%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO223+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:32 EDT 2023 % Result : Theorem 15.00s 2.68s % Output : Proof 40.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO223+3 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 : Wed Aug 30 00:04:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.57/0.60 ________ _____ % 0.57/0.60 ___ __ \_________(_)________________________________ % 0.57/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.60 (2023-06-19) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2023 % 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.60 Amanda Stjerna. % 0.57/0.60 Free software under BSD-3-Clause. % 0.57/0.60 % 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.61 Running up to 7 provers in parallel. % 0.57/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.09/1.14 Prover 4: Preprocessing ... % 3.09/1.14 Prover 1: Preprocessing ... % 3.68/1.18 Prover 3: Preprocessing ... % 3.68/1.18 Prover 0: Preprocessing ... % 4.00/1.21 Prover 6: Preprocessing ... % 4.00/1.21 Prover 5: Preprocessing ... % 4.00/1.21 Prover 2: Preprocessing ... % 6.59/1.56 Prover 5: Proving ... % 6.59/1.56 Prover 2: Proving ... % 6.59/1.61 Prover 3: Constructing countermodel ... % 7.08/1.61 Prover 6: Constructing countermodel ... % 7.08/1.63 Prover 1: Constructing countermodel ... % 8.22/1.77 Prover 3: gave up % 8.22/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.47/1.81 Prover 6: gave up % 8.72/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.72/1.85 Prover 7: Preprocessing ... % 8.72/1.86 Prover 1: gave up % 8.72/1.88 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.72/1.88 Prover 8: Preprocessing ... % 9.20/1.92 Prover 7: Warning: ignoring some quantifiers % 9.20/1.94 Prover 7: Constructing countermodel ... % 9.20/1.95 Prover 9: Preprocessing ... % 9.69/1.98 Prover 0: Proving ... % 9.69/1.99 Prover 4: Constructing countermodel ... % 9.69/2.04 Prover 8: Warning: ignoring some quantifiers % 9.69/2.05 Prover 8: Constructing countermodel ... % 11.53/2.25 Prover 8: gave up % 11.53/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.01/2.29 Prover 10: Preprocessing ... % 12.01/2.29 Prover 9: Constructing countermodel ... % 12.01/2.33 Prover 10: Warning: ignoring some quantifiers % 12.01/2.35 Prover 10: Constructing countermodel ... % 13.79/2.51 Prover 10: gave up % 13.79/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.79/2.54 Prover 11: Preprocessing ... % 14.31/2.60 Prover 7: gave up % 14.31/2.61 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 14.31/2.63 Prover 12: Preprocessing ... % 15.00/2.68 Prover 0: proved (2060ms) % 15.00/2.68 % 15.00/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.00/2.68 % 15.00/2.68 Prover 9: stopped % 15.00/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.00/2.68 Prover 5: stopped % 15.00/2.68 Prover 2: stopped % 15.00/2.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.18/2.70 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.18/2.70 Prover 16: Preprocessing ... % 15.18/2.70 Prover 13: Preprocessing ... % 15.51/2.73 Prover 12: stopped % 15.51/2.74 Prover 19: Preprocessing ... % 15.62/2.77 Prover 13: Warning: ignoring some quantifiers % 15.62/2.77 Prover 16: Warning: ignoring some quantifiers % 15.62/2.78 Prover 13: Constructing countermodel ... % 15.62/2.78 Prover 16: Constructing countermodel ... % 15.62/2.79 Prover 11: Constructing countermodel ... % 16.21/2.86 Prover 19: Warning: ignoring some quantifiers % 16.21/2.87 Prover 19: Constructing countermodel ... % 16.66/2.87 Prover 13: gave up % 17.77/3.03 Prover 19: gave up % 17.93/3.12 Prover 16: gave up % 38.91/7.04 Prover 11: Found proof (size 192) % 38.91/7.04 Prover 11: proved (4526ms) % 38.91/7.04 Prover 4: stopped % 38.91/7.04 % 38.91/7.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 38.91/7.04 % 38.91/7.06 % SZS output start Proof for theBenchmark % 39.08/7.07 Assumptions after simplification: % 39.08/7.07 --------------------------------- % 39.08/7.07 % 39.08/7.07 (ax2) % 39.08/7.12 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 39.08/7.12 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 39.08/7.12 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ~ % 39.08/7.12 $i(v1) | ~ $i(v0) | equal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 39.08/7.12 ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 39.08/7.12 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 39.08/7.12 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 39.08/7.12 (v2 = 0) & equal_lines(v0, v1) = v2)) % 39.08/7.12 % 39.08/7.12 (ax6) % 39.40/7.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 39.40/7.13 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 39.40/7.13 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 39.40/7.13 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 39.40/7.13 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 39.40/7.13 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.40/7.13 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 39.40/7.13 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 39.40/7.13 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.40/7.13 convergent_lines(v1, v2) = 0) % 39.40/7.13 % 39.40/7.13 (coipo1) % 39.40/7.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.40/7.14 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.40/7.14 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 39.40/7.14 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.40/7.14 unorthogonal_lines(v0, v1) = 0) % 39.40/7.14 % 39.40/7.14 (con) % 39.40/7.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 39.40/7.14 int] : ( ~ (v5 = 0) & equal_lines(v2, v4) = v5 & % 39.40/7.14 orthogonal_through_point(v3, v0) = v4 & orthogonal_through_point(v1, v0) = % 39.40/7.14 v3 & parallel_through_point(v1, v0) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 39.40/7.14 & $i(v0)) % 39.40/7.14 % 39.40/7.14 (cotno1) % 39.40/7.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 39.40/7.16 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 39.40/7.16 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 39.40/7.16 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 39.40/7.16 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 39.40/7.16 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 39.40/7.16 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 39.40/7.16 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 39.40/7.16 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 39.40/7.16 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 39.40/7.16 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 39.40/7.16 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 39.40/7.16 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 39.40/7.16 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 39.40/7.16 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 39.40/7.16 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 39.40/7.16 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 39.40/7.16 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 39.40/7.16 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 39.40/7.16 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 39.40/7.16 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 39.40/7.16 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 39.40/7.16 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 39.40/7.16 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 39.40/7.16 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 39.40/7.16 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 39.40/7.16 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 39.40/7.16 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 39.40/7.16 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 39.40/7.16 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 39.40/7.16 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.40/7.16 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 39.40/7.16 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 39.40/7.16 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 39.40/7.16 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 39.40/7.16 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 39.40/7.16 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 39.40/7.16 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.40/7.16 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 39.40/7.16 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.40/7.16 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 39.40/7.16 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 39.40/7.16 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 39.40/7.16 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 39.40/7.16 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.40/7.16 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 39.40/7.16 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 39.40/7.16 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.40/7.16 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 39.40/7.16 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 39.40/7.16 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 39.40/7.16 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 39.40/7.16 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 39.40/7.16 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 39.40/7.16 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 39.40/7.16 unorthogonal_lines(v1, v2) = v7))) % 39.40/7.16 % 39.40/7.16 (couo1) % 39.40/7.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 39.40/7.16 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 39.40/7.16 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.40/7.16 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 39.40/7.16 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 39.40/7.16 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 39.40/7.16 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 39.40/7.16 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 39.40/7.16 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 39.40/7.16 unorthogonal_lines(v0, v2) = 0) % 39.40/7.16 % 39.40/7.16 (cp1) % 39.40/7.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0) % 39.40/7.16 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 39.40/7.16 convergent_lines(v2, v1) = v3)) % 39.40/7.16 % 39.40/7.16 (cp2) % 39.40/7.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0) % 39.40/7.17 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 39.40/7.17 apart_point_and_line(v0, v2) = v3)) % 39.40/7.17 % 39.40/7.17 (oac1) % 39.58/7.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 39.58/7.18 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 39.58/7.18 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 39.58/7.18 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 39.58/7.18 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 39.58/7.18 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 39.58/7.18 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 39.58/7.18 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 39.58/7.18 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.58/7.18 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 39.58/7.18 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 39.58/7.18 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 39.58/7.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 39.58/7.18 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 39.58/7.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 39.58/7.18 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 39.58/7.18 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 39.58/7.18 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 39.58/7.18 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 39.58/7.18 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 39.58/7.18 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 39.58/7.18 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 39.58/7.18 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 39.58/7.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 39.58/7.18 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 39.58/7.18 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 39.58/7.18 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 39.58/7.18 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 39.58/7.18 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 39.58/7.18 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.58/7.18 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 39.58/7.18 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 39.58/7.18 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 39.58/7.18 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 39.58/7.18 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.58/7.18 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 39.58/7.18 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.18 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.58/7.18 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 39.58/7.18 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.58/7.18 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 39.58/7.18 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.18 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.58/7.18 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 39.58/7.18 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.58/7.18 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 39.58/7.18 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 39.58/7.18 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 39.58/7.18 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 39.58/7.18 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 39.58/7.18 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.18 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.58/7.18 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 39.58/7.18 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.58/7.18 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 39.58/7.18 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 39.58/7.18 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 39.58/7.18 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 39.58/7.18 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 39.58/7.18 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 39.58/7.18 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 39.58/7.18 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.18 unorthogonal_lines(v0, v1) = v4))) % 39.58/7.18 % 39.58/7.18 (occu1) % 39.58/7.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.58/7.18 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.58/7.18 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 39.58/7.18 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.58/7.18 unorthogonal_lines(v0, v1) = 0) % 39.58/7.18 % 39.58/7.18 (ooc1) % 39.58/7.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 39.58/7.18 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 39.58/7.18 unorthogonal_lines(v2, v1) = v3)) % 39.58/7.18 % 39.58/7.18 (ooc2) % 39.58/7.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 39.58/7.18 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 39.58/7.18 apart_point_and_line(v0, v2) = v3)) % 39.58/7.18 % 39.58/7.18 (ouo1) % 39.58/7.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 39.58/7.19 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ % 39.58/7.19 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 39.58/7.19 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 39.58/7.19 ((v7 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & % 39.58/7.19 apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] : ! % 39.58/7.19 [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 39.58/7.19 (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | % 39.58/7.19 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] % 39.58/7.19 : ? [v8: int] : ((v8 = 0 & unorthogonal_lines(v1, v3) = 0) | (v7 = 0 & % 39.58/7.19 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, % 39.58/7.19 v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 39.58/7.19 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) % 39.58/7.19 = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | % 39.58/7.19 ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 % 39.58/7.19 & unorthogonal_lines(v2, v3) = 0) | (v7 = 0 & apart_point_and_line(v0, % 39.58/7.19 v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0: $i] % 39.58/7.19 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 % 39.58/7.19 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 39.58/7.19 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 39.58/7.19 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 39.58/7.19 ((v7 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & % 39.58/7.19 apart_point_and_line(v0, v2) = 0))) % 39.58/7.19 % 39.58/7.19 (p1) % 39.58/7.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, % 39.58/7.19 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 39.58/7.19 distinct_lines(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 39.58/7.19 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, % 39.58/7.19 v1) = 0) % 39.58/7.19 % 39.58/7.19 (function-axioms) % 39.58/7.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 39.58/7.19 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 39.58/7.19 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.58/7.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.58/7.19 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 39.58/7.19 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 39.58/7.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 39.58/7.19 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.58/7.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.58/7.19 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 39.58/7.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 39.58/7.19 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 39.58/7.19 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.58/7.19 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 39.58/7.19 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 39.58/7.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 39.58/7.19 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.58/7.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 39.58/7.19 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 39.58/7.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 39.58/7.19 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 39.58/7.19 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 39.58/7.19 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.58/7.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.58/7.19 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 39.58/7.19 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 39.58/7.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 39.58/7.19 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.58/7.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.58/7.19 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 39.58/7.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 39.58/7.19 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 39.58/7.19 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 39.58/7.19 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 39.58/7.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 39.58/7.19 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 39.58/7.19 % 39.58/7.19 Further assumptions not needed in the proof: % 39.58/7.19 -------------------------------------------- % 39.58/7.19 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ceq1, ceq2, ceq3, ci1, % 39.58/7.19 ci2, ci3, ci4, con1, cu1, cup1, int1, orth1, par1 % 39.58/7.19 % 39.58/7.19 Those formulas are unsatisfiable: % 39.58/7.19 --------------------------------- % 39.58/7.19 % 39.58/7.19 Begin of proof % 39.58/7.19 | % 39.58/7.19 | ALPHA: (ax6) implies: % 39.58/7.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 39.58/7.20 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 39.58/7.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 39.58/7.20 | % 39.58/7.20 | ALPHA: (p1) implies: % 39.58/7.20 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_lines(v0, v1) = 0) | ~ % 39.58/7.20 | $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) % 39.58/7.20 | % 39.58/7.20 | ALPHA: (oac1) implies: % 39.58/7.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 39.58/7.20 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 39.58/7.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 39.58/7.20 | [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v1, % 39.58/7.20 | v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & % 39.58/7.20 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.20 | unorthogonal_lines(v0, v1) = v4))) % 39.58/7.20 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 39.58/7.20 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 39.58/7.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 39.58/7.20 | [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & unorthogonal_lines(v1, % 39.58/7.20 | v2) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v0, v2) = 0 & % 39.58/7.20 | convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.20 | unorthogonal_lines(v0, v1) = v4))) % 39.58/7.20 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 39.58/7.20 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) % 39.58/7.20 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 39.58/7.20 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 39.58/7.20 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 39.58/7.20 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.20 | unorthogonal_lines(v0, v1) = v4))) % 39.58/7.20 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 39.58/7.20 | (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) % 39.58/7.20 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 39.58/7.20 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & convergent_lines(v1, % 39.58/7.20 | v2) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v0, v2) = 0 & % 39.58/7.20 | convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 39.58/7.20 | unorthogonal_lines(v0, v1) = v4))) % 39.58/7.20 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 39.58/7.20 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = % 39.58/7.20 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 39.58/7.20 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 39.58/7.20 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 39.58/7.20 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 39.58/7.20 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & % 39.58/7.20 | convergent_lines(v0, v1) = v5))) % 39.58/7.20 | % 39.58/7.20 | ALPHA: (ouo1) implies: % 39.58/7.20 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 39.58/7.20 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | % 39.58/7.20 | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 39.58/7.20 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : % 39.58/7.20 | ((v8 = 0 & unorthogonal_lines(v1, v3) = 0) | (v7 = 0 & % 39.58/7.20 | apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & % 39.58/7.20 | distinct_lines(v1, v2) = v6))) % 39.58/7.20 | % 39.58/7.20 | ALPHA: (occu1) implies: % 39.58/7.20 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.58/7.20 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.58/7.20 | unorthogonal_lines(v0, v1) = 0) % 39.58/7.21 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.58/7.21 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.58/7.21 | convergent_lines(v0, v1) = 0) % 39.58/7.21 | % 39.58/7.21 | ALPHA: (cotno1) implies: % 39.58/7.21 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 39.58/7.21 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) % 39.58/7.21 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 39.58/7.21 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 39.58/7.21 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 39.58/7.21 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 39.58/7.21 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 39.58/7.21 | convergent_lines(v1, v2) = v7))) % 39.58/7.21 | % 39.58/7.21 | ALPHA: (couo1) implies: % 39.58/7.21 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 39.58/7.21 | (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = % 39.58/7.21 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, % 39.58/7.21 | v2) = 0) % 39.58/7.21 | % 39.58/7.21 | ALPHA: (ax2) implies: % 39.58/7.21 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 39.58/7.21 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 39.58/7.21 | distinct_lines(v0, v1) = 0) % 39.58/7.21 | % 39.58/7.21 | ALPHA: (function-axioms) implies: % 39.58/7.21 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 39.58/7.21 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 39.58/7.21 | (distinct_lines(v3, v2) = v0)) % 39.58/7.21 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 39.58/7.21 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 39.58/7.21 | (convergent_lines(v3, v2) = v0)) % 39.58/7.21 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 39.58/7.21 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 39.58/7.21 | (apart_point_and_line(v3, v2) = v0)) % 39.58/7.21 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 39.58/7.21 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 39.58/7.21 | (unorthogonal_lines(v3, v2) = v0)) % 39.58/7.21 | % 39.58/7.21 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 39.58/7.21 | all_38_3, all_38_4, all_38_5 gives: % 39.58/7.21 | (18) ~ (all_38_0 = 0) & equal_lines(all_38_3, all_38_1) = all_38_0 & % 39.58/7.21 | orthogonal_through_point(all_38_2, all_38_5) = all_38_1 & % 39.58/7.21 | orthogonal_through_point(all_38_4, all_38_5) = all_38_2 & % 39.58/7.21 | parallel_through_point(all_38_4, all_38_5) = all_38_3 & $i(all_38_1) & % 39.58/7.21 | $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) % 39.58/7.21 | % 39.58/7.21 | ALPHA: (18) implies: % 39.58/7.21 | (19) ~ (all_38_0 = 0) % 39.58/7.21 | (20) $i(all_38_5) % 39.58/7.21 | (21) $i(all_38_4) % 39.58/7.21 | (22) $i(all_38_3) % 39.58/7.21 | (23) $i(all_38_2) % 39.58/7.21 | (24) $i(all_38_1) % 39.58/7.21 | (25) parallel_through_point(all_38_4, all_38_5) = all_38_3 % 39.58/7.21 | (26) orthogonal_through_point(all_38_4, all_38_5) = all_38_2 % 39.58/7.21 | (27) orthogonal_through_point(all_38_2, all_38_5) = all_38_1 % 39.58/7.21 | (28) equal_lines(all_38_3, all_38_1) = all_38_0 % 39.58/7.21 | % 39.58/7.21 | GROUND_INST: instantiating (cp2) with all_38_5, all_38_4, all_38_3, % 39.58/7.21 | simplifying with (20), (21), (25) gives: % 39.58/7.21 | (29) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_3) % 39.58/7.21 | = v0) % 39.58/7.21 | % 39.58/7.21 | GROUND_INST: instantiating (cp1) with all_38_5, all_38_4, all_38_3, % 39.58/7.21 | simplifying with (20), (21), (25) gives: % 39.58/7.21 | (30) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3, all_38_4) = % 39.58/7.21 | v0) % 39.58/7.21 | % 39.58/7.21 | GROUND_INST: instantiating (ooc1) with all_38_5, all_38_4, all_38_2, % 39.58/7.21 | simplifying with (20), (21), (26) gives: % 39.58/7.21 | (31) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_2, all_38_4) = % 39.58/7.21 | v0) % 39.58/7.21 | % 39.58/7.21 | GROUND_INST: instantiating (ooc1) with all_38_5, all_38_2, all_38_1, % 39.58/7.21 | simplifying with (20), (23), (27) gives: % 39.58/7.21 | (32) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_1, all_38_2) = % 39.58/7.21 | v0) % 39.58/7.21 | % 39.58/7.22 | GROUND_INST: instantiating (ooc2) with all_38_5, all_38_2, all_38_1, % 39.58/7.22 | simplifying with (20), (23), (27) gives: % 39.58/7.22 | (33) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_1) % 39.58/7.22 | = v0) % 39.58/7.22 | % 39.58/7.22 | GROUND_INST: instantiating (13) with all_38_3, all_38_1, all_38_0, simplifying % 39.58/7.22 | with (22), (24), (28) gives: % 39.58/7.22 | (34) all_38_0 = 0 | distinct_lines(all_38_3, all_38_1) = 0 % 39.58/7.22 | % 39.58/7.22 | DELTA: instantiating (33) with fresh symbol all_45_0 gives: % 39.58/7.22 | (35) ~ (all_45_0 = 0) & apart_point_and_line(all_38_5, all_38_1) = % 39.58/7.22 | all_45_0 % 39.58/7.22 | % 39.58/7.22 | ALPHA: (35) implies: % 39.58/7.22 | (36) ~ (all_45_0 = 0) % 39.58/7.22 | (37) apart_point_and_line(all_38_5, all_38_1) = all_45_0 % 39.58/7.22 | % 39.58/7.22 | DELTA: instantiating (32) with fresh symbol all_49_0 gives: % 39.58/7.22 | (38) ~ (all_49_0 = 0) & unorthogonal_lines(all_38_1, all_38_2) = all_49_0 % 39.58/7.22 | % 39.58/7.22 | ALPHA: (38) implies: % 39.58/7.22 | (39) ~ (all_49_0 = 0) % 39.58/7.22 | (40) unorthogonal_lines(all_38_1, all_38_2) = all_49_0 % 39.58/7.22 | % 39.58/7.22 | DELTA: instantiating (31) with fresh symbol all_51_0 gives: % 39.58/7.22 | (41) ~ (all_51_0 = 0) & unorthogonal_lines(all_38_2, all_38_4) = all_51_0 % 39.58/7.22 | % 39.58/7.22 | ALPHA: (41) implies: % 39.58/7.22 | (42) ~ (all_51_0 = 0) % 39.58/7.22 | (43) unorthogonal_lines(all_38_2, all_38_4) = all_51_0 % 39.58/7.22 | % 39.58/7.22 | DELTA: instantiating (30) with fresh symbol all_53_0 gives: % 39.58/7.22 | (44) ~ (all_53_0 = 0) & convergent_lines(all_38_3, all_38_4) = all_53_0 % 39.58/7.22 | % 39.58/7.22 | ALPHA: (44) implies: % 39.58/7.22 | (45) ~ (all_53_0 = 0) % 39.58/7.22 | (46) convergent_lines(all_38_3, all_38_4) = all_53_0 % 39.58/7.22 | % 39.58/7.22 | DELTA: instantiating (29) with fresh symbol all_55_0 gives: % 39.58/7.22 | (47) ~ (all_55_0 = 0) & apart_point_and_line(all_38_5, all_38_3) = % 39.58/7.22 | all_55_0 % 39.58/7.22 | % 39.58/7.22 | ALPHA: (47) implies: % 39.58/7.22 | (48) ~ (all_55_0 = 0) % 39.58/7.22 | (49) apart_point_and_line(all_38_5, all_38_3) = all_55_0 % 39.58/7.22 | % 39.58/7.22 | BETA: splitting (34) gives: % 39.58/7.22 | % 39.58/7.22 | Case 1: % 39.58/7.22 | | % 39.58/7.22 | | (50) distinct_lines(all_38_3, all_38_1) = 0 % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (2) with all_38_3, all_38_1, simplifying with % 39.58/7.22 | | (22), (24), (50) gives: % 39.58/7.22 | | (51) convergent_lines(all_38_3, all_38_1) = 0 % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (9) with all_38_3, all_38_4, all_53_0, % 39.58/7.22 | | simplifying with (21), (22), (46) gives: % 39.58/7.22 | | (52) all_53_0 = 0 | unorthogonal_lines(all_38_3, all_38_4) = 0 % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (7) with all_38_3, all_38_2, all_38_4, all_53_0, % 39.58/7.22 | | all_51_0, simplifying with (21), (22), (23), (43), (46) gives: % 39.58/7.22 | | (53) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 39.58/7.22 | | & all_51_0 = 0 & convergent_lines(all_38_2, all_38_4) = 0) | (v2 % 39.58/7.22 | | = 0 & all_53_0 = 0 & unorthogonal_lines(all_38_3, all_38_4) = 0) % 39.58/7.22 | | | ( ~ (v1 = 0) & unorthogonal_lines(all_38_3, all_38_2) = v1) | ( % 39.58/7.22 | | ~ (v0 = 0) & convergent_lines(all_38_3, all_38_2) = v0)) % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (10) with all_38_2, all_38_4, all_51_0, % 39.58/7.22 | | simplifying with (21), (23), (43) gives: % 39.58/7.22 | | (54) all_51_0 = 0 | convergent_lines(all_38_2, all_38_4) = 0 % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (8) with all_38_5, all_38_3, all_38_1, all_38_2, % 39.58/7.22 | | all_55_0, all_49_0, simplifying with (20), (22), (23), (24), % 39.58/7.22 | | (40), (49) gives: % 39.58/7.22 | | (55) all_55_0 = 0 | all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 39.58/7.22 | | int] : ((v2 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | % 39.58/7.22 | | (v1 = 0 & apart_point_and_line(all_38_5, all_38_1) = 0) | ( ~ (v0 % 39.58/7.22 | | = 0) & distinct_lines(all_38_3, all_38_1) = v0)) % 39.58/7.22 | | % 39.58/7.22 | | GROUND_INST: instantiating (10) with all_38_1, all_38_2, all_49_0, % 39.58/7.22 | | simplifying with (23), (24), (40) gives: % 39.58/7.22 | | (56) all_49_0 = 0 | convergent_lines(all_38_1, all_38_2) = 0 % 39.58/7.22 | | % 39.58/7.22 | | DELTA: instantiating (53) with fresh symbols all_73_0, all_73_1, all_73_2, % 39.58/7.22 | | all_73_3 gives: % 39.58/7.22 | | (57) (all_73_0 = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_4) % 39.58/7.22 | | = 0) | (all_73_1 = 0 & all_53_0 = 0 & unorthogonal_lines(all_38_3, % 39.58/7.22 | | all_38_4) = 0) | ( ~ (all_73_2 = 0) & % 39.58/7.22 | | unorthogonal_lines(all_38_3, all_38_2) = all_73_2) | ( ~ (all_73_3 % 39.58/7.22 | | = 0) & convergent_lines(all_38_3, all_38_2) = all_73_3) % 39.58/7.22 | | % 39.58/7.22 | | BETA: splitting (52) gives: % 39.58/7.22 | | % 39.58/7.22 | | Case 1: % 39.58/7.22 | | | % 39.58/7.22 | | | (58) unorthogonal_lines(all_38_3, all_38_4) = 0 % 39.58/7.22 | | | % 39.58/7.22 | | | BETA: splitting (54) gives: % 39.58/7.22 | | | % 39.58/7.22 | | | Case 1: % 39.58/7.22 | | | | % 39.58/7.22 | | | | (59) convergent_lines(all_38_2, all_38_4) = 0 % 39.58/7.22 | | | | % 39.58/7.22 | | | | BETA: splitting (55) gives: % 39.58/7.22 | | | | % 39.58/7.22 | | | | Case 1: % 39.58/7.22 | | | | | % 39.58/7.22 | | | | | (60) all_55_0 = 0 % 39.58/7.22 | | | | | % 39.58/7.22 | | | | | REDUCE: (48), (60) imply: % 39.58/7.22 | | | | | (61) $false % 39.58/7.23 | | | | | % 39.58/7.23 | | | | | CLOSE: (61) is inconsistent. % 39.58/7.23 | | | | | % 39.58/7.23 | | | | Case 2: % 39.58/7.23 | | | | | % 39.58/7.23 | | | | | (62) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 39.58/7.23 | | | | | ((v2 = 0 & unorthogonal_lines(all_38_3, all_38_2) = 0) | (v1 = % 39.58/7.23 | | | | | 0 & apart_point_and_line(all_38_5, all_38_1) = 0) | ( ~ % 39.58/7.23 | | | | | (v0 = 0) & distinct_lines(all_38_3, all_38_1) = v0)) % 39.58/7.23 | | | | | % 39.58/7.23 | | | | | BETA: splitting (56) gives: % 39.58/7.23 | | | | | % 39.58/7.23 | | | | | Case 1: % 39.58/7.23 | | | | | | % 39.58/7.23 | | | | | | (63) convergent_lines(all_38_1, all_38_2) = 0 % 39.58/7.23 | | | | | | % 39.58/7.23 | | | | | | BETA: splitting (62) gives: % 39.58/7.23 | | | | | | % 39.58/7.23 | | | | | | Case 1: % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | (64) all_49_0 = 0 % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | REDUCE: (39), (64) imply: % 39.58/7.23 | | | | | | | (65) $false % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | CLOSE: (65) is inconsistent. % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | Case 2: % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | (66) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 39.58/7.23 | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | (v1 = 0 % 39.58/7.23 | | | | | | | & apart_point_and_line(all_38_5, all_38_1) = 0) | ( ~ % 39.58/7.23 | | | | | | | (v0 = 0) & distinct_lines(all_38_3, all_38_1) = v0)) % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | DELTA: instantiating (66) with fresh symbols all_213_0, all_213_1, % 39.58/7.23 | | | | | | | all_213_2 gives: % 39.58/7.23 | | | | | | | (67) (all_213_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = % 39.58/7.23 | | | | | | | 0) | (all_213_1 = 0 & apart_point_and_line(all_38_5, % 39.58/7.23 | | | | | | | all_38_1) = 0) | ( ~ (all_213_2 = 0) & % 39.58/7.23 | | | | | | | distinct_lines(all_38_3, all_38_1) = all_213_2) % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | BETA: splitting (67) gives: % 39.58/7.23 | | | | | | | % 39.58/7.23 | | | | | | | Case 1: % 39.58/7.23 | | | | | | | | % 39.58/7.23 | | | | | | | | (68) all_213_0 = 0 & unorthogonal_lines(all_38_3, all_38_2) = % 39.58/7.23 | | | | | | | | 0 % 39.58/7.23 | | | | | | | | % 39.58/7.23 | | | | | | | | ALPHA: (68) implies: % 39.58/7.23 | | | | | | | | (69) unorthogonal_lines(all_38_3, all_38_2) = 0 % 39.58/7.23 | | | | | | | | % 39.58/7.23 | | | | | | | | BETA: splitting (57) gives: % 39.58/7.23 | | | | | | | | % 39.58/7.23 | | | | | | | | Case 1: % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | (70) (all_73_0 = 0 & all_51_0 = 0 & % 39.58/7.23 | | | | | | | | | convergent_lines(all_38_2, all_38_4) = 0) | % 39.58/7.23 | | | | | | | | | (all_73_1 = 0 & all_53_0 = 0 & % 39.58/7.23 | | | | | | | | | unorthogonal_lines(all_38_3, all_38_4) = 0) % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | BETA: splitting (70) gives: % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | Case 1: % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | (71) all_73_0 = 0 & all_51_0 = 0 & % 39.58/7.23 | | | | | | | | | | convergent_lines(all_38_2, all_38_4) = 0 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | ALPHA: (71) implies: % 39.58/7.23 | | | | | | | | | | (72) all_51_0 = 0 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | REDUCE: (42), (72) imply: % 39.58/7.23 | | | | | | | | | | (73) $false % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | CLOSE: (73) is inconsistent. % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | Case 2: % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | (74) all_73_1 = 0 & all_53_0 = 0 & % 39.58/7.23 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_4) = 0 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | ALPHA: (74) implies: % 39.58/7.23 | | | | | | | | | | (75) all_53_0 = 0 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | REDUCE: (45), (75) imply: % 39.58/7.23 | | | | | | | | | | (76) $false % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | CLOSE: (76) is inconsistent. % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | End of split % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | Case 2: % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | (77) ( ~ (all_73_2 = 0) & unorthogonal_lines(all_38_3, % 39.58/7.23 | | | | | | | | | all_38_2) = all_73_2) | ( ~ (all_73_3 = 0) & % 39.58/7.23 | | | | | | | | | convergent_lines(all_38_3, all_38_2) = all_73_3) % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | BETA: splitting (77) gives: % 39.58/7.23 | | | | | | | | | % 39.58/7.23 | | | | | | | | | Case 1: % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | (78) ~ (all_73_2 = 0) & unorthogonal_lines(all_38_3, % 39.58/7.23 | | | | | | | | | | all_38_2) = all_73_2 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | ALPHA: (78) implies: % 39.58/7.23 | | | | | | | | | | (79) ~ (all_73_2 = 0) % 39.58/7.23 | | | | | | | | | | (80) unorthogonal_lines(all_38_3, all_38_2) = all_73_2 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_73_2, all_38_2, % 39.58/7.23 | | | | | | | | | | all_38_3, simplifying with (69), (80) gives: % 39.58/7.23 | | | | | | | | | | (81) all_73_2 = 0 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | REDUCE: (79), (81) imply: % 39.58/7.23 | | | | | | | | | | (82) $false % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | CLOSE: (82) is inconsistent. % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | Case 2: % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | (83) ~ (all_73_3 = 0) & convergent_lines(all_38_3, % 39.58/7.23 | | | | | | | | | | all_38_2) = all_73_3 % 39.58/7.23 | | | | | | | | | | % 39.58/7.23 | | | | | | | | | | ALPHA: (83) implies: % 39.88/7.23 | | | | | | | | | | (84) ~ (all_73_3 = 0) % 39.88/7.23 | | | | | | | | | | (85) convergent_lines(all_38_3, all_38_2) = all_73_3 % 39.88/7.23 | | | | | | | | | | % 39.88/7.23 | | | | | | | | | | GROUND_INST: instantiating (6) with all_38_3, all_38_1, % 39.88/7.23 | | | | | | | | | | all_38_2, all_49_0, simplifying with (22), (23), % 39.88/7.23 | | | | | | | | | | (24), (40), (51) gives: % 39.88/7.23 | | | | | | | | | | (86) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 39.88/7.23 | | | | | | | | | | int] : ((v3 = 0 & all_49_0 = 0 & % 39.88/7.23 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | (v2 % 39.88/7.23 | | | | | | | | | | = 0 & v1 = 0 & unorthogonal_lines(all_38_3, % 39.88/7.23 | | | | | | | | | | all_38_2) = 0 & convergent_lines(all_38_3, % 39.88/7.23 | | | | | | | | | | all_38_2) = 0) | ( ~ (v0 = 0) & % 39.88/7.23 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = v0)) % 39.88/7.23 | | | | | | | | | | % 39.88/7.23 | | | | | | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_1, % 39.88/7.23 | | | | | | | | | | all_38_4, all_53_0, simplifying with (21), (22), % 39.88/7.23 | | | | | | | | | | (24), (46), (51) gives: % 39.88/7.23 | | | | | | | | | | (87) all_53_0 = 0 | convergent_lines(all_38_1, all_38_4) % 39.88/7.23 | | | | | | | | | | = 0 % 39.88/7.23 | | | | | | | | | | % 39.88/7.23 | | | | | | | | | | GROUND_INST: instantiating (3) with all_38_3, all_38_1, % 39.88/7.23 | | | | | | | | | | all_38_2, all_73_3, simplifying with (22), (23), % 39.88/7.23 | | | | | | | | | | (24), (51), (85) gives: % 39.88/7.23 | | | | | | | | | | (88) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 39.88/7.23 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 39.88/7.23 | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.23 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | (v1 % 39.88/7.23 | | | | | | | | | | = 0 & all_73_3 = 0 & % 39.88/7.23 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( % 39.88/7.23 | | | | | | | | | | ~ (v0 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.23 | | | | | | | | | | all_38_1) = v0)) % 39.88/7.23 | | | | | | | | | | % 39.88/7.23 | | | | | | | | | | GROUND_INST: instantiating (12) with all_38_1, all_38_2, % 39.88/7.23 | | | | | | | | | | all_38_4, all_49_0, simplifying with (21), (23), % 39.88/7.24 | | | | | | | | | | (24), (40), (59) gives: % 39.88/7.24 | | | | | | | | | | (89) all_49_0 = 0 | unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_4) = 0 % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | GROUND_INST: instantiating (4) with all_38_3, all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_2, 0, simplifying with (22), (23), (24), % 39.88/7.24 | | | | | | | | | | (51), (63) gives: % 39.88/7.24 | | | | | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 39.88/7.24 | | | | | | | | | | int] : ((v3 = 0 & unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_2) = 0) | (v2 = 0 & v1 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | (v0 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_1) = v0)) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | GROUND_INST: instantiating (11) with all_38_3, all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_4, 0, 0, simplifying with (21), (22), (24), % 39.88/7.24 | | | | | | | | | | (51), (58) gives: % 39.88/7.24 | | | | | | | | | | (91) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 39.88/7.24 | | | | | | | | | | int] : ((v1 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_4) = 0) | (v0 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | ( % 39.88/7.24 | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_4) = v3) | ( ~ (v2 = 0) & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_4) = v2)) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | GROUND_INST: instantiating (5) with all_38_3, all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_2, 0, simplifying with (22), (23), (24), % 39.88/7.24 | | | | | | | | | | (51), (69) gives: % 39.88/7.24 | | | | | | | | | | (92) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 39.88/7.24 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | (v1 % 39.88/7.24 | | | | | | | | | | = 0 & convergent_lines(all_38_3, all_38_2) = 0) % 39.88/7.24 | | | | | | | | | | | ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_1) = v0)) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | DELTA: instantiating (90) with fresh symbols all_410_0, % 39.88/7.24 | | | | | | | | | | all_410_1, all_410_2, all_410_3 gives: % 39.88/7.24 | | | | | | | | | | (93) (all_410_0 = 0 & unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_2) = 0) | (all_410_1 = 0 & all_410_2 = 0 % 39.88/7.24 | | | | | | | | | | & unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | (all_410_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_1) = all_410_3) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | DELTA: instantiating (92) with fresh symbols all_416_0, % 39.88/7.24 | | | | | | | | | | all_416_1, all_416_2, all_416_3 gives: % 39.88/7.24 | | | | | | | | | | (94) (all_416_0 = 0 & all_416_1 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | % 39.88/7.24 | | | | | | | | | | (all_416_2 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_2) = 0) | ( ~ (all_416_3 = 0) & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = % 39.88/7.24 | | | | | | | | | | all_416_3) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_421_0, % 39.88/7.24 | | | | | | | | | | all_421_1, all_421_2, all_421_3 gives: % 39.88/7.24 | | | | | | | | | | (95) (all_421_2 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_4) = 0) | (all_421_3 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | (all_421_0 = 0) & unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | all_38_4) = all_421_0) | ( ~ (all_421_1 = 0) & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_4) = all_421_1) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | DELTA: instantiating (88) with fresh symbols all_463_0, % 39.88/7.24 | | | | | | | | | | all_463_1, all_463_2, all_463_3 gives: % 39.88/7.24 | | | | | | | | | | (96) (all_463_0 = 0 & all_463_1 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | % 39.88/7.24 | | | | | | | | | | (all_463_2 = 0 & all_73_3 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | (all_463_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_1) = all_463_3) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | DELTA: instantiating (86) with fresh symbols all_464_0, % 39.88/7.24 | | | | | | | | | | all_464_1, all_464_2, all_464_3 gives: % 39.88/7.24 | | | | | | | | | | (97) (all_464_0 = 0 & all_49_0 = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | % 39.88/7.24 | | | | | | | | | | (all_464_1 = 0 & all_464_2 = 0 & % 39.88/7.24 | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | (all_464_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | all_38_1) = all_464_3) % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | BETA: splitting (94) gives: % 39.88/7.24 | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | (98) all_416_0 = 0 & all_416_1 = 0 & % 39.88/7.24 | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | ALPHA: (98) implies: % 39.88/7.24 | | | | | | | | | | | (99) unorthogonal_lines(all_38_1, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | REF_CLOSE: (17), (39), (40), (99) are inconsistent by % 39.88/7.24 | | | | | | | | | | | sub-proof #2. % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | Case 2: % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | (100) (all_416_2 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_416_3 = 0) & % 39.88/7.24 | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = % 39.88/7.24 | | | | | | | | | | | all_416_3) % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | BETA: splitting (100) gives: % 39.88/7.24 | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | (101) all_416_2 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | | all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | ALPHA: (101) implies: % 39.88/7.24 | | | | | | | | | | | | (102) convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | REF_CLOSE: (15), (84), (85), (102) are inconsistent by % 39.88/7.24 | | | | | | | | | | | | sub-proof #1. % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | Case 2: % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | (103) ~ (all_416_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | | all_38_1) = all_416_3 % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | ALPHA: (103) implies: % 39.88/7.24 | | | | | | | | | | | | (104) unorthogonal_lines(all_38_3, all_38_1) = all_416_3 % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | BETA: splitting (87) gives: % 39.88/7.24 | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | (105) convergent_lines(all_38_1, all_38_4) = 0 % 39.88/7.24 | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | BETA: splitting (93) gives: % 39.88/7.24 | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | (106) all_410_0 = 0 & unorthogonal_lines(all_38_1, % 39.88/7.24 | | | | | | | | | | | | | | all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | ALPHA: (106) implies: % 39.88/7.24 | | | | | | | | | | | | | | (107) unorthogonal_lines(all_38_1, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (40), (107) are inconsistent by % 39.88/7.24 | | | | | | | | | | | | | | sub-proof #2. % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | Case 2: % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | (108) (all_410_1 = 0 & all_410_2 = 0 & % 39.88/7.24 | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.24 | | | | | | | | | | | | | | (all_410_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | | | | all_38_1) = all_410_3) % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | BETA: splitting (108) gives: % 39.88/7.24 | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | (109) all_410_1 = 0 & all_410_2 = 0 & % 39.88/7.24 | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.24 | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | ALPHA: (109) implies: % 39.88/7.24 | | | | | | | | | | | | | | | (110) convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | REF_CLOSE: (15), (84), (85), (110) are inconsistent by % 39.88/7.24 | | | | | | | | | | | | | | | sub-proof #1. % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | Case 2: % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | (111) ~ (all_410_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | | | | | all_38_1) = all_410_3 % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | ALPHA: (111) implies: % 39.88/7.24 | | | | | | | | | | | | | | | (112) ~ (all_410_3 = 0) % 39.88/7.24 | | | | | | | | | | | | | | | (113) unorthogonal_lines(all_38_3, all_38_1) = all_410_3 % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 39.88/7.24 | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | | (114) (all_421_2 = 0 & convergent_lines(all_38_3, % 39.88/7.24 | | | | | | | | | | | | | | | | all_38_4) = 0) | (all_421_3 = 0 & % 39.88/7.24 | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0) % 39.88/7.24 | | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 39.88/7.24 | | | | | | | | | | | | | | | | % 39.88/7.24 | | | | | | | | | | | | | | | | Case 1: % 39.88/7.24 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | (115) all_421_2 = 0 & convergent_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_4) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | ALPHA: (115) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | (116) convergent_lines(all_38_3, all_38_4) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_53_0, 0, all_38_4, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_3, simplifying with (46), (116) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | (117) all_53_0 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | REDUCE: (45), (117) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | (118) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | CLOSE: (118) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | (119) all_421_3 = 0 & unorthogonal_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_1) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | ALPHA: (119) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | (120) unorthogonal_lines(all_38_3, all_38_1) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | (121) all_464_0 = 0 & all_49_0 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | ALPHA: (121) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | (122) all_49_0 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | REDUCE: (39), (122) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | (123) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | (124) (all_464_1 = 0 & all_464_2 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0) | ( ~ % 39.88/7.25 | | | | | | | | | | | | | | | | | | (all_464_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | all_38_1) = all_464_3) % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | (125) all_464_1 = 0 & all_464_2 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | (126) convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (84), (85), (126) are inconsistent by % 39.88/7.25 | | | | | | | | | | | | | | | | | | | sub-proof #1. % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | (127) ~ (all_464_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | all_38_1) = all_464_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | (128) unorthogonal_lines(all_38_3, all_38_1) = all_464_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | (129) all_463_0 = 0 & all_463_1 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | (130) unorthogonal_lines(all_38_1, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (40), (130) are inconsistent by % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | (131) (all_463_2 = 0 & all_73_3 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0) | ( % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | ~ (all_463_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | all_38_1) = all_463_3) % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (132) all_463_2 = 0 & all_73_3 = 0 & % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_2) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (133) all_73_3 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (133) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (134) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (135) ~ (all_463_3 = 0) & unorthogonal_lines(all_38_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_463_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (136) unorthogonal_lines(all_38_3, all_38_1) = all_463_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_416_3, all_463_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (104), (136) % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (137) all_463_3 = all_416_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_463_3, all_38_1, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (120), (136) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (138) all_463_3 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_463_3, all_464_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (128), (136) % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (139) all_464_3 = all_463_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_410_3, all_464_3, % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_3, simplifying with (113), (128) % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (140) all_464_3 = all_410_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (140) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (141) all_463_3 = all_410_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (141) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (142) all_463_3 = all_410_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (143) all_416_3 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (142) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (144) all_416_3 = all_410_3 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (145) all_410_3 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (145) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (146) all_410_3 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (146) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | (147) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | (148) ( ~ (all_421_0 = 0) & unorthogonal_lines(all_38_1, % 39.88/7.25 | | | | | | | | | | | | | | | | all_38_4) = all_421_0) | ( ~ (all_421_1 = 0) & % 39.88/7.25 | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_4) = % 39.88/7.25 | | | | | | | | | | | | | | | | all_421_1) % 39.88/7.25 | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | (149) ~ (all_421_0 = 0) & unorthogonal_lines(all_38_1, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_4) = all_421_0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | ALPHA: (149) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | (150) ~ (all_421_0 = 0) % 39.88/7.25 | | | | | | | | | | | | | | | | | (151) unorthogonal_lines(all_38_1, all_38_4) = all_421_0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | BETA: splitting (89) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | Case 1: % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | (152) unorthogonal_lines(all_38_1, all_38_4) = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_421_0, all_38_4, % 39.88/7.25 | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (151), (152) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | | (153) all_421_0 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | REDUCE: (150), (153) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | (154) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | (155) all_49_0 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | REDUCE: (39), (155) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | | (156) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | (157) ~ (all_421_1 = 0) & convergent_lines(all_38_1, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_4) = all_421_1 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 39.88/7.25 | | | | | | | | | | | | | | | | | (158) ~ (all_421_1 = 0) % 39.88/7.25 | | | | | | | | | | | | | | | | | (159) convergent_lines(all_38_1, all_38_4) = all_421_1 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_421_1, all_38_4, % 39.88/7.25 | | | | | | | | | | | | | | | | | all_38_1, simplifying with (105), (159) gives: % 39.88/7.25 | | | | | | | | | | | | | | | | | (160) all_421_1 = 0 % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | REDUCE: (158), (160) imply: % 39.88/7.25 | | | | | | | | | | | | | | | | | (161) $false % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | Case 2: % 39.88/7.25 | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | (162) all_53_0 = 0 % 39.88/7.25 | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | REDUCE: (45), (162) imply: % 39.88/7.25 | | | | | | | | | | | | | (163) $false % 39.88/7.25 | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | | CLOSE: (163) is inconsistent. % 39.88/7.25 | | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | | End of split % 39.88/7.25 | | | | | | | | | | | | % 39.88/7.25 | | | | | | | | | | | End of split % 39.88/7.26 | | | | | | | | | | | % 39.88/7.26 | | | | | | | | | | End of split % 39.88/7.26 | | | | | | | | | | % 39.88/7.26 | | | | | | | | | End of split % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | End of split % 39.88/7.26 | | | | | | | | % 39.88/7.26 | | | | | | | Case 2: % 39.88/7.26 | | | | | | | | % 39.88/7.26 | | | | | | | | (164) (all_213_1 = 0 & apart_point_and_line(all_38_5, % 39.88/7.26 | | | | | | | | all_38_1) = 0) | ( ~ (all_213_2 = 0) & % 39.88/7.26 | | | | | | | | distinct_lines(all_38_3, all_38_1) = all_213_2) % 39.88/7.26 | | | | | | | | % 39.88/7.26 | | | | | | | | BETA: splitting (164) gives: % 39.88/7.26 | | | | | | | | % 39.88/7.26 | | | | | | | | Case 1: % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | (165) all_213_1 = 0 & apart_point_and_line(all_38_5, % 39.88/7.26 | | | | | | | | | all_38_1) = 0 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | ALPHA: (165) implies: % 39.88/7.26 | | | | | | | | | (166) apart_point_and_line(all_38_5, all_38_1) = 0 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | GROUND_INST: instantiating (16) with all_45_0, 0, all_38_1, % 39.88/7.26 | | | | | | | | | all_38_5, simplifying with (37), (166) gives: % 39.88/7.26 | | | | | | | | | (167) all_45_0 = 0 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | REDUCE: (36), (167) imply: % 39.88/7.26 | | | | | | | | | (168) $false % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | CLOSE: (168) is inconsistent. % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | Case 2: % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | (169) ~ (all_213_2 = 0) & distinct_lines(all_38_3, % 39.88/7.26 | | | | | | | | | all_38_1) = all_213_2 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | ALPHA: (169) implies: % 39.88/7.26 | | | | | | | | | (170) ~ (all_213_2 = 0) % 39.88/7.26 | | | | | | | | | (171) distinct_lines(all_38_3, all_38_1) = all_213_2 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_213_2, all_38_1, % 39.88/7.26 | | | | | | | | | all_38_3, simplifying with (50), (171) gives: % 39.88/7.26 | | | | | | | | | (172) all_213_2 = 0 % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | REDUCE: (170), (172) imply: % 39.88/7.26 | | | | | | | | | (173) $false % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | | CLOSE: (173) is inconsistent. % 39.88/7.26 | | | | | | | | | % 39.88/7.26 | | | | | | | | End of split % 39.88/7.26 | | | | | | | | % 39.88/7.26 | | | | | | | End of split % 39.88/7.26 | | | | | | | % 39.88/7.26 | | | | | | End of split % 39.88/7.26 | | | | | | % 39.88/7.26 | | | | | Case 2: % 39.88/7.26 | | | | | | % 39.88/7.26 | | | | | | (174) all_49_0 = 0 % 39.88/7.26 | | | | | | % 39.88/7.26 | | | | | | REDUCE: (39), (174) imply: % 39.88/7.26 | | | | | | (175) $false % 39.88/7.26 | | | | | | % 39.88/7.26 | | | | | | CLOSE: (175) is inconsistent. % 39.88/7.26 | | | | | | % 39.88/7.26 | | | | | End of split % 39.88/7.26 | | | | | % 39.88/7.26 | | | | End of split % 39.88/7.26 | | | | % 39.88/7.26 | | | Case 2: % 39.88/7.26 | | | | % 39.88/7.26 | | | | (176) all_51_0 = 0 % 39.88/7.26 | | | | % 39.88/7.26 | | | | REDUCE: (42), (176) imply: % 39.88/7.26 | | | | (177) $false % 39.88/7.26 | | | | % 39.88/7.26 | | | | CLOSE: (177) is inconsistent. % 39.88/7.26 | | | | % 39.88/7.26 | | | End of split % 39.88/7.26 | | | % 39.88/7.26 | | Case 2: % 39.88/7.26 | | | % 39.88/7.26 | | | (178) all_53_0 = 0 % 39.88/7.26 | | | % 39.88/7.26 | | | REDUCE: (45), (178) imply: % 39.88/7.26 | | | (179) $false % 39.88/7.26 | | | % 39.88/7.26 | | | CLOSE: (179) is inconsistent. % 39.88/7.26 | | | % 39.88/7.26 | | End of split % 39.88/7.26 | | % 39.88/7.26 | Case 2: % 39.88/7.26 | | % 39.88/7.26 | | (180) all_38_0 = 0 % 39.88/7.26 | | % 39.88/7.26 | | REDUCE: (19), (180) imply: % 39.88/7.26 | | (181) $false % 39.88/7.26 | | % 39.88/7.26 | | CLOSE: (181) is inconsistent. % 39.88/7.26 | | % 39.88/7.26 | End of split % 39.88/7.26 | % 39.88/7.26 End of proof % 39.88/7.26 % 39.88/7.26 Sub-proof #1 shows that the following formulas are inconsistent: % 39.88/7.26 ---------------------------------------------------------------- % 39.88/7.26 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 39.88/7.26 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 39.88/7.26 (convergent_lines(v3, v2) = v0)) % 39.88/7.26 (2) convergent_lines(all_38_3, all_38_2) = all_73_3 % 39.88/7.26 (3) convergent_lines(all_38_3, all_38_2) = 0 % 39.88/7.26 (4) ~ (all_73_3 = 0) % 39.88/7.26 % 39.88/7.26 Begin of proof % 39.88/7.26 | % 39.88/7.26 | GROUND_INST: instantiating (1) with 0, all_73_3, all_38_2, all_38_3, % 39.88/7.26 | simplifying with (2), (3) gives: % 39.88/7.26 | (5) all_73_3 = 0 % 39.88/7.26 | % 39.88/7.26 | REDUCE: (4), (5) imply: % 39.88/7.26 | (6) $false % 39.88/7.26 | % 39.88/7.26 | CLOSE: (6) is inconsistent. % 39.88/7.26 | % 39.88/7.26 End of proof % 39.88/7.26 % 39.88/7.26 Sub-proof #2 shows that the following formulas are inconsistent: % 39.88/7.26 ---------------------------------------------------------------- % 40.01/7.26 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 40.01/7.26 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 40.01/7.26 (unorthogonal_lines(v3, v2) = v0)) % 40.01/7.26 (2) unorthogonal_lines(all_38_1, all_38_2) = all_49_0 % 40.01/7.26 (3) unorthogonal_lines(all_38_1, all_38_2) = 0 % 40.01/7.26 (4) ~ (all_49_0 = 0) % 40.01/7.26 % 40.01/7.26 Begin of proof % 40.01/7.26 | % 40.01/7.26 | GROUND_INST: instantiating (1) with all_49_0, 0, all_38_2, all_38_1, % 40.01/7.26 | simplifying with (2), (3) gives: % 40.01/7.26 | (5) all_49_0 = 0 % 40.01/7.26 | % 40.01/7.26 | REDUCE: (4), (5) imply: % 40.01/7.26 | (6) $false % 40.01/7.26 | % 40.01/7.26 | CLOSE: (6) is inconsistent. % 40.01/7.26 | % 40.01/7.26 End of proof % 40.01/7.26 % SZS output end Proof for theBenchmark % 40.01/7.26 % 40.01/7.26 6661ms %------------------------------------------------------------------------------