%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO217+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 23:22:27 EDT 2023 % Result : Theorem 11.46s 2.24s % Output : Proof 22.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO217+2 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n028.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue Aug 29 23:05:26 EDT 2023 % 0.14/0.33 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.54/1.02 Prover 1: Preprocessing ... % 2.54/1.02 Prover 4: Preprocessing ... % 3.00/1.06 Prover 6: Preprocessing ... % 3.00/1.06 Prover 3: Preprocessing ... % 3.00/1.06 Prover 0: Preprocessing ... % 3.00/1.06 Prover 5: Preprocessing ... % 3.00/1.06 Prover 2: Preprocessing ... % 3.79/1.30 Prover 5: Proving ... % 4.69/1.32 Prover 2: Proving ... % 4.69/1.32 Prover 6: Constructing countermodel ... % 4.69/1.33 Prover 3: Constructing countermodel ... % 4.69/1.34 Prover 1: Constructing countermodel ... % 5.29/1.41 Prover 3: gave up % 5.29/1.41 Prover 1: gave up % 5.69/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.69/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.69/1.43 Prover 6: gave up % 5.69/1.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.93/1.45 Prover 8: Preprocessing ... % 5.93/1.47 Prover 7: Preprocessing ... % 5.93/1.48 Prover 9: Preprocessing ... % 5.93/1.51 Prover 7: Warning: ignoring some quantifiers % 5.93/1.53 Prover 7: Constructing countermodel ... % 6.88/1.58 Prover 4: Constructing countermodel ... % 6.88/1.58 Prover 8: Warning: ignoring some quantifiers % 6.88/1.58 Prover 0: Proving ... % 6.88/1.60 Prover 8: Constructing countermodel ... % 7.41/1.66 Prover 8: gave up % 7.57/1.67 Prover 7: gave up % 7.57/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.57/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.57/1.70 Prover 10: Preprocessing ... % 7.57/1.71 Prover 11: Preprocessing ... % 8.22/1.75 Prover 10: Warning: ignoring some quantifiers % 8.22/1.76 Prover 10: Constructing countermodel ... % 8.22/1.76 Prover 9: Constructing countermodel ... % 8.22/1.81 Prover 10: gave up % 8.79/1.84 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.79/1.89 Prover 12: Preprocessing ... % 9.44/1.95 Prover 11: Constructing countermodel ... % 9.44/2.00 Prover 12: Proving ... % 11.46/2.24 Prover 0: proved (1630ms) % 11.46/2.24 % 11.46/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.46/2.24 % 11.46/2.24 Prover 12: stopped % 11.46/2.24 Prover 2: stopped % 11.46/2.24 Prover 9: stopped % 11.46/2.24 Prover 5: stopped % 11.46/2.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.46/2.24 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.46/2.24 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.46/2.26 Prover 19: Preprocessing ... % 11.46/2.26 Prover 13: Preprocessing ... % 11.46/2.26 Prover 16: Preprocessing ... % 12.14/2.28 Prover 16: Warning: ignoring some quantifiers % 12.14/2.29 Prover 13: Warning: ignoring some quantifiers % 12.14/2.29 Prover 16: Constructing countermodel ... % 12.14/2.29 Prover 13: Constructing countermodel ... % 12.36/2.32 Prover 19: Warning: ignoring some quantifiers % 12.36/2.33 Prover 19: Constructing countermodel ... % 12.52/2.35 Prover 13: gave up % 12.52/2.36 Prover 19: gave up % 13.64/2.50 Prover 16: gave up % 21.44/3.94 Prover 11: Found proof (size 426) % 21.44/3.94 Prover 11: proved (2252ms) % 21.44/3.94 Prover 4: stopped % 21.44/3.94 % 21.44/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.44/3.94 % 21.44/3.97 % SZS output start Proof for theBenchmark % 21.44/3.98 Assumptions after simplification: % 21.44/3.98 --------------------------------- % 21.44/3.98 % 21.44/3.98 (apart6) % 21.72/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.72/4.03 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 21.72/4.03 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 21.72/4.03 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 21.72/4.03 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 21.72/4.03 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/4.03 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.72/4.03 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 21.72/4.03 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/4.03 convergent_lines(v1, v2) = 0) % 21.72/4.03 % 21.72/4.03 (coipo1) % 21.72/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.72/4.03 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/4.03 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 21.72/4.03 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/4.03 unorthogonal_lines(v0, v1) = 0) % 21.72/4.03 % 21.72/4.03 (con) % 21.72/4.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 21.72/4.03 (v4 = 0) & ~ (v3 = 0) & convergent_lines(v1, v2) = 0 & convergent_lines(v0, % 21.72/4.03 v2) = v4 & convergent_lines(v0, v1) = v3 & $i(v2) & $i(v1) & $i(v0)) % 21.72/4.03 % 21.72/4.03 (cotno1) % 21.72/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 21.72/4.05 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 21.72/4.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 21.72/4.05 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 21.72/4.05 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.72/4.05 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 21.72/4.05 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 21.72/4.05 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 21.72/4.05 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.05 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.72/4.05 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 21.72/4.05 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 21.72/4.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 21.72/4.05 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 21.72/4.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 21.72/4.05 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 21.72/4.05 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.72/4.05 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 21.72/4.05 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 21.72/4.05 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 21.72/4.05 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 21.72/4.05 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 21.72/4.05 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 21.72/4.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 21.72/4.05 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 21.72/4.05 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 21.72/4.05 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.72/4.05 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 21.72/4.05 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.72/4.05 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.72/4.05 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.72/4.05 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.72/4.05 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.72/4.05 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.72/4.05 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 21.72/4.05 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.72/4.05 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.72/4.05 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.72/4.05 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.72/4.05 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 21.72/4.05 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.72/4.05 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.72/4.05 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.72/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.72/4.05 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 21.72/4.06 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 21.72/4.06 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.72/4.06 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.72/4.06 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.72/4.06 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.72/4.06 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.72/4.06 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 21.72/4.06 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.06 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.72/4.06 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.72/4.06 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.72/4.06 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 21.72/4.06 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 21.72/4.06 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.06 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.72/4.06 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.72/4.06 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.72/4.06 unorthogonal_lines(v1, v2) = v7))) % 21.72/4.06 % 21.72/4.06 (couo1) % 21.72/4.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.72/4.06 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 21.72/4.06 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.72/4.06 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 21.72/4.06 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 21.72/4.06 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 21.72/4.06 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 21.72/4.06 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 21.72/4.06 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.72/4.06 unorthogonal_lines(v0, v2) = 0) % 21.72/4.06 % 21.72/4.06 (function-axioms) % 22.04/4.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 22.04/4.06 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.04/4.06 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.04/4.06 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 22.04/4.06 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.04/4.06 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 22.04/4.06 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.04/4.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.04/4.06 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 22.04/4.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 22.04/4.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.04/4.06 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.04/4.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.04/4.06 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 22.04/4.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.04/4.06 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 22.04/4.06 v0)) % 22.06/4.06 % 22.06/4.06 Further assumptions not needed in the proof: % 22.06/4.06 -------------------------------------------- % 22.06/4.06 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cu1 % 22.06/4.06 % 22.06/4.06 Those formulas are unsatisfiable: % 22.06/4.06 --------------------------------- % 22.06/4.06 % 22.06/4.06 Begin of proof % 22.06/4.06 | % 22.06/4.06 | ALPHA: (apart6) implies: % 22.06/4.07 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.06/4.07 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 22.06/4.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 22.06/4.07 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 22.06/4.07 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 22.06/4.07 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.06/4.07 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 22.06/4.07 | % 22.06/4.07 | ALPHA: (coipo1) implies: % 22.06/4.07 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 22.06/4.07 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 22.06/4.07 | unorthogonal_lines(v0, v1) = 0) % 22.06/4.07 | % 22.06/4.07 | ALPHA: (cotno1) implies: % 22.06/4.07 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.06/4.07 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | % 22.06/4.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 22.06/4.07 | [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & unorthogonal_lines(v0, % 22.06/4.07 | v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 22.06/4.07 | unorthogonal_lines(v1, v2) = v7))) % 22.06/4.07 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.06/4.07 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | % 22.06/4.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 22.06/4.07 | [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & unorthogonal_lines(v0, % 22.06/4.07 | v2) = 0) | (v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & % 22.06/4.07 | convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 22.06/4.07 | unorthogonal_lines(v1, v2) = v7))) % 22.06/4.07 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.06/4.07 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 22.06/4.07 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 22.06/4.07 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 22.06/4.07 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 22.06/4.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 22.06/4.07 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = % 22.06/4.07 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 22.06/4.07 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 22.06/4.07 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 22.06/4.07 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 22.06/4.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 22.06/4.07 | ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = % 22.06/4.07 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 22.06/4.07 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 22.06/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 22.06/4.07 | convergent_lines(v1, v2) = v7))) % 22.06/4.07 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 22.06/4.07 | ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = % 22.06/4.07 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 22.06/4.07 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 22.06/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 22.06/4.07 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 22.06/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 22.06/4.07 | convergent_lines(v1, v2) = v7))) % 22.06/4.08 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.06/4.08 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) % 22.06/4.08 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 22.06/4.08 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 22.06/4.08 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 22.06/4.08 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 22.06/4.08 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 22.06/4.08 | convergent_lines(v1, v2) = v7))) % 22.06/4.08 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 22.06/4.08 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, % 22.06/4.08 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 22.06/4.08 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 22.06/4.08 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 22.06/4.08 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 22.06/4.08 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 22.06/4.08 | convergent_lines(v1, v2) = v7))) % 22.06/4.08 | % 22.06/4.08 | ALPHA: (couo1) implies: % 22.06/4.08 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.06/4.08 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = % 22.06/4.08 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, % 22.06/4.08 | v1) = 0) % 22.06/4.08 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 22.06/4.08 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 22.06/4.08 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 22.06/4.08 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = % 22.06/4.08 | v5)) % 22.06/4.08 | % 22.06/4.08 | ALPHA: (function-axioms) implies: % 22.06/4.08 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.06/4.08 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.06/4.08 | (convergent_lines(v3, v2) = v0)) % 22.06/4.08 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.06/4.08 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.06/4.08 | (unorthogonal_lines(v3, v2) = v0)) % 22.06/4.08 | % 22.06/4.08 | DELTA: instantiating (con) with fresh symbols all_18_0, all_18_1, all_18_2, % 22.06/4.08 | all_18_3, all_18_4 gives: % 22.06/4.08 | (16) ~ (all_18_0 = 0) & ~ (all_18_1 = 0) & convergent_lines(all_18_3, % 22.06/4.08 | all_18_2) = 0 & convergent_lines(all_18_4, all_18_2) = all_18_0 & % 22.06/4.08 | convergent_lines(all_18_4, all_18_3) = all_18_1 & $i(all_18_2) & % 22.06/4.08 | $i(all_18_3) & $i(all_18_4) % 22.06/4.08 | % 22.06/4.08 | ALPHA: (16) implies: % 22.06/4.08 | (17) ~ (all_18_1 = 0) % 22.06/4.08 | (18) ~ (all_18_0 = 0) % 22.06/4.08 | (19) $i(all_18_4) % 22.06/4.08 | (20) $i(all_18_3) % 22.06/4.08 | (21) $i(all_18_2) % 22.06/4.08 | (22) convergent_lines(all_18_4, all_18_3) = all_18_1 % 22.06/4.08 | (23) convergent_lines(all_18_4, all_18_2) = all_18_0 % 22.06/4.08 | (24) convergent_lines(all_18_3, all_18_2) = 0 % 22.06/4.08 | % 22.06/4.08 | GROUND_INST: instantiating (2) with all_18_4, all_18_4, all_18_3, all_18_1, % 22.06/4.08 | all_18_1, simplifying with (19), (20), (22) gives: % 22.06/4.08 | (25) all_18_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.06/4.08 | convergent_lines(all_18_4, all_18_4) = v0) % 22.06/4.08 | % 22.06/4.08 | GROUND_INST: instantiating (8) with all_18_4, all_18_3, all_18_3, all_18_1, % 22.06/4.08 | all_18_1, simplifying with (19), (20), (22) gives: % 22.06/4.09 | (26) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 & % 22.06/4.09 | all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | (v0 = % 22.06/4.09 | 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( % 22.06/4.09 | ~ (v3 = 0) & unorthogonal_lines(all_18_3, all_18_3) = v3) | ( ~ % 22.06/4.09 | (v2 = 0) & convergent_lines(all_18_3, all_18_3) = v2)) % 22.06/4.09 | % 22.06/4.09 | GROUND_INST: instantiating (3) with all_18_4, all_18_3, all_18_1, simplifying % 22.06/4.09 | with (19), (20), (22) gives: % 22.06/4.09 | (27) all_18_1 = 0 | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.06/4.09 | % 22.06/4.09 | GROUND_INST: instantiating (2) with all_18_4, all_18_4, all_18_2, all_18_0, % 22.06/4.09 | all_18_0, simplifying with (19), (21), (23) gives: % 22.06/4.09 | (28) all_18_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.06/4.09 | convergent_lines(all_18_4, all_18_4) = v0) % 22.06/4.09 | % 22.06/4.09 | GROUND_INST: instantiating (8) with all_18_4, all_18_3, all_18_2, all_18_1, % 22.06/4.09 | all_18_0, simplifying with (19), (20), (21), (22), (23) gives: % 22.06/4.09 | (29) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 & % 22.06/4.09 | all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0) | (v0 = % 22.06/4.09 | 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( % 22.06/4.09 | ~ (v3 = 0) & unorthogonal_lines(all_18_3, all_18_2) = v3) | ( ~ % 22.06/4.09 | (v2 = 0) & convergent_lines(all_18_3, all_18_2) = v2)) % 22.06/4.09 | % 22.06/4.09 | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_2, all_18_0, % 22.06/4.09 | simplifying with (19), (20), (21), (23), (24) gives: % 22.06/4.09 | (30) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 22.06/4.09 | all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0) | (v1 = % 22.06/4.09 | 0 & v0 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0 & % 22.06/4.09 | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) & % 22.06/4.09 | unorthogonal_lines(all_18_3, all_18_2) = v3)) % 22.06/4.09 | % 22.06/4.09 | GROUND_INST: instantiating (4) with all_18_4, all_18_3, all_18_2, all_18_1, % 22.06/4.09 | simplifying with (19), (20), (21), (22), (24) gives: % 22.06/4.09 | (31) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 22.06/4.09 | v1 = 0 & unorthogonal_lines(all_18_4, all_18_2) = 0 & % 22.06/4.09 | convergent_lines(all_18_4, all_18_2) = 0) | (v0 = 0 & all_18_1 = 0 % 22.06/4.09 | & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~ (v3 = 0) & % 22.06/4.09 | unorthogonal_lines(all_18_3, all_18_2) = v3)) % 22.06/4.09 | % 22.06/4.09 | DELTA: instantiating (31) with fresh symbols all_28_0, all_28_1, all_28_2, % 22.06/4.09 | all_28_3 gives: % 22.06/4.09 | (32) (all_28_1 = 0 & all_28_2 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 22.06/4.09 | = 0 & convergent_lines(all_18_4, all_18_2) = 0) | (all_28_3 = 0 & % 22.06/4.09 | all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.06/4.09 | (all_28_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = all_28_0) % 22.06/4.09 | % 22.06/4.09 | DELTA: instantiating (30) with fresh symbols all_29_0, all_29_1, all_29_2, % 22.06/4.09 | all_29_3 gives: % 22.06/4.09 | (33) (all_29_1 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 22.06/4.09 | = 0) | (all_29_2 = 0 & all_29_3 = 0 & unorthogonal_lines(all_18_4, % 22.06/4.09 | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.06/4.09 | (all_29_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = all_29_0) % 22.06/4.09 | % 22.06/4.09 | DELTA: instantiating (29) with fresh symbols all_31_0, all_31_1, all_31_2, % 22.06/4.09 | all_31_3 gives: % 22.06/4.09 | (34) (all_31_2 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 22.06/4.09 | = 0) | (all_31_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.06/4.09 | all_18_3) = 0) | ( ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3, % 22.06/4.09 | all_18_2) = all_31_0) | ( ~ (all_31_1 = 0) & % 22.06/4.09 | convergent_lines(all_18_3, all_18_2) = all_31_1) % 22.06/4.09 | % 22.06/4.09 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1, all_32_2, % 22.06/4.09 | all_32_3 gives: % 22.06/4.09 | (35) (all_32_2 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) % 22.06/4.09 | = 0) | (all_32_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.06/4.09 | all_18_3) = 0) | ( ~ (all_32_0 = 0) & unorthogonal_lines(all_18_3, % 22.06/4.09 | all_18_3) = all_32_0) | ( ~ (all_32_1 = 0) & % 22.06/4.09 | convergent_lines(all_18_3, all_18_3) = all_32_1) % 22.06/4.09 | % 22.06/4.09 | BETA: splitting (32) gives: % 22.06/4.09 | % 22.06/4.09 | Case 1: % 22.06/4.09 | | % 22.06/4.10 | | (36) all_28_1 = 0 & all_28_2 = 0 & unorthogonal_lines(all_18_4, all_18_2) % 22.06/4.10 | | = 0 & convergent_lines(all_18_4, all_18_2) = 0 % 22.06/4.10 | | % 22.06/4.10 | | ALPHA: (36) implies: % 22.06/4.10 | | (37) convergent_lines(all_18_4, all_18_2) = 0 % 22.06/4.10 | | % 22.06/4.10 | | GROUND_INST: instantiating (14) with all_18_0, 0, all_18_2, all_18_4, % 22.06/4.10 | | simplifying with (23), (37) gives: % 22.06/4.10 | | (38) all_18_0 = 0 % 22.06/4.10 | | % 22.06/4.10 | | REDUCE: (18), (38) imply: % 22.06/4.10 | | (39) $false % 22.06/4.10 | | % 22.06/4.10 | | CLOSE: (39) is inconsistent. % 22.06/4.10 | | % 22.06/4.10 | Case 2: % 22.06/4.10 | | % 22.06/4.10 | | (40) (all_28_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.06/4.10 | | all_18_3) = 0) | ( ~ (all_28_0 = 0) & % 22.06/4.10 | | unorthogonal_lines(all_18_3, all_18_2) = all_28_0) % 22.06/4.10 | | % 22.06/4.10 | | BETA: splitting (40) gives: % 22.06/4.10 | | % 22.06/4.10 | | Case 1: % 22.06/4.10 | | | % 22.06/4.10 | | | (41) all_28_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.06/4.10 | | | all_18_3) = 0 % 22.06/4.10 | | | % 22.06/4.10 | | | ALPHA: (41) implies: % 22.06/4.10 | | | (42) all_18_1 = 0 % 22.06/4.10 | | | % 22.06/4.10 | | | REDUCE: (17), (42) imply: % 22.06/4.10 | | | (43) $false % 22.06/4.10 | | | % 22.06/4.10 | | | CLOSE: (43) is inconsistent. % 22.06/4.10 | | | % 22.06/4.10 | | Case 2: % 22.06/4.10 | | | % 22.24/4.10 | | | (44) ~ (all_28_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = % 22.24/4.10 | | | all_28_0 % 22.24/4.10 | | | % 22.24/4.10 | | | ALPHA: (44) implies: % 22.24/4.10 | | | (45) unorthogonal_lines(all_18_3, all_18_2) = all_28_0 % 22.24/4.10 | | | % 22.24/4.10 | | | BETA: splitting (27) gives: % 22.24/4.10 | | | % 22.24/4.10 | | | Case 1: % 22.24/4.10 | | | | % 22.24/4.10 | | | | (46) unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.24/4.10 | | | | % 22.24/4.10 | | | | BETA: splitting (33) gives: % 22.24/4.10 | | | | % 22.24/4.10 | | | | Case 1: % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | (47) all_29_1 = 0 & all_18_0 = 0 & unorthogonal_lines(all_18_4, % 22.24/4.10 | | | | | all_18_2) = 0 % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | ALPHA: (47) implies: % 22.24/4.10 | | | | | (48) all_18_0 = 0 % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | REDUCE: (18), (48) imply: % 22.24/4.10 | | | | | (49) $false % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | CLOSE: (49) is inconsistent. % 22.24/4.10 | | | | | % 22.24/4.10 | | | | Case 2: % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | (50) (all_29_2 = 0 & all_29_3 = 0 & unorthogonal_lines(all_18_4, % 22.24/4.10 | | | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0) % 22.24/4.10 | | | | | | ( ~ (all_29_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) % 22.24/4.10 | | | | | = all_29_0) % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | BETA: splitting (50) gives: % 22.24/4.10 | | | | | % 22.24/4.10 | | | | | Case 1: % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | (51) all_29_2 = 0 & all_29_3 = 0 & unorthogonal_lines(all_18_4, % 22.24/4.10 | | | | | | all_18_3) = 0 & convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | ALPHA: (51) implies: % 22.24/4.10 | | | | | | (52) convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | REF_CLOSE: (14), (17), (22), (52) are inconsistent by sub-proof #4. % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | Case 2: % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | (53) ~ (all_29_0 = 0) & unorthogonal_lines(all_18_3, all_18_2) = % 22.24/4.10 | | | | | | all_29_0 % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | ALPHA: (53) implies: % 22.24/4.10 | | | | | | (54) ~ (all_29_0 = 0) % 22.24/4.10 | | | | | | (55) unorthogonal_lines(all_18_3, all_18_2) = all_29_0 % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | BETA: splitting (34) gives: % 22.24/4.10 | | | | | | % 22.24/4.10 | | | | | | Case 1: % 22.24/4.10 | | | | | | | % 22.24/4.10 | | | | | | | (56) (all_31_2 = 0 & all_18_0 = 0 & % 22.24/4.10 | | | | | | | unorthogonal_lines(all_18_4, all_18_2) = 0) | (all_31_3 % 22.24/4.10 | | | | | | | = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.24/4.10 | | | | | | | all_18_3) = 0) % 22.24/4.10 | | | | | | | % 22.24/4.10 | | | | | | | BETA: splitting (56) gives: % 22.24/4.10 | | | | | | | % 22.24/4.10 | | | | | | | Case 1: % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | (57) all_31_2 = 0 & all_18_0 = 0 & % 22.24/4.10 | | | | | | | | unorthogonal_lines(all_18_4, all_18_2) = 0 % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | ALPHA: (57) implies: % 22.24/4.10 | | | | | | | | (58) all_18_0 = 0 % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | REDUCE: (18), (58) imply: % 22.24/4.10 | | | | | | | | (59) $false % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | CLOSE: (59) is inconsistent. % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | Case 2: % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | (60) all_31_3 = 0 & all_18_1 = 0 & % 22.24/4.10 | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | ALPHA: (60) implies: % 22.24/4.10 | | | | | | | | (61) all_18_1 = 0 % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | REDUCE: (17), (61) imply: % 22.24/4.10 | | | | | | | | (62) $false % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | | CLOSE: (62) is inconsistent. % 22.24/4.10 | | | | | | | | % 22.24/4.10 | | | | | | | End of split % 22.24/4.10 | | | | | | | % 22.24/4.10 | | | | | | Case 2: % 22.24/4.10 | | | | | | | % 22.24/4.10 | | | | | | | (63) ( ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.10 | | | | | | | all_18_2) = all_31_0) | ( ~ (all_31_1 = 0) & % 22.24/4.11 | | | | | | | convergent_lines(all_18_3, all_18_2) = all_31_1) % 22.24/4.11 | | | | | | | % 22.24/4.11 | | | | | | | BETA: splitting (63) gives: % 22.24/4.11 | | | | | | | % 22.24/4.11 | | | | | | | Case 1: % 22.24/4.11 | | | | | | | | % 22.24/4.11 | | | | | | | | (64) ~ (all_31_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.11 | | | | | | | | all_18_2) = all_31_0 % 22.24/4.11 | | | | | | | | % 22.24/4.11 | | | | | | | | ALPHA: (64) implies: % 22.24/4.11 | | | | | | | | (65) unorthogonal_lines(all_18_3, all_18_2) = all_31_0 % 22.24/4.11 | | | | | | | | % 22.24/4.11 | | | | | | | | BETA: splitting (28) gives: % 22.24/4.11 | | | | | | | | % 22.24/4.11 | | | | | | | | Case 1: % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | (66) all_18_0 = 0 % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | REDUCE: (18), (66) imply: % 22.24/4.11 | | | | | | | | | (67) $false % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | CLOSE: (67) is inconsistent. % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | Case 2: % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & % 22.24/4.11 | | | | | | | | | convergent_lines(all_18_4, all_18_4) = v0) % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | DELTA: instantiating (68) with fresh symbol all_57_0 gives: % 22.24/4.11 | | | | | | | | | (69) ~ (all_57_0 = 0) & convergent_lines(all_18_4, % 22.24/4.11 | | | | | | | | | all_18_4) = all_57_0 % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | ALPHA: (69) implies: % 22.24/4.11 | | | | | | | | | (70) convergent_lines(all_18_4, all_18_4) = all_57_0 % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | BETA: splitting (25) gives: % 22.24/4.11 | | | | | | | | | % 22.24/4.11 | | | | | | | | | Case 1: % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | (71) all_18_1 = 0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | REDUCE: (17), (71) imply: % 22.24/4.11 | | | | | | | | | | (72) $false % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | CLOSE: (72) is inconsistent. % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | Case 2: % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | DELTA: instantiating (68) with fresh symbol all_62_0 gives: % 22.24/4.11 | | | | | | | | | | (73) ~ (all_62_0 = 0) & convergent_lines(all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_4) = all_62_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | ALPHA: (73) implies: % 22.24/4.11 | | | | | | | | | | (74) ~ (all_62_0 = 0) % 22.24/4.11 | | | | | | | | | | (75) convergent_lines(all_18_4, all_18_4) = all_62_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (14) with all_57_0, all_62_0, % 22.24/4.11 | | | | | | | | | | all_18_4, all_18_4, simplifying with (70), (75) % 22.24/4.11 | | | | | | | | | | gives: % 22.24/4.11 | | | | | | | | | | (76) all_62_0 = all_57_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (15) with all_29_0, all_31_0, % 22.24/4.11 | | | | | | | | | | all_18_2, all_18_3, simplifying with (55), (65) % 22.24/4.11 | | | | | | | | | | gives: % 22.24/4.11 | | | | | | | | | | (77) all_31_0 = all_29_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (15) with all_28_0, all_31_0, % 22.24/4.11 | | | | | | | | | | all_18_2, all_18_3, simplifying with (45), (65) % 22.24/4.11 | | | | | | | | | | gives: % 22.24/4.11 | | | | | | | | | | (78) all_31_0 = all_28_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | COMBINE_EQS: (77), (78) imply: % 22.24/4.11 | | | | | | | | | | (79) all_29_0 = all_28_0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | REDUCE: (74), (76) imply: % 22.24/4.11 | | | | | | | | | | (80) ~ (all_57_0 = 0) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | REDUCE: (54), (79) imply: % 22.24/4.11 | | | | | | | | | | (81) ~ (all_28_0 = 0) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (8) with all_18_4, all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_4, all_18_1, all_57_0, simplifying with % 22.24/4.11 | | | | | | | | | | (19), (20), (22), (70) gives: % 22.24/4.11 | | | | | | | | | | (82) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 22.24/4.11 | | | | | | | | | | int] : ((v1 = 0 & all_57_0 = 0 & % 22.24/4.11 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | % 22.24/4.11 | | | | | | | | | | (v0 = 0 & all_18_1 = 0 & % 22.24/4.11 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) | ( % 22.24/4.11 | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_4) = v3) | ( ~ (v2 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = v2)) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (8) with all_18_4, all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_4, all_57_0, all_57_0, simplifying with % 22.24/4.11 | | | | | | | | | | (19), (70) gives: % 22.24/4.11 | | | | | | | | | | (83) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 22.24/4.11 | | | | | | | | | | int] : ((v1 = 0 & all_57_0 = 0 & % 22.24/4.11 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | % 22.24/4.11 | | | | | | | | | | (v0 = 0 & all_57_0 = 0 & % 22.24/4.11 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | ( % 22.24/4.11 | | | | | | | | | | ~ (v3 = 0) & unorthogonal_lines(all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_4) = v3) | ( ~ (v2 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_4, all_18_4) = v2)) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (3) with all_18_4, all_18_4, % 22.24/4.11 | | | | | | | | | | all_57_0, simplifying with (19), (70) gives: % 22.24/4.11 | | | | | | | | | | (84) all_57_0 = 0 | unorthogonal_lines(all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_4) = 0 % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (11) with all_18_4, all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3, 0, 0, simplifying with (19), (20), (46) % 22.24/4.11 | | | | | | | | | | gives: % 22.24/4.11 | | | | | | | | | | (85) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 22.24/4.11 | | | | | | | | | | int] : ((v1 = 0 & convergent_lines(all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_3) = 0) | (v0 = 0 & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.24/4.11 | | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3) = v3) | ( ~ (v2 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = v2)) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (10) with all_18_4, all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3, all_18_1, 0, simplifying with (19), % 22.24/4.11 | | | | | | | | | | (20), (22), (46) gives: % 22.24/4.11 | | | | | | | | | | (86) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 22.24/4.11 | | | | | | | | | | int] : ((v1 = 0 & convergent_lines(all_18_4, % 22.24/4.11 | | | | | | | | | | all_18_3) = 0) | (v0 = 0 & all_18_1 = 0) | ( ~ % 22.24/4.11 | | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3) = v3) | ( ~ (v2 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = v2)) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (9) with all_18_4, all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3, 0, all_18_1, simplifying with (19), % 22.24/4.11 | | | | | | | | | | (20), (22), (46) gives: % 22.24/4.11 | | | | | | | | | | (87) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 22.24/4.11 | | | | | | | | | | int] : ((v1 = 0 & all_18_1 = 0) | (v0 = 0 & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.24/4.11 | | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.11 | | | | | | | | | | all_18_3) = v3) | ( ~ (v2 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = v2)) % 22.24/4.11 | | | | | | | | | | % 22.24/4.11 | | | | | | | | | | GROUND_INST: instantiating (13) with all_18_3, all_18_2, % 22.24/4.11 | | | | | | | | | | all_18_2, all_28_0, all_28_0, simplifying with % 22.24/4.11 | | | | | | | | | | (20), (21), (45) gives: % 22.24/4.11 | | | | | | | | | | (88) all_28_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.24/4.11 | | | | | | | | | | convergent_lines(all_18_2, all_18_2) = v0) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | GROUND_INST: instantiating (12) with all_18_3, all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_2, all_28_0, simplifying with (20), (21), % 22.24/4.12 | | | | | | | | | | (24), (45) gives: % 22.24/4.12 | | | | | | | | | | (89) all_28_0 = 0 | unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | DELTA: instantiating (87) with fresh symbols all_74_0, % 22.24/4.12 | | | | | | | | | | all_74_1, all_74_2, all_74_3 gives: % 22.24/4.12 | | | | | | | | | | (90) (all_74_2 = 0 & all_18_1 = 0) | (all_74_3 = 0 & % 22.24/4.12 | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.24/4.12 | | | | | | | | | | (all_74_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_3) = all_74_0) | ( ~ (all_74_1 = 0) & % 22.24/4.12 | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_74_1) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | DELTA: instantiating (85) with fresh symbols all_75_0, % 22.24/4.12 | | | | | | | | | | all_75_1, all_75_2, all_75_3 gives: % 22.24/4.12 | | | | | | | | | | (91) (all_75_2 = 0 & convergent_lines(all_18_4, all_18_3) % 22.24/4.12 | | | | | | | | | | = 0) | (all_75_3 = 0 & convergent_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | all_18_3) = 0) | ( ~ (all_75_0 = 0) & % 22.24/4.12 | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_3) = all_75_0) % 22.24/4.12 | | | | | | | | | | | ( ~ (all_75_1 = 0) & convergent_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_3) = all_75_1) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | DELTA: instantiating (86) with fresh symbols all_83_0, % 22.24/4.12 | | | | | | | | | | all_83_1, all_83_2, all_83_3 gives: % 22.24/4.12 | | | | | | | | | | (92) (all_83_2 = 0 & convergent_lines(all_18_4, all_18_3) % 22.24/4.12 | | | | | | | | | | = 0) | (all_83_3 = 0 & all_18_1 = 0) | ( ~ % 22.24/4.12 | | | | | | | | | | (all_83_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_3) = all_83_0) | ( ~ (all_83_1 = 0) & % 22.24/4.12 | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_83_1) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | DELTA: instantiating (83) with fresh symbols all_89_0, % 22.24/4.12 | | | | | | | | | | all_89_1, all_89_2, all_89_3 gives: % 22.24/4.12 | | | | | | | | | | (93) (all_89_2 = 0 & all_57_0 = 0 & % 22.24/4.12 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | % 22.24/4.12 | | | | | | | | | | (all_89_3 = 0 & all_57_0 = 0 & % 22.24/4.12 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | ( ~ % 22.24/4.12 | | | | | | | | | | (all_89_0 = 0) & unorthogonal_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | all_18_4) = all_89_0) | ( ~ (all_89_1 = 0) & % 22.24/4.12 | | | | | | | | | | convergent_lines(all_18_4, all_18_4) = all_89_1) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | DELTA: instantiating (82) with fresh symbols all_91_0, % 22.24/4.12 | | | | | | | | | | all_91_1, all_91_2, all_91_3 gives: % 22.24/4.12 | | | | | | | | | | (94) (all_91_2 = 0 & all_57_0 = 0 & % 22.24/4.12 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | % 22.24/4.12 | | | | | | | | | | (all_91_3 = 0 & all_18_1 = 0 & % 22.24/4.12 | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.24/4.12 | | | | | | | | | | (all_91_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | all_18_4) = all_91_0) | ( ~ (all_91_1 = 0) & % 22.24/4.12 | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = all_91_1) % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | BETA: splitting (89) gives: % 22.24/4.12 | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | (95) unorthogonal_lines(all_18_3, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | BETA: splitting (35) gives: % 22.24/4.12 | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | (96) (all_32_2 = 0 & all_18_1 = 0 & % 22.24/4.12 | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) | % 22.24/4.12 | | | | | | | | | | | | (all_32_3 = 0 & all_18_1 = 0 & % 22.24/4.12 | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | BETA: splitting (96) gives: % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | (97) all_32_2 = 0 & all_18_1 = 0 & % 22.24/4.12 | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | ALPHA: (97) implies: % 22.24/4.12 | | | | | | | | | | | | | (98) all_18_1 = 0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | REDUCE: (17), (98) imply: % 22.24/4.12 | | | | | | | | | | | | | (99) $false % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | CLOSE: (99) is inconsistent. % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | (100) all_32_3 = 0 & all_18_1 = 0 & % 22.24/4.12 | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | ALPHA: (100) implies: % 22.24/4.12 | | | | | | | | | | | | | (101) all_18_1 = 0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | REDUCE: (17), (101) imply: % 22.24/4.12 | | | | | | | | | | | | | (102) $false % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | CLOSE: (102) is inconsistent. % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | End of split % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | (103) ( ~ (all_32_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | all_18_3) = all_32_0) | ( ~ (all_32_1 = 0) & % 22.24/4.12 | | | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_32_1) % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | BETA: splitting (103) gives: % 22.24/4.12 | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | (104) ~ (all_32_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | | all_18_3) = all_32_0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | ALPHA: (104) implies: % 22.24/4.12 | | | | | | | | | | | | | (105) ~ (all_32_0 = 0) % 22.24/4.12 | | | | | | | | | | | | | (106) unorthogonal_lines(all_18_3, all_18_3) = all_32_0 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | REF_CLOSE: (15), (95), (105), (106) are inconsistent by % 22.24/4.12 | | | | | | | | | | | | | sub-proof #3. % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | (107) ~ (all_32_1 = 0) & convergent_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | | all_18_3) = all_32_1 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | ALPHA: (107) implies: % 22.24/4.12 | | | | | | | | | | | | | (108) convergent_lines(all_18_3, all_18_3) = all_32_1 % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | BETA: splitting (84) gives: % 22.24/4.12 | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | (109) unorthogonal_lines(all_18_4, all_18_4) = 0 % 22.24/4.12 | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | BETA: splitting (90) gives: % 22.24/4.12 | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | (110) (all_74_2 = 0 & all_18_1 = 0) | (all_74_3 = 0 & % 22.24/4.12 | | | | | | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | (111) all_74_2 = 0 & all_18_1 = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | ALPHA: (111) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | (112) all_18_1 = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | REDUCE: (17), (112) imply: % 22.24/4.12 | | | | | | | | | | | | | | | | (113) $false % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | (114) all_74_3 = 0 & convergent_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | ALPHA: (114) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | (115) convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (115) are inconsistent by % 22.24/4.12 | | | | | | | | | | | | | | | | sub-proof #4. % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | End of split % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | (116) ( ~ (all_74_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | | | | all_18_3) = all_74_0) | ( ~ (all_74_1 = 0) & % 22.24/4.12 | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_74_1) % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 22.24/4.12 | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | (117) ~ (all_74_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | | | | | all_18_3) = all_74_0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | ALPHA: (117) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | (118) ~ (all_74_0 = 0) % 22.24/4.12 | | | | | | | | | | | | | | | | (119) unorthogonal_lines(all_18_3, all_18_3) = all_74_0 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (95), (118), (119) are inconsistent by % 22.24/4.12 | | | | | | | | | | | | | | | | sub-proof #2. % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | (120) ~ (all_74_1 = 0) & convergent_lines(all_18_3, % 22.24/4.12 | | | | | | | | | | | | | | | | all_18_3) = all_74_1 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | ALPHA: (120) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | (121) ~ (all_74_1 = 0) % 22.24/4.12 | | | | | | | | | | | | | | | | (122) convergent_lines(all_18_3, all_18_3) = all_74_1 % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 22.24/4.12 | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | (123) (all_75_2 = 0 & convergent_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | | | | | | | | all_18_3) = 0) | (all_75_3 = 0 & % 22.24/4.12 | | | | | | | | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) % 22.24/4.12 | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 22.24/4.12 | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | (124) all_75_2 = 0 & convergent_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (124) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | | | (125) convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (125) are inconsistent by % 22.24/4.12 | | | | | | | | | | | | | | | | | | sub-proof #4. % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | (126) all_75_3 = 0 & convergent_lines(all_18_4, % 22.24/4.12 | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 22.24/4.12 | | | | | | | | | | | | | | | | | | (127) convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (127) are inconsistent by % 22.24/4.12 | | | | | | | | | | | | | | | | | | sub-proof #4. % 22.24/4.12 | | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | | End of split % 22.24/4.12 | | | | | | | | | | | | | | | | | % 22.24/4.12 | | | | | | | | | | | | | | | | Case 2: % 22.24/4.12 | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | (128) ( ~ (all_75_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | all_18_3) = all_75_0) | ( ~ (all_75_1 = 0) & % 22.24/4.13 | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_75_1) % 22.24/4.13 | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | (129) ~ (all_75_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | all_18_3) = all_75_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | ALPHA: (129) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | (130) ~ (all_75_0 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | (131) unorthogonal_lines(all_18_3, all_18_3) = all_75_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_75_0, all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | all_18_3, simplifying with (95), (131) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | (132) all_75_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | REDUCE: (130), (132) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | (133) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | (134) ~ (all_75_1 = 0) & convergent_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | all_18_3) = all_75_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | ALPHA: (134) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | (135) convergent_lines(all_18_3, all_18_3) = all_75_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (136) all_28_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | REDUCE: (81), (136) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (137) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | CLOSE: (137) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (138) ? [v0: int] : ( ~ (v0 = 0) & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_2, all_18_2) = v0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (138) with fresh symbol all_118_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (139) ~ (all_118_0 = 0) & convergent_lines(all_18_2, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | all_18_2) = all_118_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (140) ~ (all_118_0 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | (141) convergent_lines(all_18_2, all_18_2) = all_118_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | (142) (all_89_2 = 0 & all_57_0 = 0 & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | (all_89_3 = 0 & all_57_0 = 0 & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (143) all_89_2 = 0 & all_57_0 = 0 & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (144) all_57_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (144) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (145) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (146) all_89_3 = 0 & all_57_0 = 0 & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_4) = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (147) all_57_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (147) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (148) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | End of split % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | (149) ( ~ (all_89_0 = 0) & unorthogonal_lines(all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | all_18_4) = all_89_0) | ( ~ (all_89_1 = 0) & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_4, all_18_4) = all_89_1) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (150) ~ (all_89_0 = 0) & unorthogonal_lines(all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | all_18_4) = all_89_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_89_0 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (152) unorthogonal_lines(all_18_4, all_18_4) = all_89_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_89_0, all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | all_18_4, simplifying with (109), (152) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (153) all_89_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (153) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (154) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (155) ~ (all_89_1 = 0) & convergent_lines(all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | all_18_4) = all_89_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (156) ~ (all_89_1 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | (157) convergent_lines(all_18_4, all_18_4) = all_89_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | (158) (all_83_2 = 0 & convergent_lines(all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0) | (all_83_3 = 0 & all_18_1 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (159) all_83_2 = 0 & convergent_lines(all_18_4, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (160) convergent_lines(all_18_4, all_18_3) = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (160) are inconsistent by % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (161) all_83_3 = 0 & all_18_1 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (162) all_18_1 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (162) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (163) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | End of split % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | (164) ( ~ (all_83_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_83_0) | ( ~ (all_83_1 = 0) & % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_3) = all_83_1) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (165) ~ (all_83_0 = 0) & unorthogonal_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_83_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (166) ~ (all_83_0 = 0) % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (167) unorthogonal_lines(all_18_3, all_18_3) = all_83_0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_83_0, all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, simplifying with (95), (167) gives: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (168) all_83_0 = 0 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (168) imply: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (169) $false % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (170) ~ (all_83_1 = 0) & convergent_lines(all_18_3, % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_83_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | (171) convergent_lines(all_18_3, all_18_3) = all_83_1 % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.24/4.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_57_0, all_89_1, % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_4, all_18_4, simplifying with (70), (157) % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (172) all_89_1 = all_57_0 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_32_1, all_75_1, % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_18_3, simplifying with (108), (135) % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (173) all_75_1 = all_32_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_75_1, all_83_1, % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_18_3, simplifying with (135), (171) % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (174) all_83_1 = all_75_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_74_1, all_83_1, % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_18_3, simplifying with (122), (171) % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (175) all_83_1 = all_74_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (175) imply: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (176) all_75_1 = all_74_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (176) implies: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (177) all_75_1 = all_74_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (177) imply: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (178) all_74_1 = all_32_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies: % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | (179) all_74_1 = all_32_1 % 22.41/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (179) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_32_1 = 0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_18_3, all_18_2, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_32_1, simplifying with (20), (21), % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (24), (108) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (181) all_32_1 = 0 | convergent_lines(all_18_2, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_18_3, all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_32_1, all_18_1, simplifying with % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (22), (108) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (182) all_32_1 = 0 | all_18_1 = 0 | ? [v0: int] : ( ~ % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_18_3, all_18_4) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | = v0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_18_3, all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_32_1, simplifying with (19), (20), % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (46), (108) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (183) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v2 = 0 & all_32_1 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_3) = 0) | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & v0 = 0 & unorthogonal_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0 & convergent_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0) | ( ~ (v3 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = v3)) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_18_2, all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_2, all_118_0, all_18_0, simplifying with % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (19), (21), (23), (141) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (184) all_118_0 = 0 | all_18_0 = 0 | ? [v0: int] : ( ~ % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_18_2, all_18_4) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | = v0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_18_4, all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4, all_18_1, 0, simplifying with (19), % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (109) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (185) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v1 = 0 & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0) | (v0 = 0 & all_18_1 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = v3) | ( ~ (v2 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = v2)) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_18_3, all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3, 0, simplifying with (19), (20), (46), % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (95) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (186) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v2 = 0 & convergent_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0) | (v1 = 0 & v0 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0) | ( % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | ~ (v3 = 0) & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = v3)) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (186) with fresh symbols all_142_0, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_142_1, all_142_2, all_142_3 gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (187) (all_142_1 = 0 & convergent_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0) | (all_142_2 = 0 & all_142_3 = % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | 0 & unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0) | ( ~ % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (all_142_0 = 0) & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_142_0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_145_0, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_145_1, all_145_2, all_145_3 gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (188) (all_145_2 = 0 & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0) | (all_145_3 = 0 & all_18_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | & unorthogonal_lines(all_18_4, all_18_3) = 0) | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_145_0 = 0) & unorthogonal_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = all_145_0) | ( ~ (all_145_1 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_145_1) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_149_0, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_149_1, all_149_2, all_149_3 gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (189) (all_149_1 = 0 & all_32_1 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_3) = 0) | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (all_149_2 = 0 & all_149_3 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0) | ( ~ % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | (all_149_0 = 0) & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_149_0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | (190) convergent_lines(all_18_2, all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_118_0 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (191) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (192) $false % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_18_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_2, all_18_4) = v0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_32_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (194) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (195) $false % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_18_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = v0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_18_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (197) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) $false % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) ? [v0: int] : ( ~ (v0 = 0) & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = v0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (199) with fresh symbol all_237_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (all_237_0 = 0) & convergent_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = all_237_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (all_237_0 = 0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) convergent_lines(all_18_3, all_18_4) = all_237_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_149_1 = 0 & all_32_1 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_32_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (204) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) $false % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) (all_149_2 = 0 & all_149_3 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0) | ( ~ % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_149_0 = 0) & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_149_0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_149_2 = 0 & all_149_3 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) unorthogonal_lines(all_18_3, all_18_4) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (70), (80), (94), (188), (202), % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209) are inconsistent by sub-proof #1. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) ~ (all_149_0 = 0) & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_149_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) convergent_lines(all_18_4, all_18_3) = all_149_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_142_1 = 0 & convergent_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) convergent_lines(all_18_3, all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_74_2 = 0 & all_18_1 = 0) | (all_74_3 = 0 & % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_4, all_18_3) = 0) % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_74_2 = 0 & all_18_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_18_1 = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (216) imply: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) $false % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_74_3 = 0 & convergent_lines(all_18_4, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) convergent_lines(all_18_4, all_18_3) = 0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (219) are inconsistent by % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_74_0 = 0) & unorthogonal_lines(all_18_3, % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_74_0 % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 22.41/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_74_0 = 0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) unorthogonal_lines(all_18_3, all_18_3) = all_74_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (95), (221), (222) are inconsistent by % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_32_2 = 0 & all_18_1 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_32_3 = 0 & all_18_1 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_32_2 = 0 & all_18_1 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_18_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (225) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_32_3 = 0 & all_18_1 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_4, all_18_3) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_18_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (228) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_32_0 = 0) & unorthogonal_lines(all_18_3, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_32_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_32_0 = 0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) unorthogonal_lines(all_18_3, all_18_3) = all_32_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (95), (231), (232) are inconsistent by % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_75_1, all_18_3, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3, simplifying with (135), (213) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_75_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (233) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_74_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (234) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_32_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (235) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) (all_142_2 = 0 & all_142_3 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0) | ( ~ % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_142_0 = 0) & convergent_lines(all_18_4, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_142_0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_142_2 = 0 & all_142_3 = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_18_3, all_18_4) = 0 & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) unorthogonal_lines(all_18_3, all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (70), (80), (94), (188), (202), % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240) are inconsistent by sub-proof #1. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) ~ (all_142_0 = 0) & convergent_lines(all_18_4, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3) = all_142_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) ~ (all_142_0 = 0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) convergent_lines(all_18_4, all_18_3) = all_142_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_18_0 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (244) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) ? [v0: int] : ( ~ (v0 = 0) & % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_18_2, all_18_4) = v0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (246) with fresh symbol all_263_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_263_0 = 0) & convergent_lines(all_18_2, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = all_263_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_263_0 = 0) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) convergent_lines(all_18_2, all_18_4) = all_263_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_18_1, all_149_0, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_18_4, simplifying with (22), (211) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_149_0 = all_18_1 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_142_0, all_149_0, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_3, all_18_4, simplifying with (211), (243) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_149_0 = all_142_0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (251) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_142_0 = all_18_1 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_142_0 = all_18_1 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_18_3, all_18_4, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_237_0, simplifying with (19), (20), (202) % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_237_0 = 0 | unorthogonal_lines(all_18_3, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_18_2, all_18_3, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_4, all_263_0, simplifying with (19), (20), % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (21), (190), (249) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_263_0 = 0 | convergent_lines(all_18_3, % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) unorthogonal_lines(all_18_3, all_18_4) = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (70), (80), (94), (188), (202), % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256), (257) are inconsistent by sub-proof #1. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_237_0 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (258) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_263_0 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (260) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_32_1 = 0 % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (262) imply: % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | (263) $false % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | (264) all_57_0 = 0 % 22.41/4.15 | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | REDUCE: (80), (264) imply: % 22.41/4.15 | | | | | | | | | | | | | | (265) $false % 22.41/4.15 | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 22.41/4.15 | | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | (266) all_28_0 = 0 % 22.41/4.15 | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | REDUCE: (81), (266) imply: % 22.41/4.15 | | | | | | | | | | | (267) $false % 22.41/4.15 | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | | CLOSE: (267) is inconsistent. % 22.41/4.15 | | | | | | | | | | | % 22.41/4.15 | | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | | % 22.41/4.15 | | | | | | | | | End of split % 22.41/4.15 | | | | | | | | | % 22.41/4.15 | | | | | | | | End of split % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | Case 2: % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | | (268) ~ (all_31_1 = 0) & convergent_lines(all_18_3, % 22.41/4.15 | | | | | | | | all_18_2) = all_31_1 % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | | ALPHA: (268) implies: % 22.41/4.15 | | | | | | | | (269) ~ (all_31_1 = 0) % 22.41/4.15 | | | | | | | | (270) convergent_lines(all_18_3, all_18_2) = all_31_1 % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_31_1, all_18_2, % 22.41/4.15 | | | | | | | | all_18_3, simplifying with (24), (270) gives: % 22.41/4.15 | | | | | | | | (271) all_31_1 = 0 % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | | REDUCE: (269), (271) imply: % 22.41/4.15 | | | | | | | | (272) $false % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | | CLOSE: (272) is inconsistent. % 22.41/4.15 | | | | | | | | % 22.41/4.15 | | | | | | | End of split % 22.41/4.15 | | | | | | | % 22.41/4.15 | | | | | | End of split % 22.41/4.15 | | | | | | % 22.41/4.15 | | | | | End of split % 22.41/4.15 | | | | | % 22.41/4.15 | | | | End of split % 22.41/4.15 | | | | % 22.41/4.15 | | | Case 2: % 22.41/4.15 | | | | % 22.41/4.15 | | | | (273) all_18_1 = 0 % 22.41/4.15 | | | | % 22.41/4.16 | | | | REDUCE: (17), (273) imply: % 22.41/4.16 | | | | (274) $false % 22.41/4.16 | | | | % 22.41/4.16 | | | | CLOSE: (274) is inconsistent. % 22.41/4.16 | | | | % 22.41/4.16 | | | End of split % 22.41/4.16 | | | % 22.41/4.16 | | End of split % 22.41/4.16 | | % 22.41/4.16 | End of split % 22.41/4.16 | % 22.41/4.16 End of proof % 22.41/4.16 % 22.41/4.16 Sub-proof #1 shows that the following formulas are inconsistent: % 22.41/4.16 ---------------------------------------------------------------- % 22.41/4.16 (1) unorthogonal_lines(all_18_3, all_18_4) = 0 % 22.41/4.16 (2) ~ (all_57_0 = 0) % 22.41/4.16 (3) (all_145_2 = 0 & convergent_lines(all_18_4, all_18_4) = 0) | (all_145_3 = % 22.41/4.16 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, all_18_3) = 0) | ( ~ % 22.41/4.16 (all_145_0 = 0) & unorthogonal_lines(all_18_3, all_18_4) = all_145_0) | % 22.41/4.16 ( ~ (all_145_1 = 0) & convergent_lines(all_18_3, all_18_4) = all_145_1) % 22.41/4.16 (4) convergent_lines(all_18_3, all_18_4) = all_237_0 % 22.41/4.16 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.41/4.16 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.41/4.16 (unorthogonal_lines(v3, v2) = v0)) % 22.41/4.16 (6) convergent_lines(all_18_4, all_18_4) = all_57_0 % 22.41/4.16 (7) convergent_lines(all_18_3, all_18_4) = 0 % 22.41/4.16 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.41/4.16 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.41/4.16 (convergent_lines(v3, v2) = v0)) % 22.41/4.16 (9) (all_91_2 = 0 & all_57_0 = 0 & unorthogonal_lines(all_18_4, all_18_4) = % 22.41/4.16 0) | (all_91_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 all_18_3) = 0) | ( ~ (all_91_0 = 0) & unorthogonal_lines(all_18_3, % 22.41/4.16 all_18_4) = all_91_0) | ( ~ (all_91_1 = 0) & % 22.41/4.16 convergent_lines(all_18_3, all_18_4) = all_91_1) % 22.41/4.16 (10) ~ (all_18_1 = 0) % 22.41/4.16 % 22.41/4.16 Begin of proof % 22.41/4.16 | % 22.41/4.16 | BETA: splitting (3) gives: % 22.41/4.16 | % 22.41/4.16 | Case 1: % 22.41/4.16 | | % 22.41/4.16 | | (11) (all_145_2 = 0 & convergent_lines(all_18_4, all_18_4) = 0) | % 22.41/4.16 | | (all_145_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 | | all_18_3) = 0) % 22.41/4.16 | | % 22.41/4.16 | | BETA: splitting (11) gives: % 22.41/4.16 | | % 22.41/4.16 | | Case 1: % 22.41/4.16 | | | % 22.41/4.16 | | | (12) all_145_2 = 0 & convergent_lines(all_18_4, all_18_4) = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | ALPHA: (12) implies: % 22.41/4.16 | | | (13) convergent_lines(all_18_4, all_18_4) = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | GROUND_INST: instantiating (8) with all_57_0, 0, all_18_4, all_18_4, % 22.41/4.16 | | | simplifying with (6), (13) gives: % 22.41/4.16 | | | (14) all_57_0 = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | REDUCE: (2), (14) imply: % 22.41/4.16 | | | (15) $false % 22.41/4.16 | | | % 22.41/4.16 | | | CLOSE: (15) is inconsistent. % 22.41/4.16 | | | % 22.41/4.16 | | Case 2: % 22.41/4.16 | | | % 22.41/4.16 | | | (16) all_145_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 | | | all_18_3) = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | ALPHA: (16) implies: % 22.41/4.16 | | | (17) all_18_1 = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | REDUCE: (10), (17) imply: % 22.41/4.16 | | | (18) $false % 22.41/4.16 | | | % 22.41/4.16 | | | CLOSE: (18) is inconsistent. % 22.41/4.16 | | | % 22.41/4.16 | | End of split % 22.41/4.16 | | % 22.41/4.16 | Case 2: % 22.41/4.16 | | % 22.41/4.16 | | (19) ( ~ (all_145_0 = 0) & unorthogonal_lines(all_18_3, all_18_4) = % 22.41/4.16 | | all_145_0) | ( ~ (all_145_1 = 0) & convergent_lines(all_18_3, % 22.41/4.16 | | all_18_4) = all_145_1) % 22.41/4.16 | | % 22.41/4.16 | | BETA: splitting (19) gives: % 22.41/4.16 | | % 22.41/4.16 | | Case 1: % 22.41/4.16 | | | % 22.41/4.16 | | | (20) ~ (all_145_0 = 0) & unorthogonal_lines(all_18_3, all_18_4) = % 22.41/4.16 | | | all_145_0 % 22.41/4.16 | | | % 22.41/4.16 | | | ALPHA: (20) implies: % 22.41/4.16 | | | (21) ~ (all_145_0 = 0) % 22.41/4.16 | | | (22) unorthogonal_lines(all_18_3, all_18_4) = all_145_0 % 22.41/4.16 | | | % 22.41/4.16 | | | GROUND_INST: instantiating (5) with 0, all_145_0, all_18_4, all_18_3, % 22.41/4.16 | | | simplifying with (1), (22) gives: % 22.41/4.16 | | | (23) all_145_0 = 0 % 22.41/4.16 | | | % 22.41/4.16 | | | REDUCE: (21), (23) imply: % 22.41/4.16 | | | (24) $false % 22.41/4.16 | | | % 22.41/4.16 | | | CLOSE: (24) is inconsistent. % 22.41/4.16 | | | % 22.41/4.16 | | Case 2: % 22.41/4.16 | | | % 22.41/4.16 | | | (25) ~ (all_145_1 = 0) & convergent_lines(all_18_3, all_18_4) = % 22.41/4.16 | | | all_145_1 % 22.41/4.16 | | | % 22.41/4.16 | | | ALPHA: (25) implies: % 22.41/4.16 | | | (26) convergent_lines(all_18_3, all_18_4) = all_145_1 % 22.41/4.16 | | | % 22.41/4.16 | | | BETA: splitting (9) gives: % 22.41/4.16 | | | % 22.41/4.16 | | | Case 1: % 22.41/4.16 | | | | % 22.41/4.16 | | | | (27) (all_91_2 = 0 & all_57_0 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 | | | | all_18_4) = 0) | (all_91_3 = 0 & all_18_1 = 0 & % 22.41/4.16 | | | | unorthogonal_lines(all_18_4, all_18_3) = 0) % 22.41/4.16 | | | | % 22.41/4.16 | | | | BETA: splitting (27) gives: % 22.41/4.16 | | | | % 22.41/4.16 | | | | Case 1: % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | (28) all_91_2 = 0 & all_57_0 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 | | | | | all_18_4) = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | ALPHA: (28) implies: % 22.41/4.16 | | | | | (29) all_57_0 = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | REDUCE: (2), (29) imply: % 22.41/4.16 | | | | | (30) $false % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | CLOSE: (30) is inconsistent. % 22.41/4.16 | | | | | % 22.41/4.16 | | | | Case 2: % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | (31) all_91_3 = 0 & all_18_1 = 0 & unorthogonal_lines(all_18_4, % 22.41/4.16 | | | | | all_18_3) = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | ALPHA: (31) implies: % 22.41/4.16 | | | | | (32) all_18_1 = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | REDUCE: (10), (32) imply: % 22.41/4.16 | | | | | (33) $false % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | CLOSE: (33) is inconsistent. % 22.41/4.16 | | | | | % 22.41/4.16 | | | | End of split % 22.41/4.16 | | | | % 22.41/4.16 | | | Case 2: % 22.41/4.16 | | | | % 22.41/4.16 | | | | (34) ( ~ (all_91_0 = 0) & unorthogonal_lines(all_18_3, all_18_4) = % 22.41/4.16 | | | | all_91_0) | ( ~ (all_91_1 = 0) & convergent_lines(all_18_3, % 22.41/4.16 | | | | all_18_4) = all_91_1) % 22.41/4.16 | | | | % 22.41/4.16 | | | | BETA: splitting (34) gives: % 22.41/4.16 | | | | % 22.41/4.16 | | | | Case 1: % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | (35) ~ (all_91_0 = 0) & unorthogonal_lines(all_18_3, all_18_4) = % 22.41/4.16 | | | | | all_91_0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | ALPHA: (35) implies: % 22.41/4.16 | | | | | (36) ~ (all_91_0 = 0) % 22.41/4.16 | | | | | (37) unorthogonal_lines(all_18_3, all_18_4) = all_91_0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | GROUND_INST: instantiating (5) with 0, all_91_0, all_18_4, all_18_3, % 22.41/4.16 | | | | | simplifying with (1), (37) gives: % 22.41/4.16 | | | | | (38) all_91_0 = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | REDUCE: (36), (38) imply: % 22.41/4.16 | | | | | (39) $false % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | CLOSE: (39) is inconsistent. % 22.41/4.16 | | | | | % 22.41/4.16 | | | | Case 2: % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | (40) ~ (all_91_1 = 0) & convergent_lines(all_18_3, all_18_4) = % 22.41/4.16 | | | | | all_91_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | ALPHA: (40) implies: % 22.41/4.16 | | | | | (41) ~ (all_91_1 = 0) % 22.41/4.16 | | | | | (42) convergent_lines(all_18_3, all_18_4) = all_91_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | GROUND_INST: instantiating (8) with 0, all_145_1, all_18_4, all_18_3, % 22.41/4.16 | | | | | simplifying with (7), (26) gives: % 22.41/4.16 | | | | | (43) all_145_1 = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | GROUND_INST: instantiating (8) with all_145_1, all_237_0, all_18_4, % 22.41/4.16 | | | | | all_18_3, simplifying with (4), (26) gives: % 22.41/4.16 | | | | | (44) all_237_0 = all_145_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | GROUND_INST: instantiating (8) with all_91_1, all_237_0, all_18_4, % 22.41/4.16 | | | | | all_18_3, simplifying with (4), (42) gives: % 22.41/4.16 | | | | | (45) all_237_0 = all_91_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | COMBINE_EQS: (44), (45) imply: % 22.41/4.16 | | | | | (46) all_145_1 = all_91_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | SIMP: (46) implies: % 22.41/4.16 | | | | | (47) all_145_1 = all_91_1 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | COMBINE_EQS: (43), (47) imply: % 22.41/4.16 | | | | | (48) all_91_1 = 0 % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | REDUCE: (41), (48) imply: % 22.41/4.16 | | | | | (49) $false % 22.41/4.16 | | | | | % 22.41/4.16 | | | | | CLOSE: (49) is inconsistent. % 22.41/4.16 | | | | | % 22.41/4.16 | | | | End of split % 22.41/4.16 | | | | % 22.41/4.16 | | | End of split % 22.41/4.16 | | | % 22.41/4.16 | | End of split % 22.41/4.16 | | % 22.41/4.16 | End of split % 22.41/4.16 | % 22.41/4.16 End of proof % 22.41/4.16 % 22.41/4.16 Sub-proof #2 shows that the following formulas are inconsistent: % 22.41/4.16 ---------------------------------------------------------------- % 22.41/4.16 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.41/4.16 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.41/4.16 (unorthogonal_lines(v3, v2) = v0)) % 22.41/4.16 (2) unorthogonal_lines(all_18_3, all_18_3) = all_74_0 % 22.41/4.16 (3) unorthogonal_lines(all_18_3, all_18_3) = 0 % 22.41/4.16 (4) ~ (all_74_0 = 0) % 22.41/4.16 % 22.41/4.16 Begin of proof % 22.41/4.16 | % 22.41/4.16 | GROUND_INST: instantiating (1) with 0, all_74_0, all_18_3, all_18_3, % 22.41/4.16 | simplifying with (2), (3) gives: % 22.41/4.16 | (5) all_74_0 = 0 % 22.41/4.16 | % 22.41/4.16 | REDUCE: (4), (5) imply: % 22.41/4.16 | (6) $false % 22.41/4.16 | % 22.41/4.16 | CLOSE: (6) is inconsistent. % 22.41/4.16 | % 22.41/4.16 End of proof % 22.41/4.16 % 22.41/4.16 Sub-proof #3 shows that the following formulas are inconsistent: % 22.41/4.16 ---------------------------------------------------------------- % 22.41/4.16 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.41/4.16 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.41/4.16 (unorthogonal_lines(v3, v2) = v0)) % 22.41/4.16 (2) unorthogonal_lines(all_18_3, all_18_3) = all_32_0 % 22.41/4.16 (3) unorthogonal_lines(all_18_3, all_18_3) = 0 % 22.41/4.16 (4) ~ (all_32_0 = 0) % 22.41/4.16 % 22.41/4.16 Begin of proof % 22.41/4.16 | % 22.41/4.16 | GROUND_INST: instantiating (1) with 0, all_32_0, all_18_3, all_18_3, % 22.41/4.16 | simplifying with (2), (3) gives: % 22.41/4.16 | (5) all_32_0 = 0 % 22.41/4.16 | % 22.41/4.16 | REDUCE: (4), (5) imply: % 22.41/4.16 | (6) $false % 22.41/4.16 | % 22.41/4.16 | CLOSE: (6) is inconsistent. % 22.41/4.16 | % 22.41/4.16 End of proof % 22.41/4.16 % 22.41/4.16 Sub-proof #4 shows that the following formulas are inconsistent: % 22.41/4.16 ---------------------------------------------------------------- % 22.41/4.16 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.41/4.16 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.41/4.16 (convergent_lines(v3, v2) = v0)) % 22.41/4.16 (2) convergent_lines(all_18_4, all_18_3) = all_18_1 % 22.41/4.16 (3) convergent_lines(all_18_4, all_18_3) = 0 % 22.41/4.16 (4) ~ (all_18_1 = 0) % 22.41/4.16 % 22.41/4.16 Begin of proof % 22.41/4.17 | % 22.41/4.17 | GROUND_INST: instantiating (1) with all_18_1, 0, all_18_3, all_18_4, % 22.41/4.17 | simplifying with (2), (3) gives: % 22.41/4.17 | (5) all_18_1 = 0 % 22.41/4.17 | % 22.41/4.17 | REDUCE: (4), (5) imply: % 22.41/4.17 | (6) $false % 22.41/4.17 | % 22.41/4.17 | CLOSE: (6) is inconsistent. % 22.41/4.17 | % 22.41/4.17 End of proof % 22.41/4.17 % SZS output end Proof for theBenchmark % 22.41/4.17 % 22.41/4.17 3585ms %------------------------------------------------------------------------------