%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO217+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 23:22:26 EDT 2023 % Result : Theorem 11.55s 2.31s % Output : Proof 22.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO217+1 : TPTP v8.1.2. Released v3.3.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n013.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 19:33:16 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.61 Running up to 7 provers in parallel. % 0.66/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.39/1.06 Prover 4: Preprocessing ... % 2.39/1.06 Prover 1: Preprocessing ... % 2.97/1.11 Prover 5: Preprocessing ... % 2.97/1.11 Prover 3: Preprocessing ... % 2.97/1.11 Prover 0: Preprocessing ... % 2.97/1.11 Prover 6: Preprocessing ... % 2.97/1.11 Prover 2: Preprocessing ... % 5.13/1.39 Prover 5: Proving ... % 5.13/1.39 Prover 6: Constructing countermodel ... % 5.13/1.40 Prover 2: Proving ... % 5.13/1.40 Prover 3: Constructing countermodel ... % 5.13/1.40 Prover 1: Constructing countermodel ... % 5.41/1.50 Prover 6: gave up % 5.41/1.50 Prover 1: gave up % 5.41/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.41/1.51 Prover 3: gave up % 5.41/1.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.02/1.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.02/1.53 Prover 8: Preprocessing ... % 6.02/1.54 Prover 7: Preprocessing ... % 6.02/1.55 Prover 9: Preprocessing ... % 6.52/1.61 Prover 4: Constructing countermodel ... % 6.52/1.61 Prover 7: Warning: ignoring some quantifiers % 6.52/1.61 Prover 0: Proving ... % 6.52/1.62 Prover 7: Constructing countermodel ... % 6.52/1.63 Prover 8: Warning: ignoring some quantifiers % 6.52/1.64 Prover 8: Constructing countermodel ... % 7.30/1.72 Prover 8: gave up % 7.58/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.58/1.76 Prover 7: gave up % 7.58/1.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.58/1.77 Prover 10: Preprocessing ... % 7.58/1.80 Prover 11: Preprocessing ... % 8.11/1.81 Prover 9: Constructing countermodel ... % 8.11/1.82 Prover 10: Warning: ignoring some quantifiers % 8.11/1.83 Prover 10: Constructing countermodel ... % 8.69/1.90 Prover 10: gave up % 8.69/1.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.69/1.92 Prover 12: Preprocessing ... % 9.71/2.04 Prover 12: Proving ... % 9.71/2.04 Prover 11: Constructing countermodel ... % 11.55/2.30 Prover 0: proved (1682ms) % 11.55/2.30 % 11.55/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.55/2.31 % 11.55/2.31 Prover 9: stopped % 11.55/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.55/2.31 Prover 12: stopped % 11.94/2.33 Prover 5: stopped % 11.94/2.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.94/2.33 Prover 2: stopped % 11.94/2.33 Prover 13: Preprocessing ... % 11.94/2.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.94/2.34 Prover 19: Preprocessing ... % 11.94/2.35 Prover 13: Warning: ignoring some quantifiers % 11.94/2.35 Prover 16: Preprocessing ... % 11.94/2.35 Prover 13: Constructing countermodel ... % 11.94/2.38 Prover 16: Warning: ignoring some quantifiers % 11.94/2.39 Prover 16: Constructing countermodel ... % 12.58/2.41 Prover 13: gave up % 12.58/2.43 Prover 19: Warning: ignoring some quantifiers % 12.58/2.43 Prover 19: Constructing countermodel ... % 12.58/2.47 Prover 19: gave up % 13.17/2.52 Prover 16: gave up % 20.89/3.94 Prover 11: Found proof (size 338) % 20.89/3.94 Prover 11: proved (2174ms) % 20.89/3.94 Prover 4: stopped % 20.89/3.94 % 20.89/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.89/3.94 % 21.14/3.97 % SZS output start Proof for theBenchmark % 21.14/3.97 Assumptions after simplification: % 21.14/3.97 --------------------------------- % 21.14/3.97 % 21.14/3.97 (ax6) % 21.14/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.14/4.02 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 21.14/4.02 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 21.14/4.02 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 21.14/4.02 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 21.14/4.02 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.14/4.02 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.14/4.02 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 21.14/4.02 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.14/4.02 convergent_lines(v1, v2) = 0) % 21.14/4.02 % 21.14/4.02 (coipo1) % 21.14/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.14/4.02 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.14/4.02 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 21.14/4.03 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.14/4.03 unorthogonal_lines(v0, v1) = 0) % 21.14/4.03 % 21.14/4.03 (con) % 21.14/4.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 21.14/4.03 (v4 = 0) & ~ (v3 = 0) & convergent_lines(v1, v2) = 0 & convergent_lines(v0, % 21.14/4.03 v2) = v4 & convergent_lines(v0, v1) = v3 & $i(v2) & $i(v1) & $i(v0)) % 21.14/4.03 % 21.14/4.03 (cotno1) % 21.52/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 21.52/4.05 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 21.52/4.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 21.52/4.05 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | % 21.52/4.05 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.05 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 21.52/4.05 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 21.52/4.05 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 21.52/4.05 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.05 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 21.52/4.05 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 21.52/4.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 21.52/4.05 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~ % 21.52/4.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 21.52/4.05 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = % 21.52/4.05 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.05 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, % 21.52/4.05 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 21.52/4.05 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, % 21.52/4.05 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 21.52/4.05 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1, % 21.52/4.05 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: % 21.52/4.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 21.52/4.05 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 21.52/4.05 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 21.52/4.05 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.52/4.05 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 21.52/4.05 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.52/4.05 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.52/4.05 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.05 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.52/4.05 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.52/4.05 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.52/4.05 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : % 21.52/4.05 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ % 21.52/4.05 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.52/4.05 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.05 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.52/4.05 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 21.52/4.05 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.52/4.05 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.52/4.05 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.52/4.05 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 21.52/4.05 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 21.52/4.05 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.52/4.05 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.52/4.05 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.05 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.52/4.05 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 21.52/4.05 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 % 21.52/4.05 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] % 21.52/4.05 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~ % 21.52/4.05 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & % 21.52/4.05 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 % 21.52/4.05 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.05 unorthogonal_lines(v1, v2) = v7))) % 21.52/4.05 % 21.52/4.05 (couo1) % 21.52/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.52/4.05 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 21.52/4.05 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.52/4.05 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] : % 21.52/4.05 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, % 21.52/4.05 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | % 21.52/4.05 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 21.52/4.05 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ % 21.52/4.05 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.52/4.05 unorthogonal_lines(v0, v2) = 0) % 21.52/4.05 % 21.52/4.05 (function-axioms) % 21.52/4.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.52/4.05 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 21.52/4.06 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.52/4.06 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 21.52/4.06 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.52/4.06 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 21.52/4.06 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.52/4.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.52/4.06 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 21.52/4.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.52/4.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 21.52/4.06 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.52/4.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.52/4.06 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 21.52/4.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.52/4.06 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 21.52/4.06 v0)) % 21.52/4.06 % 21.52/4.06 Further assumptions not needed in the proof: % 21.52/4.06 -------------------------------------------- % 21.52/4.06 apart1, apart2, apart3, apart4, apart5, ceq1, ceq2, ceq3, ci1, ci2, ci3, ci4, % 21.52/4.06 cu1 % 21.52/4.06 % 21.52/4.06 Those formulas are unsatisfiable: % 21.52/4.06 --------------------------------- % 21.52/4.06 % 21.52/4.06 Begin of proof % 21.52/4.06 | % 21.52/4.06 | ALPHA: (ax6) implies: % 21.52/4.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.52/4.06 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 21.52/4.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0) % 21.52/4.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 21.52/4.06 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ % 21.52/4.06 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.52/4.06 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 21.52/4.06 | % 21.52/4.06 | ALPHA: (coipo1) implies: % 21.52/4.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.52/4.06 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.52/4.06 | unorthogonal_lines(v0, v1) = 0) % 21.52/4.06 | % 21.52/4.06 | ALPHA: (cotno1) implies: % 21.52/4.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.52/4.06 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | % 21.52/4.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 21.52/4.06 | [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & unorthogonal_lines(v0, % 21.52/4.06 | v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & % 21.52/4.06 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.06 | unorthogonal_lines(v1, v2) = v7))) % 21.52/4.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.52/4.06 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | % 21.52/4.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? % 21.52/4.06 | [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & unorthogonal_lines(v0, % 21.52/4.06 | v2) = 0) | (v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & % 21.52/4.06 | convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) & % 21.52/4.06 | unorthogonal_lines(v1, v2) = v7))) % 21.52/4.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.52/4.06 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) % 21.52/4.06 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : % 21.52/4.06 | ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 21.52/4.07 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 21.52/4.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.52/4.07 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = % 21.52/4.07 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 21.52/4.07 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & % 21.52/4.07 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | % 21.52/4.07 | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) % 21.52/4.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 21.52/4.07 | ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = % 21.52/4.07 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 21.52/4.07 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 21.52/4.07 | convergent_lines(v1, v2) = v7))) % 21.52/4.07 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 21.52/4.07 | ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = % 21.52/4.07 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 21.52/4.07 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.07 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 21.52/4.07 | convergent_lines(v1, v2) = v7))) % 21.52/4.07 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 21.52/4.07 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) % 21.52/4.07 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 21.52/4.07 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.07 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.07 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 21.52/4.07 | convergent_lines(v1, v2) = v7))) % 21.52/4.07 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] % 21.52/4.07 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, % 21.52/4.07 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : % 21.52/4.07 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & % 21.52/4.07 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & % 21.52/4.07 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) & % 21.52/4.07 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & % 21.52/4.07 | convergent_lines(v1, v2) = v7))) % 21.52/4.07 | % 21.52/4.07 | ALPHA: (couo1) implies: % 21.52/4.07 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.52/4.07 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = % 21.52/4.07 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, % 21.52/4.07 | v1) = 0) % 21.52/4.07 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] % 21.52/4.07 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 21.52/4.07 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.52/4.07 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = % 21.52/4.07 | v5)) % 21.52/4.07 | % 21.52/4.07 | ALPHA: (function-axioms) implies: % 21.52/4.07 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.52/4.07 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 21.52/4.07 | (convergent_lines(v3, v2) = v0)) % 21.52/4.08 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.52/4.08 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 21.52/4.08 | (unorthogonal_lines(v3, v2) = v0)) % 21.52/4.08 | % 21.52/4.08 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2, % 21.52/4.08 | all_20_3, all_20_4 gives: % 21.52/4.08 | (16) ~ (all_20_0 = 0) & ~ (all_20_1 = 0) & convergent_lines(all_20_3, % 21.52/4.08 | all_20_2) = 0 & convergent_lines(all_20_4, all_20_2) = all_20_0 & % 21.52/4.08 | convergent_lines(all_20_4, all_20_3) = all_20_1 & $i(all_20_2) & % 21.52/4.08 | $i(all_20_3) & $i(all_20_4) % 21.52/4.08 | % 21.52/4.08 | ALPHA: (16) implies: % 21.52/4.08 | (17) ~ (all_20_1 = 0) % 21.52/4.08 | (18) ~ (all_20_0 = 0) % 21.52/4.08 | (19) $i(all_20_4) % 21.52/4.08 | (20) $i(all_20_3) % 21.52/4.08 | (21) $i(all_20_2) % 21.52/4.08 | (22) convergent_lines(all_20_4, all_20_3) = all_20_1 % 21.52/4.08 | (23) convergent_lines(all_20_4, all_20_2) = all_20_0 % 21.52/4.08 | (24) convergent_lines(all_20_3, all_20_2) = 0 % 21.52/4.08 | % 21.52/4.08 | GROUND_INST: instantiating (2) with all_20_4, all_20_4, all_20_3, all_20_1, % 21.52/4.08 | all_20_1, simplifying with (19), (20), (22) gives: % 21.68/4.08 | (25) all_20_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 21.68/4.08 | convergent_lines(all_20_4, all_20_4) = v0) % 21.68/4.08 | % 21.68/4.08 | GROUND_INST: instantiating (8) with all_20_4, all_20_3, all_20_3, all_20_1, % 21.68/4.08 | all_20_1, simplifying with (19), (20), (22) gives: % 21.68/4.08 | (26) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 & % 21.68/4.08 | all_20_1 = 0 & unorthogonal_lines(all_20_4, all_20_3) = 0) | (v0 = % 21.68/4.08 | 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, all_20_3) = 0) | ( % 21.68/4.08 | ~ (v3 = 0) & unorthogonal_lines(all_20_3, all_20_3) = v3) | ( ~ % 21.68/4.08 | (v2 = 0) & convergent_lines(all_20_3, all_20_3) = v2)) % 21.68/4.08 | % 21.68/4.08 | GROUND_INST: instantiating (3) with all_20_4, all_20_3, all_20_1, simplifying % 21.68/4.08 | with (19), (20), (22) gives: % 21.68/4.08 | (27) all_20_1 = 0 | unorthogonal_lines(all_20_4, all_20_3) = 0 % 21.68/4.08 | % 21.68/4.08 | GROUND_INST: instantiating (8) with all_20_4, all_20_3, all_20_2, all_20_1, % 21.68/4.08 | all_20_0, simplifying with (19), (20), (21), (22), (23) gives: % 21.68/4.08 | (28) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0 & % 21.68/4.08 | all_20_0 = 0 & unorthogonal_lines(all_20_4, all_20_2) = 0) | (v0 = % 21.68/4.08 | 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, all_20_3) = 0) | ( % 21.68/4.08 | ~ (v3 = 0) & unorthogonal_lines(all_20_3, all_20_2) = v3) | ( ~ % 21.68/4.08 | (v2 = 0) & convergent_lines(all_20_3, all_20_2) = v2)) % 21.68/4.08 | % 21.68/4.08 | GROUND_INST: instantiating (5) with all_20_4, all_20_3, all_20_2, all_20_0, % 21.68/4.08 | simplifying with (19), (20), (21), (23), (24) gives: % 21.68/4.08 | (29) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 21.68/4.08 | all_20_0 = 0 & unorthogonal_lines(all_20_4, all_20_2) = 0) | (v1 = % 21.68/4.08 | 0 & v0 = 0 & unorthogonal_lines(all_20_4, all_20_3) = 0 & % 21.68/4.08 | convergent_lines(all_20_4, all_20_3) = 0) | ( ~ (v3 = 0) & % 21.68/4.08 | unorthogonal_lines(all_20_3, all_20_2) = v3)) % 21.68/4.08 | % 21.68/4.09 | GROUND_INST: instantiating (4) with all_20_4, all_20_3, all_20_2, all_20_1, % 21.68/4.09 | simplifying with (19), (20), (21), (22), (24) gives: % 21.68/4.09 | (30) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0 & % 21.68/4.09 | v1 = 0 & unorthogonal_lines(all_20_4, all_20_2) = 0 & % 21.68/4.09 | convergent_lines(all_20_4, all_20_2) = 0) | (v0 = 0 & all_20_1 = 0 % 21.68/4.09 | & unorthogonal_lines(all_20_4, all_20_3) = 0) | ( ~ (v3 = 0) & % 21.68/4.09 | unorthogonal_lines(all_20_3, all_20_2) = v3)) % 21.68/4.09 | % 21.68/4.09 | DELTA: instantiating (30) with fresh symbols all_33_0, all_33_1, all_33_2, % 21.68/4.09 | all_33_3 gives: % 21.68/4.09 | (31) (all_33_1 = 0 & all_33_2 = 0 & unorthogonal_lines(all_20_4, all_20_2) % 21.68/4.09 | = 0 & convergent_lines(all_20_4, all_20_2) = 0) | (all_33_3 = 0 & % 21.68/4.09 | all_20_1 = 0 & unorthogonal_lines(all_20_4, all_20_3) = 0) | ( ~ % 21.68/4.09 | (all_33_0 = 0) & unorthogonal_lines(all_20_3, all_20_2) = all_33_0) % 21.68/4.09 | % 21.68/4.09 | DELTA: instantiating (29) with fresh symbols all_34_0, all_34_1, all_34_2, % 21.68/4.09 | all_34_3 gives: % 21.68/4.09 | (32) (all_34_1 = 0 & all_20_0 = 0 & unorthogonal_lines(all_20_4, all_20_2) % 21.68/4.09 | = 0) | (all_34_2 = 0 & all_34_3 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | all_20_3) = 0 & convergent_lines(all_20_4, all_20_3) = 0) | ( ~ % 21.68/4.09 | (all_34_0 = 0) & unorthogonal_lines(all_20_3, all_20_2) = all_34_0) % 21.68/4.09 | % 21.68/4.09 | DELTA: instantiating (28) with fresh symbols all_36_0, all_36_1, all_36_2, % 21.68/4.09 | all_36_3 gives: % 21.68/4.09 | (33) (all_36_2 = 0 & all_20_0 = 0 & unorthogonal_lines(all_20_4, all_20_2) % 21.68/4.09 | = 0) | (all_36_3 = 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | all_20_3) = 0) | ( ~ (all_36_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.09 | all_20_2) = all_36_0) | ( ~ (all_36_1 = 0) & % 21.68/4.09 | convergent_lines(all_20_3, all_20_2) = all_36_1) % 21.68/4.09 | % 21.68/4.09 | DELTA: instantiating (26) with fresh symbols all_38_0, all_38_1, all_38_2, % 21.68/4.09 | all_38_3 gives: % 21.68/4.09 | (34) (all_38_2 = 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, all_20_3) % 21.68/4.09 | = 0) | (all_38_3 = 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | all_20_3) = 0) | ( ~ (all_38_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.09 | all_20_3) = all_38_0) | ( ~ (all_38_1 = 0) & % 21.68/4.09 | convergent_lines(all_20_3, all_20_3) = all_38_1) % 21.68/4.09 | % 21.68/4.09 | BETA: splitting (27) gives: % 21.68/4.09 | % 21.68/4.09 | Case 1: % 21.68/4.09 | | % 21.68/4.09 | | (35) unorthogonal_lines(all_20_4, all_20_3) = 0 % 21.68/4.09 | | % 21.68/4.09 | | BETA: splitting (32) gives: % 21.68/4.09 | | % 21.68/4.09 | | Case 1: % 21.68/4.09 | | | % 21.68/4.09 | | | (36) all_34_1 = 0 & all_20_0 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | | | all_20_2) = 0 % 21.68/4.09 | | | % 21.68/4.09 | | | ALPHA: (36) implies: % 21.68/4.09 | | | (37) all_20_0 = 0 % 21.68/4.09 | | | % 21.68/4.09 | | | REDUCE: (18), (37) imply: % 21.68/4.09 | | | (38) $false % 21.68/4.09 | | | % 21.68/4.09 | | | CLOSE: (38) is inconsistent. % 21.68/4.09 | | | % 21.68/4.09 | | Case 2: % 21.68/4.09 | | | % 21.68/4.09 | | | (39) (all_34_2 = 0 & all_34_3 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | | | all_20_3) = 0 & convergent_lines(all_20_4, all_20_3) = 0) | ( % 21.68/4.09 | | | ~ (all_34_0 = 0) & unorthogonal_lines(all_20_3, all_20_2) = % 21.68/4.09 | | | all_34_0) % 21.68/4.09 | | | % 21.68/4.09 | | | BETA: splitting (39) gives: % 21.68/4.09 | | | % 21.68/4.09 | | | Case 1: % 21.68/4.09 | | | | % 21.68/4.09 | | | | (40) all_34_2 = 0 & all_34_3 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.09 | | | | all_20_3) = 0 & convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.09 | | | | % 21.68/4.09 | | | | ALPHA: (40) implies: % 21.68/4.09 | | | | (41) convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.09 | | | | % 21.68/4.09 | | | | REF_CLOSE: (14), (17), (22), (41) are inconsistent by sub-proof #2. % 21.68/4.09 | | | | % 21.68/4.09 | | | Case 2: % 21.68/4.09 | | | | % 21.68/4.09 | | | | (42) ~ (all_34_0 = 0) & unorthogonal_lines(all_20_3, all_20_2) = % 21.68/4.09 | | | | all_34_0 % 21.68/4.09 | | | | % 21.68/4.09 | | | | ALPHA: (42) implies: % 21.68/4.09 | | | | (43) ~ (all_34_0 = 0) % 21.68/4.09 | | | | (44) unorthogonal_lines(all_20_3, all_20_2) = all_34_0 % 21.68/4.09 | | | | % 21.68/4.09 | | | | BETA: splitting (25) gives: % 21.68/4.09 | | | | % 21.68/4.09 | | | | Case 1: % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | (45) all_20_1 = 0 % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | REDUCE: (17), (45) imply: % 21.68/4.09 | | | | | (46) $false % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | CLOSE: (46) is inconsistent. % 21.68/4.09 | | | | | % 21.68/4.09 | | | | Case 2: % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | (47) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_20_4, % 21.68/4.09 | | | | | all_20_4) = v0) % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | DELTA: instantiating (47) with fresh symbol all_54_0 gives: % 21.68/4.09 | | | | | (48) ~ (all_54_0 = 0) & convergent_lines(all_20_4, all_20_4) = % 21.68/4.09 | | | | | all_54_0 % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | ALPHA: (48) implies: % 21.68/4.09 | | | | | (49) convergent_lines(all_20_4, all_20_4) = all_54_0 % 21.68/4.09 | | | | | % 21.68/4.09 | | | | | DELTA: instantiating (47) with fresh symbol all_59_0 gives: % 21.68/4.10 | | | | | (50) ~ (all_59_0 = 0) & convergent_lines(all_20_4, all_20_4) = % 21.68/4.10 | | | | | all_59_0 % 21.68/4.10 | | | | | % 21.68/4.10 | | | | | ALPHA: (50) implies: % 21.68/4.10 | | | | | (51) ~ (all_59_0 = 0) % 21.68/4.10 | | | | | (52) convergent_lines(all_20_4, all_20_4) = all_59_0 % 21.68/4.10 | | | | | % 21.68/4.10 | | | | | BETA: splitting (31) gives: % 21.68/4.10 | | | | | % 21.68/4.10 | | | | | Case 1: % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | (53) all_33_1 = 0 & all_33_2 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.10 | | | | | | all_20_2) = 0 & convergent_lines(all_20_4, all_20_2) = 0 % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | ALPHA: (53) implies: % 21.68/4.10 | | | | | | (54) convergent_lines(all_20_4, all_20_2) = 0 % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | GROUND_INST: instantiating (14) with all_20_0, 0, all_20_2, % 21.68/4.10 | | | | | | all_20_4, simplifying with (23), (54) gives: % 21.68/4.10 | | | | | | (55) all_20_0 = 0 % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | REDUCE: (18), (55) imply: % 21.68/4.10 | | | | | | (56) $false % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | CLOSE: (56) is inconsistent. % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | Case 2: % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | (57) (all_33_3 = 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.10 | | | | | | all_20_3) = 0) | ( ~ (all_33_0 = 0) & % 21.68/4.10 | | | | | | unorthogonal_lines(all_20_3, all_20_2) = all_33_0) % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | BETA: splitting (57) gives: % 21.68/4.10 | | | | | | % 21.68/4.10 | | | | | | Case 1: % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | (58) all_33_3 = 0 & all_20_1 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.10 | | | | | | | all_20_3) = 0 % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | ALPHA: (58) implies: % 21.68/4.10 | | | | | | | (59) all_20_1 = 0 % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | REDUCE: (17), (59) imply: % 21.68/4.10 | | | | | | | (60) $false % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | CLOSE: (60) is inconsistent. % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | Case 2: % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | (61) ~ (all_33_0 = 0) & unorthogonal_lines(all_20_3, all_20_2) % 21.68/4.10 | | | | | | | = all_33_0 % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | ALPHA: (61) implies: % 21.68/4.10 | | | | | | | (62) unorthogonal_lines(all_20_3, all_20_2) = all_33_0 % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | BETA: splitting (33) gives: % 21.68/4.10 | | | | | | | % 21.68/4.10 | | | | | | | Case 1: % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | (63) (all_36_2 = 0 & all_20_0 = 0 & % 21.68/4.10 | | | | | | | | unorthogonal_lines(all_20_4, all_20_2) = 0) | % 21.68/4.10 | | | | | | | | (all_36_3 = 0 & all_20_1 = 0 & % 21.68/4.10 | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0) % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | BETA: splitting (63) gives: % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | Case 1: % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | (64) all_36_2 = 0 & all_20_0 = 0 & % 21.68/4.10 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_2) = 0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | ALPHA: (64) implies: % 21.68/4.10 | | | | | | | | | (65) all_20_0 = 0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | REDUCE: (18), (65) imply: % 21.68/4.10 | | | | | | | | | (66) $false % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | CLOSE: (66) is inconsistent. % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | Case 2: % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | (67) all_36_3 = 0 & all_20_1 = 0 & % 21.68/4.10 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | ALPHA: (67) implies: % 21.68/4.10 | | | | | | | | | (68) all_20_1 = 0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | REDUCE: (17), (68) imply: % 21.68/4.10 | | | | | | | | | (69) $false % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | CLOSE: (69) is inconsistent. % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | End of split % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | Case 2: % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | (70) ( ~ (all_36_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.10 | | | | | | | | all_20_2) = all_36_0) | ( ~ (all_36_1 = 0) & % 21.68/4.10 | | | | | | | | convergent_lines(all_20_3, all_20_2) = all_36_1) % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | BETA: splitting (70) gives: % 21.68/4.10 | | | | | | | | % 21.68/4.10 | | | | | | | | Case 1: % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | (71) ~ (all_36_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.10 | | | | | | | | | all_20_2) = all_36_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | ALPHA: (71) implies: % 21.68/4.10 | | | | | | | | | (72) unorthogonal_lines(all_20_3, all_20_2) = all_36_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (14) with all_54_0, all_59_0, % 21.68/4.10 | | | | | | | | | all_20_4, all_20_4, simplifying with (49), (52) % 21.68/4.10 | | | | | | | | | gives: % 21.68/4.10 | | | | | | | | | (73) all_59_0 = all_54_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (15) with all_34_0, all_36_0, % 21.68/4.10 | | | | | | | | | all_20_2, all_20_3, simplifying with (44), (72) % 21.68/4.10 | | | | | | | | | gives: % 21.68/4.10 | | | | | | | | | (74) all_36_0 = all_34_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (15) with all_33_0, all_36_0, % 21.68/4.10 | | | | | | | | | all_20_2, all_20_3, simplifying with (62), (72) % 21.68/4.10 | | | | | | | | | gives: % 21.68/4.10 | | | | | | | | | (75) all_36_0 = all_33_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | COMBINE_EQS: (74), (75) imply: % 21.68/4.10 | | | | | | | | | (76) all_34_0 = all_33_0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | REDUCE: (51), (73) imply: % 21.68/4.10 | | | | | | | | | (77) ~ (all_54_0 = 0) % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | REDUCE: (43), (76) imply: % 21.68/4.10 | | | | | | | | | (78) ~ (all_33_0 = 0) % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (8) with all_20_4, all_20_4, % 21.68/4.10 | | | | | | | | | all_20_4, all_54_0, all_54_0, simplifying with % 21.68/4.10 | | | | | | | | | (19), (49) gives: % 21.68/4.10 | | | | | | | | | (79) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 21.68/4.10 | | | | | | | | | int] : ((v1 = 0 & all_54_0 = 0 & % 21.68/4.10 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | (v0 % 21.68/4.10 | | | | | | | | | = 0 & all_54_0 = 0 & unorthogonal_lines(all_20_4, % 21.68/4.10 | | | | | | | | | all_20_4) = 0) | ( ~ (v3 = 0) & % 21.68/4.10 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = v3) | ( ~ % 21.68/4.10 | | | | | | | | | (v2 = 0) & convergent_lines(all_20_4, all_20_4) = % 21.68/4.10 | | | | | | | | | v2)) % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (3) with all_20_4, all_20_4, % 21.68/4.10 | | | | | | | | | all_54_0, simplifying with (19), (49) gives: % 21.68/4.10 | | | | | | | | | (80) all_54_0 = 0 | unorthogonal_lines(all_20_4, all_20_4) % 21.68/4.10 | | | | | | | | | = 0 % 21.68/4.10 | | | | | | | | | % 21.68/4.10 | | | | | | | | | GROUND_INST: instantiating (11) with all_20_4, all_20_3, % 21.68/4.10 | | | | | | | | | all_20_3, 0, 0, simplifying with (19), (20), (35) % 21.68/4.10 | | | | | | | | | gives: % 21.68/4.10 | | | | | | | | | (81) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 21.68/4.10 | | | | | | | | | int] : ((v1 = 0 & convergent_lines(all_20_4, % 21.68/4.10 | | | | | | | | | all_20_3) = 0) | (v0 = 0 & % 21.68/4.10 | | | | | | | | | convergent_lines(all_20_4, all_20_3) = 0) | ( ~ % 21.68/4.10 | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_20_3, all_20_3) % 21.68/4.10 | | | | | | | | | = v3) | ( ~ (v2 = 0) & convergent_lines(all_20_3, % 21.68/4.10 | | | | | | | | | all_20_3) = v2)) % 21.68/4.10 | | | | | | | | | % 21.68/4.11 | | | | | | | | | GROUND_INST: instantiating (10) with all_20_4, all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3, all_20_1, 0, simplifying with (19), % 21.68/4.11 | | | | | | | | | (20), (22), (35) gives: % 21.68/4.11 | | | | | | | | | (82) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 21.68/4.11 | | | | | | | | | int] : ((v1 = 0 & convergent_lines(all_20_4, % 21.68/4.11 | | | | | | | | | all_20_3) = 0) | (v0 = 0 & all_20_1 = 0) | ( ~ % 21.68/4.11 | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_20_3, all_20_3) % 21.68/4.11 | | | | | | | | | = v3) | ( ~ (v2 = 0) & convergent_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3) = v2)) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | GROUND_INST: instantiating (9) with all_20_4, all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3, 0, all_20_1, simplifying with (19), % 21.68/4.11 | | | | | | | | | (20), (22), (35) gives: % 21.68/4.11 | | | | | | | | | (83) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 21.68/4.11 | | | | | | | | | int] : ((v1 = 0 & all_20_1 = 0) | (v0 = 0 & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_4, all_20_3) = 0) | ( ~ % 21.68/4.11 | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_20_3, all_20_3) % 21.68/4.11 | | | | | | | | | = v3) | ( ~ (v2 = 0) & convergent_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3) = v2)) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | GROUND_INST: instantiating (9) with all_20_4, all_20_3, % 21.68/4.11 | | | | | | | | | all_20_4, 0, all_54_0, simplifying with (19), % 21.68/4.11 | | | | | | | | | (20), (35), (49) gives: % 21.68/4.11 | | | | | | | | | (84) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 21.68/4.11 | | | | | | | | | int] : ((v1 = 0 & all_54_0 = 0 & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | (v0 % 21.68/4.11 | | | | | | | | | = 0 & convergent_lines(all_20_4, all_20_3) = 0) | % 21.68/4.11 | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_4) = v3) | ( ~ (v2 = 0) & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_3, all_20_4) = v2)) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | GROUND_INST: instantiating (13) with all_20_3, all_20_2, % 21.68/4.11 | | | | | | | | | all_20_2, all_33_0, all_33_0, simplifying with % 21.68/4.11 | | | | | | | | | (20), (21), (62) gives: % 21.68/4.11 | | | | | | | | | (85) all_33_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_2, all_20_2) = v0) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | GROUND_INST: instantiating (12) with all_20_3, all_20_3, % 21.68/4.11 | | | | | | | | | all_20_2, all_33_0, simplifying with (20), (21), % 21.68/4.11 | | | | | | | | | (24), (62) gives: % 21.68/4.11 | | | | | | | | | (86) all_33_0 = 0 | unorthogonal_lines(all_20_3, all_20_3) % 21.68/4.11 | | | | | | | | | = 0 % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | DELTA: instantiating (81) with fresh symbols all_81_0, % 21.68/4.11 | | | | | | | | | all_81_1, all_81_2, all_81_3 gives: % 21.68/4.11 | | | | | | | | | (87) (all_81_2 = 0 & convergent_lines(all_20_4, all_20_3) = % 21.68/4.11 | | | | | | | | | 0) | (all_81_3 = 0 & convergent_lines(all_20_4, % 21.68/4.11 | | | | | | | | | all_20_3) = 0) | ( ~ (all_81_0 = 0) & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_3, all_20_3) = all_81_0) | % 21.68/4.11 | | | | | | | | | ( ~ (all_81_1 = 0) & convergent_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3) = all_81_1) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | DELTA: instantiating (83) with fresh symbols all_82_0, % 21.68/4.11 | | | | | | | | | all_82_1, all_82_2, all_82_3 gives: % 21.68/4.11 | | | | | | | | | (88) (all_82_2 = 0 & all_20_1 = 0) | (all_82_3 = 0 & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_4, all_20_3) = 0) | ( ~ % 21.68/4.11 | | | | | | | | | (all_82_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_3) = all_82_0) | ( ~ (all_82_1 = 0) & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_82_1) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | DELTA: instantiating (82) with fresh symbols all_83_0, % 21.68/4.11 | | | | | | | | | all_83_1, all_83_2, all_83_3 gives: % 21.68/4.11 | | | | | | | | | (89) (all_83_2 = 0 & convergent_lines(all_20_4, all_20_3) = % 21.68/4.11 | | | | | | | | | 0) | (all_83_3 = 0 & all_20_1 = 0) | ( ~ (all_83_0 = % 21.68/4.11 | | | | | | | | | 0) & unorthogonal_lines(all_20_3, all_20_3) = % 21.68/4.11 | | | | | | | | | all_83_0) | ( ~ (all_83_1 = 0) & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_83_1) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | DELTA: instantiating (84) with fresh symbols all_89_0, % 21.68/4.11 | | | | | | | | | all_89_1, all_89_2, all_89_3 gives: % 21.68/4.11 | | | | | | | | | (90) (all_89_2 = 0 & all_54_0 = 0 & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | % 21.68/4.11 | | | | | | | | | (all_89_3 = 0 & convergent_lines(all_20_4, all_20_3) = % 21.68/4.11 | | | | | | | | | 0) | ( ~ (all_89_0 = 0) & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = all_89_0) | % 21.68/4.11 | | | | | | | | | ( ~ (all_89_1 = 0) & convergent_lines(all_20_3, % 21.68/4.11 | | | | | | | | | all_20_4) = all_89_1) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | DELTA: instantiating (79) with fresh symbols all_94_0, % 21.68/4.11 | | | | | | | | | all_94_1, all_94_2, all_94_3 gives: % 21.68/4.11 | | | | | | | | | (91) (all_94_2 = 0 & all_54_0 = 0 & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | % 21.68/4.11 | | | | | | | | | (all_94_3 = 0 & all_54_0 = 0 & % 21.68/4.11 | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | ( ~ % 21.68/4.11 | | | | | | | | | (all_94_0 = 0) & unorthogonal_lines(all_20_4, % 21.68/4.11 | | | | | | | | | all_20_4) = all_94_0) | ( ~ (all_94_1 = 0) & % 21.68/4.11 | | | | | | | | | convergent_lines(all_20_4, all_20_4) = all_94_1) % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | BETA: splitting (80) gives: % 21.68/4.11 | | | | | | | | | % 21.68/4.11 | | | | | | | | | Case 1: % 21.68/4.11 | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | (92) unorthogonal_lines(all_20_4, all_20_4) = 0 % 21.68/4.11 | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | BETA: splitting (86) gives: % 21.68/4.11 | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | Case 1: % 21.68/4.11 | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | (93) unorthogonal_lines(all_20_3, all_20_3) = 0 % 21.68/4.11 | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | BETA: splitting (34) gives: % 21.68/4.11 | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | Case 1: % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | (94) (all_38_2 = 0 & all_20_1 = 0 & % 21.68/4.11 | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0) | % 21.68/4.11 | | | | | | | | | | | | (all_38_3 = 0 & all_20_1 = 0 & % 21.68/4.11 | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0) % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | BETA: splitting (94) gives: % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | Case 1: % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | (95) all_38_2 = 0 & all_20_1 = 0 & % 21.68/4.11 | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | ALPHA: (95) implies: % 21.68/4.11 | | | | | | | | | | | | | (96) all_20_1 = 0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | REDUCE: (17), (96) imply: % 21.68/4.11 | | | | | | | | | | | | | (97) $false % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | CLOSE: (97) is inconsistent. % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | Case 2: % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | (98) all_38_3 = 0 & all_20_1 = 0 & % 21.68/4.11 | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_3) = 0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | ALPHA: (98) implies: % 21.68/4.11 | | | | | | | | | | | | | (99) all_20_1 = 0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | REDUCE: (17), (99) imply: % 21.68/4.11 | | | | | | | | | | | | | (100) $false % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | CLOSE: (100) is inconsistent. % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | End of split % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | Case 2: % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | (101) ( ~ (all_38_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.11 | | | | | | | | | | | | all_20_3) = all_38_0) | ( ~ (all_38_1 = 0) & % 21.68/4.11 | | | | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_38_1) % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | BETA: splitting (101) gives: % 21.68/4.11 | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | Case 1: % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | (102) ~ (all_38_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.11 | | | | | | | | | | | | | all_20_3) = all_38_0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | ALPHA: (102) implies: % 21.68/4.11 | | | | | | | | | | | | | (103) ~ (all_38_0 = 0) % 21.68/4.11 | | | | | | | | | | | | | (104) unorthogonal_lines(all_20_3, all_20_3) = all_38_0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_38_0, all_20_3, % 21.68/4.11 | | | | | | | | | | | | | all_20_3, simplifying with (93), (104) gives: % 21.68/4.11 | | | | | | | | | | | | | (105) all_38_0 = 0 % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | REDUCE: (103), (105) imply: % 21.68/4.11 | | | | | | | | | | | | | (106) $false % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.11 | | | | | | | | | | | | Case 2: % 21.68/4.11 | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | (107) ~ (all_38_1 = 0) & convergent_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | all_20_3) = all_38_1 % 21.68/4.12 | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | ALPHA: (107) implies: % 21.68/4.12 | | | | | | | | | | | | | (108) convergent_lines(all_20_3, all_20_3) = all_38_1 % 21.68/4.12 | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | BETA: splitting (87) gives: % 21.68/4.12 | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | (109) (all_81_2 = 0 & convergent_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | all_20_3) = 0) | (all_81_3 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | convergent_lines(all_20_4, all_20_3) = 0) % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | BETA: splitting (109) gives: % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | (110) all_81_2 = 0 & convergent_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | ALPHA: (110) implies: % 21.68/4.12 | | | | | | | | | | | | | | | (111) convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (111) are inconsistent by % 21.68/4.12 | | | | | | | | | | | | | | | sub-proof #2. % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | (112) all_81_3 = 0 & convergent_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | ALPHA: (112) implies: % 21.68/4.12 | | | | | | | | | | | | | | | (113) convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (113) are inconsistent by % 21.68/4.12 | | | | | | | | | | | | | | | sub-proof #2. % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | End of split % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | (114) ( ~ (all_81_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | all_20_3) = all_81_0) | ( ~ (all_81_1 = 0) & % 21.68/4.12 | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_81_1) % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | BETA: splitting (114) gives: % 21.68/4.12 | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | (115) ~ (all_81_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | all_20_3) = all_81_0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | ALPHA: (115) implies: % 21.68/4.12 | | | | | | | | | | | | | | | (116) ~ (all_81_0 = 0) % 21.68/4.12 | | | | | | | | | | | | | | | (117) unorthogonal_lines(all_20_3, all_20_3) = all_81_0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_81_0, all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | all_20_3, simplifying with (93), (117) gives: % 21.68/4.12 | | | | | | | | | | | | | | | (118) all_81_0 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | REDUCE: (116), (118) imply: % 21.68/4.12 | | | | | | | | | | | | | | | (119) $false % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | (120) ~ (all_81_1 = 0) & convergent_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | all_20_3) = all_81_1 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | ALPHA: (120) implies: % 21.68/4.12 | | | | | | | | | | | | | | | (121) ~ (all_81_1 = 0) % 21.68/4.12 | | | | | | | | | | | | | | | (122) convergent_lines(all_20_3, all_20_3) = all_81_1 % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 21.68/4.12 | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | (123) all_33_0 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | REDUCE: (78), (123) imply: % 21.68/4.12 | | | | | | | | | | | | | | | | (124) $false % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | (125) ? [v0: int] : ( ~ (v0 = 0) & % 21.68/4.12 | | | | | | | | | | | | | | | | convergent_lines(all_20_2, all_20_2) = v0) % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | DELTA: instantiating (125) with fresh symbol all_133_0 % 21.68/4.12 | | | | | | | | | | | | | | | | gives: % 21.68/4.12 | | | | | | | | | | | | | | | | (126) ~ (all_133_0 = 0) & convergent_lines(all_20_2, % 21.68/4.12 | | | | | | | | | | | | | | | | all_20_2) = all_133_0 % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | (127) ~ (all_133_0 = 0) % 21.68/4.12 | | | | | | | | | | | | | | | | (128) convergent_lines(all_20_2, all_20_2) = all_133_0 % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | (129) (all_82_2 = 0 & all_20_1 = 0) | (all_82_3 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | | | | convergent_lines(all_20_4, all_20_3) = 0) % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | (130) all_82_2 = 0 & all_20_1 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (130) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (131) all_20_1 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | REDUCE: (17), (131) imply: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (132) $false % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | (133) all_82_3 = 0 & convergent_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | | | | all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (133) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (134) convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (134) are inconsistent by % 21.68/4.12 | | | | | | | | | | | | | | | | | | sub-proof #2. % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | End of split % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | (135) ( ~ (all_82_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | | | all_20_3) = all_82_0) | ( ~ (all_82_1 = 0) & % 21.68/4.12 | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_82_1) % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | (136) ~ (all_82_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | | | | all_20_3) = all_82_0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (136) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (137) ~ (all_82_0 = 0) % 21.68/4.12 | | | | | | | | | | | | | | | | | | (138) unorthogonal_lines(all_20_3, all_20_3) = all_82_0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_82_0, all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | | | | all_20_3, simplifying with (93), (138) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (139) all_82_0 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | REDUCE: (137), (139) imply: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (140) $false % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | (141) ~ (all_82_1 = 0) & convergent_lines(all_20_3, % 21.68/4.12 | | | | | | | | | | | | | | | | | | all_20_3) = all_82_1 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | ALPHA: (141) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | (142) convergent_lines(all_20_3, all_20_3) = all_82_1 % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | (143) (all_94_2 = 0 & all_54_0 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | (all_94_3 = 0 & all_54_0 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0) % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (144) all_94_2 = 0 & all_54_0 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (145) all_54_0 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (145) imply: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (146) $false % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (147) all_94_3 = 0 & all_54_0 = 0 & % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_4, all_20_4) = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (148) all_54_0 = 0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (148) imply: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (149) $false % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | End of split % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | (150) ( ~ (all_94_0 = 0) & unorthogonal_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | | | | | all_20_4) = all_94_0) | ( ~ (all_94_1 = 0) & % 21.68/4.12 | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_4, all_20_4) = all_94_1) % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (151) ~ (all_94_0 = 0) & unorthogonal_lines(all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | all_20_4) = all_94_0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies: % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (152) ~ (all_94_0 = 0) % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | (153) unorthogonal_lines(all_20_4, all_20_4) = all_94_0 % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_94_0, all_20_4, % 21.68/4.12 | | | | | | | | | | | | | | | | | | | | all_20_4, simplifying with (92), (153) gives: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | (154) all_94_0 = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (154) imply: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | (155) $false % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | (156) ~ (all_94_1 = 0) & convergent_lines(all_20_4, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | all_20_4) = all_94_1 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | (157) ~ (all_94_1 = 0) % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | (158) convergent_lines(all_20_4, all_20_4) = all_94_1 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | (159) (all_83_2 = 0 & convergent_lines(all_20_4, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0) | (all_83_3 = 0 & all_20_1 = 0) % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (160) all_83_2 = 0 & convergent_lines(all_20_4, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (161) convergent_lines(all_20_4, all_20_3) = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (161) are inconsistent by % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (162) all_83_3 = 0 & all_20_1 = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (163) all_20_1 = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (163) imply: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (164) $false % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | End of split % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | (165) ( ~ (all_83_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_83_0) | ( ~ (all_83_1 = 0) & % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_3) = all_83_1) % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (166) ~ (all_83_0 = 0) & unorthogonal_lines(all_20_3, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_83_0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_83_0 = 0) % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (168) unorthogonal_lines(all_20_3, all_20_3) = all_83_0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_83_0, all_20_3, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, simplifying with (93), (168) gives: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (169) all_83_0 = 0 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (169) imply: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (170) $false % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_83_1 = 0) & convergent_lines(all_20_3, % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_83_1 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | (172) convergent_lines(all_20_3, all_20_3) = all_83_1 % 21.68/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_54_0, all_94_1, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_4, all_20_4, simplifying with (49), (158) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (173) all_94_1 = all_54_0 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_82_1, all_83_1, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_20_3, simplifying with (142), (172) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (174) all_83_1 = all_82_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_81_1, all_83_1, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_20_3, simplifying with (122), (172) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (175) all_83_1 = all_81_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_38_1, all_83_1, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_20_3, simplifying with (108), (172) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (176) all_83_1 = all_38_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (175) imply: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (177) all_82_1 = all_81_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (176) imply: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (178) all_82_1 = all_38_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (178) imply: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (179) all_81_1 = all_38_1 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (179) imply: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_38_1 = 0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_20_3, all_20_2, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_38_1, simplifying with (20), (21), % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (24), (108) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (181) all_38_1 = 0 | convergent_lines(all_20_2, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_20_3, all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_38_1, all_20_1, simplifying with % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (19), (20), (22), (108) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (182) all_38_1 = 0 | all_20_1 = 0 | ? [v0: int] : ( ~ % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_20_3, all_20_4) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | = v0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_20_3, all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_38_1, simplifying with (19), (20), % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (35), (108) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (183) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v2 = 0 & all_38_1 = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_3) = 0) | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & v0 = 0 & unorthogonal_lines(all_20_3, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_4) = 0 & convergent_lines(all_20_3, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_4) = 0) | ( ~ (v3 = 0) & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_4, all_20_3) = v3)) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_20_2, all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_2, all_133_0, all_20_0, simplifying with % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (19), (21), (23), (128) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (184) all_133_0 = 0 | all_20_0 = 0 | ? [v0: int] : ( ~ % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_20_2, all_20_4) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | = v0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_20_3, all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3, 0, simplifying with (19), (20), (35), % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (93) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (185) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v2 = 0 & convergent_lines(all_20_3, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0) | (v1 = 0 & v0 = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0) | ( % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | ~ (v3 = 0) & convergent_lines(all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = v3)) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_183_0, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_183_1, all_183_2, all_183_3 gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (186) (all_183_1 = 0 & convergent_lines(all_20_3, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0) | (all_183_2 = 0 & all_183_3 = % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | 0 & unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0) | ( ~ % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (all_183_0 = 0) & convergent_lines(all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_183_0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_191_0, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_191_1, all_191_2, all_191_3 gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (187) (all_191_1 = 0 & all_38_1 = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_3) = 0) | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (all_191_2 = 0 & all_191_3 = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0) | ( ~ % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | (all_191_0 = 0) & convergent_lines(all_20_4, % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_191_0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | (188) all_133_0 = 0 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (188) imply: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | (189) $false % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | (190) all_20_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_2, all_20_4) = v0) % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | | (191) all_38_1 = 0 % 21.92/4.13 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (191) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | (192) $false % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | (193) all_20_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = v0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_20_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (194) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (195) $false % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (196) ? [v0: int] : ( ~ (v0 = 0) & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = v0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (196) with fresh symbol all_242_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_242_0 = 0) & convergent_lines(all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_20_4) = all_242_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_242_0 = 0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | (199) convergent_lines(all_20_3, all_20_4) = all_242_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (200) convergent_lines(all_20_2, all_20_3) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_183_1 = 0 & convergent_lines(all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) convergent_lines(all_20_3, all_20_3) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_83_1, all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3, simplifying with (172), (202) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_83_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (203) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_82_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (204) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_82_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (205) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_81_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (206) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_81_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (207) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_38_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (208) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_38_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (209) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) $false % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) (all_183_2 = 0 & all_183_3 = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0) | ( ~ % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_183_0 = 0) & convergent_lines(all_20_4, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_183_0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_183_2 = 0 & all_183_3 = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) convergent_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) unorthogonal_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (22), (77), (90), (199), (213), % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) are inconsistent by sub-proof #1. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_183_0 = 0) & convergent_lines(all_20_4, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_183_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) ~ (all_183_0 = 0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) convergent_lines(all_20_4, all_20_3) = all_183_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_20_0 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (218) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) $false % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ? [v0: int] : ( ~ (v0 = 0) & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_2, all_20_4) = v0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (220) with fresh symbol all_287_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_287_0 = 0) & convergent_lines(all_20_2, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_4) = all_287_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_287_0 = 0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) convergent_lines(all_20_2, all_20_4) = all_287_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_191_1 = 0 & all_38_1 = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_3) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_38_1 = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (225) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) $false % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) (all_191_2 = 0 & all_191_3 = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0) | ( ~ % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_191_0 = 0) & convergent_lines(all_20_4, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_191_0) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_191_2 = 0 & all_191_3 = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_20_3, all_20_4) = 0 & % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) convergent_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) unorthogonal_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (22), (77), (90), (199), (229), % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) are inconsistent by sub-proof #1. % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_191_0 = 0) & convergent_lines(all_20_4, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3) = all_191_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) convergent_lines(all_20_4, all_20_3) = all_191_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_20_1, all_191_0, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_20_4, simplifying with (22), (232) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_191_0 = all_20_1 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_183_0, all_191_0, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_3, all_20_4, simplifying with (217), (232) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_191_0 = all_183_0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (234) imply: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_183_0 = all_20_1 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_20_3, all_20_4, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_242_0, simplifying with (19), (20), (199) % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_242_0 = 0 | unorthogonal_lines(all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_20_2, all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_4, all_287_0, simplifying with (19), (20), % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (21), (200), (223) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_287_0 = 0 | convergent_lines(all_20_3, % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) convergent_lines(all_20_3, all_20_4) = 0 % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) unorthogonal_lines(all_20_3, all_20_4) = 0 % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (17), (22), (77), (90), (199), (238), % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) are inconsistent by sub-proof #1. % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_242_0 = 0 % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (240) imply: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) $false % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_287_0 = 0 % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (242) imply: % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) $false % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent. % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 21.92/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_38_1 = 0 % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (244) imply: % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (245) $false % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | Case 2: % 22.00/4.15 | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | (246) all_33_0 = 0 % 22.00/4.15 | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | REDUCE: (78), (246) imply: % 22.00/4.15 | | | | | | | | | | | (247) $false % 22.00/4.15 | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | | CLOSE: (247) is inconsistent. % 22.00/4.15 | | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | | % 22.00/4.15 | | | | | | | | | Case 2: % 22.00/4.15 | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | (248) all_54_0 = 0 % 22.00/4.15 | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | REDUCE: (77), (248) imply: % 22.00/4.15 | | | | | | | | | | (249) $false % 22.00/4.15 | | | | | | | | | | % 22.00/4.15 | | | | | | | | | | CLOSE: (249) is inconsistent. % 22.00/4.15 | | | | | | | | | | % 22.00/4.15 | | | | | | | | | End of split % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | Case 2: % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | | (250) ~ (all_36_1 = 0) & convergent_lines(all_20_3, % 22.00/4.15 | | | | | | | | | all_20_2) = all_36_1 % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | | ALPHA: (250) implies: % 22.00/4.15 | | | | | | | | | (251) ~ (all_36_1 = 0) % 22.00/4.15 | | | | | | | | | (252) convergent_lines(all_20_3, all_20_2) = all_36_1 % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_36_1, all_20_2, % 22.00/4.15 | | | | | | | | | all_20_3, simplifying with (24), (252) gives: % 22.00/4.15 | | | | | | | | | (253) all_36_1 = 0 % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | | REDUCE: (251), (253) imply: % 22.00/4.15 | | | | | | | | | (254) $false % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | | CLOSE: (254) is inconsistent. % 22.00/4.15 | | | | | | | | | % 22.00/4.15 | | | | | | | | End of split % 22.00/4.15 | | | | | | | | % 22.00/4.15 | | | | | | | End of split % 22.00/4.15 | | | | | | | % 22.00/4.15 | | | | | | End of split % 22.00/4.15 | | | | | | % 22.00/4.15 | | | | | End of split % 22.00/4.15 | | | | | % 22.00/4.15 | | | | End of split % 22.00/4.15 | | | | % 22.00/4.15 | | | End of split % 22.00/4.15 | | | % 22.00/4.15 | | End of split % 22.00/4.15 | | % 22.00/4.15 | Case 2: % 22.00/4.15 | | % 22.00/4.15 | | (255) all_20_1 = 0 % 22.00/4.15 | | % 22.00/4.15 | | REDUCE: (17), (255) imply: % 22.00/4.15 | | (256) $false % 22.00/4.15 | | % 22.00/4.15 | | CLOSE: (256) is inconsistent. % 22.00/4.15 | | % 22.00/4.15 | End of split % 22.00/4.15 | % 22.00/4.15 End of proof % 22.00/4.15 % 22.00/4.15 Sub-proof #1 shows that the following formulas are inconsistent: % 22.00/4.15 ---------------------------------------------------------------- % 22.00/4.15 (1) convergent_lines(all_20_3, all_20_4) = 0 % 22.00/4.15 (2) ~ (all_54_0 = 0) % 22.00/4.15 (3) (all_89_2 = 0 & all_54_0 = 0 & unorthogonal_lines(all_20_4, all_20_4) = % 22.00/4.15 0) | (all_89_3 = 0 & convergent_lines(all_20_4, all_20_3) = 0) | ( ~ % 22.00/4.15 (all_89_0 = 0) & unorthogonal_lines(all_20_3, all_20_4) = all_89_0) | ( % 22.00/4.15 ~ (all_89_1 = 0) & convergent_lines(all_20_3, all_20_4) = all_89_1) % 22.00/4.15 (4) convergent_lines(all_20_4, all_20_3) = all_20_1 % 22.00/4.15 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.00/4.15 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.00/4.15 (convergent_lines(v3, v2) = v0)) % 22.00/4.15 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.00/4.15 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 22.00/4.15 (unorthogonal_lines(v3, v2) = v0)) % 22.00/4.15 (7) ~ (all_20_1 = 0) % 22.00/4.15 (8) unorthogonal_lines(all_20_3, all_20_4) = 0 % 22.00/4.15 (9) convergent_lines(all_20_3, all_20_4) = all_242_0 % 22.00/4.15 % 22.00/4.15 Begin of proof % 22.00/4.15 | % 22.00/4.15 | BETA: splitting (3) gives: % 22.00/4.15 | % 22.00/4.15 | Case 1: % 22.00/4.15 | | % 22.00/4.15 | | (10) (all_89_2 = 0 & all_54_0 = 0 & unorthogonal_lines(all_20_4, % 22.00/4.15 | | all_20_4) = 0) | (all_89_3 = 0 & convergent_lines(all_20_4, % 22.00/4.15 | | all_20_3) = 0) % 22.00/4.15 | | % 22.00/4.15 | | BETA: splitting (10) gives: % 22.00/4.15 | | % 22.00/4.15 | | Case 1: % 22.00/4.15 | | | % 22.00/4.15 | | | (11) all_89_2 = 0 & all_54_0 = 0 & unorthogonal_lines(all_20_4, % 22.00/4.15 | | | all_20_4) = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | ALPHA: (11) implies: % 22.00/4.15 | | | (12) all_54_0 = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | REDUCE: (2), (12) imply: % 22.00/4.15 | | | (13) $false % 22.00/4.15 | | | % 22.00/4.15 | | | CLOSE: (13) is inconsistent. % 22.00/4.15 | | | % 22.00/4.15 | | Case 2: % 22.00/4.15 | | | % 22.00/4.15 | | | (14) all_89_3 = 0 & convergent_lines(all_20_4, all_20_3) = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | ALPHA: (14) implies: % 22.00/4.15 | | | (15) convergent_lines(all_20_4, all_20_3) = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | REF_CLOSE: (4), (5), (7), (15) are inconsistent by sub-proof #2. % 22.00/4.15 | | | % 22.00/4.15 | | End of split % 22.00/4.15 | | % 22.00/4.15 | Case 2: % 22.00/4.15 | | % 22.00/4.15 | | (16) ( ~ (all_89_0 = 0) & unorthogonal_lines(all_20_3, all_20_4) = % 22.00/4.15 | | all_89_0) | ( ~ (all_89_1 = 0) & convergent_lines(all_20_3, % 22.00/4.15 | | all_20_4) = all_89_1) % 22.00/4.15 | | % 22.00/4.15 | | BETA: splitting (16) gives: % 22.00/4.15 | | % 22.00/4.15 | | Case 1: % 22.00/4.15 | | | % 22.00/4.15 | | | (17) ~ (all_89_0 = 0) & unorthogonal_lines(all_20_3, all_20_4) = % 22.00/4.15 | | | all_89_0 % 22.00/4.15 | | | % 22.00/4.15 | | | ALPHA: (17) implies: % 22.00/4.15 | | | (18) ~ (all_89_0 = 0) % 22.00/4.15 | | | (19) unorthogonal_lines(all_20_3, all_20_4) = all_89_0 % 22.00/4.15 | | | % 22.00/4.15 | | | GROUND_INST: instantiating (6) with 0, all_89_0, all_20_4, all_20_3, % 22.00/4.15 | | | simplifying with (8), (19) gives: % 22.00/4.15 | | | (20) all_89_0 = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | REDUCE: (18), (20) imply: % 22.00/4.15 | | | (21) $false % 22.00/4.15 | | | % 22.00/4.15 | | | CLOSE: (21) is inconsistent. % 22.00/4.15 | | | % 22.00/4.15 | | Case 2: % 22.00/4.15 | | | % 22.00/4.15 | | | (22) ~ (all_89_1 = 0) & convergent_lines(all_20_3, all_20_4) = % 22.00/4.15 | | | all_89_1 % 22.00/4.15 | | | % 22.00/4.15 | | | ALPHA: (22) implies: % 22.00/4.15 | | | (23) ~ (all_89_1 = 0) % 22.00/4.15 | | | (24) convergent_lines(all_20_3, all_20_4) = all_89_1 % 22.00/4.15 | | | % 22.00/4.15 | | | GROUND_INST: instantiating (5) with all_89_1, all_242_0, all_20_4, % 22.00/4.15 | | | all_20_3, simplifying with (9), (24) gives: % 22.00/4.15 | | | (25) all_242_0 = all_89_1 % 22.00/4.15 | | | % 22.00/4.15 | | | GROUND_INST: instantiating (5) with 0, all_242_0, all_20_4, all_20_3, % 22.00/4.15 | | | simplifying with (1), (9) gives: % 22.00/4.15 | | | (26) all_242_0 = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | COMBINE_EQS: (25), (26) imply: % 22.00/4.15 | | | (27) all_89_1 = 0 % 22.00/4.15 | | | % 22.00/4.15 | | | REDUCE: (23), (27) imply: % 22.00/4.15 | | | (28) $false % 22.00/4.15 | | | % 22.00/4.15 | | | CLOSE: (28) is inconsistent. % 22.00/4.15 | | | % 22.00/4.15 | | End of split % 22.00/4.15 | | % 22.00/4.15 | End of split % 22.00/4.15 | % 22.00/4.15 End of proof % 22.00/4.15 % 22.00/4.15 Sub-proof #2 shows that the following formulas are inconsistent: % 22.00/4.15 ---------------------------------------------------------------- % 22.00/4.15 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.00/4.15 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 22.00/4.15 (convergent_lines(v3, v2) = v0)) % 22.00/4.15 (2) convergent_lines(all_20_4, all_20_3) = all_20_1 % 22.00/4.15 (3) convergent_lines(all_20_4, all_20_3) = 0 % 22.00/4.15 (4) ~ (all_20_1 = 0) % 22.00/4.15 % 22.00/4.15 Begin of proof % 22.00/4.15 | % 22.00/4.15 | GROUND_INST: instantiating (1) with all_20_1, 0, all_20_3, all_20_4, % 22.00/4.15 | simplifying with (2), (3) gives: % 22.00/4.15 | (5) all_20_1 = 0 % 22.00/4.15 | % 22.00/4.15 | REDUCE: (4), (5) imply: % 22.00/4.15 | (6) $false % 22.00/4.15 | % 22.00/4.15 | CLOSE: (6) is inconsistent. % 22.00/4.15 | % 22.00/4.15 End of proof % 22.00/4.15 % SZS output end Proof for theBenchmark % 22.00/4.15 % 22.00/4.16 3551ms %------------------------------------------------------------------------------