TSTP Solution File: GEO212+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO212+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:22:22 EDT 2023
% Result : Theorem 12.65s 2.57s
% Output : Proof 21.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO212+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 20:55:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.74/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.74/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.74/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.74/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.74/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.74/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.74/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.80/1.12 Prover 4: Preprocessing ...
% 2.80/1.12 Prover 1: Preprocessing ...
% 2.80/1.17 Prover 6: Preprocessing ...
% 2.80/1.17 Prover 2: Preprocessing ...
% 2.80/1.17 Prover 3: Preprocessing ...
% 2.80/1.17 Prover 0: Preprocessing ...
% 2.80/1.17 Prover 5: Preprocessing ...
% 4.86/1.46 Prover 5: Proving ...
% 4.86/1.47 Prover 2: Proving ...
% 4.86/1.49 Prover 3: Constructing countermodel ...
% 5.56/1.51 Prover 6: Constructing countermodel ...
% 5.56/1.52 Prover 1: Constructing countermodel ...
% 6.17/1.67 Prover 3: gave up
% 6.17/1.67 Prover 6: gave up
% 6.17/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.17/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.17/1.68 Prover 4: Constructing countermodel ...
% 7.07/1.71 Prover 1: gave up
% 7.12/1.72 Prover 0: Proving ...
% 7.12/1.72 Prover 7: Preprocessing ...
% 7.12/1.72 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.12/1.75 Prover 8: Preprocessing ...
% 7.12/1.76 Prover 9: Preprocessing ...
% 7.12/1.77 Prover 7: Warning: ignoring some quantifiers
% 7.12/1.79 Prover 7: Constructing countermodel ...
% 7.81/1.85 Prover 8: Warning: ignoring some quantifiers
% 7.81/1.86 Prover 7: gave up
% 7.81/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.81/1.87 Prover 8: Constructing countermodel ...
% 7.81/1.92 Prover 10: Preprocessing ...
% 8.84/1.97 Prover 10: Warning: ignoring some quantifiers
% 8.84/1.98 Prover 10: Constructing countermodel ...
% 8.84/2.01 Prover 8: gave up
% 8.84/2.02 Prover 10: gave up
% 8.84/2.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.84/2.03 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 9.61/2.06 Prover 11: Preprocessing ...
% 9.61/2.06 Prover 12: Preprocessing ...
% 9.61/2.09 Prover 9: Constructing countermodel ...
% 10.03/2.14 Prover 12: Proving ...
% 11.03/2.27 Prover 11: Constructing countermodel ...
% 12.65/2.56 Prover 0: proved (1927ms)
% 12.65/2.57
% 12.65/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.65/2.57
% 12.65/2.57 Prover 9: stopped
% 12.65/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.65/2.58 Prover 5: stopped
% 12.65/2.58 Prover 12: stopped
% 12.65/2.58 Prover 2: stopped
% 12.65/2.58 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.65/2.58 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.74/2.62 Prover 16: Preprocessing ...
% 13.74/2.62 Prover 13: Preprocessing ...
% 13.74/2.62 Prover 19: Preprocessing ...
% 13.74/2.64 Prover 16: Warning: ignoring some quantifiers
% 13.74/2.65 Prover 16: Constructing countermodel ...
% 14.12/2.67 Prover 13: Warning: ignoring some quantifiers
% 14.12/2.67 Prover 13: Constructing countermodel ...
% 14.12/2.68 Prover 19: Warning: ignoring some quantifiers
% 14.12/2.69 Prover 19: Constructing countermodel ...
% 14.12/2.71 Prover 13: gave up
% 14.55/2.71 Prover 16: gave up
% 14.55/2.73 Prover 19: gave up
% 19.56/3.70 Prover 11: Found proof (size 633)
% 19.56/3.70 Prover 11: proved (1679ms)
% 19.56/3.70 Prover 4: stopped
% 19.56/3.70
% 19.56/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.56/3.70
% 20.04/3.76 % SZS output start Proof for theBenchmark
% 20.04/3.78 Assumptions after simplification:
% 20.04/3.78 ---------------------------------
% 20.04/3.78
% 20.04/3.78 (apart3)
% 20.36/3.81 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 20.36/3.81
% 20.36/3.81 (apart6)
% 20.36/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 20.36/3.82 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 20.36/3.82 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 20.36/3.82 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 20.36/3.82 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~
% 20.36/3.82 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.82 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.36/3.82 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 20.36/3.82 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.82 convergent_lines(v1, v2) = 0)
% 20.36/3.82
% 20.36/3.82 (con)
% 20.36/3.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~
% 20.36/3.83 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 &
% 20.36/3.83 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v2) = v3 & $i(v2) &
% 20.36/3.83 $i(v1) & $i(v0))
% 20.36/3.83
% 20.36/3.83 (oac1)
% 20.36/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 20.36/3.85 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) |
% 20.36/3.85 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7:
% 20.36/3.85 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.85 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.85 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 20.36/3.85 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 20.36/3.85 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~
% 20.36/3.85 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 20.36/3.85 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.85 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 20.36/3.85 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 20.36/3.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 20.36/3.85 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~
% 20.36/3.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int]
% 20.36/3.85 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 =
% 20.36/3.85 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.85 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 20.36/3.85 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 20.36/3.85 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 20.36/3.85 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 20.36/3.85 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 20.36/3.85 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 20.36/3.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 20.36/3.85 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 20.36/3.85 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 20.36/3.85 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 20.36/3.85 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~
% 20.36/3.85 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 20.36/3.85 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 20.36/3.85 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 20.36/3.85 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 20.36/3.85 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.36/3.85 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 20.36/3.85 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 20.36/3.85 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.36/3.85 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 20.36/3.85 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 20.36/3.85 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 20.36/3.85 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 20.36/3.85 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 20.36/3.85 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.36/3.85 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~
% 20.36/3.85 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 20.36/3.85 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 20.36/3.85 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~
% 20.36/3.85 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 20.36/3.85 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85 unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.85
% 20.36/3.85 (occu1)
% 20.36/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 20.36/3.85 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.85 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 20.36/3.85 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.85 unorthogonal_lines(v0, v1) = 0)
% 20.36/3.85
% 20.36/3.85 (function-axioms)
% 20.36/3.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.36/3.86 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 20.36/3.86 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 20.36/3.86 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 20.36/3.86 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.36/3.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 20.36/3.86 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.36/3.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 20.36/3.86 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 20.36/3.86 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 20.36/3.86 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 20.36/3.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.36/3.86 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 20.36/3.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 20.36/3.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 20.36/3.86 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 20.36/3.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.36/3.86 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 20.36/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.36/3.86 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 20.36/3.86 v0))
% 20.36/3.86
% 20.36/3.86 Further assumptions not needed in the proof:
% 20.36/3.86 --------------------------------------------
% 20.36/3.86 apart1, apart2, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cp1, cp2, cu1,
% 20.36/3.86 cup1, ooc1, ooc2, ouo1
% 20.36/3.86
% 20.36/3.86 Those formulas are unsatisfiable:
% 20.36/3.86 ---------------------------------
% 20.36/3.86
% 20.36/3.86 Begin of proof
% 20.36/3.86 |
% 20.36/3.86 | ALPHA: (apart6) implies:
% 20.36/3.86 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 20.36/3.86 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 20.36/3.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 20.36/3.86 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 20.36/3.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 20.36/3.86 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~
% 20.36/3.86 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.86 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 20.36/3.86 |
% 20.36/3.86 | ALPHA: (occu1) implies:
% 20.36/3.86 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 20.36/3.87 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.87 | unorthogonal_lines(v0, v1) = 0)
% 20.36/3.87 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 20.36/3.87 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 20.36/3.87 | convergent_lines(v0, v1) = 0)
% 20.36/3.87 |
% 20.36/3.87 | ALPHA: (oac1) implies:
% 20.36/3.87 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.87 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.87 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 20.36/3.87 | [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v1,
% 20.36/3.87 | v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 &
% 20.36/3.87 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87 | unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.87 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.87 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3)
% 20.36/3.87 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 20.36/3.87 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87 | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87 | convergent_lines(v0, v1) = v4)))
% 20.36/3.87 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.87 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0)
% 20.36/3.87 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 20.36/3.87 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87 | unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.87 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.87 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) =
% 20.36/3.87 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 20.36/3.87 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87 | convergent_lines(v0, v1) = v4)))
% 20.36/3.88 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.88 | (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) =
% 20.36/3.88 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 20.36/3.88 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.88 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.88 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 20.36/3.88 | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.88 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 20.36/3.88 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) =
% 20.36/3.88 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 20.36/3.88 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.88 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.88 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 20.36/3.88 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 20.36/3.88 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 20.36/3.88 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) =
% 20.36/3.88 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 20.36/3.88 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.88 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.88 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.88 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.88 | convergent_lines(v0, v1) = v5)))
% 20.36/3.89 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 20.36/3.89 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2)
% 20.36/3.89 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 20.36/3.89 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89 | convergent_lines(v0, v1) = v5)))
% 20.36/3.89 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 20.36/3.89 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2)
% 20.36/3.89 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 20.36/3.89 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89 | convergent_lines(v0, v1) = v5)))
% 20.36/3.89 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 20.36/3.89 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0,
% 20.36/3.89 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] :
% 20.36/3.89 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89 | convergent_lines(v0, v1) = v5)))
% 20.36/3.89 |
% 20.36/3.89 | ALPHA: (function-axioms) implies:
% 20.36/3.90 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 20.36/3.90 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 20.36/3.90 | (convergent_lines(v3, v2) = v0))
% 20.36/3.90 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 20.36/3.90 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 20.36/3.90 | (unorthogonal_lines(v3, v2) = v0))
% 20.36/3.90 |
% 20.36/3.90 | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2,
% 20.36/3.90 | all_23_3, all_23_4 gives:
% 20.36/3.90 | (18) ~ (all_23_0 = 0) & ~ (all_23_1 = 0) & unorthogonal_lines(all_23_3,
% 20.36/3.90 | all_23_2) = all_23_0 & unorthogonal_lines(all_23_4, all_23_3) = 0 &
% 20.36/3.90 | convergent_lines(all_23_4, all_23_2) = all_23_1 & $i(all_23_2) &
% 20.36/3.90 | $i(all_23_3) & $i(all_23_4)
% 20.36/3.90 |
% 20.36/3.90 | ALPHA: (18) implies:
% 20.36/3.90 | (19) ~ (all_23_1 = 0)
% 20.36/3.90 | (20) ~ (all_23_0 = 0)
% 20.36/3.90 | (21) $i(all_23_4)
% 20.36/3.90 | (22) $i(all_23_3)
% 20.36/3.90 | (23) $i(all_23_2)
% 20.36/3.90 | (24) convergent_lines(all_23_4, all_23_2) = all_23_1
% 20.36/3.90 | (25) unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.36/3.90 | (26) unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.36/3.90 |
% 20.36/3.90 | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_2, all_23_1,
% 20.36/3.90 | all_23_1, simplifying with (21), (23), (24) gives:
% 20.36/3.91 | (27) all_23_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 20.36/3.91 | convergent_lines(all_23_4, all_23_4) = v0)
% 20.36/3.91 |
% 20.36/3.91 | GROUND_INST: instantiating (12) with all_23_4, all_23_4, all_23_2, all_23_1,
% 20.36/3.91 | all_23_1, simplifying with (21), (23), (24) gives:
% 20.36/3.91 | (28) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.91 | all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (v2 =
% 20.36/3.91 | 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (
% 20.36/3.91 | ~ (v1 = 0) & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~
% 20.36/3.91 | (v0 = 0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.36/3.91 |
% 20.36/3.91 | GROUND_INST: instantiating (4) with all_23_4, all_23_2, all_23_1, simplifying
% 20.36/3.91 | with (21), (23), (24) gives:
% 20.36/3.91 | (29) all_23_1 = 0 | unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.36/3.91 |
% 20.36/3.91 | GROUND_INST: instantiating (15) with all_23_4, all_23_4, all_23_3, 0, 0,
% 20.36/3.91 | simplifying with (21), (22), (25) gives:
% 20.36/3.91 | (30) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.91 | convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0 &
% 20.36/3.91 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) &
% 20.36/3.91 | unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = 0) &
% 20.36/3.91 | convergent_lines(all_23_4, all_23_4) = v0))
% 20.36/3.91 |
% 20.36/3.91 | GROUND_INST: instantiating (9) with all_23_4, all_23_3, all_23_3, 0,
% 20.36/3.91 | simplifying with (21), (22), (25) gives:
% 20.36/3.92 | (31) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.92 | v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 20.36/3.92 | convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 &
% 20.36/3.92 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92 | convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92 |
% 20.36/3.92 | GROUND_INST: instantiating (7) with all_23_4, all_23_3, all_23_2, all_23_1,
% 20.36/3.92 | simplifying with (21), (22), (23), (24), (25) gives:
% 20.36/3.92 | (32) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.92 | v2 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0 &
% 20.36/3.92 | convergent_lines(all_23_3, all_23_2) = 0) | (v1 = 0 & all_23_1 = 0
% 20.36/3.92 | & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92 | convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92 |
% 20.36/3.92 | GROUND_INST: instantiating (15) with all_23_3, all_23_3, all_23_2, all_23_0,
% 20.36/3.92 | all_23_0, simplifying with (22), (23), (26) gives:
% 20.36/3.92 | (33) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.92 | all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92 | & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.36/3.92 | (v1 = 0) & unorthogonal_lines(all_23_3, all_23_3) = v1) | ( ~ (v0
% 20.36/3.92 | = 0) & convergent_lines(all_23_3, all_23_3) = v0))
% 20.36/3.92 |
% 20.36/3.92 | GROUND_INST: instantiating (11) with all_23_4, all_23_3, all_23_2, all_23_0,
% 20.36/3.92 | simplifying with (21), (22), (23), (25), (26) gives:
% 20.36/3.92 | (34) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.92 | all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92 | & v1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 20.36/3.92 | convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92 | convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92 |
% 20.36/3.92 | GROUND_INST: instantiating (14) with all_23_4, all_23_3, all_23_2, all_23_1,
% 20.36/3.92 | all_23_0, simplifying with (21), (22), (23), (24), (26) gives:
% 20.36/3.92 | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.92 | all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92 | & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.92 | (v1 = 0) & unorthogonal_lines(all_23_4, all_23_3) = v1) | ( ~ (v0
% 20.36/3.92 | = 0) & convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92 |
% 20.36/3.92 | GROUND_INST: instantiating (13) with all_23_3, all_23_4, all_23_2, all_23_0,
% 20.36/3.92 | all_23_1, simplifying with (21), (22), (23), (24), (26) gives:
% 20.36/3.93 | (36) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 20.36/3.93 | all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (v2 =
% 20.36/3.93 | 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.36/3.93 | (v1 = 0) & unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0
% 20.36/3.93 | = 0) & convergent_lines(all_23_3, all_23_4) = v0))
% 20.36/3.93 |
% 20.36/3.93 | GROUND_INST: instantiating (5) with all_23_3, all_23_2, all_23_0, simplifying
% 20.36/3.93 | with (22), (23), (26) gives:
% 20.36/3.93 | (37) all_23_0 = 0 | convergent_lines(all_23_3, all_23_2) = 0
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1, all_30_2,
% 20.36/3.93 | all_30_3 gives:
% 20.36/3.93 | (38) (all_30_0 = 0 & all_30_1 = 0 & unorthogonal_lines(all_23_3, all_23_3)
% 20.36/3.93 | = 0 & convergent_lines(all_23_3, all_23_3) = 0) | (all_30_2 = 0 &
% 20.36/3.93 | convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_30_3 = 0) &
% 20.36/3.93 | convergent_lines(all_23_4, all_23_3) = all_30_3)
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (30) with fresh symbols all_31_0, all_31_1, all_31_2,
% 20.36/3.93 | all_31_3 gives:
% 20.36/3.93 | (39) (all_31_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (all_31_1
% 20.36/3.93 | = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_31_2 = 0)
% 20.36/3.93 | & unorthogonal_lines(all_23_4, all_23_4) = all_31_2) | ( ~ (all_31_3
% 20.36/3.93 | = 0) & convergent_lines(all_23_4, all_23_4) = all_31_3)
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2,
% 20.36/3.93 | all_32_3 gives:
% 20.36/3.93 | (40) (all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_23_3, all_23_2)
% 20.36/3.93 | = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (all_32_2 = 0 &
% 20.36/3.93 | all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.93 | (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_32_3)
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (34) with fresh symbols all_33_0, all_33_1, all_33_2,
% 20.36/3.93 | all_33_3 gives:
% 20.36/3.93 | (41) (all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.36/3.93 | 0) | (all_33_1 = 0 & all_33_2 = 0 & unorthogonal_lines(all_23_4,
% 20.36/3.93 | all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.93 | (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_33_3)
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (33) with fresh symbols all_34_0, all_34_1, all_34_2,
% 20.36/3.93 | all_34_3 gives:
% 20.36/3.93 | (42) (all_34_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.36/3.93 | 0) | (all_34_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 20.36/3.93 | all_23_2) = 0) | ( ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 20.36/3.93 | all_23_3) = all_34_2) | ( ~ (all_34_3 = 0) &
% 20.36/3.93 | convergent_lines(all_23_3, all_23_3) = all_34_3)
% 20.36/3.93 |
% 20.36/3.93 | DELTA: instantiating (28) with fresh symbols all_35_0, all_35_1, all_35_2,
% 20.36/3.93 | all_35_3 gives:
% 21.03/3.93 | (43) (all_35_0 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2)
% 21.03/3.93 | = 0) | (all_35_1 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.93 | all_23_2) = 0) | ( ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.03/3.93 | all_23_4) = all_35_2) | ( ~ (all_35_3 = 0) &
% 21.03/3.93 | convergent_lines(all_23_4, all_23_4) = all_35_3)
% 21.03/3.93 |
% 21.03/3.93 | DELTA: instantiating (36) with fresh symbols all_36_0, all_36_1, all_36_2,
% 21.03/3.93 | all_36_3 gives:
% 21.03/3.93 | (44) (all_36_0 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2)
% 21.03/3.93 | = 0) | (all_36_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 21.03/3.93 | all_23_2) = 0) | ( ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.03/3.93 | all_23_4) = all_36_2) | ( ~ (all_36_3 = 0) &
% 21.03/3.93 | convergent_lines(all_23_3, all_23_4) = all_36_3)
% 21.03/3.93 |
% 21.03/3.93 | DELTA: instantiating (35) with fresh symbols all_37_0, all_37_1, all_37_2,
% 21.03/3.93 | all_37_3 gives:
% 21.03/3.93 | (45) (all_37_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 21.03/3.93 | 0) | (all_37_1 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.93 | all_23_2) = 0) | ( ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.03/3.93 | all_23_3) = all_37_2) | ( ~ (all_37_3 = 0) &
% 21.03/3.93 | convergent_lines(all_23_4, all_23_3) = all_37_3)
% 21.03/3.93 |
% 21.03/3.93 | BETA: splitting (29) gives:
% 21.03/3.93 |
% 21.03/3.93 | Case 1:
% 21.03/3.93 | |
% 21.03/3.93 | | (46) unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.03/3.93 | |
% 21.03/3.93 | | BETA: splitting (37) gives:
% 21.03/3.93 | |
% 21.03/3.93 | | Case 1:
% 21.03/3.93 | | |
% 21.03/3.93 | | | (47) convergent_lines(all_23_3, all_23_2) = 0
% 21.03/3.93 | | |
% 21.03/3.93 | | | BETA: splitting (40) gives:
% 21.03/3.93 | | |
% 21.03/3.93 | | | Case 1:
% 21.03/3.93 | | | |
% 21.03/3.93 | | | | (48) all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_23_3,
% 21.03/3.93 | | | | all_23_2) = 0 & convergent_lines(all_23_3, all_23_2) = 0
% 21.03/3.93 | | | |
% 21.03/3.93 | | | | ALPHA: (48) implies:
% 21.03/3.93 | | | | (49) unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.03/3.94 | | | |
% 21.03/3.94 | | | | REF_CLOSE: (17), (20), (26), (49) are inconsistent by sub-proof #6.
% 21.03/3.94 | | | |
% 21.03/3.94 | | | Case 2:
% 21.03/3.94 | | | |
% 21.03/3.94 | | | | (50) (all_32_2 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.94 | | | | all_23_2) = 0) | ( ~ (all_32_3 = 0) &
% 21.03/3.94 | | | | convergent_lines(all_23_4, all_23_3) = all_32_3)
% 21.03/3.94 | | | |
% 21.03/3.94 | | | | BETA: splitting (50) gives:
% 21.03/3.94 | | | |
% 21.03/3.94 | | | | Case 1:
% 21.03/3.94 | | | | |
% 21.03/3.94 | | | | | (51) all_32_2 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.94 | | | | | all_23_2) = 0
% 21.03/3.94 | | | | |
% 21.03/3.94 | | | | | ALPHA: (51) implies:
% 21.03/3.94 | | | | | (52) all_23_1 = 0
% 21.03/3.94 | | | | |
% 21.03/3.94 | | | | | REDUCE: (19), (52) imply:
% 21.03/3.94 | | | | | (53) $false
% 21.03/3.94 | | | | |
% 21.03/3.94 | | | | | CLOSE: (53) is inconsistent.
% 21.03/3.94 | | | | |
% 21.03/3.94 | | | | Case 2:
% 21.03/3.94 | | | | |
% 21.07/3.94 | | | | | (54) ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 21.07/3.94 | | | | | all_32_3
% 21.07/3.94 | | | | |
% 21.07/3.94 | | | | | ALPHA: (54) implies:
% 21.07/3.94 | | | | | (55) convergent_lines(all_23_4, all_23_3) = all_32_3
% 21.07/3.94 | | | | |
% 21.07/3.94 | | | | | BETA: splitting (27) gives:
% 21.07/3.94 | | | | |
% 21.07/3.94 | | | | | Case 1:
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | (56) all_23_1 = 0
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | REDUCE: (19), (56) imply:
% 21.07/3.94 | | | | | | (57) $false
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | CLOSE: (57) is inconsistent.
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | Case 2:
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.07/3.94 | | | | | | all_23_4) = v0)
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | DELTA: instantiating (58) with fresh symbol all_51_0 gives:
% 21.07/3.94 | | | | | | (59) ~ (all_51_0 = 0) & convergent_lines(all_23_4, all_23_4) =
% 21.07/3.94 | | | | | | all_51_0
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | ALPHA: (59) implies:
% 21.07/3.94 | | | | | | (60) ~ (all_51_0 = 0)
% 21.07/3.94 | | | | | | (61) convergent_lines(all_23_4, all_23_4) = all_51_0
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | BETA: splitting (41) gives:
% 21.07/3.94 | | | | | |
% 21.07/3.94 | | | | | | Case 1:
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | (62) all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 21.07/3.94 | | | | | | | all_23_2) = 0
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | ALPHA: (62) implies:
% 21.07/3.94 | | | | | | | (63) all_23_0 = 0
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | REDUCE: (20), (63) imply:
% 21.07/3.94 | | | | | | | (64) $false
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | CLOSE: (64) is inconsistent.
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | Case 2:
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | (65) (all_33_1 = 0 & all_33_2 = 0 &
% 21.07/3.94 | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 21.07/3.94 | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.07/3.94 | | | | | | | (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 21.07/3.94 | | | | | | | all_33_3)
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | BETA: splitting (65) gives:
% 21.07/3.94 | | | | | | |
% 21.07/3.94 | | | | | | | Case 1:
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | (66) all_33_1 = 0 & all_33_2 = 0 &
% 21.07/3.94 | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 21.07/3.94 | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | ALPHA: (66) implies:
% 21.07/3.94 | | | | | | | | (67) convergent_lines(all_23_4, all_23_2) = 0
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | REF_CLOSE: (16), (19), (24), (67) are inconsistent by sub-proof
% 21.07/3.94 | | | | | | | | #5.
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | Case 2:
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | (68) ~ (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3)
% 21.07/3.94 | | | | | | | | = all_33_3
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | ALPHA: (68) implies:
% 21.07/3.94 | | | | | | | | (69) ~ (all_33_3 = 0)
% 21.07/3.94 | | | | | | | | (70) convergent_lines(all_23_4, all_23_3) = all_33_3
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | BETA: splitting (45) gives:
% 21.07/3.94 | | | | | | | |
% 21.07/3.94 | | | | | | | | Case 1:
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | (71) (all_37_0 = 0 & all_23_0 = 0 &
% 21.07/3.94 | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) |
% 21.07/3.94 | | | | | | | | | (all_37_1 = 0 & all_23_1 = 0 &
% 21.07/3.94 | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0)
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | BETA: splitting (71) gives:
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | Case 1:
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | (72) all_37_0 = 0 & all_23_0 = 0 &
% 21.07/3.94 | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | ALPHA: (72) implies:
% 21.07/3.94 | | | | | | | | | | (73) all_23_0 = 0
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | REDUCE: (20), (73) imply:
% 21.07/3.94 | | | | | | | | | | (74) $false
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | CLOSE: (74) is inconsistent.
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | Case 2:
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | (75) all_37_1 = 0 & all_23_1 = 0 &
% 21.07/3.94 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | ALPHA: (75) implies:
% 21.07/3.94 | | | | | | | | | | (76) all_23_1 = 0
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | REDUCE: (19), (76) imply:
% 21.07/3.94 | | | | | | | | | | (77) $false
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | CLOSE: (77) is inconsistent.
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | End of split
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | Case 2:
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | (78) ( ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.94 | | | | | | | | | all_23_3) = all_37_2) | ( ~ (all_37_3 = 0) &
% 21.07/3.94 | | | | | | | | | convergent_lines(all_23_4, all_23_3) = all_37_3)
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | BETA: splitting (78) gives:
% 21.07/3.94 | | | | | | | | |
% 21.07/3.94 | | | | | | | | | Case 1:
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | (79) ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.94 | | | | | | | | | | all_23_3) = all_37_2
% 21.07/3.94 | | | | | | | | | |
% 21.07/3.94 | | | | | | | | | | ALPHA: (79) implies:
% 21.07/3.94 | | | | | | | | | | (80) ~ (all_37_2 = 0)
% 21.07/3.95 | | | | | | | | | | (81) unorthogonal_lines(all_23_4, all_23_3) = all_37_2
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_37_2, all_23_3,
% 21.07/3.95 | | | | | | | | | | all_23_4, simplifying with (25), (81) gives:
% 21.07/3.95 | | | | | | | | | | (82) all_37_2 = 0
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | REDUCE: (80), (82) imply:
% 21.07/3.95 | | | | | | | | | | (83) $false
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | CLOSE: (83) is inconsistent.
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | Case 2:
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | (84) ~ (all_37_3 = 0) & convergent_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3) = all_37_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | ALPHA: (84) implies:
% 21.07/3.95 | | | | | | | | | | (85) convergent_lines(all_23_4, all_23_3) = all_37_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_33_3, all_37_3,
% 21.07/3.95 | | | | | | | | | | all_23_3, all_23_4, simplifying with (70), (85)
% 21.07/3.95 | | | | | | | | | | gives:
% 21.07/3.95 | | | | | | | | | | (86) all_37_3 = all_33_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_37_3,
% 21.07/3.95 | | | | | | | | | | all_23_3, all_23_4, simplifying with (55), (85)
% 21.07/3.95 | | | | | | | | | | gives:
% 21.07/3.95 | | | | | | | | | | (87) all_37_3 = all_32_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | COMBINE_EQS: (86), (87) imply:
% 21.07/3.95 | | | | | | | | | | (88) all_33_3 = all_32_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | SIMP: (88) implies:
% 21.07/3.95 | | | | | | | | | | (89) all_33_3 = all_32_3
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | REDUCE: (69), (89) imply:
% 21.07/3.95 | | | | | | | | | | (90) ~ (all_32_3 = 0)
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_4, all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4, all_51_0, all_51_0, simplifying with
% 21.07/3.95 | | | | | | | | | | (21), (61) gives:
% 21.07/3.95 | | | | | | | | | | (91) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & all_51_0 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.07/3.95 | | | | | | | | | | (v2 = 0 & all_51_0 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.07/3.95 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_3,
% 21.07/3.95 | | | | | | | | | | all_23_4, all_51_0, simplifying with (21), (22),
% 21.07/3.95 | | | | | | | | | | (25), (61) gives:
% 21.07/3.95 | | | | | | | | | | (92) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) | (v1
% 21.07/3.95 | | | | | | | | | | = 0 & all_51_0 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.07/3.95 | | | | | | | | | | ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_4, all_23_4,
% 21.07/3.95 | | | | | | | | | | all_51_0, simplifying with (21), (61) gives:
% 21.07/3.95 | | | | | | | | | | (93) all_51_0 = 0 | unorthogonal_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4) = 0
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_4, all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3, all_32_3, all_32_3, simplifying with
% 21.07/3.95 | | | | | | | | | | (21), (22), (55) gives:
% 21.07/3.95 | | | | | | | | | | (94) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & all_32_3 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.07/3.95 | | | | | | | | | | (v2 = 0 & all_32_3 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.07/3.95 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3, all_32_3, 0, simplifying with (21),
% 21.07/3.95 | | | | | | | | | | (22), (25), (55) gives:
% 21.07/3.95 | | | | | | | | | | (95) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3) = 0) | (v2 = 0 & all_32_3 = 0) | ( ~
% 21.07/3.95 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_3, 0, all_32_3, simplifying with (21),
% 21.07/3.95 | | | | | | | | | | (22), (25), (55) gives:
% 21.07/3.95 | | | | | | | | | | (96) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & all_32_3 = 0) | (v2 = 0 &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.07/3.95 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_3,
% 21.07/3.95 | | | | | | | | | | all_23_3, all_32_3, simplifying with (21), (22),
% 21.07/3.95 | | | | | | | | | | (25), (55) gives:
% 21.07/3.95 | | | | | | | | | | (97) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.95 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.95 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0) | (v1
% 21.07/3.95 | | | | | | | | | | = 0 & all_32_3 = 0) | ( ~ (v0 = 0) &
% 21.07/3.95 | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = v0))
% 21.07/3.95 | | | | | | | | | |
% 21.07/3.95 | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_3, all_23_3,
% 21.07/3.95 | | | | | | | | | | all_23_2, 0, 0, simplifying with (22), (23), (47)
% 21.07/3.95 | | | | | | | | | | gives:
% 21.07/3.96 | | | | | | | | | | (98) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.96 | | | | | | | | | | int] : ((v3 = 0 & unorthogonal_lines(all_23_3,
% 21.07/3.96 | | | | | | | | | | all_23_2) = 0) | (v2 = 0 &
% 21.07/3.96 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0) | (
% 21.07/3.96 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_23_3,
% 21.07/3.96 | | | | | | | | | | all_23_3) = v1) | ( ~ (v0 = 0) &
% 21.07/3.96 | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = v0))
% 21.07/3.96 | | | | | | | | | |
% 21.07/3.96 | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_2,
% 21.07/3.96 | | | | | | | | | | all_23_2, 0, simplifying with (22), (23), (47)
% 21.07/3.96 | | | | | | | | | | gives:
% 21.07/3.96 | | | | | | | | | | (99) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 21.07/3.96 | | | | | | | | | | int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.07/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.07/3.96 | | | | | | | | | | = 0 & unorthogonal_lines(all_23_3, all_23_2) =
% 21.07/3.96 | | | | | | | | | | 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_23_3,
% 21.07/3.96 | | | | | | | | | | all_23_2) = v0))
% 21.07/3.96 | | | | | | | | | |
% 21.07/3.96 | | | | | | | | | | GROUND_INST: instantiating (8) with all_23_3, all_23_2,
% 21.07/3.96 | | | | | | | | | | all_23_2, all_23_0, simplifying with (22), (23),
% 21.07/3.96 | | | | | | | | | | (26), (47) gives:
% 21.07/3.96 | | | | | | | | | | (100) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.07/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.07/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.07/3.96 | | | | | | | | | | = 0 & all_23_0 = 0) | ( ~ (v0 = 0) &
% 21.07/3.96 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = v0))
% 21.07/3.96 | | | | | | | | | |
% 21.07/3.96 | | | | | | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4,
% 21.07/3.96 | | | | | | | | | | all_23_2, 0, 0, simplifying with (21), (23), (46)
% 21.07/3.96 | | | | | | | | | | gives:
% 21.07/3.96 | | | | | | | | | | (101) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.07/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.07/3.96 | | | | | | | | | | all_23_2) = 0) | (v2 = 0 &
% 21.07/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.07/3.96 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.96 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.96 | | | | | | | | | |
% 21.07/3.96 | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 21.07/3.96 | | | | | | | | | | all_23_2, 0, simplifying with (21), (23), (46)
% 21.07/3.96 | | | | | | | | | | gives:
% 21.18/3.96 | | | | | | | | | | (102) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.18/3.96 | | | | | | | | | | = 0 & convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/3.96 | | | | | | | | | | | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2, all_23_1, 0, simplifying with (21),
% 21.18/3.96 | | | | | | | | | | (23), (24), (46) gives:
% 21.18/3.96 | | | | | | | | | | (103) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2) = 0) | (v2 = 0 & all_23_1 = 0) | (
% 21.18/3.96 | | | | | | | | | | ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2, 0, all_23_1, simplifying with (21),
% 21.18/3.96 | | | | | | | | | | (23), (24), (46) gives:
% 21.18/3.96 | | | | | | | | | | (104) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & all_23_1 = 0) | (v2 = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.96 | | | | | | | | | | (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 21.18/3.96 | | | | | | | | | | all_23_3, 0, simplifying with (21), (22), (23),
% 21.18/3.96 | | | | | | | | | | (25), (46) gives:
% 21.18/3.96 | | | | | | | | | | (105) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | (v1
% 21.18/3.96 | | | | | | | | | | = 0 & convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.96 | | | | | | | | | | | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96 | | | | | | | | | | all_23_2, all_23_1, simplifying with (21), (23),
% 21.18/3.96 | | | | | | | | | | (24), (46) gives:
% 21.18/3.96 | | | | | | | | | | (106) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.18/3.96 | | | | | | | | | | = 0 & all_23_1 = 0) | ( ~ (v0 = 0) &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96 | | | | | | | | | | all_23_3, all_32_3, simplifying with (21), (22),
% 21.18/3.96 | | | | | | | | | | (23), (46), (55) gives:
% 21.18/3.96 | | | | | | | | | | (107) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) | (v1
% 21.18/3.96 | | | | | | | | | | = 0 & all_32_3 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.18/3.96 | | | | | | | | | | ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96 | | | | | | | | | | all_23_4, all_51_0, simplifying with (21), (23),
% 21.18/3.96 | | | | | | | | | | (46), (61) gives:
% 21.18/3.96 | | | | | | | | | | (108) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/3.96 | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.18/3.96 | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0) | (v1
% 21.18/3.96 | | | | | | | | | | = 0 & all_51_0 = 0 &
% 21.18/3.96 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.18/3.96 | | | | | | | | | | ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96 | | | | | | | | | | all_23_2) = v0))
% 21.18/3.96 | | | | | | | | | |
% 21.18/3.96 | | | | | | | | | | DELTA: instantiating (100) with fresh symbols all_71_0,
% 21.18/3.96 | | | | | | | | | | all_71_1, all_71_2, all_71_3 gives:
% 21.18/3.97 | | | | | | | | | | (109) (all_71_0 = 0 & all_71_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_71_2 = 0 & all_23_0 = 0) | ( ~ (all_71_3 = 0)
% 21.18/3.97 | | | | | | | | | | & unorthogonal_lines(all_23_3, all_23_2) =
% 21.18/3.97 | | | | | | | | | | all_71_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_72_0,
% 21.18/3.97 | | | | | | | | | | all_72_1, all_72_2, all_72_3 gives:
% 21.18/3.97 | | | | | | | | | | (110) (all_72_0 = 0 & all_72_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_72_2 = 0 & all_32_3 = 0) | ( ~ (all_72_3 = 0)
% 21.18/3.97 | | | | | | | | | | & convergent_lines(all_23_4, all_23_3) =
% 21.18/3.97 | | | | | | | | | | all_72_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (96) with fresh symbols all_73_0,
% 21.18/3.97 | | | | | | | | | | all_73_1, all_73_2, all_73_3 gives:
% 21.18/3.97 | | | | | | | | | | (111) (all_73_0 = 0 & all_32_3 = 0) | (all_73_1 = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_73_2) | ( ~ (all_73_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_73_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (95) with fresh symbols all_74_0,
% 21.18/3.97 | | | | | | | | | | all_74_1, all_74_2, all_74_3 gives:
% 21.18/3.97 | | | | | | | | | | (112) (all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_3) = 0) | (all_74_1 = 0 & all_32_3 = 0)
% 21.18/3.97 | | | | | | | | | | | ( ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_74_2) | ( ~ (all_74_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_74_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (106) with fresh symbols all_77_0,
% 21.18/3.97 | | | | | | | | | | all_77_1, all_77_2, all_77_3 gives:
% 21.18/3.97 | | | | | | | | | | (113) (all_77_0 = 0 & all_77_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_77_2 = 0 & all_23_1 = 0) | ( ~ (all_77_3 = 0)
% 21.18/3.97 | | | | | | | | | | & convergent_lines(all_23_4, all_23_2) =
% 21.18/3.97 | | | | | | | | | | all_77_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_78_0,
% 21.18/3.97 | | | | | | | | | | all_78_1, all_78_2, all_78_3 gives:
% 21.18/3.97 | | | | | | | | | | (114) (all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_2) = 0) | (all_78_1 = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_78_2) | ( ~ (all_78_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_78_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (105) with fresh symbols all_79_0,
% 21.18/3.97 | | | | | | | | | | all_79_1, all_79_2, all_79_3 gives:
% 21.18/3.97 | | | | | | | | | | (115) (all_79_0 = 0 & all_79_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_79_2 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_3) = 0) | ( ~ (all_79_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_79_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (99) with fresh symbols all_80_0,
% 21.18/3.97 | | | | | | | | | | all_80_1, all_80_2, all_80_3 gives:
% 21.18/3.97 | | | | | | | | | | (116) (all_80_0 = 0 & all_80_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.18/3.97 | | | | | | | | | | all_23_2) = 0) | ( ~ (all_80_3 = 0) &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) =
% 21.18/3.97 | | | | | | | | | | all_80_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_82_0,
% 21.18/3.97 | | | | | | | | | | all_82_1, all_82_2, all_82_3 gives:
% 21.18/3.97 | | | | | | | | | | (117) (all_82_0 = 0 & all_23_1 = 0) | (all_82_1 = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_82_2) | ( ~ (all_82_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_82_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_83_0,
% 21.18/3.97 | | | | | | | | | | all_83_1, all_83_2, all_83_3 gives:
% 21.18/3.97 | | | | | | | | | | (118) (all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_2) = 0) | (all_83_1 = 0 & all_23_1 = 0)
% 21.18/3.97 | | | | | | | | | | | ( ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_83_2) | ( ~ (all_83_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_83_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_84_0,
% 21.18/3.97 | | | | | | | | | | all_84_1, all_84_2, all_84_3 gives:
% 21.18/3.97 | | | | | | | | | | (119) (all_84_0 = 0 & all_84_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_84_2 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_2) = 0) | ( ~ (all_84_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_84_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_85_0,
% 21.18/3.97 | | | | | | | | | | all_85_1, all_85_2, all_85_3 gives:
% 21.18/3.97 | | | | | | | | | | (120) (all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.18/3.97 | | | | | | | | | | all_23_2) = 0) | (all_85_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/3.97 | | | | | | | | | | all_23_3) = all_85_2) | ( ~ (all_85_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = all_85_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (92) with fresh symbols all_88_0,
% 21.18/3.97 | | | | | | | | | | all_88_1, all_88_2, all_88_3 gives:
% 21.18/3.97 | | | | | | | | | | (121) (all_88_0 = 0 & all_88_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_88_2 = 0 & all_51_0 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_3) = all_88_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_89_0,
% 21.18/3.97 | | | | | | | | | | all_89_1, all_89_2, all_89_3 gives:
% 21.18/3.97 | | | | | | | | | | (122) (all_89_0 = 0 & all_89_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_89_2 = 0 & all_51_0 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_2) = all_89_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (107) with fresh symbols all_90_0,
% 21.18/3.97 | | | | | | | | | | all_90_1, all_90_2, all_90_3 gives:
% 21.18/3.97 | | | | | | | | | | (123) (all_90_0 = 0 & all_90_1 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_90_2 = 0 & all_32_3 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_2) = all_90_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (94) with fresh symbols all_91_0,
% 21.18/3.97 | | | | | | | | | | all_91_1, all_91_2, all_91_3 gives:
% 21.18/3.97 | | | | | | | | | | (124) (all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_91_2) | ( ~ (all_91_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_91_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_92_0,
% 21.18/3.97 | | | | | | | | | | all_92_1, all_92_2, all_92_3 gives:
% 21.18/3.97 | | | | | | | | | | (125) (all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.18/3.97 | | | | | | | | | | (all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.97 | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97 | | | | | | | | | | (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | all_23_4) = all_92_2) | ( ~ (all_92_3 = 0) &
% 21.18/3.97 | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_92_3)
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | BETA: splitting (93) gives:
% 21.18/3.97 | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | Case 1:
% 21.18/3.97 | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | (126) unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.97 | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | BETA: splitting (112) gives:
% 21.18/3.97 | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | Case 1:
% 21.18/3.97 | | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | | (127) (all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97 | | | | | | | | | | | | all_23_3) = 0) | (all_74_1 = 0 & all_32_3 = 0)
% 21.18/3.97 | | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | | BETA: splitting (127) gives:
% 21.18/3.97 | | | | | | | | | | | |
% 21.18/3.97 | | | | | | | | | | | | Case 1:
% 21.18/3.97 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | (128) all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | ALPHA: (128) implies:
% 21.18/3.98 | | | | | | | | | | | | | (129) convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (129) are inconsistent by
% 21.18/3.98 | | | | | | | | | | | | | sub-proof #4.
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | (130) all_74_1 = 0 & all_32_3 = 0
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | ALPHA: (130) implies:
% 21.18/3.98 | | | | | | | | | | | | | (131) all_32_3 = 0
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | REDUCE: (90), (131) imply:
% 21.18/3.98 | | | | | | | | | | | | | (132) $false
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | End of split
% 21.18/3.98 | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | (133) ( ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | all_23_4) = all_74_2) | ( ~ (all_74_3 = 0) &
% 21.18/3.98 | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_74_3)
% 21.18/3.98 | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | BETA: splitting (133) gives:
% 21.18/3.98 | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | (134) ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | all_23_4) = all_74_2
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | ALPHA: (134) implies:
% 21.18/3.98 | | | | | | | | | | | | | (135) ~ (all_74_2 = 0)
% 21.18/3.98 | | | | | | | | | | | | | (136) unorthogonal_lines(all_23_4, all_23_4) = all_74_2
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_74_2, all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | all_23_4, simplifying with (126), (136) gives:
% 21.18/3.98 | | | | | | | | | | | | | (137) all_74_2 = 0
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | REDUCE: (135), (137) imply:
% 21.18/3.98 | | | | | | | | | | | | | (138) $false
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | (139) ~ (all_74_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | all_23_4) = all_74_3
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | ALPHA: (139) implies:
% 21.18/3.98 | | | | | | | | | | | | | (140) convergent_lines(all_23_4, all_23_4) = all_74_3
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 21.18/3.98 | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | (141) (all_73_0 = 0 & all_32_3 = 0) | (all_73_1 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | (142) all_73_0 = 0 & all_32_3 = 0
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | (143) all_32_3 = 0
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | REDUCE: (90), (143) imply:
% 21.18/3.98 | | | | | | | | | | | | | | | (144) $false
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | (145) all_73_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | (146) convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (146) are inconsistent by
% 21.18/3.98 | | | | | | | | | | | | | | | sub-proof #4.
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | End of split
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | (147) ( ~ (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | all_23_4) = all_73_2) | ( ~ (all_73_3 = 0) &
% 21.18/3.98 | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_73_3)
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 21.18/3.98 | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | (148) ~ (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | all_23_4) = all_73_2
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | (149) ~ (all_73_2 = 0)
% 21.18/3.98 | | | | | | | | | | | | | | | (150) unorthogonal_lines(all_23_4, all_23_4) = all_73_2
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_73_2, all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (150) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | (151) all_73_2 = 0
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | REDUCE: (149), (151) imply:
% 21.18/3.98 | | | | | | | | | | | | | | | (152) $false
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | (153) ~ (all_73_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | all_23_4) = all_73_3
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | (154) convergent_lines(all_23_4, all_23_4) = all_73_3
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 21.18/3.98 | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | (155) (all_31_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | all_23_3) = 0) | (all_31_1 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | (156) all_31_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (157) convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (157) are inconsistent by
% 21.18/3.98 | | | | | | | | | | | | | | | | | sub-proof #4.
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | (158) all_31_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (159) convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (159) are inconsistent by
% 21.18/3.98 | | | | | | | | | | | | | | | | | sub-proof #4.
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | End of split
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | (160) ( ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | all_23_4) = all_31_2) | ( ~ (all_31_3 = 0) &
% 21.18/3.98 | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_31_3)
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | (161) ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | | all_23_4) = all_31_2
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (162) ~ (all_31_2 = 0)
% 21.18/3.98 | | | | | | | | | | | | | | | | | (163) unorthogonal_lines(all_23_4, all_23_4) = all_31_2
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_31_2, all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (163) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (164) all_31_2 = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | REDUCE: (162), (164) imply:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (165) $false
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | (166) ~ (all_31_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98 | | | | | | | | | | | | | | | | | all_23_4) = all_31_3
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | | | (167) convergent_lines(all_23_4, all_23_4) = all_31_3
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | (168) (all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | (all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98 | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 21.18/3.98 | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | (169) all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | (170) all_32_3 = 0
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | REDUCE: (90), (170) imply:
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | (171) $false
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent.
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98 | | | | | | | | | | | | | | | | | | |
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | (172) all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.98 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (173) all_32_3 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | REDUCE: (90), (173) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (174) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99 | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | (175) ( ~ (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | all_23_4) = all_91_2) | ( ~ (all_91_3 = 0) &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_91_3)
% 21.18/3.99 | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (176) ~ (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | all_23_4) = all_91_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (177) ~ (all_91_2 = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (178) unorthogonal_lines(all_23_4, all_23_4) = all_91_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_91_2, all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (178) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (179) all_91_2 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | REDUCE: (177), (179) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (180) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (181) ~ (all_91_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | all_23_4) = all_91_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | (182) convergent_lines(all_23_4, all_23_4) = all_91_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | (183) (all_35_0 = 0 & all_23_1 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | (all_35_1 = 0 & all_23_1 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (184) all_35_0 = 0 & all_23_1 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (185) all_23_1 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (185) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (186) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (187) all_35_1 = 0 & all_23_1 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (188) all_23_1 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (188) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (189) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | (190) ( ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | all_23_4) = all_35_2) | ( ~ (all_35_3 = 0) &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_35_3)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_35_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_35_2 = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (193) unorthogonal_lines(all_23_4, all_23_4) = all_35_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_35_2, all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (193) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (194) all_35_2 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (194) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (195) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (196) ~ (all_35_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_35_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_35_3 = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | (198) convergent_lines(all_23_4, all_23_4) = all_35_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | (199) (all_82_0 = 0 & all_23_1 = 0) | (all_82_1 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (200) all_82_0 = 0 & all_23_1 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (201) all_23_1 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (201) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (202) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (203) all_82_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (204) convergent_lines(all_23_4, all_23_2) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (204) are inconsistent by
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | (205) ( ~ (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_82_2) | ( ~ (all_82_3 = 0) &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_82_3)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_82_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (207) ~ (all_82_2 = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (208) unorthogonal_lines(all_23_4, all_23_4) = all_82_2
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_82_2, all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (208) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (209) all_82_2 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (209) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (210) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (211) ~ (all_82_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_82_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | (212) convergent_lines(all_23_4, all_23_4) = all_82_3
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | (all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0)
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_51_0 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (215) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (216) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_51_0 = 0
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (218) imply:
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | (219) $false
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/3.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | (220) ( ~ (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_92_2) | ( ~ (all_92_3 = 0) &
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_92_3)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_92_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_92_2 = 0)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (223) unorthogonal_lines(all_23_4, all_23_4) = all_92_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_92_2, all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (223) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_92_2 = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (224) imply:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (225) $false
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_92_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_92_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | (227) convergent_lines(all_23_4, all_23_4) = all_92_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_78_1 = 0 &
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (230) are inconsistent by
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_78_1 = 0 & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (232) are inconsistent by
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (233) ( ~ (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_78_2) | ( ~ (all_78_3 = 0) &
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_78_3)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_78_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_78_2 = 0)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) unorthogonal_lines(all_23_4, all_23_4) = all_78_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_78_2, all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (236) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_78_2 = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (235), (237) imply:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) $false
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (all_78_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_78_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) convergent_lines(all_23_4, all_23_4) = all_78_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) (all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_83_1 = 0 & all_23_1 = 0)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (243) are inconsistent by
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_83_1 = 0 & all_23_1 = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_23_1 = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (245) imply:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ( ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_83_2) | ( ~ (all_83_3 = 0) &
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_4) = all_83_3)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_83_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_83_2 = 0)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) unorthogonal_lines(all_23_4, all_23_4) = all_83_2
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_83_2, all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (126), (250) gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_83_2 = 0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (251) imply:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) $false
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_83_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_83_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) convergent_lines(all_23_4, all_23_4) = all_83_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_51_0, all_73_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (61), (154)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_73_3 = all_51_0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_51_0, all_78_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (61), (240)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_78_3 = all_51_0
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_74_3, all_78_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (140), (240)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_78_3 = all_74_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_82_3, all_83_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (212), (254)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_83_3 = all_82_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_73_3, all_83_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (154), (254)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_83_3 = all_73_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_35_3, all_83_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (198), (254)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_83_3 = all_35_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_78_3, all_91_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (182), (240)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_91_3 = all_78_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_91_3, all_92_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (182), (227)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_92_3 = all_91_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_31_3, all_92_3,
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_4, simplifying with (167), (227)
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_92_3 = all_31_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (263) imply:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_91_3 = all_31_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (264) implies:
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_91_3 = all_31_3
% 21.18/4.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (265) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_78_3 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_78_3 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_82_3 = all_73_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (260) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_82_3 = all_35_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (269) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_73_3 = all_35_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_73_3 = all_35_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_74_3 = all_51_0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (267) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_74_3 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_51_0 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_51_0 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (271) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_51_0 = all_35_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (276) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_51_0 = all_35_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (277) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_35_3 = all_31_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (278) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_31_3 = 0)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, 0, simplifying with (21), (22), (25),
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0 & convergent_lines(all_23_4, all_23_4) =
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = v0))
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (280) with fresh symbols all_142_0,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_142_1, all_142_2, all_142_3 gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_142_0 = 0 & all_142_1 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) =
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_142_3)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_30_0 = 0 & all_30_1 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (22), (283) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) (all_30_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | ( ~ (all_30_3 = 0) &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) = all_30_3)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_30_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) convergent_lines(all_23_4, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (287) are inconsistent by
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_30_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_30_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) convergent_lines(all_23_4, all_23_3) = all_30_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_30_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (55), (289)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_32_3 = all_30_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (290) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_30_3 = 0)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) (all_34_0 = 0 & all_23_0 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_34_1 = 0 & all_23_0 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_34_0 = 0 & all_23_0 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_23_0 = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (294) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_34_1 = 0 & all_23_0 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_23_0 = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (297) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) ( ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_34_2) | ( ~ (all_34_3 = 0) &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = all_34_3)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_34_2
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) ~ (all_34_2 = 0)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) unorthogonal_lines(all_23_3, all_23_3) = all_34_2
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_2, simplifying with (22), (302) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_34_2 = 0 | convergent_lines(all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (22), (304) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_34_2 = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (306) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_34_3 = 0) & convergent_lines(all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_34_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_34_3 = 0)
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) convergent_lines(all_23_3, all_23_3) = all_34_3
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_72_0 = 0 & all_72_1 = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_34_3, all_23_3,
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (310), (312) gives:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_34_3 = 0
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (313) imply:
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) $false
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent.
% 21.18/4.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) (all_72_2 = 0 & all_32_3 = 0) | ( ~ (all_72_3 = 0)
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & convergent_lines(all_23_4, all_23_3) =
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_72_3)
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_72_2 = 0 & all_32_3 = 0
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_32_3 = 0
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (317) imply:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_30_3 = 0
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_30_3 = 0
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (319) imply:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) $false
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent.
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_72_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_72_3
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) ~ (all_72_3 = 0)
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) convergent_lines(all_23_4, all_23_3) = all_72_3
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_30_3, all_72_3,
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (289), (323)
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_72_3 = all_30_3
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_3, all_23_2,
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_34_3, simplifying with (22), (23),
% 21.18/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (310) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_34_3 = 0 | convergent_lines(all_23_2,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_23_3, all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_34_3, all_30_3, simplifying with
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (21), (22), (289), (310) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_34_3 = 0 | all_30_3 = 0 | ? [v0: int] : ( ~
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & convergent_lines(all_23_3, all_23_4)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_3, all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_3, simplifying with (22), (310) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_34_3 = 0 | unorthogonal_lines(all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) (all_36_0 = 0 & all_23_1 = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_36_1 = 0 & all_23_0 = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_36_0 = 0 & all_23_1 = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_23_1 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (330) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_36_1 = 0 & all_23_0 = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_23_0 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (333) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) ( ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_36_2) | ( ~ (all_36_3 = 0) &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = all_36_3)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_36_2
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_36_2 = 0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) unorthogonal_lines(all_23_3, all_23_4) = all_36_2
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_34_3 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (339) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_30_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = v0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_30_3 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (342) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ? [v0: int] : ( ~ (v0 = 0) &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = v0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (344) with fresh symbol all_193_0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_193_0 = 0) & convergent_lines(all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_193_0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_193_0 = 0)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) convergent_lines(all_23_3, all_23_4) = all_193_0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_142_0 = 0 & all_142_1 = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) unorthogonal_lines(all_23_3, all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_36_2, all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (338), (349) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_36_2 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (350) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) =
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_142_3)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) convergent_lines(all_23_4, all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (167), (279), (354) are inconsistent by
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_3, all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_193_0, simplifying with (21), (22), (347)
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_193_0 = 0 | unorthogonal_lines(all_23_3,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) unorthogonal_lines(all_23_3, all_23_4) = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_36_2, all_23_4,
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (338), (356) gives:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_36_2 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (357) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_193_0 = 0
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (359) imply:
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) $false
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_36_3 = 0) & convergent_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_36_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_36_3 = 0)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) convergent_lines(all_23_3, all_23_4) = all_36_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_88_0 = 0 & all_88_1 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (362), (363), (366) are inconsistent by
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) (all_88_2 = 0 & all_51_0 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_88_3)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_88_2 = 0 & all_51_0 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_51_0 = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (369) imply:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_31_3 = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (370) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_31_3 = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (371) imply:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) $false
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_88_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_88_3 = 0)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) convergent_lines(all_23_4, all_23_3) = all_88_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) unorthogonal_lines(all_23_3, all_23_3) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_142_0 = 0 & all_142_1 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (362), (363), (378) are inconsistent by
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_3) =
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_142_3)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) convergent_lines(all_23_4, all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (167), (279), (381) are inconsistent by
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) ~ (all_142_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_142_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) convergent_lines(all_23_4, all_23_3) = all_142_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) (all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_85_1 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) = 0)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (386) are inconsistent by
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_85_1 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (388) are inconsistent by
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) ( ~ (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_85_2) | ( ~ (all_85_3 = 0) &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_3) = all_85_3)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) ~ (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_85_2
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_85_2 = 0)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) unorthogonal_lines(all_23_3, all_23_3) = all_85_2
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_85_2, all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, simplifying with (376), (392) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_85_2 = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (393) imply:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) $false
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (394) is inconsistent.
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_30_3, all_142_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (289), (383)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_142_3 = all_30_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_88_3, all_142_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, all_23_4, simplifying with (375), (383)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_142_3 = all_88_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (396) imply:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_88_3 = all_30_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_88_3 = all_30_3
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_2, all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, 0, all_30_3, simplifying with (21),
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (289), (364) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_30_3 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & unorthogonal_lines(all_23_2, all_23_3)
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v1 = 0) &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = v1) |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v0 = 0) & convergent_lines(all_23_2,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = v0))
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_2, all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3, 0, 0, simplifying with (21), (22), (23),
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (364) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | (v2 = 0 &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0) |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = v0))
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_36_3, simplifying with (21), (22),
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (363), (364) gives:
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_36_3 = 0 | convergent_lines(all_23_2,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = 0
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_23_2, all_23_3,
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_0, simplifying with (22), (23),
% 21.46/4.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (26), (364) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & all_23_0 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v2 = 0 & v1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0 & convergent_lines(all_23_2,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (v0 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = v0))
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (400) with fresh symbols all_223_0,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_223_1, all_223_2, all_223_3 gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) (all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | (all_223_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0) | (
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_223_2) | ( ~ (all_223_3 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_223_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (402) with fresh symbols all_233_0,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_233_1, all_233_2, all_233_3 gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) (all_233_0 = 0 & all_23_0 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_3, all_23_2) = 0) |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_233_1 = 0 & all_233_2 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_233_3 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = all_233_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (399) with fresh symbols all_237_0,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_237_1, all_237_2, all_237_3 gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) (all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | ( ~ (all_237_2 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_237_2) | ( ~ (all_237_3 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_237_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) convergent_lines(all_23_2, all_23_4) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_71_0 = 0 & all_71_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (408) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (409) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) (all_71_2 = 0 & all_23_0 = 0) | ( ~ (all_71_3 = 0)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & unorthogonal_lines(all_23_3, all_23_2) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_71_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_71_2 = 0 & all_23_0 = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_23_0 = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (412) imply:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_71_3 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_71_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_71_3 = 0)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) unorthogonal_lines(all_23_3, all_23_2) = all_71_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_23_0, all_71_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_3, simplifying with (26), (416)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_71_3 = all_23_0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_77_0 = 0 & all_77_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (419) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_77_2 = 0 & all_23_1 = 0) | ( ~ (all_77_3 = 0)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & convergent_lines(all_23_4, all_23_2) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_77_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_77_2 = 0 & all_23_1 = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_23_1 = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (423) imply:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (424) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (all_77_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_77_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) convergent_lines(all_23_4, all_23_2) = all_77_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_77_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (24), (426)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_77_3 = all_23_1
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_79_0 = 0 & all_79_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (428) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (429), (apart3) are
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) (all_79_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | ( ~ (all_79_3 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_79_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_79_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) convergent_lines(all_23_4, all_23_3) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (432) are inconsistent by
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) ~ (all_79_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_79_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) ~ (all_79_3 = 0)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) convergent_lines(all_23_4, all_23_2) = all_79_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_79_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (24), (435)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_79_3 = all_23_1
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_80_0 = 0 & all_80_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (438) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (all_80_3 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_3, all_23_2) =
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_80_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (442) are inconsistent by
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_80_3 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_80_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_80_3 = 0)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) unorthogonal_lines(all_23_3, all_23_2) = all_80_3
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_23_0, all_80_3,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_3, simplifying with (26), (445)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_80_3 = all_23_0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_84_0 = 0 & all_84_1 = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (448) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) $false
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent.
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) (all_84_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | ( ~ (all_84_3 = 0) &
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_4, all_23_2) = all_84_3)
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_84_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) convergent_lines(all_23_4, all_23_2) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (452) are inconsistent by
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) ~ (all_84_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_84_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (453) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) convergent_lines(all_23_4, all_23_2) = all_84_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_84_3,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (24), (454)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_84_3 = all_23_1
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_89_0 = 0 & all_89_1 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) unorthogonal_lines(all_23_2, all_23_4) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) (all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0) | (all_223_1 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) convergent_lines(all_23_4, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (460) are inconsistent by
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_223_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (461) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (462), (apart3) are
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) ( ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_223_2) | ( ~ (all_223_3 = 0) &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) =
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_223_3)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_223_2
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) ~ (all_223_2 = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) unorthogonal_lines(all_23_2, all_23_4) = all_223_2
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_223_2, all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, simplifying with (457), (466) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_223_2 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (465), (467) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) ~ (all_223_3 = 0) & convergent_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_223_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (all_223_3 = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) convergent_lines(all_23_2, all_23_4) = all_223_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (405) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) (all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_30_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (474) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (475) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (477), (apart3) are
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) ( ~ (all_237_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_237_2) | ( ~ (all_237_3 = 0) &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_4) =
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_237_3)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) ~ (all_237_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_237_2
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) ~ (all_237_2 = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) unorthogonal_lines(all_23_2, all_23_4) = all_237_2
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_237_2, all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, simplifying with (457), (481) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_237_2 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (480), (482) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (483) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) ~ (all_237_3 = 0) & convergent_lines(all_23_2,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4) = all_237_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) convergent_lines(all_23_2, all_23_4) = all_237_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_237_3, all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, simplifying with (406), (485) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_237_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_223_3, all_237_3,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_4, all_23_2, simplifying with (471), (485)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_237_3 = all_223_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (486), (487) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_223_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (488) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (489) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) (all_89_2 = 0 & all_51_0 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_89_3)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_89_2 = 0 & all_51_0 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_51_0 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (492) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_31_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_31_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (494) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (495) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_89_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) convergent_lines(all_23_4, all_23_2) = all_89_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_89_3,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (24), (497)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_89_3 = all_23_1
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_90_0 = 0 & all_90_1 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (500), (apart3) are
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) (all_90_2 = 0 & all_32_3 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_90_3)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_90_2 = 0 & all_32_3 = 0 &
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_32_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (503) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_30_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_30_3 = 0
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (505) imply:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) $false
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) ~ (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = all_90_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (507) implies:
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) ~ (all_90_3 = 0)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) convergent_lines(all_23_4, all_23_2) = all_90_3
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_90_3,
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_4, simplifying with (24), (509)
% 21.46/4.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_90_3 = all_23_1
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_4,
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2, all_23_1, simplifying with (21), (23),
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (406) gives:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_23_1 = 0 | convergent_lines(all_23_2,
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (23), (512) gives:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) $false
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (513) is inconsistent.
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_23_1 = 0
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.46/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (514) imply:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) $false
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent.
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_36_3 = 0
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (516) imply:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) $false
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (517) is inconsistent.
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_34_3 = 0
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (518) imply:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) $false
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_34_3 = 0
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (520) imply:
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) $false
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent.
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | Case 2:
% 21.64/4.06 | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | (522) all_51_0 = 0
% 21.64/4.06 | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | REDUCE: (60), (522) imply:
% 21.64/4.06 | | | | | | | | | | | (523) $false
% 21.64/4.06 | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | | CLOSE: (523) is inconsistent.
% 21.64/4.06 | | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | | |
% 21.64/4.06 | | | | | | | | | End of split
% 21.64/4.06 | | | | | | | | |
% 21.64/4.06 | | | | | | | | End of split
% 21.64/4.06 | | | | | | | |
% 21.64/4.06 | | | | | | | End of split
% 21.64/4.06 | | | | | | |
% 21.64/4.06 | | | | | | End of split
% 21.64/4.06 | | | | | |
% 21.64/4.06 | | | | | End of split
% 21.64/4.06 | | | | |
% 21.64/4.06 | | | | End of split
% 21.64/4.06 | | | |
% 21.64/4.06 | | | End of split
% 21.64/4.06 | | |
% 21.64/4.06 | | Case 2:
% 21.64/4.06 | | |
% 21.64/4.06 | | | (524) all_23_0 = 0
% 21.64/4.06 | | |
% 21.64/4.06 | | | REDUCE: (20), (524) imply:
% 21.64/4.06 | | | (525) $false
% 21.64/4.06 | | |
% 21.64/4.06 | | | CLOSE: (525) is inconsistent.
% 21.64/4.06 | | |
% 21.64/4.06 | | End of split
% 21.64/4.06 | |
% 21.64/4.06 | Case 2:
% 21.64/4.06 | |
% 21.64/4.06 | | (526) all_23_1 = 0
% 21.64/4.06 | |
% 21.64/4.06 | | REDUCE: (19), (526) imply:
% 21.64/4.06 | | (527) $false
% 21.64/4.06 | |
% 21.64/4.06 | | CLOSE: (527) is inconsistent.
% 21.64/4.06 | |
% 21.64/4.06 | End of split
% 21.64/4.06 |
% 21.64/4.06 End of proof
% 21.64/4.06
% 21.64/4.06 Sub-proof #1 shows that the following formulas are inconsistent:
% 21.64/4.06 ----------------------------------------------------------------
% 21.64/4.06 (1) unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.64/4.06 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.06 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 21.64/4.06 (unorthogonal_lines(v3, v2) = v0))
% 21.64/4.06 (3) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 21.64/4.06 (4) (all_233_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0)
% 21.64/4.06 | (all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2, all_23_2)
% 21.64/4.06 = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~ (all_233_3 = 0) &
% 21.64/4.06 unorthogonal_lines(all_23_2, all_23_3) = all_233_3)
% 21.64/4.06 (5) ~ (all_23_0 = 0)
% 21.64/4.06 (6) $i(all_23_2)
% 21.64/4.06
% 21.64/4.06 Begin of proof
% 21.64/4.06 |
% 21.64/4.06 | BETA: splitting (4) gives:
% 21.64/4.06 |
% 21.64/4.06 | Case 1:
% 21.64/4.06 | |
% 21.64/4.06 | | (7) all_233_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 21.64/4.06 | | 0
% 21.64/4.06 | |
% 21.64/4.06 | | ALPHA: (7) implies:
% 21.64/4.06 | | (8) all_23_0 = 0
% 21.64/4.06 | |
% 21.64/4.06 | | REDUCE: (5), (8) imply:
% 21.64/4.06 | | (9) $false
% 21.64/4.06 | |
% 21.64/4.06 | | CLOSE: (9) is inconsistent.
% 21.64/4.06 | |
% 21.64/4.06 | Case 2:
% 21.64/4.06 | |
% 21.64/4.06 | | (10) (all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2,
% 21.64/4.06 | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 21.64/4.06 | | (all_233_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 21.64/4.06 | | all_233_3)
% 21.64/4.06 | |
% 21.64/4.06 | | BETA: splitting (10) gives:
% 21.64/4.06 | |
% 21.64/4.06 | | Case 1:
% 21.64/4.06 | | |
% 21.64/4.06 | | | (11) all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2,
% 21.64/4.06 | | | all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0
% 21.64/4.06 | | |
% 21.64/4.06 | | | ALPHA: (11) implies:
% 21.64/4.06 | | | (12) convergent_lines(all_23_2, all_23_2) = 0
% 21.64/4.06 | | |
% 21.64/4.06 | | | GROUND_INST: instantiating (3) with all_23_2, simplifying with (6), (12)
% 21.64/4.06 | | | gives:
% 21.64/4.06 | | | (13) $false
% 21.64/4.06 | | |
% 21.64/4.06 | | | CLOSE: (13) is inconsistent.
% 21.64/4.06 | | |
% 21.64/4.06 | | Case 2:
% 21.64/4.06 | | |
% 21.64/4.06 | | | (14) ~ (all_233_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 21.64/4.06 | | | all_233_3
% 21.64/4.06 | | |
% 21.64/4.06 | | | ALPHA: (14) implies:
% 21.64/4.06 | | | (15) ~ (all_233_3 = 0)
% 21.64/4.06 | | | (16) unorthogonal_lines(all_23_2, all_23_3) = all_233_3
% 21.64/4.06 | | |
% 21.64/4.06 | | | GROUND_INST: instantiating (2) with 0, all_233_3, all_23_3, all_23_2,
% 21.64/4.06 | | | simplifying with (1), (16) gives:
% 21.64/4.06 | | | (17) all_233_3 = 0
% 21.64/4.06 | | |
% 21.64/4.06 | | | REDUCE: (15), (17) imply:
% 21.64/4.06 | | | (18) $false
% 21.64/4.06 | | |
% 21.64/4.06 | | | CLOSE: (18) is inconsistent.
% 21.64/4.06 | | |
% 21.64/4.06 | | End of split
% 21.64/4.06 | |
% 21.64/4.06 | End of split
% 21.64/4.06 |
% 21.64/4.06 End of proof
% 21.64/4.06
% 21.64/4.06 Sub-proof #2 shows that the following formulas are inconsistent:
% 21.64/4.06 ----------------------------------------------------------------
% 21.64/4.06 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.06 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 21.64/4.06 (convergent_lines(v3, v2) = v0))
% 21.64/4.06 (2) convergent_lines(all_23_3, all_23_4) = all_36_3
% 21.64/4.06 (3) convergent_lines(all_23_3, all_23_4) = 0
% 21.64/4.06 (4) ~ (all_36_3 = 0)
% 21.64/4.06
% 21.64/4.06 Begin of proof
% 21.64/4.06 |
% 21.64/4.06 | GROUND_INST: instantiating (1) with 0, all_36_3, all_23_4, all_23_3,
% 21.64/4.06 | simplifying with (2), (3) gives:
% 21.64/4.06 | (5) all_36_3 = 0
% 21.64/4.06 |
% 21.64/4.06 | REDUCE: (4), (5) imply:
% 21.64/4.06 | (6) $false
% 21.64/4.06 |
% 21.64/4.06 | CLOSE: (6) is inconsistent.
% 21.64/4.06 |
% 21.64/4.06 End of proof
% 21.64/4.06
% 21.64/4.06 Sub-proof #3 shows that the following formulas are inconsistent:
% 21.64/4.06 ----------------------------------------------------------------
% 21.64/4.06 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.06 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 21.64/4.06 (convergent_lines(v3, v2) = v0))
% 21.64/4.06 (2) convergent_lines(all_23_4, all_23_4) = all_31_3
% 21.64/4.06 (3) convergent_lines(all_23_4, all_23_4) = 0
% 21.64/4.06 (4) ~ (all_31_3 = 0)
% 21.64/4.06
% 21.64/4.06 Begin of proof
% 21.64/4.06 |
% 21.64/4.06 | GROUND_INST: instantiating (1) with all_31_3, 0, all_23_4, all_23_4,
% 21.64/4.06 | simplifying with (2), (3) gives:
% 21.64/4.06 | (5) all_31_3 = 0
% 21.64/4.06 |
% 21.64/4.06 | REDUCE: (4), (5) imply:
% 21.64/4.06 | (6) $false
% 21.64/4.06 |
% 21.64/4.06 | CLOSE: (6) is inconsistent.
% 21.64/4.06 |
% 21.64/4.06 End of proof
% 21.64/4.06
% 21.64/4.06 Sub-proof #4 shows that the following formulas are inconsistent:
% 21.64/4.06 ----------------------------------------------------------------
% 21.64/4.06 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.06 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 21.64/4.06 (convergent_lines(v3, v2) = v0))
% 21.64/4.06 (2) convergent_lines(all_23_4, all_23_3) = all_32_3
% 21.64/4.06 (3) convergent_lines(all_23_4, all_23_3) = 0
% 21.64/4.06 (4) ~ (all_32_3 = 0)
% 21.64/4.06
% 21.64/4.06 Begin of proof
% 21.64/4.06 |
% 21.64/4.06 | GROUND_INST: instantiating (1) with all_32_3, 0, all_23_3, all_23_4,
% 21.64/4.06 | simplifying with (2), (3) gives:
% 21.64/4.06 | (5) all_32_3 = 0
% 21.64/4.07 |
% 21.64/4.07 | REDUCE: (4), (5) imply:
% 21.64/4.07 | (6) $false
% 21.64/4.07 |
% 21.64/4.07 | CLOSE: (6) is inconsistent.
% 21.64/4.07 |
% 21.64/4.07 End of proof
% 21.64/4.07
% 21.64/4.07 Sub-proof #5 shows that the following formulas are inconsistent:
% 21.64/4.07 ----------------------------------------------------------------
% 21.64/4.07 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.07 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 21.64/4.07 (convergent_lines(v3, v2) = v0))
% 21.64/4.07 (2) convergent_lines(all_23_4, all_23_2) = all_23_1
% 21.64/4.07 (3) convergent_lines(all_23_4, all_23_2) = 0
% 21.64/4.07 (4) ~ (all_23_1 = 0)
% 21.64/4.07
% 21.64/4.07 Begin of proof
% 21.64/4.07 |
% 21.64/4.07 | GROUND_INST: instantiating (1) with all_23_1, 0, all_23_2, all_23_4,
% 21.64/4.07 | simplifying with (2), (3) gives:
% 21.64/4.07 | (5) all_23_1 = 0
% 21.64/4.07 |
% 21.64/4.07 | REDUCE: (4), (5) imply:
% 21.64/4.07 | (6) $false
% 21.64/4.07 |
% 21.64/4.07 | CLOSE: (6) is inconsistent.
% 21.64/4.07 |
% 21.64/4.07 End of proof
% 21.64/4.07
% 21.64/4.07 Sub-proof #6 shows that the following formulas are inconsistent:
% 21.64/4.07 ----------------------------------------------------------------
% 21.64/4.07 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.64/4.07 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 21.64/4.07 (unorthogonal_lines(v3, v2) = v0))
% 21.64/4.07 (2) unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 21.64/4.07 (3) unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.64/4.07 (4) ~ (all_23_0 = 0)
% 21.64/4.07
% 21.64/4.07 Begin of proof
% 21.64/4.07 |
% 21.64/4.07 | GROUND_INST: instantiating (1) with all_23_0, 0, all_23_2, all_23_3,
% 21.64/4.07 | simplifying with (2), (3) gives:
% 21.64/4.07 | (5) all_23_0 = 0
% 21.64/4.07 |
% 21.64/4.07 | REDUCE: (4), (5) imply:
% 21.64/4.07 | (6) $false
% 21.64/4.07 |
% 21.64/4.07 | CLOSE: (6) is inconsistent.
% 21.64/4.07 |
% 21.64/4.07 End of proof
% 21.64/4.07 % SZS output end Proof for theBenchmark
% 21.64/4.07
% 21.64/4.07 3451ms
%------------------------------------------------------------------------------