | all_97_2, all_97_3 gives: % 23.08/4.13 | | | | (198) unorthogonal_lines(all_25_2, all_25_4) = all_97_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_97_3 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_4) = all_97_2 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_4) = all_97_1 & ( ~ (all_97_3 % 23.08/4.13 | | | | = 0) | (all_97_0 = 0 & all_97_1 = 0) | (all_97_2 = 0 & % 23.08/4.13 | | | | all_48_3 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (198) implies: % 23.08/4.13 | | | | (199) unorthogonal_lines(all_25_3, all_25_2) = all_97_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (158) with fresh symbols all_105_0, all_105_1, % 23.08/4.13 | | | | all_105_2, all_105_3 gives: % 23.08/4.13 | | | | (200) unorthogonal_lines(all_25_4, all_25_2) = all_105_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_4, all_25_4) = all_105_2 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_2) = all_105_1 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_105_3 & ( ~ % 23.08/4.13 | | | | (all_105_2 = 0) | ~ (all_105_3 = 0) | all_105_0 = 0 | % 23.08/4.13 | | | | (all_105_1 = 0 & all_25_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (200) implies: % 23.08/4.13 | | | | (201) convergent_lines(all_25_4, all_25_4) = all_105_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (164) with fresh symbols all_107_0, all_107_1, % 23.08/4.13 | | | | all_107_2, all_107_3 gives: % 23.08/4.13 | | | | (202) unorthogonal_lines(all_25_3, all_25_2) = all_107_1 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_4) = all_107_2 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_4) = all_107_3 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_2) = all_107_0 & ( ~ % 23.08/4.13 | | | | (all_107_2 = 0) | ~ (all_107_3 = 0) | all_107_1 = 0 | % 23.08/4.13 | | | | (all_107_0 = 0 & all_25_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (202) implies: % 23.08/4.13 | | | | (203) unorthogonal_lines(all_25_3, all_25_2) = all_107_1 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (184) with fresh symbols all_109_0, all_109_1, % 23.08/4.13 | | | | all_109_2, all_109_3 gives: % 23.08/4.13 | | | | (204) unorthogonal_lines(all_25_2, all_25_4) = all_109_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_109_3 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_4) = all_109_1 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_4) = all_109_2 & ( ~ % 23.08/4.13 | | | | (all_109_3 = 0) | (all_109_0 = 0 & all_109_1 = 0) | % 23.08/4.13 | | | | (all_109_2 = 0 & all_48_2 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (204) implies: % 23.08/4.13 | | | | (205) unorthogonal_lines(all_25_3, all_25_2) = all_109_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (183) with fresh symbols all_113_0, all_113_1, % 23.08/4.13 | | | | all_113_2, all_113_3 gives: % 23.08/4.13 | | | | (206) unorthogonal_lines(all_25_4, all_25_3) = all_113_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_4, all_25_4) = all_113_2 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_3) = all_113_1 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_113_3 & ( ~ % 23.08/4.13 | | | | (all_113_2 = 0) | ~ (all_113_3 = 0) | all_113_0 = 0 | % 23.08/4.13 | | | | (all_113_1 = 0 & all_36_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (206) implies: % 23.08/4.13 | | | | (207) convergent_lines(all_25_4, all_25_4) = all_113_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (163) with fresh symbols all_115_0, all_115_1, % 23.08/4.13 | | | | all_115_2, all_115_3 gives: % 23.08/4.13 | | | | (208) unorthogonal_lines(all_25_3, all_25_2) = all_115_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_3) = all_115_2 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_2) = all_115_1 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_3) = all_115_3 & ( ~ % 23.08/4.13 | | | | (all_115_2 = 0) | ~ (all_115_3 = 0) | all_115_0 = 0 | % 23.08/4.13 | | | | (all_115_1 = 0 & all_25_0 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (208) implies: % 23.08/4.13 | | | | (209) unorthogonal_lines(all_25_3, all_25_2) = all_115_0 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (182) with fresh symbols all_117_0, all_117_1, % 23.08/4.13 | | | | all_117_2, all_117_3 gives: % 23.08/4.13 | | | | (210) unorthogonal_lines(all_25_4, all_25_3) = all_117_1 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_4, all_25_4) = all_117_2 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_3) = all_117_0 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_117_3 & ( ~ % 23.08/4.13 | | | | (all_117_2 = 0) | ~ (all_117_3 = 0) | all_117_1 = 0 | % 23.08/4.13 | | | | (all_117_0 = 0 & all_36_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (210) implies: % 23.08/4.13 | | | | (211) convergent_lines(all_25_4, all_25_4) = all_117_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (178) with fresh symbols all_119_0, all_119_1, % 23.08/4.13 | | | | all_119_2, all_119_3 gives: % 23.08/4.13 | | | | (212) unorthogonal_lines(all_25_2, all_25_4) = all_119_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_4, all_25_2) = all_119_3 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_4) = all_119_1 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_119_2 & ( ~ % 23.08/4.13 | | | | (all_119_3 = 0) | (all_119_0 = 0 & all_119_1 = 0) | % 23.08/4.13 | | | | (all_119_2 = 0 & all_36_2 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (212) implies: % 23.08/4.13 | | | | (213) convergent_lines(all_25_4, all_25_4) = all_119_2 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (162) with fresh symbols all_121_0, all_121_1, % 23.08/4.13 | | | | all_121_2, all_121_3 gives: % 23.08/4.13 | | | | (214) unorthogonal_lines(all_25_3, all_25_2) = all_121_1 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_3) = all_121_2 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_2) = all_121_0 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_3) = all_121_3 & ( ~ % 23.08/4.13 | | | | (all_121_2 = 0) | ~ (all_121_3 = 0) | all_121_1 = 0 | % 23.08/4.13 | | | | (all_121_0 = 0 & all_25_0 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (214) implies: % 23.08/4.13 | | | | (215) unorthogonal_lines(all_25_3, all_25_2) = all_121_1 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (157) with fresh symbols all_123_0, all_123_1, % 23.08/4.13 | | | | all_123_2, all_123_3 gives: % 23.08/4.13 | | | | (216) unorthogonal_lines(all_25_4, all_25_2) = all_123_1 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_4, all_25_4) = all_123_2 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_2) = all_123_0 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_123_3 & ( ~ % 23.08/4.13 | | | | (all_123_2 = 0) | ~ (all_123_3 = 0) | all_123_1 = 0 | % 23.08/4.13 | | | | (all_123_0 = 0 & all_25_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (216) implies: % 23.08/4.13 | | | | (217) convergent_lines(all_25_4, all_25_4) = all_123_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (167) with fresh symbols all_125_0, all_125_1, % 23.08/4.13 | | | | all_125_2, all_125_3 gives: % 23.08/4.13 | | | | (218) unorthogonal_lines(all_25_2, all_25_2) = all_125_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_125_3 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_2) = all_125_1 & % 23.08/4.13 | | | | convergent_lines(all_25_3, all_25_2) = all_125_2 & ( ~ % 23.08/4.13 | | | | (all_125_3 = 0) | (all_125_0 = 0 & all_125_1 = 0) | % 23.08/4.13 | | | | (all_125_2 = 0 & all_25_0 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (218) implies: % 23.08/4.13 | | | | (219) unorthogonal_lines(all_25_3, all_25_2) = all_125_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (165) with fresh symbols all_129_0, all_129_1, % 23.08/4.13 | | | | all_129_2, all_129_3 gives: % 23.08/4.13 | | | | (220) unorthogonal_lines(all_25_2, all_25_3) = all_129_0 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_2) = all_129_3 & % 23.08/4.13 | | | | unorthogonal_lines(all_25_3, all_25_3) = all_129_2 & % 23.08/4.13 | | | | convergent_lines(all_25_2, all_25_3) = all_129_1 & ( ~ % 23.08/4.13 | | | | (all_129_3 = 0) | (all_129_0 = 0 & all_129_1 = 0) | % 23.08/4.13 | | | | (all_129_2 = 0 & all_38_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (220) implies: % 23.08/4.13 | | | | (221) unorthogonal_lines(all_25_3, all_25_2) = all_129_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | DELTA: instantiating (181) with fresh symbols all_141_0, all_141_1, % 23.08/4.13 | | | | all_141_2, all_141_3 gives: % 23.08/4.13 | | | | (222) unorthogonal_lines(all_25_4, all_25_4) = all_141_2 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_3) = all_141_0 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_3) = all_141_1 & % 23.08/4.13 | | | | convergent_lines(all_25_4, all_25_4) = all_141_3 & ( ~ % 23.08/4.13 | | | | (all_141_2 = 0) | ~ (all_141_3 = 0) | (all_141_0 = 0 & % 23.08/4.13 | | | | all_36_1 = 0) | (all_141_1 = 0 & all_36_1 = 0)) % 23.08/4.13 | | | | % 23.08/4.13 | | | | ALPHA: (222) implies: % 23.08/4.13 | | | | (223) convergent_lines(all_25_4, all_25_4) = all_141_3 % 23.08/4.13 | | | | % 23.08/4.13 | | | | BETA: splitting (169) gives: % 23.08/4.13 | | | | % 23.08/4.13 | | | | Case 1: % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | (224) all_32_0 = 0 % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | REDUCE: (44), (224) imply: % 23.08/4.13 | | | | | (225) $false % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | CLOSE: (225) is inconsistent. % 23.08/4.13 | | | | | % 23.08/4.13 | | | | Case 2: % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | (226) ? [v0: any] : ? [v1: any] : (convergent_lines(all_25_4, % 23.08/4.13 | | | | | all_25_4) = v1 & distinct_lines(all_25_4, all_25_4) = v0 % 23.08/4.13 | | | | | & ( ~ (v0 = 0) | v1 = 0)) % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | DELTA: instantiating (226) with fresh symbols all_154_0, all_154_1 % 23.08/4.13 | | | | | gives: % 23.08/4.13 | | | | | (227) convergent_lines(all_25_4, all_25_4) = all_154_0 & % 23.08/4.13 | | | | | distinct_lines(all_25_4, all_25_4) = all_154_1 & ( ~ % 23.08/4.13 | | | | | (all_154_1 = 0) | all_154_0 = 0) % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | ALPHA: (227) implies: % 23.08/4.13 | | | | | (228) convergent_lines(all_25_4, all_25_4) = all_154_0 % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | BETA: splitting (170) gives: % 23.08/4.13 | | | | | % 23.08/4.13 | | | | | Case 1: % 23.08/4.13 | | | | | | % 23.08/4.13 | | | | | | (229) all_32_0 = 0 % 23.08/4.13 | | | | | | % 23.08/4.13 | | | | | | REDUCE: (44), (229) imply: % 23.08/4.13 | | | | | | (230) $false % 23.08/4.13 | | | | | | % 23.08/4.13 | | | | | | CLOSE: (230) is inconsistent. % 23.08/4.13 | | | | | | % 23.08/4.13 | | | | | Case 2: % 23.08/4.13 | | | | | | % 23.08/4.14 | | | | | | (231) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 23.08/4.14 | | | | | | (apart_point_and_line(all_32_1, all_25_4) = v3 & % 23.08/4.14 | | | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.14 | | | | | | distinct_lines(all_25_4, all_25_4) = v1 & % 23.08/4.14 | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ (v1 = 0) | % 23.08/4.14 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.14 | | | | | | % 23.08/4.14 | | | | | | DELTA: instantiating (231) with fresh symbols all_164_0, all_164_1, % 23.08/4.14 | | | | | | all_164_2, all_164_3 gives: % 23.08/4.14 | | | | | | (232) apart_point_and_line(all_32_1, all_25_4) = all_164_0 & % 23.08/4.14 | | | | | | apart_point_and_line(all_32_1, all_25_4) = all_164_1 & % 23.08/4.14 | | | | | | distinct_lines(all_25_4, all_25_4) = all_164_2 & % 23.08/4.14 | | | | | | distinct_points(all_32_1, all_32_1) = all_164_3 & ( ~ % 23.08/4.14 | | | | | | (all_164_2 = 0) | ~ (all_164_3 = 0) | all_164_0 = 0 | % 23.08/4.14 | | | | | | all_164_1 = 0) % 23.08/4.14 | | | | | | % 23.08/4.14 | | | | | | ALPHA: (232) implies: % 23.08/4.14 | | | | | | (233) apart_point_and_line(all_32_1, all_25_4) = all_164_1 % 23.08/4.14 | | | | | | (234) apart_point_and_line(all_32_1, all_25_4) = all_164_0 % 23.08/4.14 | | | | | | % 23.08/4.14 | | | | | | BETA: splitting (171) gives: % 23.08/4.14 | | | | | | % 23.08/4.14 | | | | | | Case 1: % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | (235) all_34_0 = 0 % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | REDUCE: (48), (235) imply: % 23.08/4.14 | | | | | | | (236) $false % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | CLOSE: (236) is inconsistent. % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | Case 2: % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | (237) all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 23.08/4.14 | | | | | | | : (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.08/4.14 | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.14 | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = 0) % 23.08/4.14 | | | | | | | | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | BETA: splitting (174) gives: % 23.08/4.14 | | | | | | | % 23.08/4.14 | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | (238) all_34_0 = 0 % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | REDUCE: (48), (238) imply: % 23.08/4.14 | | | | | | | | (239) $false % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | CLOSE: (239) is inconsistent. % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | (240) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 23.08/4.14 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.14 | | | | | | | | all_25_3) = v2 & apart_point_and_line(all_32_1, % 23.08/4.14 | | | | | | | | all_25_4) = v3 & distinct_lines(all_25_4, all_25_3) % 23.08/4.14 | | | | | | | | = v1 & distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.14 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | BETA: splitting (173) gives: % 23.08/4.14 | | | | | | | | % 23.08/4.14 | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | (241) all_34_0 = 0 % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | REDUCE: (48), (241) imply: % 23.08/4.14 | | | | | | | | | (242) $false % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | CLOSE: (242) is inconsistent. % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | (243) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : % 23.08/4.14 | | | | | | | | | (convergent_lines(all_25_3, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ (v0 = % 23.08/4.14 | | | | | | | | | 0) | v1 = 0)) % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | BETA: splitting (172) gives: % 23.08/4.14 | | | | | | | | | % 23.08/4.14 | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | (244) all_34_0 = 0 % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | REDUCE: (48), (244) imply: % 23.08/4.14 | | | | | | | | | | (245) $false % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | CLOSE: (245) is inconsistent. % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | (246) all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | [v2: any] : (unorthogonal_lines(all_25_3, all_25_2) % 23.08/4.14 | | | | | | | | | | = v2 & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.14 | | | | | | | | | | v1 & distinct_lines(all_25_4, all_25_3) = v0 & ( % 23.08/4.14 | | | | | | | | | | ~ (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | BETA: splitting (180) gives: % 23.08/4.14 | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | (247) all_36_1 = 0 % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | REDUCE: (154), (247) imply: % 23.08/4.14 | | | | | | | | | | | (248) $false % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | CLOSE: (248) is inconsistent. % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | (249) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | [v2: any] : (unorthogonal_lines(all_25_3, % 23.08/4.14 | | | | | | | | | | | all_25_3) = v2 & % 23.08/4.14 | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | BETA: splitting (179) gives: % 23.08/4.14 | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | (250) all_36_1 = 0 % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | REDUCE: (154), (250) imply: % 23.08/4.14 | | | | | | | | | | | | (251) $false % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | (252) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | | [v2: any] : (unorthogonal_lines(all_25_3, % 23.08/4.14 | | | | | | | | | | | | all_25_3) = v2 & % 23.08/4.14 | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | BETA: splitting (176) gives: % 23.08/4.14 | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | (253) all_34_0 = 0 % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | REDUCE: (48), (253) imply: % 23.08/4.14 | | | | | | | | | | | | | (254) $false % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | (255) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 23.08/4.14 | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_25_3) = v2 & % 23.08/4.14 | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v3 & % 23.08/4.14 | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | BETA: splitting (175) gives: % 23.08/4.14 | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | (256) all_34_0 = 0 % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | REDUCE: (48), (256) imply: % 23.08/4.14 | | | | | | | | | | | | | | (257) $false % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | CLOSE: (257) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | (258) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 23.08/4.14 | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_25_3) = v3 & % 23.08/4.14 | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.14 | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | BETA: splitting (177) gives: % 23.08/4.14 | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | (259) all_34_0 = 0 % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | REDUCE: (48), (259) imply: % 23.08/4.14 | | | | | | | | | | | | | | | (260) $false % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | (261) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : % 23.08/4.14 | | | | | | | | | | | | | | | (apart_point_and_line(all_32_1, all_25_3) = v3 & % 23.08/4.14 | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.14 | | | | | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v1 & % 23.08/4.14 | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 23.08/4.14 | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | (262) all_32_0 = 0 % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | REDUCE: (44), (262) imply: % 23.08/4.14 | | | | | | | | | | | | | | | | (263) $false % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | (264) all_25_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 23.08/4.14 | | | | | | | | | | | | | | | | [v2: any] : (unorthogonal_lines(all_25_4, % 23.08/4.14 | | | | | | | | | | | | | | | | all_25_2) = v2 & % 23.08/4.14 | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_3) = v1 & % 23.08/4.14 | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 23.08/4.14 | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | Case 1: % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | (265) all_25_1 = 0 % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | REDUCE: (23), (265) imply: % 23.08/4.14 | | | | | | | | | | | | | | | | | (266) $false % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | Case 2: % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | (267) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.08/4.14 | | | | | | | | | | | | | | | | | (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.08/4.14 | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.14 | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.14 | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | DELTA: instantiating (267) with fresh symbols all_220_0, % 23.08/4.14 | | | | | | | | | | | | | | | | | all_220_1, all_220_2 gives: % 23.08/4.14 | | | | | | | | | | | | | | | | | (268) unorthogonal_lines(all_25_3, all_25_2) = all_220_0 % 23.08/4.14 | | | | | | | | | | | | | | | | | & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.14 | | | | | | | | | | | | | | | | | all_220_1 & distinct_lines(all_25_3, all_25_4) = % 23.08/4.14 | | | | | | | | | | | | | | | | | all_220_2 & ( ~ (all_220_2 = 0) | all_220_0 = 0 | % 23.08/4.14 | | | | | | | | | | | | | | | | | all_220_1 = 0) % 23.08/4.14 | | | | | | | | | | | | | | | | | % 23.08/4.14 | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 23.08/4.14 | | | | | | | | | | | | | | | | | (269) distinct_lines(all_25_3, all_25_4) = all_220_2 % 23.08/4.14 | | | | | | | | | | | | | | | | | (270) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.14 | | | | | | | | | | | | | | | | | all_220_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | (271) unorthogonal_lines(all_25_3, all_25_2) = all_220_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | (272) ~ (all_220_2 = 0) | all_220_0 = 0 | all_220_1 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | (273) all_32_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | REDUCE: (44), (273) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | (274) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | (275) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 23.08/4.15 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_25_3) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | DELTA: instantiating (275) with fresh symbols all_225_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_225_1, all_225_2, all_225_3 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | (276) apart_point_and_line(all_32_1, all_25_3) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_225_1 & apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_25_4) = all_225_0 & distinct_lines(all_25_4, % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_25_3) = all_225_2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = all_225_3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | ( ~ (all_225_2 = 0) | ~ (all_225_3 = 0) | % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_225_0 = 0 | all_225_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | (277) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | all_225_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (278) all_32_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (278) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (279) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (280) ? [v0: any] : ? [v1: any] : % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (convergent_lines(all_25_3, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (v0 = 0) | v1 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (280) with fresh symbols all_230_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | all_230_1 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (281) convergent_lines(all_25_3, all_25_4) = all_230_0 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = all_230_1 & ( % 23.08/4.15 | | | | | | | | | | | | | | | | | | | ~ (all_230_1 = 0) | all_230_0 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | (282) distinct_lines(all_25_3, all_25_4) = all_230_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (283) all_25_1 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (283) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (284) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (285) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (unorthogonal_lines(all_25_3, all_25_2) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbols all_240_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | all_240_1, all_240_2 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (286) unorthogonal_lines(all_25_3, all_25_2) = all_240_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | all_240_1 & distinct_lines(all_25_4, all_25_3) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | all_240_2 & ( ~ (all_240_2 = 0) | all_240_0 = 0 | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | all_240_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (287) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | all_240_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | (288) unorthogonal_lines(all_25_3, all_25_2) = all_240_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (289) all_34_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (289) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (290) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (291) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (unorthogonal_lines(all_25_3, all_25_3) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (291) with fresh symbols all_245_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | all_245_1, all_245_2 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (292) unorthogonal_lines(all_25_3, all_25_3) = all_245_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | all_245_1 & distinct_lines(all_25_4, all_25_3) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | all_245_2 & ( ~ (all_245_2 = 0) | all_245_0 = 0 | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | all_245_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | (293) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | all_245_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (294) all_34_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (294) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (295) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (296) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (unorthogonal_lines(all_25_3, all_25_3) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (296) with fresh symbols all_250_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | all_250_1, all_250_2 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (297) unorthogonal_lines(all_25_3, all_25_3) = all_250_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | & apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | all_250_1 & distinct_lines(all_25_3, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | all_250_2 & ( ~ (all_250_2 = 0) | all_250_0 = 0 | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | all_250_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (298) distinct_lines(all_25_3, all_25_4) = all_250_2 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | (299) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | all_250_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (300) all_32_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (300) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (301) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (302) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (302) with fresh symbols all_255_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_255_1, all_255_2, all_255_3 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (303) apart_point_and_line(all_32_1, all_25_3) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_255_1 & apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_255_0 & distinct_lines(all_25_3, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_255_2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = all_255_3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_255_2 = 0) | ~ (all_255_3 = 0) | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_255_0 = 0 | all_255_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (304) distinct_lines(all_25_3, all_25_4) = all_255_2 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | (305) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | all_255_0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (306) all_32_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (306) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (307) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (308) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = v3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (308) with fresh symbols all_260_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_260_1, all_260_2, all_260_3 gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (309) apart_point_and_line(all_32_1, all_25_3) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_260_0 & apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_260_1 & distinct_lines(all_25_3, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_260_2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = all_260_3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_260_2 = 0) | ~ (all_260_3 = 0) | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_260_0 = 0 | all_260_1 = 0) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (310) distinct_lines(all_25_3, all_25_4) = all_260_2 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (311) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | all_260_1 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_32_0 = 0 % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (312) imply: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | (313) $false % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent. % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | (314) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_32_1, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = v3 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_4) = v2 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_4, all_25_3) = v1 & % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = v0 & ( ~ % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (314) with fresh symbols all_265_0, % 23.08/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | all_265_1, all_265_2, all_265_3 gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | (315) apart_point_and_line(all_32_1, all_25_3) = % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | all_265_0 & apart_point_and_line(all_32_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4) = all_265_1 & distinct_lines(all_25_4, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3) = all_265_2 & % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_32_1, all_32_1) = all_265_3 & % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_265_2 = 0) | ~ (all_265_3 = 0) | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | all_265_0 = 0 | all_265_1 = 0) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | (316) apart_point_and_line(all_32_1, all_25_4) = % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | all_265_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_25_0 = 0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (317) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (318) $false % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (unorthogonal_lines(all_25_4, all_25_2) = v2 & % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_32_1, all_25_3) = v1 & % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_25_3, all_25_4) = v0 & ( ~ % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0)) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_270_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_270_1, all_270_2 gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (320) unorthogonal_lines(all_25_4, all_25_2) = all_270_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | & apart_point_and_line(all_32_1, all_25_3) = % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_270_1 & distinct_lines(all_25_3, all_25_4) = % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_270_2 & ( ~ (all_270_2 = 0) | all_270_0 = 0 | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_270_1 = 0) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) distinct_lines(all_25_3, all_25_4) = all_270_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_220_2, all_255_2, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_3, simplifying with (269), (304) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_255_2 = all_220_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_255_2, all_260_2, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_3, simplifying with (304), (310) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_260_2 = all_255_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_230_1, all_260_2, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_3, simplifying with (282), (310) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_260_2 = all_230_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_255_2, all_270_2, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_3, simplifying with (304), (321) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_270_2 = all_255_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_250_2, all_270_2, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_3, simplifying with (298), (321) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_270_2 = all_250_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_83_3, all_105_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (187), (201) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_105_3 = all_83_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_36_3, all_123_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (53), (217) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_123_3 = all_36_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_117_3, all_123_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (211), (217) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_123_3 = all_117_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_123_3, all_141_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (217), (223) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_141_3 = all_123_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_119_2, all_141_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (213), (223) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_141_3 = all_119_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_117_3, all_154_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (211), (228) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_154_0 = all_117_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_113_3, all_154_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (207), (228) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_154_0 = all_113_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_105_3, all_154_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_25_4, simplifying with (201), (228) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_154_0 = all_105_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_220_1, all_225_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (270), (277) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_225_0 = all_220_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_225_0, all_245_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (277), (293) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_245_1 = all_225_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_245_1, all_255_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (293), (305) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_255_0 = all_245_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_32_0, all_260_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (45), (311) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_260_1 = all_32_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_250_1, all_260_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (299), (311) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_260_1 = all_250_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_240_1, all_260_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (287), (311) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_260_1 = all_240_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_220_1, all_260_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (270), (311) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_260_1 = all_220_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_164_0, all_260_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (234), (311) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_260_1 = all_164_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_255_0, all_265_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (305), (316) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_265_1 = all_255_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_164_1, all_265_1, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_4, all_32_1, simplifying with (233), (316) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_265_1 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_25_0, all_89_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (30), (192) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_89_0 = all_25_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_89_0, all_91_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (192), (194) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_91_3 = all_89_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_91_3, all_97_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (194), (199) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_97_3 = all_91_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_109_3, all_115_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (205), (209) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_115_0 = all_109_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_91_2, all_115_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (195), (209) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_115_0 = all_91_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_89_0, all_115_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (192), (209) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_115_0 = all_89_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_89_1, all_115_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (191), (209) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_115_0 = all_89_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_87_1, all_125_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (189), (219) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_125_3 = all_87_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_97_3, all_129_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (199), (221) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_129_3 = all_97_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_95_3, all_129_3, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (197), (221) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_129_3 = all_95_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_129_3, all_220_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (221), (271) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_220_0 = all_129_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_121_1, all_220_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (215), (271) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_220_0 = all_121_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_125_3, all_240_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (219), (288) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_240_0 = all_125_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_107_1, all_240_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (203), (288) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_240_0 = all_107_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_97_3, all_240_0, % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_2, all_25_3, simplifying with (199), (288) % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_240_0 = all_97_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (326) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_255_2 = all_250_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_255_2 = all_250_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (344) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_255_0 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (362) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_255_0 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (341) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_250_1 = all_220_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (338), (339) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_250_1 = all_32_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (340) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_250_1 = all_240_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (342) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_250_1 = all_164_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (324) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_255_2 = all_230_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (368) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_255_2 = all_230_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (363) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_245_1 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (370) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_245_1 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (361) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_250_2 = all_220_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (369) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_250_2 = all_230_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (366) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_240_1 = all_32_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (366) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_240_1 = all_220_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (367) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_240_1 = all_164_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (373) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_230_1 = all_220_2 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (371) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_225_0 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (378) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_225_0 = all_164_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (358) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_125_3 = all_107_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (380) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_125_3 = all_107_1 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (358), (359) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_107_1 = all_97_3 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (376) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_220_1 = all_164_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (383) implies: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_220_1 = all_164_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (376) imply: % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_164_0 = all_32_0 % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (379) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_220_1 = all_164_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (386) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_220_1 = all_164_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (355), (356) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_129_3 = all_121_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (388) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_129_3 = all_121_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (384), (387) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_164_0 = all_164_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_164_0 = all_164_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (391) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_164_1 = all_32_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (392) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_164_1 = all_32_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (333) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_117_3 = all_113_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (394) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_117_3 = all_113_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (334) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_113_3 = all_105_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (331) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_123_3 = all_119_2 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_123_3 = all_119_2 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (389) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_121_1 = all_95_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (389) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_121_1 = all_97_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (381) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_107_1 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_107_1 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (398) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_119_2 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (398) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_119_2 = all_117_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (400) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_97_3 = all_95_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (405) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_97_3 = all_95_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (404) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_117_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (407) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_117_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (408) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_113_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (409) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_113_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (349) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_109_3 = all_91_2 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (351) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_109_3 = all_89_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (350) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_109_3 = all_89_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (396), (410) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_105_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (414) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_105_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (412) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_91_2 = all_89_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (413) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_91_2 = all_89_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (402) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_97_3 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (418) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_97_3 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (415) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_83_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (420) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_83_3 = all_36_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (419) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_95_3 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (406) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_95_3 = all_91_3 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (422), (423) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_91_3 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (424) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_91_3 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (416), (417) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_89_0 = all_89_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (426) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_89_0 = all_89_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (425) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_89_0 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (428) implies: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_89_0 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (345), (427) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_89_1 = all_25_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (429) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_89_1 = all_87_1 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (431) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_87_1 = all_25_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (422), (432) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_95_3 = all_25_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (433) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_121_1 = all_25_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (393) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_220_1 = all_32_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (434) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_220_0 = all_25_0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_220_2 = 0) % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) distinct_lines(all_25_3, all_25_4) = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_220_2, 0, all_25_4, % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_25_3, simplifying with (269), (438) gives: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_220_2 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (439) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) $false % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent. % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_36_3 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (441) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) convergent_lines(all_25_4, all_25_4) = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_25_4, simplifying % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (25), (442) gives: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) $false % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent. % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_220_0 = 0 | all_220_1 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_220_0 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (436), (445) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_25_0 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (446) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) $false % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (447) is inconsistent. % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_220_1 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (448) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_32_0 = 0 % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (449) imply: % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) $false % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (450) is inconsistent. % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | | % 23.08/4.17 | | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | | % 23.08/4.17 | | | | | | | | | End of split % 23.08/4.17 | | | | | | | | | % 23.08/4.17 | | | | | | | | End of split % 23.08/4.17 | | | | | | | | % 23.08/4.17 | | | | | | | End of split % 23.08/4.17 | | | | | | | % 23.08/4.17 | | | | | | End of split % 23.08/4.17 | | | | | | % 23.08/4.17 | | | | | End of split % 23.08/4.17 | | | | | % 23.08/4.17 | | | | End of split % 23.08/4.17 | | | | % 23.08/4.17 | | | Case 2: % 23.08/4.17 | | | | % 23.08/4.17 | | | | (451) (all_40_0 = 0 & all_40_1 = 0) | (all_40_2 = 0 & all_25_1 = 0) % 23.08/4.17 | | | | % 23.08/4.17 | | | | BETA: splitting (451) gives: % 23.08/4.17 | | | | % 23.08/4.17 | | | | Case 1: % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | (452) all_40_0 = 0 & all_40_1 = 0 % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | ALPHA: (452) implies: % 23.08/4.17 | | | | | (453) all_40_0 = 0 % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | COMBINE_EQS: (120), (453) imply: % 23.08/4.17 | | | | | (454) all_25_0 = 0 % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | REDUCE: (24), (454) imply: % 23.08/4.17 | | | | | (455) $false % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | CLOSE: (455) is inconsistent. % 23.08/4.17 | | | | | % 23.08/4.17 | | | | Case 2: % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | (456) all_40_2 = 0 & all_25_1 = 0 % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | ALPHA: (456) implies: % 23.08/4.17 | | | | | (457) all_25_1 = 0 % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | REDUCE: (23), (457) imply: % 23.08/4.17 | | | | | (458) $false % 23.08/4.17 | | | | | % 23.08/4.17 | | | | | CLOSE: (458) is inconsistent. % 23.08/4.17 | | | | | % 23.08/4.17 | | | | End of split % 23.08/4.17 | | | | % 23.08/4.17 | | | End of split % 23.08/4.17 | | | % 23.08/4.17 | | Case 2: % 23.08/4.17 | | | % 23.08/4.17 | | | (459) all_25_1 = 0 % 23.08/4.17 | | | % 23.08/4.17 | | | REDUCE: (23), (459) imply: % 23.08/4.17 | | | (460) $false % 23.08/4.17 | | | % 23.08/4.17 | | | CLOSE: (460) is inconsistent. % 23.08/4.17 | | | % 23.08/4.17 | | End of split % 23.08/4.17 | | % 23.08/4.17 | Case 2: % 23.08/4.17 | | % 23.08/4.17 | | (461) all_25_0 = 0 % 23.08/4.17 | | % 23.08/4.17 | | REDUCE: (24), (461) imply: % 23.08/4.17 | | (462) $false % 23.08/4.17 | | % 23.08/4.17 | | CLOSE: (462) is inconsistent. % 23.08/4.17 | | % 23.08/4.17 | End of split % 23.08/4.17 | % 23.08/4.17 End of proof % 23.08/4.18 % SZS output end Proof for theBenchmark % 23.08/4.18 % 23.08/4.18 3575ms %------------------------------------------------------------------------------