%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO213+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 : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 23:22:23 EDT 2023

% Result   : Theorem 12.89s 2.42s
% Output   : Proof 20.89s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO213+2 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 23:10:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.66/0.63  ________       _____
% 0.66/0.63  ___  __ \_________(_)________________________________
% 0.66/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.66/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.66/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.66/0.63  
% 0.66/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.63  (2023-06-19)
% 0.66/0.63  
% 0.66/0.63  (c) Philipp Rümmer, 2009-2023
% 0.66/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.63                Amanda Stjerna.
% 0.66/0.63  Free software under BSD-3-Clause.
% 0.66/0.63  
% 0.66/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.63  
% 0.66/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.64  Running up to 7 provers in parallel.
% 0.76/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.61/1.06  Prover 4: Preprocessing ...
% 2.61/1.06  Prover 1: Preprocessing ...
% 3.00/1.10  Prover 6: Preprocessing ...
% 3.00/1.10  Prover 0: Preprocessing ...
% 3.00/1.10  Prover 5: Preprocessing ...
% 3.00/1.10  Prover 3: Preprocessing ...
% 3.00/1.10  Prover 2: Preprocessing ...
% 5.08/1.37  Prover 5: Proving ...
% 5.08/1.39  Prover 2: Proving ...
% 5.08/1.43  Prover 1: Constructing countermodel ...
% 5.08/1.43  Prover 6: Constructing countermodel ...
% 5.08/1.45  Prover 3: Constructing countermodel ...
% 6.41/1.56  Prover 3: gave up
% 6.41/1.56  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.41/1.58  Prover 6: gave up
% 6.41/1.58  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.41/1.60  Prover 1: gave up
% 6.41/1.60  Prover 4: Constructing countermodel ...
% 6.41/1.60  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.41/1.61  Prover 8: Preprocessing ...
% 6.41/1.61  Prover 0: Proving ...
% 6.41/1.61  Prover 7: Preprocessing ...
% 6.94/1.63  Prover 9: Preprocessing ...
% 7.27/1.68  Prover 7: Warning: ignoring some quantifiers
% 7.27/1.70  Prover 7: Constructing countermodel ...
% 7.92/1.76  Prover 7: gave up
% 7.92/1.77  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.92/1.77  Prover 8: Warning: ignoring some quantifiers
% 8.12/1.79  Prover 8: Constructing countermodel ...
% 8.12/1.82  Prover 10: Preprocessing ...
% 8.58/1.89  Prover 10: Warning: ignoring some quantifiers
% 8.58/1.89  Prover 8: gave up
% 8.58/1.89  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.58/1.90  Prover 10: Constructing countermodel ...
% 9.11/1.91  Prover 11: Preprocessing ...
% 9.11/1.92  Prover 9: Constructing countermodel ...
% 9.11/1.94  Prover 10: gave up
% 9.11/1.96  Prover 12: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 9.56/1.98  Prover 12: Preprocessing ...
% 10.19/2.07  Prover 12: Proving ...
% 10.72/2.13  Prover 11: Constructing countermodel ...
% 12.89/2.41  Prover 0: proved (1767ms)
% 12.89/2.42  
% 12.89/2.42  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.89/2.42  
% 12.89/2.42  Prover 9: stopped
% 12.89/2.42  Prover 2: stopped
% 12.89/2.42  Prover 12: stopped
% 12.89/2.42  Prover 5: stopped
% 12.89/2.42  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.89/2.42  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.89/2.42  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.14/2.45  Prover 13: Preprocessing ...
% 13.14/2.45  Prover 16: Preprocessing ...
% 13.14/2.46  Prover 19: Preprocessing ...
% 13.14/2.47  Prover 16: Warning: ignoring some quantifiers
% 13.14/2.48  Prover 13: Warning: ignoring some quantifiers
% 13.14/2.48  Prover 16: Constructing countermodel ...
% 13.14/2.48  Prover 13: Constructing countermodel ...
% 13.14/2.51  Prover 13: gave up
% 13.14/2.52  Prover 16: gave up
% 13.76/2.53  Prover 19: Warning: ignoring some quantifiers
% 13.76/2.54  Prover 19: Constructing countermodel ...
% 13.76/2.58  Prover 19: gave up
% 19.36/3.61  Prover 11: Found proof (size 662)
% 19.36/3.61  Prover 11: proved (1718ms)
% 19.36/3.61  Prover 4: stopped
% 19.36/3.61  
% 19.36/3.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.36/3.61  
% 19.78/3.65  % SZS output start Proof for theBenchmark
% 19.78/3.66  Assumptions after simplification:
% 19.78/3.66  ---------------------------------
% 19.78/3.66  
% 19.78/3.66    (apart3)
% 19.98/3.68     ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) |  ~ $i(v0))
% 19.98/3.68  
% 19.98/3.68    (apart6)
% 19.98/3.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 19.98/3.69      0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0,
% 19.98/3.69          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 =
% 19.98/3.69          0) & convergent_lines(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.98/3.69    [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~
% 19.98/3.69      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.69      convergent_lines(v0, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 19.98/3.69    [v3: int] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~
% 19.98/3.69      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.69      convergent_lines(v1, v2) = 0)
% 19.98/3.69  
% 19.98/3.69    (ceq3)
% 19.98/3.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (distinct_lines(v0,
% 19.98/3.69          v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) &
% 19.98/3.69        convergent_lines(v0, v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 19.98/3.69      (convergent_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | distinct_lines(v0,
% 19.98/3.69        v1) = 0)
% 19.98/3.69  
% 19.98/3.69    (con)
% 19.98/3.69     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] :  ? [v4: int] : ( ~
% 19.98/3.70      (v4 = 0) &  ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 &
% 19.98/3.70      unorthogonal_lines(v0, v1) = 0 & distinct_lines(v0, v2) = v3 & $i(v2) &
% 19.98/3.70      $i(v1) & $i(v0))
% 19.98/3.70  
% 19.98/3.70    (oac1)
% 19.98/3.72     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any] : ( ~
% 19.98/3.72      (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) | 
% 19.98/3.72      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] :  ? [v7:
% 19.98/3.72        int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) |
% 19.98/3.72        (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 19.98/3.72          unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 19.98/3.72            v1) = v5))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :
% 19.98/3.72     ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~
% 19.98/3.72      (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 19.98/3.72      [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 19.98/3.72          convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 19.98/3.72            v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0:
% 19.98/3.72      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any] : ( ~
% 19.98/3.72      (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ~
% 19.98/3.72      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] :  ? [v7: int]
% 19.98/3.72      :  ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 =
% 19.98/3.72          0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 19.98/3.72          unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 19.98/3.72            v1) = v5))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :
% 19.98/3.72     ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0,
% 19.98/3.72          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 19.98/3.72        int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 19.98/3.72            v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0:
% 19.98/3.72      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 19.98/3.72          v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1)
% 19.98/3.72      |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] :
% 19.98/3.72      ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 19.98/3.72            = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] : 
% 19.98/3.72    ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~
% 19.98/3.72      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 19.98/3.72        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 19.98/3.72          convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 19.98/3.72            = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i]
% 19.98/3.72    :  ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~
% 19.98/3.72      (unorthogonal_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 19.98/3.72      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 19.98/3.72          & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.72          convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.98/3.72      $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~
% 19.98/3.72      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 19.98/3.72        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 19.98/3.72          & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.72          unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.98/3.72      $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~
% 19.98/3.72      (convergent_lines(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 19.98/3.72      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 19.98/3.72            = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] : 
% 19.98/3.72    ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~
% 19.98/3.72      (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 19.98/3.72      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 19.98/3.72          & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.72          convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.98/3.72      $i] :  ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) |  ~
% 19.98/3.72      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 19.98/3.72        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 19.98/3.72          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 19.98/3.72            = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i]
% 19.98/3.72    :  ! [v2: $i] :  ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) |  ~
% 19.98/3.72      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 19.98/3.72        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.72          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 19.98/3.72          & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.72          unorthogonal_lines(v0, v1) = v4)))
% 19.98/3.72  
% 19.98/3.72    (occu1)
% 19.98/3.72     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 19.98/3.72      (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.72      convergent_lines(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] :
% 19.98/3.72    (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.72      unorthogonal_lines(v0, v1) = 0)
% 19.98/3.72  
% 19.98/3.72    (function-axioms)
% 19.98/3.73     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 19.98/3.73      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 19.98/3.73          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 19.98/3.73    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 19.98/3.73      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.98/3.73      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 19.98/3.73      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.98/3.73      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 19.98/3.73      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 19.98/3.73    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 19.98/3.73      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 19.98/3.73      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 19.98/3.73      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 19.98/3.73        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 19.98/3.73      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 19.98/3.73      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 19.98/3.73      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 19.98/3.73      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 19.98/3.73      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.98/3.73    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 19.98/3.73        v0))
% 19.98/3.73  
% 19.98/3.73  Further assumptions not needed in the proof:
% 19.98/3.73  --------------------------------------------
% 19.98/3.73  apart1, apart2, apart4, apart5, ceq1, ceq2, con1, con2, cp1, cp2, cu1, cup1,
% 19.98/3.73  ooc1, ooc2, ouo1
% 19.98/3.73  
% 19.98/3.73  Those formulas are unsatisfiable:
% 19.98/3.73  ---------------------------------
% 19.98/3.73  
% 19.98/3.73  Begin of proof
% 19.98/3.73  | 
% 19.98/3.73  | ALPHA: (apart6) implies:
% 19.98/3.73  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 19.98/3.73  |          (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 19.98/3.73  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 19.98/3.73  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 19.98/3.73  |          (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 19.98/3.73  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 19.98/3.73  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] :
% 19.98/3.73  |        (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~
% 19.98/3.73  |          (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.73  |           ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 19.98/3.73  | 
% 19.98/3.73  | ALPHA: (ceq3) implies:
% 19.98/3.73  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 19.98/3.73  |          (distinct_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 19.98/3.73  |          : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 19.98/3.73  | 
% 19.98/3.73  | ALPHA: (occu1) implies:
% 19.98/3.73  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 19.98/3.73  |          (convergent_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.73  |          unorthogonal_lines(v0, v1) = 0)
% 19.98/3.73  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 19.98/3.73  |          (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.98/3.73  |          convergent_lines(v0, v1) = 0)
% 19.98/3.73  | 
% 19.98/3.73  | ALPHA: (oac1) implies:
% 19.98/3.74  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 19.98/3.74  |          (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 19.98/3.74  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ?
% 19.98/3.74  |          [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v1,
% 19.98/3.74  |                v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 &
% 19.98/3.74  |              unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.74  |              unorthogonal_lines(v0, v1) = v4)))
% 19.98/3.74  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 19.98/3.74  |          (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 19.98/3.74  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ?
% 19.98/3.74  |          [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 & unorthogonal_lines(v1,
% 19.98/3.74  |                v2) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v0, v2) = 0 &
% 19.98/3.74  |              convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.74  |              unorthogonal_lines(v0, v1) = v4)))
% 19.98/3.74  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 19.98/3.74  |          (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3)
% 19.98/3.74  |          |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] : 
% 19.98/3.74  |          ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.74  |              unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 19.98/3.74  |            (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.74  |              convergent_lines(v0, v1) = v4)))
% 19.98/3.74  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 19.98/3.74  |           (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) =
% 19.98/3.74  |             0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 19.98/3.74  |             int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 19.98/3.74  |               unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 19.98/3.74  |             (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 19.98/3.74  |               unorthogonal_lines(v0, v1) = v4)))
% 20.32/3.74  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.32/3.74  |           (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) =
% 20.32/3.74  |             0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 20.32/3.74  |             int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.32/3.74  |               unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.32/3.74  |             (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.32/3.74  |               convergent_lines(v0, v1) = v4)))
% 20.32/3.75  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.32/3.75  |           (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) =
% 20.32/3.75  |             0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 20.32/3.75  |             int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.32/3.75  |               convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.32/3.75  |               unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 20.32/3.75  |             ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 20.32/3.75  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.32/3.75  |         : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) =
% 20.32/3.75  |             v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.32/3.75  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.32/3.75  |               unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.32/3.75  |               unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.32/3.75  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.32/3.75  |               convergent_lines(v0, v1) = v5)))
% 20.32/3.75  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.32/3.75  |         : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2)
% 20.32/3.75  |             = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.32/3.75  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.32/3.75  |               unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.32/3.75  |               convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.32/3.75  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.32/3.75  |               convergent_lines(v0, v1) = v5)))
% 20.32/3.75  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.32/3.75  |         : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2)
% 20.32/3.75  |             = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.32/3.75  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.32/3.75  |               convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.32/3.75  |               unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.32/3.75  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.32/3.75  |               convergent_lines(v0, v1) = v5)))
% 20.32/3.75  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.32/3.75  |         : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0,
% 20.32/3.75  |               v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : 
% 20.32/3.75  |           ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.32/3.75  |               convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.32/3.75  |               convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.32/3.75  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.32/3.75  |               convergent_lines(v0, v1) = v5)))
% 20.32/3.75  | 
% 20.32/3.75  | ALPHA: (function-axioms) implies:
% 20.32/3.75  |   (17)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 20.32/3.75  |         :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.32/3.75  |           (convergent_lines(v3, v2) = v0))
% 20.32/3.75  |   (18)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 20.32/3.75  |         :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.32/3.75  |           (unorthogonal_lines(v3, v2) = v0))
% 20.32/3.75  | 
% 20.32/3.75  | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2,
% 20.32/3.75  |        all_23_3, all_23_4 gives:
% 20.32/3.76  |   (19)   ~ (all_23_0 = 0) &  ~ (all_23_1 = 0) & unorthogonal_lines(all_23_3,
% 20.32/3.76  |           all_23_2) = all_23_0 & unorthogonal_lines(all_23_4, all_23_3) = 0 &
% 20.32/3.76  |         distinct_lines(all_23_4, all_23_2) = all_23_1 & $i(all_23_2) &
% 20.32/3.76  |         $i(all_23_3) & $i(all_23_4)
% 20.32/3.76  | 
% 20.32/3.76  | ALPHA: (19) implies:
% 20.32/3.76  |   (20)   ~ (all_23_1 = 0)
% 20.32/3.76  |   (21)   ~ (all_23_0 = 0)
% 20.32/3.76  |   (22)  $i(all_23_4)
% 20.32/3.76  |   (23)  $i(all_23_3)
% 20.32/3.76  |   (24)  $i(all_23_2)
% 20.32/3.76  |   (25)  distinct_lines(all_23_4, all_23_2) = all_23_1
% 20.32/3.76  |   (26)  unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.32/3.76  |   (27)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.32/3.76  | 
% 20.32/3.76  | GROUND_INST: instantiating (4) with all_23_4, all_23_2, all_23_1, simplifying
% 20.32/3.76  |              with (22), (24), (25) gives:
% 20.32/3.76  |   (28)  all_23_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 20.32/3.76  |           convergent_lines(all_23_4, all_23_2) = v0)
% 20.32/3.76  | 
% 20.32/3.76  | GROUND_INST: instantiating (16) with all_23_4, all_23_4, all_23_3, 0, 0,
% 20.32/3.76  |              simplifying with (22), (23), (26) gives:
% 20.32/3.76  |   (29)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.32/3.76  |             convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0 &
% 20.32/3.76  |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) &
% 20.32/3.76  |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = 0) &
% 20.32/3.76  |             convergent_lines(all_23_4, all_23_4) = v0))
% 20.32/3.76  | 
% 20.32/3.76  | GROUND_INST: instantiating (11) with all_23_4, all_23_3, all_23_3, 0,
% 20.32/3.76  |              simplifying with (22), (23), (26) gives:
% 20.32/3.76  |   (30)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.32/3.76  |             v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 20.32/3.76  |             convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 &
% 20.32/3.76  |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v0 = 0) &
% 20.32/3.76  |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.32/3.76  | 
% 20.32/3.76  | GROUND_INST: instantiating (16) with all_23_3, all_23_3, all_23_2, all_23_0,
% 20.32/3.76  |              all_23_0, simplifying with (23), (24), (27) gives:
% 20.32/3.76  |   (31)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.32/3.76  |             all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.32/3.76  |             & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.32/3.76  |             (v1 = 0) & unorthogonal_lines(all_23_3, all_23_3) = v1) | ( ~ (v0
% 20.32/3.76  |               = 0) & convergent_lines(all_23_3, all_23_3) = v0))
% 20.32/3.76  | 
% 20.32/3.76  | GROUND_INST: instantiating (12) with all_23_4, all_23_3, all_23_2, all_23_0,
% 20.32/3.76  |              simplifying with (22), (23), (24), (26), (27) gives:
% 20.43/3.77  |   (32)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.43/3.77  |             all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.43/3.77  |             & v1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 20.43/3.77  |             convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.43/3.77  |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.43/3.77  | 
% 20.43/3.77  | GROUND_INST: instantiating (6) with all_23_3, all_23_2, all_23_0, simplifying
% 20.43/3.77  |              with (23), (24), (27) gives:
% 20.43/3.77  |   (33)  all_23_0 = 0 | convergent_lines(all_23_3, all_23_2) = 0
% 20.43/3.77  | 
% 20.43/3.77  | DELTA: instantiating (30) with fresh symbols all_30_0, all_30_1, all_30_2,
% 20.43/3.77  |        all_30_3 gives:
% 20.43/3.77  |   (34)  (all_30_0 = 0 & all_30_1 = 0 & unorthogonal_lines(all_23_3, all_23_3)
% 20.43/3.77  |           = 0 & convergent_lines(all_23_3, all_23_3) = 0) | (all_30_2 = 0 &
% 20.43/3.77  |           convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_30_3 = 0) &
% 20.43/3.77  |           convergent_lines(all_23_4, all_23_3) = all_30_3)
% 20.43/3.77  | 
% 20.43/3.77  | DELTA: instantiating (29) with fresh symbols all_31_0, all_31_1, all_31_2,
% 20.43/3.77  |        all_31_3 gives:
% 20.43/3.77  |   (35)  (all_31_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (all_31_1
% 20.43/3.77  |           = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_31_2 = 0)
% 20.43/3.77  |           & unorthogonal_lines(all_23_4, all_23_4) = all_31_2) | ( ~ (all_31_3
% 20.43/3.77  |             = 0) & convergent_lines(all_23_4, all_23_4) = all_31_3)
% 20.43/3.77  | 
% 20.43/3.77  | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2,
% 20.43/3.77  |        all_32_3 gives:
% 20.43/3.77  |   (36)  (all_32_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.43/3.77  |           0) | (all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.77  |             all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.43/3.77  |           (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_32_3)
% 20.43/3.77  | 
% 20.43/3.77  | DELTA: instantiating (31) with fresh symbols all_33_0, all_33_1, all_33_2,
% 20.43/3.77  |        all_33_3 gives:
% 20.43/3.77  |   (37)  (all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.43/3.77  |           0) | (all_33_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 20.43/3.77  |             all_23_2) = 0) | ( ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3,
% 20.43/3.77  |             all_23_3) = all_33_2) | ( ~ (all_33_3 = 0) &
% 20.43/3.77  |           convergent_lines(all_23_3, all_23_3) = all_33_3)
% 20.43/3.77  | 
% 20.43/3.77  | BETA: splitting (33) gives:
% 20.43/3.77  | 
% 20.43/3.77  | Case 1:
% 20.43/3.77  | | 
% 20.43/3.77  | |   (38)  convergent_lines(all_23_3, all_23_2) = 0
% 20.43/3.77  | | 
% 20.43/3.77  | | BETA: splitting (28) gives:
% 20.43/3.77  | | 
% 20.43/3.77  | | Case 1:
% 20.43/3.77  | | | 
% 20.43/3.77  | | |   (39)  all_23_1 = 0
% 20.43/3.77  | | | 
% 20.43/3.77  | | | REDUCE: (20), (39) imply:
% 20.43/3.77  | | |   (40)  $false
% 20.43/3.77  | | | 
% 20.43/3.77  | | | CLOSE: (40) is inconsistent.
% 20.43/3.77  | | | 
% 20.43/3.77  | | Case 2:
% 20.43/3.77  | | | 
% 20.43/3.77  | | |   (41)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4, all_23_2)
% 20.43/3.77  | | |           = v0)
% 20.43/3.77  | | | 
% 20.43/3.77  | | | DELTA: instantiating (41) with fresh symbol all_40_0 gives:
% 20.43/3.77  | | |   (42)   ~ (all_40_0 = 0) & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.77  | | |         all_40_0
% 20.43/3.77  | | | 
% 20.43/3.77  | | | ALPHA: (42) implies:
% 20.43/3.77  | | |   (43)   ~ (all_40_0 = 0)
% 20.43/3.77  | | |   (44)  convergent_lines(all_23_4, all_23_2) = all_40_0
% 20.43/3.77  | | | 
% 20.43/3.77  | | | BETA: splitting (36) gives:
% 20.43/3.77  | | | 
% 20.43/3.77  | | | Case 1:
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | |   (45)  all_32_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 20.43/3.77  | | | |           all_23_2) = 0
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | | ALPHA: (45) implies:
% 20.43/3.77  | | | |   (46)  all_23_0 = 0
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | | REDUCE: (21), (46) imply:
% 20.43/3.77  | | | |   (47)  $false
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | | CLOSE: (47) is inconsistent.
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | Case 2:
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | |   (48)  (all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.77  | | | |             all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) |
% 20.43/3.77  | | | |         ( ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 20.43/3.77  | | | |           all_32_3)
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | | BETA: splitting (48) gives:
% 20.43/3.77  | | | | 
% 20.43/3.77  | | | | Case 1:
% 20.43/3.77  | | | | | 
% 20.43/3.77  | | | | |   (49)  all_32_1 = 0 & all_32_2 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.77  | | | | |           all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0
% 20.43/3.77  | | | | | 
% 20.43/3.77  | | | | | ALPHA: (49) implies:
% 20.43/3.77  | | | | |   (50)  convergent_lines(all_23_4, all_23_2) = 0
% 20.43/3.77  | | | | | 
% 20.43/3.77  | | | | | GROUND_INST: instantiating (17) with 0, all_40_0, all_23_2, all_23_4,
% 20.43/3.77  | | | | |              simplifying with (44), (50) gives:
% 20.43/3.78  | | | | |   (51)  all_40_0 = 0
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | REDUCE: (43), (51) imply:
% 20.43/3.78  | | | | |   (52)  $false
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | CLOSE: (52) is inconsistent.
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | Case 2:
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | |   (53)   ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 20.43/3.78  | | | | |         all_32_3
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | ALPHA: (53) implies:
% 20.43/3.78  | | | | |   (54)   ~ (all_32_3 = 0)
% 20.43/3.78  | | | | |   (55)  convergent_lines(all_23_4, all_23_3) = all_32_3
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_3,
% 20.43/3.78  | | | | |              all_32_3, all_32_3, simplifying with (22), (23), (55)
% 20.43/3.78  | | | | |              gives:
% 20.43/3.78  | | | | |   (56)  all_32_3 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 20.43/3.78  | | | | |           convergent_lines(all_23_4, all_23_4) = v0)
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4, all_23_3,
% 20.43/3.78  | | | | |              all_32_3, all_32_3, simplifying with (22), (23), (55)
% 20.43/3.78  | | | | |              gives:
% 20.43/3.78  | | | | |   (57)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & all_32_3 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.78  | | | | |               all_23_3) = 0) | (v2 = 0 & all_32_3 = 0 &
% 20.43/3.78  | | | | |             unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0)
% 20.43/3.78  | | | | |             & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.78  | | | | |               0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4, all_23_3,
% 20.43/3.78  | | | | |              all_32_3, 0, simplifying with (22), (23), (26), (55)
% 20.43/3.78  | | | | |              gives:
% 20.43/3.78  | | | | |   (58)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0
% 20.43/3.78  | | | | |             & all_32_3 = 0) | ( ~ (v1 = 0) &
% 20.43/3.78  | | | | |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.78  | | | | |               0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4, all_23_3, 0,
% 20.43/3.78  | | | | |              all_32_3, simplifying with (22), (23), (26), (55) gives:
% 20.43/3.78  | | | | |   (59)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & all_32_3 = 0) | (v2 = 0 &
% 20.43/3.78  | | | | |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) &
% 20.43/3.78  | | | | |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.78  | | | | |               0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3, all_23_3,
% 20.43/3.78  | | | | |              all_32_3, simplifying with (22), (23), (26), (55) gives:
% 20.43/3.78  | | | | |   (60)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0
% 20.43/3.78  | | | | |             & convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 &
% 20.43/3.78  | | | | |             all_32_3 = 0) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 20.43/3.78  | | | | |               all_23_3) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_2,
% 20.43/3.78  | | | | |              all_40_0, all_40_0, simplifying with (22), (24), (44)
% 20.43/3.78  | | | | |              gives:
% 20.43/3.78  | | | | |   (61)  all_40_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 20.43/3.78  | | | | |           convergent_lines(all_23_4, all_23_4) = v0)
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4, all_23_2,
% 20.43/3.78  | | | | |              all_40_0, all_40_0, simplifying with (22), (24), (44)
% 20.43/3.78  | | | | |              gives:
% 20.43/3.78  | | | | |   (62)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.78  | | | | |               all_23_2) = 0) | (v2 = 0 & all_40_0 = 0 &
% 20.43/3.78  | | | | |             unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (v1 = 0)
% 20.43/3.78  | | | | |             & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.78  | | | | |               0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (14) with all_23_3, all_23_4, all_23_2,
% 20.43/3.78  | | | | |              all_23_0, all_40_0, simplifying with (22), (23), (24),
% 20.43/3.78  | | | | |              (27), (44) gives:
% 20.43/3.78  | | | | |   (63)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.78  | | | | |         ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.78  | | | | |               all_23_2) = 0) | (v2 = 0 & all_23_0 = 0 &
% 20.43/3.78  | | | | |             convergent_lines(all_23_3, all_23_2) = 0) | ( ~ (v1 = 0) &
% 20.43/3.78  | | | | |             unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.78  | | | | |               0) & convergent_lines(all_23_3, all_23_4) = v0))
% 20.43/3.78  | | | | | 
% 20.43/3.78  | | | | | GROUND_INST: instantiating (5) with all_23_4, all_23_2, all_40_0,
% 20.43/3.78  | | | | |              simplifying with (22), (24), (44) gives:
% 20.43/3.79  | | | | |   (64)  all_40_0 = 0 | unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | GROUND_INST: instantiating (7) with all_23_3, all_23_2, all_23_2, 0,
% 20.43/3.79  | | | | |              simplifying with (23), (24), (38) gives:
% 20.43/3.79  | | | | |   (65)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.79  | | | | |         ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0
% 20.43/3.79  | | | | |             & convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 &
% 20.43/3.79  | | | | |             unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~ (v0 = 0)
% 20.43/3.79  | | | | |             & unorthogonal_lines(all_23_3, all_23_2) = v0))
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | GROUND_INST: instantiating (13) with all_23_3, all_23_4, all_23_2, 0,
% 20.43/3.79  | | | | |              all_40_0, simplifying with (22), (23), (24), (38), (44)
% 20.43/3.79  | | | | |              gives:
% 20.43/3.79  | | | | |   (66)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.79  | | | | |         ((v3 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.79  | | | | |               all_23_2) = 0) | (v2 = 0 & unorthogonal_lines(all_23_3,
% 20.43/3.79  | | | | |               all_23_2) = 0) | ( ~ (v1 = 0) &
% 20.43/3.79  | | | | |             unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0 =
% 20.43/3.79  | | | | |               0) & convergent_lines(all_23_3, all_23_4) = v0))
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | GROUND_INST: instantiating (10) with all_23_3, all_23_2, all_23_2,
% 20.43/3.79  | | | | |              all_23_0, simplifying with (23), (24), (27), (38) gives:
% 20.43/3.79  | | | | |   (67)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :
% 20.43/3.79  | | | | |         ((v3 = 0 & v2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0
% 20.43/3.79  | | | | |             & convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0 &
% 20.43/3.79  | | | | |             all_23_0 = 0) | ( ~ (v0 = 0) &
% 20.43/3.79  | | | | |             unorthogonal_lines(all_23_3, all_23_2) = v0))
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (65) with fresh symbols all_57_0, all_57_1,
% 20.43/3.79  | | | | |        all_57_2, all_57_3 gives:
% 20.43/3.79  | | | | |   (68)  (all_57_0 = 0 & all_57_1 = 0 & unorthogonal_lines(all_23_2,
% 20.43/3.79  | | | | |             all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0)
% 20.43/3.79  | | | | |         | (all_57_2 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0)
% 20.43/3.79  | | | | |         | ( ~ (all_57_3 = 0) & unorthogonal_lines(all_23_3, all_23_2)
% 20.43/3.79  | | | | |           = all_57_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (58) with fresh symbols all_58_0, all_58_1,
% 20.43/3.79  | | | | |        all_58_2, all_58_3 gives:
% 20.43/3.79  | | | | |   (69)  (all_58_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) |
% 20.43/3.79  | | | | |         (all_58_1 = 0 & all_32_3 = 0) | ( ~ (all_58_2 = 0) &
% 20.43/3.79  | | | | |           unorthogonal_lines(all_23_4, all_23_4) = all_58_2) | ( ~
% 20.43/3.79  | | | | |           (all_58_3 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.79  | | | | |           all_58_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (60) with fresh symbols all_60_0, all_60_1,
% 20.43/3.79  | | | | |        all_60_2, all_60_3 gives:
% 20.43/3.79  | | | | |   (70)  (all_60_0 = 0 & all_60_1 = 0 & unorthogonal_lines(all_23_3,
% 20.43/3.79  | | | | |             all_23_3) = 0 & convergent_lines(all_23_3, all_23_3) = 0)
% 20.43/3.79  | | | | |         | (all_60_2 = 0 & all_32_3 = 0) | ( ~ (all_60_3 = 0) &
% 20.43/3.79  | | | | |           convergent_lines(all_23_4, all_23_3) = all_60_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (59) with fresh symbols all_61_0, all_61_1,
% 20.43/3.79  | | | | |        all_61_2, all_61_3 gives:
% 20.43/3.79  | | | | |   (71)  (all_61_0 = 0 & all_32_3 = 0) | (all_61_1 = 0 &
% 20.43/3.79  | | | | |           convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_61_2 =
% 20.43/3.79  | | | | |             0) & unorthogonal_lines(all_23_4, all_23_4) = all_61_2) |
% 20.43/3.79  | | | | |         ( ~ (all_61_3 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.79  | | | | |           all_61_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (67) with fresh symbols all_62_0, all_62_1,
% 20.43/3.79  | | | | |        all_62_2, all_62_3 gives:
% 20.43/3.79  | | | | |   (72)  (all_62_0 = 0 & all_62_1 = 0 & unorthogonal_lines(all_23_2,
% 20.43/3.79  | | | | |             all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0)
% 20.43/3.79  | | | | |         | (all_62_2 = 0 & all_23_0 = 0) | ( ~ (all_62_3 = 0) &
% 20.43/3.79  | | | | |           unorthogonal_lines(all_23_3, all_23_2) = all_62_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (66) with fresh symbols all_65_0, all_65_1,
% 20.43/3.79  | | | | |        all_65_2, all_65_3 gives:
% 20.43/3.79  | | | | |   (73)  (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.79  | | | | |             all_23_2) = 0) | (all_65_1 = 0 &
% 20.43/3.79  | | | | |           unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~ (all_65_2
% 20.43/3.79  | | | | |             = 0) & unorthogonal_lines(all_23_3, all_23_4) = all_65_2)
% 20.43/3.79  | | | | |         | ( ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) =
% 20.43/3.79  | | | | |           all_65_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (63) with fresh symbols all_66_0, all_66_1,
% 20.43/3.79  | | | | |        all_66_2, all_66_3 gives:
% 20.43/3.79  | | | | |   (74)  (all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.79  | | | | |             all_23_2) = 0) | (all_66_1 = 0 & all_23_0 = 0 &
% 20.43/3.79  | | | | |           convergent_lines(all_23_3, all_23_2) = 0) | ( ~ (all_66_2 =
% 20.43/3.79  | | | | |             0) & unorthogonal_lines(all_23_3, all_23_4) = all_66_2) |
% 20.43/3.79  | | | | |         ( ~ (all_66_3 = 0) & convergent_lines(all_23_3, all_23_4) =
% 20.43/3.79  | | | | |           all_66_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (62) with fresh symbols all_67_0, all_67_1,
% 20.43/3.79  | | | | |        all_67_2, all_67_3 gives:
% 20.43/3.79  | | | | |   (75)  (all_67_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.79  | | | | |             all_23_2) = 0) | (all_67_1 = 0 & all_40_0 = 0 &
% 20.43/3.79  | | | | |           unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (all_67_2
% 20.43/3.79  | | | | |             = 0) & unorthogonal_lines(all_23_4, all_23_4) = all_67_2)
% 20.43/3.79  | | | | |         | ( ~ (all_67_3 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.79  | | | | |           all_67_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | DELTA: instantiating (57) with fresh symbols all_68_0, all_68_1,
% 20.43/3.79  | | | | |        all_68_2, all_68_3 gives:
% 20.43/3.79  | | | | |   (76)  (all_68_0 = 0 & all_32_3 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.79  | | | | |             all_23_3) = 0) | (all_68_1 = 0 & all_32_3 = 0 &
% 20.43/3.79  | | | | |           unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~ (all_68_2
% 20.43/3.79  | | | | |             = 0) & unorthogonal_lines(all_23_4, all_23_4) = all_68_2)
% 20.43/3.79  | | | | |         | ( ~ (all_68_3 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.79  | | | | |           all_68_3)
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | BETA: splitting (64) gives:
% 20.43/3.79  | | | | | 
% 20.43/3.79  | | | | | Case 1:
% 20.43/3.79  | | | | | | 
% 20.43/3.79  | | | | | |   (77)  unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.43/3.79  | | | | | | 
% 20.43/3.79  | | | | | | BETA: splitting (61) gives:
% 20.43/3.79  | | | | | | 
% 20.43/3.79  | | | | | | Case 1:
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | |   (78)  all_40_0 = 0
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | REDUCE: (43), (78) imply:
% 20.43/3.79  | | | | | | |   (79)  $false
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | CLOSE: (79) is inconsistent.
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | Case 2:
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | |   (80)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 20.43/3.79  | | | | | | |             all_23_4) = v0)
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | DELTA: instantiating (80) with fresh symbol all_76_0 gives:
% 20.43/3.79  | | | | | | |   (81)   ~ (all_76_0 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.79  | | | | | | |         all_76_0
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | ALPHA: (81) implies:
% 20.43/3.79  | | | | | | |   (82)  convergent_lines(all_23_4, all_23_4) = all_76_0
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | BETA: splitting (56) gives:
% 20.43/3.79  | | | | | | | 
% 20.43/3.79  | | | | | | | Case 1:
% 20.43/3.79  | | | | | | | | 
% 20.43/3.79  | | | | | | | |   (83)  all_32_3 = 0
% 20.43/3.79  | | | | | | | | 
% 20.43/3.79  | | | | | | | | REDUCE: (54), (83) imply:
% 20.43/3.79  | | | | | | | |   (84)  $false
% 20.43/3.79  | | | | | | | | 
% 20.43/3.79  | | | | | | | | CLOSE: (84) is inconsistent.
% 20.43/3.79  | | | | | | | | 
% 20.43/3.79  | | | | | | | Case 2:
% 20.43/3.79  | | | | | | | | 
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | DELTA: instantiating (80) with fresh symbol all_81_0 gives:
% 20.43/3.80  | | | | | | | |   (85)   ~ (all_81_0 = 0) & convergent_lines(all_23_4, all_23_4)
% 20.43/3.80  | | | | | | | |         = all_81_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | ALPHA: (85) implies:
% 20.43/3.80  | | | | | | | |   (86)   ~ (all_81_0 = 0)
% 20.43/3.80  | | | | | | | |   (87)  convergent_lines(all_23_4, all_23_4) = all_81_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | DELTA: instantiating (80) with fresh symbol all_86_0 gives:
% 20.43/3.80  | | | | | | | |   (88)   ~ (all_86_0 = 0) & convergent_lines(all_23_4, all_23_4)
% 20.43/3.80  | | | | | | | |         = all_86_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | ALPHA: (88) implies:
% 20.43/3.80  | | | | | | | |   (89)  convergent_lines(all_23_4, all_23_4) = all_86_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (17) with all_81_0, all_86_0,
% 20.43/3.80  | | | | | | | |              all_23_4, all_23_4, simplifying with (87), (89)
% 20.43/3.80  | | | | | | | |              gives:
% 20.43/3.80  | | | | | | | |   (90)  all_86_0 = all_81_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (17) with all_76_0, all_86_0,
% 20.43/3.80  | | | | | | | |              all_23_4, all_23_4, simplifying with (82), (89)
% 20.43/3.80  | | | | | | | |              gives:
% 20.43/3.80  | | | | | | | |   (91)  all_86_0 = all_76_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | COMBINE_EQS: (90), (91) imply:
% 20.43/3.80  | | | | | | | |   (92)  all_81_0 = all_76_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | SIMP: (92) implies:
% 20.43/3.80  | | | | | | | |   (93)  all_81_0 = all_76_0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | REDUCE: (86), (93) imply:
% 20.43/3.80  | | | | | | | |   (94)   ~ (all_76_0 = 0)
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4,
% 20.43/3.80  | | | | | | | |              all_23_4, all_76_0, all_76_0, simplifying with
% 20.43/3.80  | | | | | | | |              (22), (82) gives:
% 20.43/3.80  | | | | | | | |   (95)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |           int] : ((v3 = 0 & all_76_0 = 0 &
% 20.43/3.80  | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = 0) | (v2 =
% 20.43/3.80  | | | | | | | |             0 & all_76_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.80  | | | | | | | |               all_23_4) = 0) | ( ~ (v1 = 0) &
% 20.43/3.80  | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~
% 20.43/3.80  | | | | | | | |             (v0 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.80  | | | | | | | |             v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3,
% 20.43/3.80  | | | | | | | |              all_23_4, all_76_0, simplifying with (22), (23),
% 20.43/3.80  | | | | | | | |              (26), (82) gives:
% 20.43/3.80  | | | | | | | |   (96)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |           int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.80  | | | | | | | |             unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.43/3.80  | | | | | | | |             convergent_lines(all_23_3, all_23_4) = 0) | (v1 = 0
% 20.43/3.80  | | | | | | | |             & all_76_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.80  | | | | | | | |               all_23_4) = 0) | ( ~ (v0 = 0) &
% 20.43/3.80  | | | | | | | |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (5) with all_23_4, all_23_4,
% 20.43/3.80  | | | | | | | |              all_76_0, simplifying with (22), (82) gives:
% 20.43/3.80  | | | | | | | |   (97)  all_76_0 = 0 | unorthogonal_lines(all_23_4, all_23_4) =
% 20.43/3.80  | | | | | | | |         0
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (16) with all_23_4, all_23_4,
% 20.43/3.80  | | | | | | | |              all_23_2, 0, 0, simplifying with (22), (24), (77)
% 20.43/3.80  | | | | | | | |              gives:
% 20.43/3.80  | | | | | | | |   (98)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |           int] : ((v3 = 0 & convergent_lines(all_23_4, all_23_2)
% 20.43/3.80  | | | | | | | |             = 0) | (v2 = 0 & convergent_lines(all_23_4,
% 20.43/3.80  | | | | | | | |               all_23_2) = 0) | ( ~ (v1 = 0) &
% 20.43/3.80  | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~
% 20.43/3.80  | | | | | | | |             (v0 = 0) & convergent_lines(all_23_4, all_23_4) =
% 20.43/3.80  | | | | | | | |             v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_2,
% 20.43/3.80  | | | | | | | |              all_23_2, 0, simplifying with (22), (24), (77)
% 20.43/3.80  | | | | | | | |              gives:
% 20.43/3.80  | | | | | | | |   (99)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |           int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.80  | | | | | | | |             unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.43/3.80  | | | | | | | |             convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0
% 20.43/3.80  | | | | | | | |             & convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.43/3.80  | | | | | | | |             (v0 = 0) & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.80  | | | | | | | |             v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4,
% 20.43/3.80  | | | | | | | |              all_23_2, all_40_0, 0, simplifying with (22), (24),
% 20.43/3.80  | | | | | | | |              (44), (77) gives:
% 20.43/3.80  | | | | | | | |   (100)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |            int] : ((v3 = 0 & convergent_lines(all_23_4,
% 20.43/3.80  | | | | | | | |                all_23_2) = 0) | (v2 = 0 & all_40_0 = 0) | ( ~
% 20.43/3.80  | | | | | | | |              (v1 = 0) & unorthogonal_lines(all_23_4, all_23_4) =
% 20.43/3.80  | | | | | | | |              v1) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 20.43/3.80  | | | | | | | |                all_23_4) = v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4,
% 20.43/3.80  | | | | | | | |              all_23_2, 0, all_40_0, simplifying with (22), (24),
% 20.43/3.80  | | | | | | | |              (44), (77) gives:
% 20.43/3.80  | | | | | | | |   (101)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |            int] : ((v3 = 0 & all_40_0 = 0) | (v2 = 0 &
% 20.43/3.80  | | | | | | | |              convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v1
% 20.43/3.80  | | | | | | | |                = 0) & unorthogonal_lines(all_23_4, all_23_4) =
% 20.43/3.80  | | | | | | | |              v1) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 20.43/3.80  | | | | | | | |                all_23_4) = v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_2,
% 20.43/3.80  | | | | | | | |              all_23_3, 0, simplifying with (22), (23), (24),
% 20.43/3.80  | | | | | | | |              (26), (77) gives:
% 20.43/3.80  | | | | | | | |   (102)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |            int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.80  | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.43/3.80  | | | | | | | |              convergent_lines(all_23_2, all_23_3) = 0) | (v1 = 0
% 20.43/3.80  | | | | | | | |              & convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 20.43/3.80  | | | | | | | |              (v0 = 0) & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.80  | | | | | | | |              v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.80  | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 20.43/3.80  | | | | | | | |              all_23_2, all_40_0, simplifying with (22), (24),
% 20.43/3.80  | | | | | | | |              (44), (77) gives:
% 20.43/3.80  | | | | | | | |   (103)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.80  | | | | | | | |            int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.80  | | | | | | | |              unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.43/3.80  | | | | | | | |              convergent_lines(all_23_2, all_23_2) = 0) | (v1 = 0
% 20.43/3.80  | | | | | | | |              & all_40_0 = 0) | ( ~ (v0 = 0) &
% 20.43/3.80  | | | | | | | |              convergent_lines(all_23_4, all_23_2) = v0))
% 20.43/3.80  | | | | | | | | 
% 20.43/3.81  | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 20.43/3.81  | | | | | | | |              all_23_3, all_32_3, simplifying with (22), (23),
% 20.43/3.81  | | | | | | | |              (24), (55), (77) gives:
% 20.43/3.81  | | | | | | | |   (104)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.81  | | | | | | | |            int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.81  | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.43/3.81  | | | | | | | |              convergent_lines(all_23_2, all_23_3) = 0) | (v1 = 0
% 20.43/3.81  | | | | | | | |              & all_32_3 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.81  | | | | | | | |                all_23_3) = 0) | ( ~ (v0 = 0) &
% 20.43/3.81  | | | | | | | |              convergent_lines(all_23_4, all_23_2) = v0))
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 20.43/3.81  | | | | | | | |              all_23_4, all_76_0, simplifying with (22), (24),
% 20.43/3.81  | | | | | | | |              (77), (82) gives:
% 20.43/3.81  | | | | | | | |   (105)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 20.43/3.81  | | | | | | | |            int] : ((v3 = 0 & v2 = 0 &
% 20.43/3.81  | | | | | | | |              unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 20.43/3.81  | | | | | | | |              convergent_lines(all_23_2, all_23_4) = 0) | (v1 = 0
% 20.43/3.81  | | | | | | | |              & all_76_0 = 0 & unorthogonal_lines(all_23_4,
% 20.43/3.81  | | | | | | | |                all_23_4) = 0) | ( ~ (v0 = 0) &
% 20.43/3.81  | | | | | | | |              convergent_lines(all_23_4, all_23_2) = v0))
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (103) with fresh symbols all_97_0,
% 20.43/3.81  | | | | | | | |        all_97_1, all_97_2, all_97_3 gives:
% 20.43/3.81  | | | | | | | |   (106)  (all_97_0 = 0 & all_97_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) | (all_97_2
% 20.43/3.81  | | | | | | | |            = 0 & all_40_0 = 0) | ( ~ (all_97_3 = 0) &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_97_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (102) with fresh symbols all_98_0,
% 20.43/3.81  | | | | | | | |        all_98_1, all_98_2, all_98_3 gives:
% 20.43/3.81  | | | | | | | |   (107)  (all_98_0 = 0 & all_98_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_2, all_23_3) = 0) | (all_98_2
% 20.43/3.81  | | | | | | | |            = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_98_3 = 0) & convergent_lines(all_23_4, all_23_2)
% 20.43/3.81  | | | | | | | |            = all_98_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (101) with fresh symbols all_99_0,
% 20.43/3.81  | | | | | | | |        all_99_1, all_99_2, all_99_3 gives:
% 20.43/3.81  | | | | | | | |   (108)  (all_99_0 = 0 & all_40_0 = 0) | (all_99_1 = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_99_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_4) = all_99_2) | ( ~ (all_99_3 = 0) &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_99_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (100) with fresh symbols all_100_0,
% 20.43/3.81  | | | | | | | |        all_100_1, all_100_2, all_100_3 gives:
% 20.43/3.81  | | | | | | | |   (109)  (all_100_0 = 0 & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.81  | | | | | | | |            0) | (all_100_1 = 0 & all_40_0 = 0) | ( ~ (all_100_2
% 20.43/3.81  | | | | | | | |              = 0) & unorthogonal_lines(all_23_4, all_23_4) =
% 20.43/3.81  | | | | | | | |            all_100_2) | ( ~ (all_100_3 = 0) &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_100_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (99) with fresh symbols all_102_0,
% 20.43/3.81  | | | | | | | |        all_102_1, all_102_2, all_102_3 gives:
% 20.43/3.81  | | | | | | | |   (110)  (all_102_0 = 0 & all_102_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) |
% 20.43/3.81  | | | | | | | |          (all_102_2 = 0 & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.81  | | | | | | | |            0) | ( ~ (all_102_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_2) = all_102_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (98) with fresh symbols all_103_0,
% 20.43/3.81  | | | | | | | |        all_103_1, all_103_2, all_103_3 gives:
% 20.43/3.81  | | | | | | | |   (111)  (all_103_0 = 0 & convergent_lines(all_23_4, all_23_2) =
% 20.43/3.81  | | | | | | | |            0) | (all_103_1 = 0 & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_2) = 0) | ( ~ (all_103_2 = 0) &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = all_103_2) |
% 20.43/3.81  | | | | | | | |          ( ~ (all_103_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_4) = all_103_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (105) with fresh symbols all_104_0,
% 20.43/3.81  | | | | | | | |        all_104_1, all_104_2, all_104_3 gives:
% 20.43/3.81  | | | | | | | |   (112)  (all_104_0 = 0 & all_104_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_2, all_23_4) = 0) |
% 20.43/3.81  | | | | | | | |          (all_104_2 = 0 & all_76_0 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_104_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_2) = all_104_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (104) with fresh symbols all_105_0,
% 20.43/3.81  | | | | | | | |        all_105_1, all_105_2, all_105_3 gives:
% 20.43/3.81  | | | | | | | |   (113)  (all_105_0 = 0 & all_105_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_2, all_23_3) = 0) |
% 20.43/3.81  | | | | | | | |          (all_105_2 = 0 & all_32_3 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_105_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_2) = all_105_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (96) with fresh symbols all_107_0,
% 20.43/3.81  | | | | | | | |        all_107_1, all_107_2, all_107_3 gives:
% 20.43/3.81  | | | | | | | |   (114)  (all_107_0 = 0 & all_107_1 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_3, all_23_4) = 0) |
% 20.43/3.81  | | | | | | | |          (all_107_2 = 0 & all_76_0 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_107_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_3) = all_107_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | DELTA: instantiating (95) with fresh symbols all_108_0,
% 20.43/3.81  | | | | | | | |        all_108_1, all_108_2, all_108_3 gives:
% 20.43/3.81  | | | | | | | |   (115)  (all_108_0 = 0 & all_76_0 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 20.43/3.81  | | | | | | | |          (all_108_1 = 0 & all_76_0 = 0 &
% 20.43/3.81  | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 20.43/3.81  | | | | | | | |            (all_108_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.81  | | | | | | | |              all_23_4) = all_108_2) | ( ~ (all_108_3 = 0) &
% 20.43/3.81  | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_108_3)
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | BETA: splitting (34) gives:
% 20.43/3.81  | | | | | | | | 
% 20.43/3.81  | | | | | | | | Case 1:
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | |   (116)  all_30_0 = 0 & all_30_1 = 0 &
% 20.43/3.81  | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 20.43/3.81  | | | | | | | | |          convergent_lines(all_23_3, all_23_3) = 0
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | ALPHA: (116) implies:
% 20.43/3.81  | | | | | | | | |   (117)  convergent_lines(all_23_3, all_23_3) = 0
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 20.43/3.81  | | | | | | | | |              with (23), (117) gives:
% 20.43/3.81  | | | | | | | | |   (118)  $false
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | CLOSE: (118) is inconsistent.
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | Case 2:
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | |   (119)  (all_30_2 = 0 & convergent_lines(all_23_4, all_23_3)
% 20.43/3.81  | | | | | | | | |            = 0) | ( ~ (all_30_3 = 0) &
% 20.43/3.81  | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = all_30_3)
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | BETA: splitting (119) gives:
% 20.43/3.81  | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | Case 1:
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | |   (120)  all_30_2 = 0 & convergent_lines(all_23_4, all_23_3)
% 20.43/3.81  | | | | | | | | | |          = 0
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | | ALPHA: (120) implies:
% 20.43/3.81  | | | | | | | | | |   (121)  convergent_lines(all_23_4, all_23_3) = 0
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | | GROUND_INST: instantiating (17) with all_32_3, 0, all_23_3,
% 20.43/3.81  | | | | | | | | | |              all_23_4, simplifying with (55), (121) gives:
% 20.43/3.81  | | | | | | | | | |   (122)  all_32_3 = 0
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | | REDUCE: (54), (122) imply:
% 20.43/3.81  | | | | | | | | | |   (123)  $false
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | | CLOSE: (123) is inconsistent.
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | Case 2:
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | |   (124)   ~ (all_30_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.81  | | | | | | | | | |            all_23_3) = all_30_3
% 20.43/3.81  | | | | | | | | | | 
% 20.43/3.81  | | | | | | | | | | ALPHA: (124) implies:
% 20.43/3.82  | | | | | | | | | |   (125)   ~ (all_30_3 = 0)
% 20.43/3.82  | | | | | | | | | |   (126)  convergent_lines(all_23_4, all_23_3) = all_30_3
% 20.43/3.82  | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | BETA: splitting (97) gives:
% 20.43/3.82  | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | |   (127)  unorthogonal_lines(all_23_4, all_23_4) = 0
% 20.43/3.82  | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | BETA: splitting (69) gives:
% 20.43/3.82  | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | |   (128)  (all_58_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | |              all_23_3) = 0) | (all_58_1 = 0 & all_32_3 = 0)
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | BETA: splitting (128) gives:
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | |   (129)  all_58_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | |            all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | ALPHA: (129) implies:
% 20.43/3.82  | | | | | | | | | | | | |   (130)  convergent_lines(all_23_4, all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (130) are inconsistent by
% 20.43/3.82  | | | | | | | | | | | | |            sub-proof #7.
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | |   (131)  all_58_1 = 0 & all_32_3 = 0
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | ALPHA: (131) implies:
% 20.43/3.82  | | | | | | | | | | | | |   (132)  all_32_3 = 0
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | REDUCE: (54), (132) imply:
% 20.43/3.82  | | | | | | | | | | | | |   (133)  $false
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | End of split
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | |   (134)  ( ~ (all_58_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | |              all_23_4) = all_58_2) | ( ~ (all_58_3 = 0) &
% 20.43/3.82  | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_58_3)
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | BETA: splitting (134) gives:
% 20.43/3.82  | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | |   (135)   ~ (all_58_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | |            all_23_4) = all_58_2
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | ALPHA: (135) implies:
% 20.43/3.82  | | | | | | | | | | | | |   (136)   ~ (all_58_2 = 0)
% 20.43/3.82  | | | | | | | | | | | | |   (137)  unorthogonal_lines(all_23_4, all_23_4) = all_58_2
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_58_2, all_23_4,
% 20.43/3.82  | | | | | | | | | | | | |              all_23_4, simplifying with (127), (137) gives:
% 20.43/3.82  | | | | | | | | | | | | |   (138)  all_58_2 = 0
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | REDUCE: (136), (138) imply:
% 20.43/3.82  | | | | | | | | | | | | |   (139)  $false
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | |   (140)   ~ (all_58_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | |            all_23_4) = all_58_3
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | ALPHA: (140) implies:
% 20.43/3.82  | | | | | | | | | | | | |   (141)   ~ (all_58_3 = 0)
% 20.43/3.82  | | | | | | | | | | | | |   (142)  convergent_lines(all_23_4, all_23_4) = all_58_3
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 20.43/3.82  | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | |   (143)  (all_68_0 = 0 & all_32_3 = 0 &
% 20.43/3.82  | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 20.43/3.82  | | | | | | | | | | | | | |          (all_68_1 = 0 & all_32_3 = 0 &
% 20.43/3.82  | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0)
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | |   (144)  all_68_0 = 0 & all_32_3 = 0 &
% 20.43/3.82  | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 20.43/3.82  | | | | | | | | | | | | | | |   (145)  all_32_3 = 0
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | REDUCE: (54), (145) imply:
% 20.43/3.82  | | | | | | | | | | | | | | |   (146)  $false
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | |   (147)  all_68_1 = 0 & all_32_3 = 0 &
% 20.43/3.82  | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 20.43/3.82  | | | | | | | | | | | | | | |   (148)  all_32_3 = 0
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | REDUCE: (54), (148) imply:
% 20.43/3.82  | | | | | | | | | | | | | | |   (149)  $false
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | End of split
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | |   (150)  ( ~ (all_68_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | |              all_23_4) = all_68_2) | ( ~ (all_68_3 = 0) &
% 20.43/3.82  | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_68_3)
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 20.43/3.82  | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | |   (151)   ~ (all_68_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | |            all_23_4) = all_68_2
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 20.43/3.82  | | | | | | | | | | | | | | |   (152)   ~ (all_68_2 = 0)
% 20.43/3.82  | | | | | | | | | | | | | | |   (153)  unorthogonal_lines(all_23_4, all_23_4) = all_68_2
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_68_2, all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (153) gives:
% 20.43/3.82  | | | | | | | | | | | | | | |   (154)  all_68_2 = 0
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | REDUCE: (152), (154) imply:
% 20.43/3.82  | | | | | | | | | | | | | | |   (155)  $false
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | |   (156)   ~ (all_68_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | |            all_23_4) = all_68_3
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 20.43/3.82  | | | | | | | | | | | | | | |   (157)  convergent_lines(all_23_4, all_23_4) = all_68_3
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 20.43/3.82  | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | |   (158)  (all_31_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | |              all_23_3) = 0) | (all_31_1 = 0 &
% 20.43/3.82  | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = 0)
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (159)  all_31_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (160)  convergent_lines(all_23_4, all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (160) are inconsistent by
% 20.43/3.82  | | | | | | | | | | | | | | | | |            sub-proof #7.
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (161)  all_31_1 = 0 & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (162)  convergent_lines(all_23_4, all_23_3) = 0
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (162) are inconsistent by
% 20.43/3.82  | | | | | | | | | | | | | | | | |            sub-proof #7.
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | End of split
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | |   (163)  ( ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | |              all_23_4) = all_31_2) | ( ~ (all_31_3 = 0) &
% 20.43/3.82  | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_31_3)
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 20.43/3.82  | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (164)   ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | | |            all_23_4) = all_31_2
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (165)   ~ (all_31_2 = 0)
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (166)  unorthogonal_lines(all_23_4, all_23_4) = all_31_2
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_31_2, all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (166) gives:
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (167)  all_31_2 = 0
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | REDUCE: (165), (167) imply:
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (168)  $false
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.82  | | | | | | | | | | | | | | | | | 
% 20.43/3.82  | | | | | | | | | | | | | | | | |   (169)   ~ (all_31_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.82  | | | | | | | | | | | | | | | | |            all_23_4) = all_31_3
% 20.43/3.83  | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | |   (170)  convergent_lines(all_23_4, all_23_4) = all_31_3
% 20.43/3.83  | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | |   (171)  (all_100_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_100_1 = 0 & all_40_0 =
% 20.43/3.83  | | | | | | | | | | | | | | | | | |            0)
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (172)  all_100_0 = 0 & convergent_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (173)  convergent_lines(all_23_4, all_23_2) = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (173) are inconsistent by
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (174)  all_100_1 = 0 & all_40_0 = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (175)  all_40_0 = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | REDUCE: (43), (175) imply:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (176)  $false
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | End of split
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | |   (177)  ( ~ (all_100_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | |              all_23_4) = all_100_2) | ( ~ (all_100_3 = 0) &
% 20.43/3.83  | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) =
% 20.43/3.83  | | | | | | | | | | | | | | | | | |            all_100_3)
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (178)   ~ (all_100_2 = 0) & unorthogonal_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |            all_23_4) = all_100_2
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (179)   ~ (all_100_2 = 0)
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (180)  unorthogonal_lines(all_23_4, all_23_4) = all_100_2
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_100_2, all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (180) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (181)  all_100_2 = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | REDUCE: (179), (181) imply:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (182)  $false
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_100_3 = 0) & convergent_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |            all_23_4) = all_100_3
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | |   (184)  convergent_lines(all_23_4, all_23_4) = all_100_3
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | |   (185)  (all_61_0 = 0 & all_32_3 = 0) | (all_61_1 = 0 &
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = 0)
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |   (186)  all_61_0 = 0 & all_32_3 = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |   (187)  all_32_3 = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (187) imply:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |   (188)  $false
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |   (189)  all_61_1 = 0 & convergent_lines(all_23_4,
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |   (190)  convergent_lines(all_23_4, all_23_3) = 0
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (190) are inconsistent by
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | |            sub-proof #7.
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | End of split
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 20.43/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | |   (191)  ( ~ (all_61_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_61_2) | ( ~ (all_61_3 = 0) &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_61_3)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (192)   ~ (all_61_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_61_2
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (193)   ~ (all_61_2 = 0)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (194)  unorthogonal_lines(all_23_4, all_23_4) = all_61_2
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_61_2, all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (194) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (195)  all_61_2 = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (195) imply:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (196)  $false
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (197)   ~ (all_61_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_61_3
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | |   (198)  convergent_lines(all_23_4, all_23_4) = all_61_3
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_103_0 = 0 & convergent_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_103_1 = 0 &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_103_0 = 0 & convergent_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (201)  convergent_lines(all_23_4, all_23_2) = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (201) are inconsistent by
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_103_1 = 0 & convergent_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (203)  convergent_lines(all_23_4, all_23_2) = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (203) are inconsistent by
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |   (204)  ( ~ (all_103_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_103_2) | ( ~ (all_103_3 = 0) &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) =
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | |            all_103_3)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (205)   ~ (all_103_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_103_2
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (206)   ~ (all_103_2 = 0)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (207)  unorthogonal_lines(all_23_4, all_23_4) = all_103_2
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_103_2, all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (207) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_103_2 = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (208) imply:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (209)  $false
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (210)   ~ (all_103_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_103_3
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | |   (211)  convergent_lines(all_23_4, all_23_4) = all_103_3
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | |   (212)  (all_67_0 = 0 & all_40_0 = 0 &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | |          (all_67_1 = 0 & all_40_0 = 0 &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0)
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_67_0 = 0 & all_40_0 = 0 &
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_40_0 = 0
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (214) imply:
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  $false
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.83  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_67_1 = 0 & all_40_0 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_40_0 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (217) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | |   (219)  ( ~ (all_67_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_67_2) | ( ~ (all_67_3 = 0) &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_67_3)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (220)   ~ (all_67_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_67_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (221)   ~ (all_67_2 = 0)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  unorthogonal_lines(all_23_4, all_23_4) = all_67_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_67_2, all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (222) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_67_2 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (221), (223) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (225)   ~ (all_67_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_67_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  convergent_lines(all_23_4, all_23_4) = all_67_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  (all_108_0 = 0 & all_76_0 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_108_1 = 0 & all_76_0 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_108_0 = 0 & all_76_0 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_76_0 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (229) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_108_1 = 0 & all_76_0 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_76_0 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (232) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  ( ~ (all_108_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_108_2) | ( ~ (all_108_3 = 0) &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) =
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_108_3)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)   ~ (all_108_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_108_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_108_2 = 0)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  unorthogonal_lines(all_23_4, all_23_4) = all_108_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_108_2, all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (237) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_108_2 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (238) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)   ~ (all_108_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_108_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  convergent_lines(all_23_4, all_23_4) = all_108_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  (all_99_0 = 0 & all_40_0 = 0) | (all_99_1 = 0 &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_99_0 = 0 & all_40_0 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_40_0 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (244) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_99_1 = 0 & convergent_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  convergent_lines(all_23_4, all_23_2) = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (247) are inconsistent by
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  ( ~ (all_99_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_99_2) | ( ~ (all_99_3 = 0) &
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_99_3)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)   ~ (all_99_2 = 0) & unorthogonal_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_99_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)   ~ (all_99_2 = 0)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  unorthogonal_lines(all_23_4, all_23_4) = all_99_2
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_99_2, all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (127), (251) gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_99_2 = 0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  $false
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)   ~ (all_99_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_99_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  convergent_lines(all_23_4, all_23_4) = all_99_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_58_3, all_61_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (142), (198)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_61_3 = all_58_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_68_3, all_99_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (157), (255)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_99_3 = all_68_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_68_3, all_100_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (157), (184)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_100_3 = all_68_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_67_3, all_100_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (184), (226)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_100_3 = all_67_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_61_3, all_100_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (184), (198)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_100_3 = all_61_3
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_76_0, all_103_3,
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (82), (211)
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_103_3 = all_76_0
% 20.73/3.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_99_3, all_103_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (211), (255)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_103_3 = all_99_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_99_3, all_108_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (241), (255)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_108_3 = all_99_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_31_3, all_108_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (170), (241)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_108_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_32_3, all_30_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (55), (126)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_32_3 = all_30_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (264) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_99_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_99_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (262) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_99_3 = all_76_0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_99_3 = all_76_0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_68_3 = all_67_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_68_3 = all_67_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (260) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_67_3 = all_61_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (269) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_76_0 = all_68_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (269) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_76_0 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_68_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_68_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (276) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_67_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_67_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (278) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_61_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_61_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (280) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_58_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_58_3 = all_31_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (282) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)   ~ (all_31_3 = 0)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_23_4, all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, 0, simplifying with (22), (23), (26),
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (127) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              convergent_lines(all_23_3, all_23_4) = 0) |
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v1 = 0 & convergent_lines(all_23_4, all_23_4) =
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              0) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_3) = v0))
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbols all_160_0,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_160_1, all_160_2, all_160_3 gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  (all_160_0 = 0 & all_160_1 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = 0) |
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_160_2 = 0 & convergent_lines(all_23_4,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = 0) | ( ~ (all_160_3 = 0) &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) =
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_160_3)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  (all_33_0 = 0 & all_23_0 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0) |
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_33_1 = 0 & all_23_0 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_33_0 = 0 & all_23_0 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_2) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_23_0 = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (288) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  $false
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_33_1 = 0 & all_23_0 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_2) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_23_0 = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (291) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  $false
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  ( ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_33_2) | ( ~ (all_33_3 = 0) &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_3) = all_33_3)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)   ~ (all_33_2 = 0) & unorthogonal_lines(all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_33_2
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)   ~ (all_33_2 = 0)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  unorthogonal_lines(all_23_3, all_23_3) = all_33_2
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_33_2, simplifying with (23), (296) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_33_2 = 0 | convergent_lines(all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  convergent_lines(all_23_3, all_23_3) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (298) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  $false
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_33_2 = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (300) imply:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  $false
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)   ~ (all_33_3 = 0) & convergent_lines(all_23_3,
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_33_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)   ~ (all_33_3 = 0)
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  convergent_lines(all_23_3, all_23_3) = all_33_3
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_60_0 = 0 & all_60_1 = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_3) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  convergent_lines(all_23_3, all_23_3) = 0
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (306) gives:
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  $false
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 20.73/3.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  (all_60_2 = 0 & all_32_3 = 0) | ( ~ (all_60_3 = 0)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & convergent_lines(all_23_4, all_23_3) =
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_60_3)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_60_2 = 0 & all_32_3 = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_32_3 = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (310) imply:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_30_3 = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_30_3 = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (312) imply:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  $false
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent.
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)   ~ (all_60_3 = 0) & convergent_lines(all_23_4,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_60_3
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)   ~ (all_60_3 = 0)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  convergent_lines(all_23_4, all_23_3) = all_60_3
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_3, all_60_3,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (126), (316)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_60_3 = all_30_3
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_3, all_23_2,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_33_3, simplifying with (23), (24),
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (38), (304) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_33_3 = 0 | convergent_lines(all_23_2,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_23_3, all_23_4,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_33_3, all_30_3, simplifying with
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (22), (23), (126), (304) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_33_3 = 0 | all_30_3 = 0 |  ? [v0: int] : ( ~
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v0 = 0) & convergent_lines(all_23_3, all_23_4)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = v0)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_57_0 = 0 & all_57_1 = 0 &
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  convergent_lines(all_23_2, all_23_2) = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (24), (321) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  $false
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  (all_57_2 = 0 & unorthogonal_lines(all_23_3,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_57_3 = 0) &
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_2) =
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_3)
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_57_2 = 0 & unorthogonal_lines(all_23_3,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, 0, all_23_2,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (27), (325) gives:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_23_0 = 0
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (326) imply:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  $false
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent.
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)   ~ (all_57_3 = 0) & unorthogonal_lines(all_23_3,
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_57_3
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 20.73/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)   ~ (all_57_3 = 0)
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  unorthogonal_lines(all_23_3, all_23_2) = all_57_3
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  convergent_lines(all_23_2, all_23_3) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_33_3 = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (332) imply:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  $false
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_30_3 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = v0)
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_30_3 = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (335) imply:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  $false
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)   ? [v0: int] : ( ~ (v0 = 0) &
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = v0)
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (337) with fresh symbol all_214_0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)   ~ (all_214_0 = 0) & convergent_lines(all_23_3,
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_214_0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)   ~ (all_214_0 = 0)
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  convergent_lines(all_23_3, all_23_4) = all_214_0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_160_0 = 0 & all_160_1 = 0 &
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (21), (27), (43), (73), (330), (342),
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (343) are inconsistent by sub-proof #4.
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  (all_160_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = 0) | ( ~ (all_160_3 = 0) &
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) =
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_160_3)
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_160_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  convergent_lines(all_23_4, all_23_4) = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_31_3, 0, all_23_4,
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (170), (346) gives:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  all_31_3 = 0
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (347) imply:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  $false
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent.
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)   ~ (all_160_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_160_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  convergent_lines(all_23_4, all_23_3) = all_160_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_107_0 = 0 & all_107_1 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (21), (27), (43), (73), (330), (352),
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (353) are inconsistent by sub-proof #4.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  (all_107_2 = 0 & all_76_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_107_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_107_3)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_107_2 = 0 & all_76_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_76_0 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (356) imply:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_31_3 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (357) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_31_3 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (358) imply:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  $false
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)   ~ (all_107_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_107_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)   ~ (all_107_3 = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  convergent_lines(all_23_4, all_23_3) = all_107_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_3, all_160_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (126), (350)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  all_160_3 = all_30_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_107_3, all_160_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (350), (362)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_160_3 = all_107_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, all_57_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_3, simplifying with (27), (330)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_57_3 = all_23_0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (363), (364) imply:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_107_3 = all_30_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (366) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  all_107_3 = all_30_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_62_0 = 0 & all_62_1 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (24), (369) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  $false
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  (all_62_2 = 0 & all_23_0 = 0) | ( ~ (all_62_3 = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & unorthogonal_lines(all_23_3, all_23_2) =
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_62_3)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_62_2 = 0 & all_23_0 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  all_23_0 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (373) imply:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)  $false
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)   ~ (all_62_3 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_62_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)   ~ (all_62_3 = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)  unorthogonal_lines(all_23_3, all_23_2) = all_62_3
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_23_0, all_62_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_3, simplifying with (27), (377)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_62_3 = all_23_0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  (all_65_0 = 0 & all_40_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_65_1 = 0 & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  all_65_0 = 0 & all_40_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  all_40_0 = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (381) imply:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  $false
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (382) is inconsistent.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  all_65_1 = 0 & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (27), (330), (384) are inconsistent by
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  ( ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_65_2) | ( ~ (all_65_3 = 0) &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = all_65_3)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)   ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_65_2
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)   ~ (all_65_2 = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  unorthogonal_lines(all_23_3, all_23_4) = all_65_2
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)  (all_66_0 = 0 & all_40_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_66_1 = 0 & all_23_0 = 0 &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0)
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (389) are inconsistent by sub-proof
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #3.
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (390)  ( ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_66_2) | ( ~ (all_66_3 = 0) &
% 20.89/3.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = all_66_3)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (391)   ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_66_2
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (392)   ~ (all_66_2 = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (393)  unorthogonal_lines(all_23_3, all_23_4) = all_66_2
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_65_2, all_66_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_3, simplifying with (388), (393)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (394)  all_66_2 = all_65_2
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_4,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_214_0, simplifying with (22), (23), (340)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (395)  all_214_0 = 0 | unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (396)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (387), (388), (396) are inconsistent by
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (397)  all_214_0 = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (397) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (398)  $false
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (399)   ~ (all_66_3 = 0) & convergent_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_66_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (400)  convergent_lines(all_23_3, all_23_4) = all_66_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_214_0, all_66_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_3, simplifying with (340), (400)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (401)  all_214_0 = all_66_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (401) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (402)   ~ (all_66_3 = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_4,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_66_3, simplifying with (22), (23), (400)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (403)  all_66_3 = 0 | unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (404)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (387), (388), (404) are inconsistent by
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (405)  all_66_3 = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (402), (405) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (406)  $false
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (407)   ~ (all_65_3 = 0) & convergent_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_65_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (408)  convergent_lines(all_23_3, all_23_4) = all_65_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_214_0, all_65_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_3, simplifying with (340), (408)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (409)  all_214_0 = all_65_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (409) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (410)   ~ (all_65_3 = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (411)  (all_66_0 = 0 & all_40_0 = 0 &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_66_1 = 0 & all_23_0 = 0 &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (411) are inconsistent by sub-proof
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #3.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (412)  ( ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_66_2) | ( ~ (all_66_3 = 0) &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = all_66_3)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (413)   ~ (all_66_2 = 0) & unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_66_2
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (414)   ~ (all_66_2 = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (415)  unorthogonal_lines(all_23_3, all_23_4) = all_66_2
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_4,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_66_2, simplifying with (22), (23), (415)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (416)  all_66_2 = 0 | convergent_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (417)  convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_65_3, all_23_4,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (408), (417) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (418)  all_65_3 = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (410), (418) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (419)  $false
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (419) is inconsistent.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (420)  all_66_2 = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (414), (420) imply:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (421)  $false
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent.
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (422)   ~ (all_66_3 = 0) & convergent_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_66_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (423)   ~ (all_66_3 = 0)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (424)  convergent_lines(all_23_3, all_23_4) = all_66_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_65_3, all_66_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_3, simplifying with (408), (424)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (425)  all_66_3 = all_65_3
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_23_4,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, 0, all_30_3, simplifying with (22),
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (23), (24), (126), (331) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & all_30_3 = 0 &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v2 = 0 & unorthogonal_lines(all_23_2, all_23_3)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = 0) | ( ~ (v1 = 0) &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_4) = v1) |
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ( ~ (v0 = 0) & convergent_lines(all_23_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_4) = v0))
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_23_2, all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, 0, simplifying with (23), (24), (38),
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (331) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_3, all_23_2) = 0) |
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v2 = 0 & v1 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_2) = 0 & convergent_lines(all_23_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = v0))
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_65_3, simplifying with (22), (23),
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24), (331), (408) gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)  all_65_3 = 0 | convergent_lines(all_23_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (427) with fresh symbols all_269_0,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_269_1, all_269_2, all_269_3 gives:
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  (all_269_0 = 0 & unorthogonal_lines(all_23_3,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_269_1 = 0 & all_269_2 =
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            0 & unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_269_3 = 0) & unorthogonal_lines(all_23_2,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_269_3)
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (426) with fresh symbols all_278_0,
% 20.89/3.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_278_1, all_278_2, all_278_3 gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  (all_278_0 = 0 & all_30_3 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_278_1 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_278_2 = 0) &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_4) =
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_278_2) | ( ~ (all_278_3 = 0) &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_278_3)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  convergent_lines(all_23_2, all_23_4) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  all_97_0 = 0 & all_97_1 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)  convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (24), (433) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)  $false
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  (all_97_2 = 0 & all_40_0 = 0) | ( ~ (all_97_3 = 0)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & convergent_lines(all_23_4, all_23_2) =
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_97_3)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_97_2 = 0 & all_40_0 = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  all_40_0 = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (437) imply:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  $false
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)   ~ (all_97_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_97_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  convergent_lines(all_23_4, all_23_2) = all_97_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_97_3,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (44), (440)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_97_3 = all_40_0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_98_0 = 0 & all_98_1 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (443),
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (apart3) are inconsistent by sub-proof #1.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  (all_98_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_98_3 = 0) &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_98_3)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_98_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  convergent_lines(all_23_4, all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (125), (126), (446) are inconsistent by
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #7.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)   ~ (all_98_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_98_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)   ~ (all_98_3 = 0)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  convergent_lines(all_23_4, all_23_2) = all_98_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_98_3,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (44), (449)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  all_98_3 = all_40_0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_102_0 = 0 & all_102_1 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (24), (452) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  $false
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (453) is inconsistent.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  (all_102_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_102_3 = 0) &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) =
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_102_3)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  all_102_2 = 0 & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (455) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  convergent_lines(all_23_4, all_23_2) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (44), (456) are inconsistent by
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)   ~ (all_102_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_102_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (457) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  convergent_lines(all_23_4, all_23_2) = all_102_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_102_3,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (44), (458)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_102_3 = all_40_0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  all_104_0 = 0 & all_104_1 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_4) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  unorthogonal_lines(all_23_2, all_23_4) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  (all_278_0 = 0 & all_30_3 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_278_1 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_278_0 = 0 & all_30_3 = 0 &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  all_30_3 = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (464) imply:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  $false
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_278_1 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (467),
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (apart3) are inconsistent by sub-proof #1.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  ( ~ (all_278_2 = 0) & unorthogonal_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_278_2) | ( ~ (all_278_3 = 0) &
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_278_3)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_278_2 = 0) & unorthogonal_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_278_2
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)   ~ (all_278_2 = 0)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  unorthogonal_lines(all_23_2, all_23_4) = all_278_2
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_278_2, all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, simplifying with (461), (471) gives:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_278_2 = 0
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (472) imply:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  $false
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent.
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)   ~ (all_278_3 = 0) & convergent_lines(all_23_2,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_278_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)   ~ (all_278_3 = 0)
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  convergent_lines(all_23_2, all_23_4) = all_278_3
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_278_3, all_23_4,
% 20.89/3.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, simplifying with (431), (476) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_278_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (477) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  (all_104_2 = 0 & all_76_0 = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_104_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = all_104_3)
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  all_104_2 = 0 & all_76_0 = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  all_76_0 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (481) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_31_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (482) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_31_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (483) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (484) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)   ~ (all_104_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_104_3
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  convergent_lines(all_23_4, all_23_2) = all_104_3
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_104_3,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (44), (486)
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_104_3 = all_40_0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_105_0 = 0 & all_105_1 = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_3) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (24), (27), (330), (429), (489),
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (apart3) are inconsistent by sub-proof #1.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  (all_105_2 = 0 & all_32_3 = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_105_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = all_105_3)
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_105_2 = 0 & all_32_3 = 0 &
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_32_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (492) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_30_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_30_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (494) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (495) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)   ~ (all_105_3 = 0) & convergent_lines(all_23_4,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_105_3
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)   ~ (all_105_3 = 0)
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  convergent_lines(all_23_4, all_23_2) = all_105_3
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_40_0, all_105_3,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (44), (498)
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_105_3 = all_40_0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_4,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_40_0, simplifying with (22), (24),
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (44), (431) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_40_0 = 0 | convergent_lines(all_23_2,
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (24), (501) gives:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (502) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_40_0 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (503) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (504) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_65_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (410), (505) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  all_33_3 = 0
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (507) imply:
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  $false
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | Case 2:
% 20.89/3.90  | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | |   (509)  all_76_0 = 0
% 20.89/3.90  | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | REDUCE: (94), (509) imply:
% 20.89/3.90  | | | | | | | | | | |   (510)  $false
% 20.89/3.90  | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | | CLOSE: (510) is inconsistent.
% 20.89/3.90  | | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | | 
% 20.89/3.90  | | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | | 
% 20.89/3.90  | | | | | | | | End of split
% 20.89/3.90  | | | | | | | | 
% 20.89/3.90  | | | | | | | End of split
% 20.89/3.90  | | | | | | | 
% 20.89/3.90  | | | | | | End of split
% 20.89/3.90  | | | | | | 
% 20.89/3.90  | | | | | Case 2:
% 20.89/3.90  | | | | | | 
% 20.89/3.90  | | | | | |   (511)  all_40_0 = 0
% 20.89/3.90  | | | | | | 
% 20.89/3.90  | | | | | | REDUCE: (43), (511) imply:
% 20.89/3.90  | | | | | |   (512)  $false
% 20.89/3.90  | | | | | | 
% 20.89/3.90  | | | | | | CLOSE: (512) is inconsistent.
% 20.89/3.90  | | | | | | 
% 20.89/3.90  | | | | | End of split
% 20.89/3.90  | | | | | 
% 20.89/3.90  | | | | End of split
% 20.89/3.90  | | | | 
% 20.89/3.90  | | | End of split
% 20.89/3.90  | | | 
% 20.89/3.90  | | End of split
% 20.89/3.90  | | 
% 20.89/3.90  | Case 2:
% 20.89/3.90  | | 
% 20.89/3.90  | |   (513)  all_23_0 = 0
% 20.89/3.90  | | 
% 20.89/3.90  | | REDUCE: (21), (513) imply:
% 20.89/3.90  | |   (514)  $false
% 20.89/3.90  | | 
% 20.89/3.90  | | CLOSE: (514) is inconsistent.
% 20.89/3.90  | | 
% 20.89/3.90  | End of split
% 20.89/3.90  | 
% 20.89/3.90  End of proof
% 20.89/3.90  
% 20.89/3.90  Sub-proof #1 shows that the following formulas are inconsistent:
% 20.89/3.90  ----------------------------------------------------------------
% 20.89/3.90    (1)  unorthogonal_lines(all_23_3, all_23_2) = all_57_3
% 20.89/3.90    (2)   ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) |  ~ $i(v0))
% 20.89/3.90    (3)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 20.89/3.90    (4)   ~ (all_23_0 = 0)
% 20.89/3.90    (5)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.89/3.90    (6)  (all_269_0 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0) | (all_269_1
% 20.89/3.90           = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 20.89/3.90           convergent_lines(all_23_2, all_23_2) = 0) | ( ~ (all_269_3 = 0) &
% 20.89/3.90           unorthogonal_lines(all_23_2, all_23_3) = all_269_3)
% 20.89/3.90    (7)  $i(all_23_2)
% 20.89/3.91    (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.91         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.89/3.91           (unorthogonal_lines(v3, v2) = v0))
% 20.89/3.91  
% 20.89/3.91  Begin of proof
% 20.89/3.91  | 
% 20.89/3.91  | BETA: splitting (6) gives:
% 20.89/3.91  | 
% 20.89/3.91  | Case 1:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (9)  all_269_0 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.91  | | 
% 20.89/3.91  | | ALPHA: (9) implies:
% 20.89/3.91  | |   (10)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.91  | | 
% 20.89/3.91  | | REF_CLOSE: (1), (4), (5), (8), (10) are inconsistent by sub-proof #5.
% 20.89/3.91  | | 
% 20.89/3.91  | Case 2:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (11)  (all_269_1 = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.91  | |             all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 20.89/3.91  | |           (all_269_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 20.89/3.91  | |           all_269_3)
% 20.89/3.91  | | 
% 20.89/3.91  | | BETA: splitting (11) gives:
% 20.89/3.91  | | 
% 20.89/3.91  | | Case 1:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (12)  all_269_1 = 0 & all_269_2 = 0 & unorthogonal_lines(all_23_2,
% 20.89/3.91  | | |           all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (12) implies:
% 20.89/3.91  | | |   (13)  convergent_lines(all_23_2, all_23_2) = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | GROUND_INST: instantiating (2) with all_23_2, simplifying with (7), (13)
% 20.89/3.91  | | |              gives:
% 20.89/3.91  | | |   (14)  $false
% 20.89/3.91  | | | 
% 20.89/3.91  | | | CLOSE: (14) is inconsistent.
% 20.89/3.91  | | | 
% 20.89/3.91  | | Case 2:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (15)   ~ (all_269_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 20.89/3.91  | | |         all_269_3
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (15) implies:
% 20.89/3.91  | | |   (16)   ~ (all_269_3 = 0)
% 20.89/3.91  | | |   (17)  unorthogonal_lines(all_23_2, all_23_3) = all_269_3
% 20.89/3.91  | | | 
% 20.89/3.91  | | | GROUND_INST: instantiating (8) with 0, all_269_3, all_23_3, all_23_2,
% 20.89/3.91  | | |              simplifying with (3), (17) gives:
% 20.89/3.91  | | |   (18)  all_269_3 = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | REDUCE: (16), (18) imply:
% 20.89/3.91  | | |   (19)  $false
% 20.89/3.91  | | | 
% 20.89/3.91  | | | CLOSE: (19) is inconsistent.
% 20.89/3.91  | | | 
% 20.89/3.91  | | End of split
% 20.89/3.91  | | 
% 20.89/3.91  | End of split
% 20.89/3.91  | 
% 20.89/3.91  End of proof
% 20.89/3.91  
% 20.89/3.91  Sub-proof #2 shows that the following formulas are inconsistent:
% 20.89/3.91  ----------------------------------------------------------------
% 20.89/3.91    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.91         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.89/3.91           (unorthogonal_lines(v3, v2) = v0))
% 20.89/3.91    (2)  unorthogonal_lines(all_23_3, all_23_4) = all_65_2
% 20.89/3.91    (3)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.91    (4)   ~ (all_65_2 = 0)
% 20.89/3.91  
% 20.89/3.91  Begin of proof
% 20.89/3.91  | 
% 20.89/3.91  | GROUND_INST: instantiating (1) with 0, all_65_2, all_23_4, all_23_3,
% 20.89/3.91  |              simplifying with (2), (3) gives:
% 20.89/3.91  |   (5)  all_65_2 = 0
% 20.89/3.91  | 
% 20.89/3.91  | REDUCE: (4), (5) imply:
% 20.89/3.91  |   (6)  $false
% 20.89/3.91  | 
% 20.89/3.91  | CLOSE: (6) is inconsistent.
% 20.89/3.91  | 
% 20.89/3.91  End of proof
% 20.89/3.91  
% 20.89/3.91  Sub-proof #3 shows that the following formulas are inconsistent:
% 20.89/3.91  ----------------------------------------------------------------
% 20.89/3.91    (1)  (all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2) =
% 20.89/3.91           0) | (all_66_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 20.89/3.91             all_23_2) = 0)
% 20.89/3.91    (2)   ~ (all_40_0 = 0)
% 20.89/3.91    (3)   ~ (all_23_0 = 0)
% 20.89/3.91  
% 20.89/3.91  Begin of proof
% 20.89/3.91  | 
% 20.89/3.91  | BETA: splitting (1) gives:
% 20.89/3.91  | 
% 20.89/3.91  | Case 1:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (4)  all_66_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2)
% 20.89/3.91  | |        = 0
% 20.89/3.91  | | 
% 20.89/3.91  | | ALPHA: (4) implies:
% 20.89/3.91  | |   (5)  all_40_0 = 0
% 20.89/3.91  | | 
% 20.89/3.91  | | REDUCE: (2), (5) imply:
% 20.89/3.91  | |   (6)  $false
% 20.89/3.91  | | 
% 20.89/3.91  | | CLOSE: (6) is inconsistent.
% 20.89/3.91  | | 
% 20.89/3.91  | Case 2:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (7)  all_66_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.89/3.91  | |        0
% 20.89/3.91  | | 
% 20.89/3.91  | | ALPHA: (7) implies:
% 20.89/3.91  | |   (8)  all_23_0 = 0
% 20.89/3.91  | | 
% 20.89/3.91  | | REDUCE: (3), (8) imply:
% 20.89/3.91  | |   (9)  $false
% 20.89/3.91  | | 
% 20.89/3.91  | | CLOSE: (9) is inconsistent.
% 20.89/3.91  | | 
% 20.89/3.91  | End of split
% 20.89/3.91  | 
% 20.89/3.91  End of proof
% 20.89/3.91  
% 20.89/3.91  Sub-proof #4 shows that the following formulas are inconsistent:
% 20.89/3.91  ----------------------------------------------------------------
% 20.89/3.91    (1)  unorthogonal_lines(all_23_3, all_23_2) = all_57_3
% 20.89/3.91    (2)   ~ (all_23_0 = 0)
% 20.89/3.91    (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.91         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.89/3.91           (convergent_lines(v3, v2) = v0))
% 20.89/3.91    (4)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.89/3.91    (5)  (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4, all_23_2) =
% 20.89/3.91           0) | (all_65_1 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.89/3.91           (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) = all_65_2) | (
% 20.89/3.91           ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) = all_65_3)
% 20.89/3.91    (6)   ~ (all_40_0 = 0)
% 20.89/3.91    (7)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 20.89/3.91    (8)  convergent_lines(all_23_3, all_23_4) = 0
% 20.89/3.91    (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.91         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.89/3.91           (unorthogonal_lines(v3, v2) = v0))
% 20.89/3.91  
% 20.89/3.91  Begin of proof
% 20.89/3.91  | 
% 20.89/3.91  | BETA: splitting (5) gives:
% 20.89/3.91  | 
% 20.89/3.91  | Case 1:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (10)  (all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.89/3.91  | |             all_23_2) = 0) | (all_65_1 = 0 & unorthogonal_lines(all_23_3,
% 20.89/3.91  | |             all_23_2) = 0)
% 20.89/3.91  | | 
% 20.89/3.91  | | BETA: splitting (10) gives:
% 20.89/3.91  | | 
% 20.89/3.91  | | Case 1:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (11)  all_65_0 = 0 & all_40_0 = 0 & unorthogonal_lines(all_23_4,
% 20.89/3.91  | | |           all_23_2) = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (11) implies:
% 20.89/3.91  | | |   (12)  all_40_0 = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | REDUCE: (6), (12) imply:
% 20.89/3.91  | | |   (13)  $false
% 20.89/3.91  | | | 
% 20.89/3.91  | | | CLOSE: (13) is inconsistent.
% 20.89/3.91  | | | 
% 20.89/3.91  | | Case 2:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (14)  all_65_1 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (14) implies:
% 20.89/3.91  | | |   (15)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | REF_CLOSE: (1), (2), (4), (9), (15) are inconsistent by sub-proof #5.
% 20.89/3.91  | | | 
% 20.89/3.91  | | End of split
% 20.89/3.91  | | 
% 20.89/3.91  | Case 2:
% 20.89/3.91  | | 
% 20.89/3.91  | |   (16)  ( ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) =
% 20.89/3.91  | |           all_65_2) | ( ~ (all_65_3 = 0) & convergent_lines(all_23_3,
% 20.89/3.91  | |             all_23_4) = all_65_3)
% 20.89/3.91  | | 
% 20.89/3.91  | | BETA: splitting (16) gives:
% 20.89/3.91  | | 
% 20.89/3.91  | | Case 1:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (17)   ~ (all_65_2 = 0) & unorthogonal_lines(all_23_3, all_23_4) =
% 20.89/3.91  | | |         all_65_2
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (17) implies:
% 20.89/3.91  | | |   (18)   ~ (all_65_2 = 0)
% 20.89/3.91  | | |   (19)  unorthogonal_lines(all_23_3, all_23_4) = all_65_2
% 20.89/3.91  | | | 
% 20.89/3.91  | | | GROUND_INST: instantiating (9) with 0, all_65_2, all_23_4, all_23_3,
% 20.89/3.91  | | |              simplifying with (7), (19) gives:
% 20.89/3.91  | | |   (20)  all_65_2 = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | REDUCE: (18), (20) imply:
% 20.89/3.91  | | |   (21)  $false
% 20.89/3.91  | | | 
% 20.89/3.91  | | | CLOSE: (21) is inconsistent.
% 20.89/3.91  | | | 
% 20.89/3.91  | | Case 2:
% 20.89/3.91  | | | 
% 20.89/3.91  | | |   (22)   ~ (all_65_3 = 0) & convergent_lines(all_23_3, all_23_4) =
% 20.89/3.91  | | |         all_65_3
% 20.89/3.91  | | | 
% 20.89/3.91  | | | ALPHA: (22) implies:
% 20.89/3.91  | | |   (23)   ~ (all_65_3 = 0)
% 20.89/3.91  | | |   (24)  convergent_lines(all_23_3, all_23_4) = all_65_3
% 20.89/3.91  | | | 
% 20.89/3.91  | | | GROUND_INST: instantiating (3) with 0, all_65_3, all_23_4, all_23_3,
% 20.89/3.91  | | |              simplifying with (8), (24) gives:
% 20.89/3.91  | | |   (25)  all_65_3 = 0
% 20.89/3.91  | | | 
% 20.89/3.91  | | | REDUCE: (23), (25) imply:
% 20.89/3.91  | | |   (26)  $false
% 20.89/3.91  | | | 
% 20.89/3.91  | | | CLOSE: (26) is inconsistent.
% 20.89/3.91  | | | 
% 20.89/3.91  | | End of split
% 20.89/3.91  | | 
% 20.89/3.91  | End of split
% 20.89/3.91  | 
% 20.89/3.91  End of proof
% 20.89/3.91  
% 20.89/3.91  Sub-proof #5 shows that the following formulas are inconsistent:
% 20.89/3.91  ----------------------------------------------------------------
% 20.89/3.91    (1)  unorthogonal_lines(all_23_3, all_23_2) = all_57_3
% 20.89/3.91    (2)   ~ (all_23_0 = 0)
% 20.89/3.91    (3)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 20.89/3.91    (4)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.89/3.92    (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.92         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.89/3.92           (unorthogonal_lines(v3, v2) = v0))
% 20.89/3.92  
% 20.89/3.92  Begin of proof
% 20.89/3.92  | 
% 20.89/3.92  | GROUND_INST: instantiating (5) with all_23_0, all_57_3, all_23_2, all_23_3,
% 20.89/3.92  |              simplifying with (1), (4) gives:
% 20.89/3.92  |   (6)  all_57_3 = all_23_0
% 20.89/3.92  | 
% 20.89/3.92  | GROUND_INST: instantiating (5) with 0, all_57_3, all_23_2, all_23_3,
% 20.89/3.92  |              simplifying with (1), (3) gives:
% 20.89/3.92  |   (7)  all_57_3 = 0
% 20.89/3.92  | 
% 20.89/3.92  | COMBINE_EQS: (6), (7) imply:
% 20.89/3.92  |   (8)  all_23_0 = 0
% 20.89/3.92  | 
% 20.89/3.92  | REDUCE: (2), (8) imply:
% 20.89/3.92  |   (9)  $false
% 20.89/3.92  | 
% 20.89/3.92  | CLOSE: (9) is inconsistent.
% 20.89/3.92  | 
% 20.89/3.92  End of proof
% 20.89/3.92  
% 20.89/3.92  Sub-proof #6 shows that the following formulas are inconsistent:
% 20.89/3.92  ----------------------------------------------------------------
% 20.89/3.92    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.92         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.89/3.92           (convergent_lines(v3, v2) = v0))
% 20.89/3.92    (2)  convergent_lines(all_23_4, all_23_2) = all_40_0
% 20.89/3.92    (3)  convergent_lines(all_23_4, all_23_2) = 0
% 20.89/3.92    (4)   ~ (all_40_0 = 0)
% 20.89/3.92  
% 20.89/3.92  Begin of proof
% 20.89/3.92  | 
% 20.89/3.92  | GROUND_INST: instantiating (1) with 0, all_40_0, all_23_2, all_23_4,
% 20.89/3.92  |              simplifying with (2), (3) gives:
% 20.89/3.92  |   (5)  all_40_0 = 0
% 20.89/3.92  | 
% 20.89/3.92  | REDUCE: (4), (5) imply:
% 20.89/3.92  |   (6)  $false
% 20.89/3.92  | 
% 20.89/3.92  | CLOSE: (6) is inconsistent.
% 20.89/3.92  | 
% 20.89/3.92  End of proof
% 20.89/3.92  
% 20.89/3.92  Sub-proof #7 shows that the following formulas are inconsistent:
% 20.89/3.92  ----------------------------------------------------------------
% 20.89/3.92    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 20.89/3.92         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.89/3.92           (convergent_lines(v3, v2) = v0))
% 20.89/3.92    (2)  convergent_lines(all_23_4, all_23_3) = all_30_3
% 20.89/3.92    (3)  convergent_lines(all_23_4, all_23_3) = 0
% 20.89/3.92    (4)   ~ (all_30_3 = 0)
% 20.89/3.92  
% 20.89/3.92  Begin of proof
% 20.89/3.92  | 
% 20.89/3.92  | GROUND_INST: instantiating (1) with all_30_3, 0, all_23_3, all_23_4,
% 20.89/3.92  |              simplifying with (2), (3) gives:
% 20.89/3.92  |   (5)  all_30_3 = 0
% 20.89/3.92  | 
% 20.89/3.92  | REDUCE: (4), (5) imply:
% 20.89/3.92  |   (6)  $false
% 20.89/3.92  | 
% 20.89/3.92  | CLOSE: (6) is inconsistent.
% 20.89/3.92  | 
% 20.89/3.92  End of proof
% 20.89/3.92  % SZS output end Proof for theBenchmark
% 20.89/3.92  
% 20.89/3.92  3289ms
%------------------------------------------------------------------------------