TSTP Solution File: GEO212+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO212+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 23:22:22 EDT 2023

% Result   : Theorem 12.65s 2.57s
% Output   : Proof 21.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO212+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 20:55:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.74/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.74/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.74/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.74/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.74/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.74/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.74/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.80/1.12  Prover 4: Preprocessing ...
% 2.80/1.12  Prover 1: Preprocessing ...
% 2.80/1.17  Prover 6: Preprocessing ...
% 2.80/1.17  Prover 2: Preprocessing ...
% 2.80/1.17  Prover 3: Preprocessing ...
% 2.80/1.17  Prover 0: Preprocessing ...
% 2.80/1.17  Prover 5: Preprocessing ...
% 4.86/1.46  Prover 5: Proving ...
% 4.86/1.47  Prover 2: Proving ...
% 4.86/1.49  Prover 3: Constructing countermodel ...
% 5.56/1.51  Prover 6: Constructing countermodel ...
% 5.56/1.52  Prover 1: Constructing countermodel ...
% 6.17/1.67  Prover 3: gave up
% 6.17/1.67  Prover 6: gave up
% 6.17/1.67  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.17/1.67  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.17/1.68  Prover 4: Constructing countermodel ...
% 7.07/1.71  Prover 1: gave up
% 7.12/1.72  Prover 0: Proving ...
% 7.12/1.72  Prover 7: Preprocessing ...
% 7.12/1.72  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.12/1.75  Prover 8: Preprocessing ...
% 7.12/1.76  Prover 9: Preprocessing ...
% 7.12/1.77  Prover 7: Warning: ignoring some quantifiers
% 7.12/1.79  Prover 7: Constructing countermodel ...
% 7.81/1.85  Prover 8: Warning: ignoring some quantifiers
% 7.81/1.86  Prover 7: gave up
% 7.81/1.86  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.81/1.87  Prover 8: Constructing countermodel ...
% 7.81/1.92  Prover 10: Preprocessing ...
% 8.84/1.97  Prover 10: Warning: ignoring some quantifiers
% 8.84/1.98  Prover 10: Constructing countermodel ...
% 8.84/2.01  Prover 8: gave up
% 8.84/2.02  Prover 10: gave up
% 8.84/2.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.84/2.03  Prover 12: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 9.61/2.06  Prover 11: Preprocessing ...
% 9.61/2.06  Prover 12: Preprocessing ...
% 9.61/2.09  Prover 9: Constructing countermodel ...
% 10.03/2.14  Prover 12: Proving ...
% 11.03/2.27  Prover 11: Constructing countermodel ...
% 12.65/2.56  Prover 0: proved (1927ms)
% 12.65/2.57  
% 12.65/2.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.65/2.57  
% 12.65/2.57  Prover 9: stopped
% 12.65/2.58  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.65/2.58  Prover 5: stopped
% 12.65/2.58  Prover 12: stopped
% 12.65/2.58  Prover 2: stopped
% 12.65/2.58  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.65/2.58  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.74/2.62  Prover 16: Preprocessing ...
% 13.74/2.62  Prover 13: Preprocessing ...
% 13.74/2.62  Prover 19: Preprocessing ...
% 13.74/2.64  Prover 16: Warning: ignoring some quantifiers
% 13.74/2.65  Prover 16: Constructing countermodel ...
% 14.12/2.67  Prover 13: Warning: ignoring some quantifiers
% 14.12/2.67  Prover 13: Constructing countermodel ...
% 14.12/2.68  Prover 19: Warning: ignoring some quantifiers
% 14.12/2.69  Prover 19: Constructing countermodel ...
% 14.12/2.71  Prover 13: gave up
% 14.55/2.71  Prover 16: gave up
% 14.55/2.73  Prover 19: gave up
% 19.56/3.70  Prover 11: Found proof (size 633)
% 19.56/3.70  Prover 11: proved (1679ms)
% 19.56/3.70  Prover 4: stopped
% 19.56/3.70  
% 19.56/3.70  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.56/3.70  
% 20.04/3.76  % SZS output start Proof for theBenchmark
% 20.04/3.78  Assumptions after simplification:
% 20.04/3.78  ---------------------------------
% 20.04/3.78  
% 20.04/3.78    (apart3)
% 20.36/3.81     ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) |  ~ $i(v0))
% 20.36/3.81  
% 20.36/3.81    (apart6)
% 20.36/3.82     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 20.36/3.82      0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0,
% 20.36/3.82          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 =
% 20.36/3.82          0) & convergent_lines(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 20.36/3.82    [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~
% 20.36/3.82      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.82      convergent_lines(v0, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 20.36/3.82    [v3: int] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~
% 20.36/3.82      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.82      convergent_lines(v1, v2) = 0)
% 20.36/3.82  
% 20.36/3.82    (con)
% 20.36/3.83     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] :  ? [v4: int] : ( ~
% 20.36/3.83      (v4 = 0) &  ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 &
% 20.36/3.83      unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v2) = v3 & $i(v2) &
% 20.36/3.83      $i(v1) & $i(v0))
% 20.36/3.83  
% 20.36/3.83    (oac1)
% 20.36/3.85     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any] : ( ~
% 20.36/3.85      (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) | 
% 20.36/3.85      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] :  ? [v7:
% 20.36/3.85        int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.85        (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.85          unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 20.36/3.85            v1) = v5))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :
% 20.36/3.85     ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~
% 20.36/3.85      (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 20.36/3.85      [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.85          convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 20.36/3.85            v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0:
% 20.36/3.85      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any] : ( ~
% 20.36/3.85      (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ~
% 20.36/3.85      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6: int] :  ? [v7: int]
% 20.36/3.85      :  ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 =
% 20.36/3.85          0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.85          unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 20.36/3.85            v1) = v5))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :
% 20.36/3.85     ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0,
% 20.36/3.85          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.36/3.85        int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 20.36/3.85            v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0:
% 20.36/3.85      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 20.36/3.85          v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1)
% 20.36/3.85      |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] :
% 20.36/3.85      ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85            = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] : 
% 20.36/3.85    ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~
% 20.36/3.85      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 20.36/3.85        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85          convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85            = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i]
% 20.36/3.85    :  ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~
% 20.36/3.85      (unorthogonal_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 20.36/3.85      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85          & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85          convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.36/3.85      $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~
% 20.36/3.85      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 20.36/3.85        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85          & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85          unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.36/3.85      $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~
% 20.36/3.85      (convergent_lines(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 20.36/3.85      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85            = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] : 
% 20.36/3.85    ! [v2: $i] :  ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~
% 20.36/3.85      (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 20.36/3.85      [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85          & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85          convergent_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.36/3.85      $i] :  ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) |  ~
% 20.36/3.85      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 20.36/3.85        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.85          unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 20.36/3.85            = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i]
% 20.36/3.85    :  ! [v2: $i] :  ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) |  ~
% 20.36/3.85      (convergent_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 20.36/3.85        int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.85          unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 20.36/3.85          & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.85          unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.85  
% 20.36/3.85    (occu1)
% 20.36/3.85     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 20.36/3.85      (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.85      convergent_lines(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] :
% 20.36/3.85    (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.85      unorthogonal_lines(v0, v1) = 0)
% 20.36/3.85  
% 20.36/3.85    (function-axioms)
% 20.36/3.86     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.36/3.86      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 20.36/3.86          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 20.36/3.86    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 20.36/3.86      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.36/3.86      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 20.36/3.86      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.36/3.86      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 20.36/3.86      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 20.36/3.86    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 20.36/3.86      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 20.36/3.86      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.36/3.86      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 20.36/3.86        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 20.36/3.86      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.36/3.86      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 20.36/3.86      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.36/3.86      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 20.36/3.86      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 20.36/3.86    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 20.36/3.86        v0))
% 20.36/3.86  
% 20.36/3.86  Further assumptions not needed in the proof:
% 20.36/3.86  --------------------------------------------
% 20.36/3.86  apart1, apart2, apart4, apart5, ceq1, ceq2, ceq3, con1, con2, cp1, cp2, cu1,
% 20.36/3.86  cup1, ooc1, ooc2, ouo1
% 20.36/3.86  
% 20.36/3.86  Those formulas are unsatisfiable:
% 20.36/3.86  ---------------------------------
% 20.36/3.86  
% 20.36/3.86  Begin of proof
% 20.36/3.86  | 
% 20.36/3.86  | ALPHA: (apart6) implies:
% 20.36/3.86  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 20.36/3.86  |          (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.86  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 20.36/3.86  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 20.36/3.86  |          (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.86  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 20.36/3.86  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] :
% 20.36/3.86  |        (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~
% 20.36/3.86  |          (convergent_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.86  |           ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 20.36/3.86  | 
% 20.36/3.86  | ALPHA: (occu1) implies:
% 20.36/3.86  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 20.36/3.87  |          (convergent_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.87  |          unorthogonal_lines(v0, v1) = 0)
% 20.36/3.87  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 20.36/3.87  |          (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.36/3.87  |          convergent_lines(v0, v1) = 0)
% 20.36/3.87  | 
% 20.36/3.87  | ALPHA: (oac1) implies:
% 20.36/3.87  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.87  |          (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |
% 20.36/3.87  |           ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ?
% 20.36/3.87  |          [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v1,
% 20.36/3.87  |                v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 &
% 20.36/3.87  |              unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87  |              unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.87  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.87  |          (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3)
% 20.36/3.87  |          |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] : 
% 20.36/3.87  |          ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87  |              unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87  |            (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87  |              convergent_lines(v0, v1) = v4)))
% 20.36/3.87  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.87  |          (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0)
% 20.36/3.87  |          |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] : 
% 20.36/3.87  |          ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87  |              unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87  |            (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87  |              unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.87  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.87  |          (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) =
% 20.36/3.87  |            0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 20.36/3.87  |            int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 20.36/3.87  |              unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 20.36/3.87  |            (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 20.36/3.87  |              convergent_lines(v0, v1) = v4)))
% 20.36/3.88  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.88  |           (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) =
% 20.36/3.88  |             0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 20.36/3.88  |             int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.88  |               convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.88  |               unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 20.36/3.88  |             ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 20.36/3.88  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 20.36/3.88  |           (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) =
% 20.36/3.88  |             0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 20.36/3.88  |             int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 20.36/3.88  |               convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 20.36/3.88  |               unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 20.36/3.88  |             ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 20.36/3.88  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.36/3.88  |         : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) =
% 20.36/3.88  |             v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.36/3.88  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.88  |               unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.88  |               unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.88  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.88  |               convergent_lines(v0, v1) = v5)))
% 20.36/3.89  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.36/3.89  |         : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2)
% 20.36/3.89  |             = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.36/3.89  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89  |               unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89  |               convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89  |               convergent_lines(v0, v1) = v5)))
% 20.36/3.89  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.36/3.89  |         : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2)
% 20.36/3.89  |             = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] :  ? [v6:
% 20.36/3.89  |             int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89  |               convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89  |               unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89  |               convergent_lines(v0, v1) = v5)))
% 20.36/3.89  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] :  ! [v4: any]
% 20.36/3.89  |         : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0,
% 20.36/3.89  |               v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : 
% 20.36/3.89  |           ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 20.36/3.89  |               convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 20.36/3.89  |               convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 20.36/3.89  |               unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 20.36/3.89  |               convergent_lines(v0, v1) = v5)))
% 20.36/3.89  | 
% 20.36/3.89  | ALPHA: (function-axioms) implies:
% 20.36/3.90  |   (16)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 20.36/3.90  |         :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 20.36/3.90  |           (convergent_lines(v3, v2) = v0))
% 20.36/3.90  |   (17)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 20.36/3.90  |         :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 20.36/3.90  |           (unorthogonal_lines(v3, v2) = v0))
% 20.36/3.90  | 
% 20.36/3.90  | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2,
% 20.36/3.90  |        all_23_3, all_23_4 gives:
% 20.36/3.90  |   (18)   ~ (all_23_0 = 0) &  ~ (all_23_1 = 0) & unorthogonal_lines(all_23_3,
% 20.36/3.90  |           all_23_2) = all_23_0 & unorthogonal_lines(all_23_4, all_23_3) = 0 &
% 20.36/3.90  |         convergent_lines(all_23_4, all_23_2) = all_23_1 & $i(all_23_2) &
% 20.36/3.90  |         $i(all_23_3) & $i(all_23_4)
% 20.36/3.90  | 
% 20.36/3.90  | ALPHA: (18) implies:
% 20.36/3.90  |   (19)   ~ (all_23_1 = 0)
% 20.36/3.90  |   (20)   ~ (all_23_0 = 0)
% 20.36/3.90  |   (21)  $i(all_23_4)
% 20.36/3.90  |   (22)  $i(all_23_3)
% 20.36/3.90  |   (23)  $i(all_23_2)
% 20.36/3.90  |   (24)  convergent_lines(all_23_4, all_23_2) = all_23_1
% 20.36/3.90  |   (25)  unorthogonal_lines(all_23_4, all_23_3) = 0
% 20.36/3.90  |   (26)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 20.36/3.90  | 
% 20.36/3.90  | GROUND_INST: instantiating (3) with all_23_4, all_23_4, all_23_2, all_23_1,
% 20.36/3.90  |              all_23_1, simplifying with (21), (23), (24) gives:
% 20.36/3.91  |   (27)  all_23_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 20.36/3.91  |           convergent_lines(all_23_4, all_23_4) = v0)
% 20.36/3.91  | 
% 20.36/3.91  | GROUND_INST: instantiating (12) with all_23_4, all_23_4, all_23_2, all_23_1,
% 20.36/3.91  |              all_23_1, simplifying with (21), (23), (24) gives:
% 20.36/3.91  |   (28)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.91  |             all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (v2 =
% 20.36/3.91  |             0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (
% 20.36/3.91  |             ~ (v1 = 0) & unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~
% 20.36/3.91  |             (v0 = 0) & convergent_lines(all_23_4, all_23_4) = v0))
% 20.36/3.91  | 
% 20.36/3.91  | GROUND_INST: instantiating (4) with all_23_4, all_23_2, all_23_1, simplifying
% 20.36/3.91  |              with (21), (23), (24) gives:
% 20.36/3.91  |   (29)  all_23_1 = 0 | unorthogonal_lines(all_23_4, all_23_2) = 0
% 20.36/3.91  | 
% 20.36/3.91  | GROUND_INST: instantiating (15) with all_23_4, all_23_4, all_23_3, 0, 0,
% 20.36/3.91  |              simplifying with (21), (22), (25) gives:
% 20.36/3.91  |   (30)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.91  |             convergent_lines(all_23_4, all_23_3) = 0) | (v2 = 0 &
% 20.36/3.91  |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v1 = 0) &
% 20.36/3.91  |             unorthogonal_lines(all_23_4, all_23_4) = v1) | ( ~ (v0 = 0) &
% 20.36/3.91  |             convergent_lines(all_23_4, all_23_4) = v0))
% 20.36/3.91  | 
% 20.36/3.91  | GROUND_INST: instantiating (9) with all_23_4, all_23_3, all_23_3, 0,
% 20.36/3.91  |              simplifying with (21), (22), (25) gives:
% 20.36/3.92  |   (31)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.92  |             v2 = 0 & unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 20.36/3.92  |             convergent_lines(all_23_3, all_23_3) = 0) | (v1 = 0 &
% 20.36/3.92  |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92  |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92  | 
% 20.36/3.92  | GROUND_INST: instantiating (7) with all_23_4, all_23_3, all_23_2, all_23_1,
% 20.36/3.92  |              simplifying with (21), (22), (23), (24), (25) gives:
% 20.36/3.92  |   (32)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.92  |             v2 = 0 & unorthogonal_lines(all_23_3, all_23_2) = 0 &
% 20.36/3.92  |             convergent_lines(all_23_3, all_23_2) = 0) | (v1 = 0 & all_23_1 = 0
% 20.36/3.92  |             & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92  |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92  | 
% 20.36/3.92  | GROUND_INST: instantiating (15) with all_23_3, all_23_3, all_23_2, all_23_0,
% 20.36/3.92  |              all_23_0, simplifying with (22), (23), (26) gives:
% 20.36/3.92  |   (33)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.92  |             all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92  |             & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.36/3.92  |             (v1 = 0) & unorthogonal_lines(all_23_3, all_23_3) = v1) | ( ~ (v0
% 20.36/3.92  |               = 0) & convergent_lines(all_23_3, all_23_3) = v0))
% 20.36/3.92  | 
% 20.36/3.92  | GROUND_INST: instantiating (11) with all_23_4, all_23_3, all_23_2, all_23_0,
% 20.36/3.92  |              simplifying with (21), (22), (23), (25), (26) gives:
% 20.36/3.92  |   (34)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.92  |             all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92  |             & v1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 20.36/3.92  |             convergent_lines(all_23_4, all_23_2) = 0) | ( ~ (v0 = 0) &
% 20.36/3.92  |             convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92  | 
% 20.36/3.92  | GROUND_INST: instantiating (14) with all_23_4, all_23_3, all_23_2, all_23_1,
% 20.36/3.92  |              all_23_0, simplifying with (21), (22), (23), (24), (26) gives:
% 20.36/3.92  |   (35)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.92  |             all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (v2 = 0
% 20.36/3.92  |             & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.92  |             (v1 = 0) & unorthogonal_lines(all_23_4, all_23_3) = v1) | ( ~ (v0
% 20.36/3.92  |               = 0) & convergent_lines(all_23_4, all_23_3) = v0))
% 20.36/3.92  | 
% 20.36/3.92  | GROUND_INST: instantiating (13) with all_23_3, all_23_4, all_23_2, all_23_0,
% 20.36/3.92  |              all_23_1, simplifying with (21), (22), (23), (24), (26) gives:
% 20.36/3.93  |   (36)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 20.36/3.93  |             all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | (v2 =
% 20.36/3.93  |             0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0) | ( ~
% 20.36/3.93  |             (v1 = 0) & unorthogonal_lines(all_23_3, all_23_4) = v1) | ( ~ (v0
% 20.36/3.93  |               = 0) & convergent_lines(all_23_3, all_23_4) = v0))
% 20.36/3.93  | 
% 20.36/3.93  | GROUND_INST: instantiating (5) with all_23_3, all_23_2, all_23_0, simplifying
% 20.36/3.93  |              with (22), (23), (26) gives:
% 20.36/3.93  |   (37)  all_23_0 = 0 | convergent_lines(all_23_3, all_23_2) = 0
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1, all_30_2,
% 20.36/3.93  |        all_30_3 gives:
% 20.36/3.93  |   (38)  (all_30_0 = 0 & all_30_1 = 0 & unorthogonal_lines(all_23_3, all_23_3)
% 20.36/3.93  |           = 0 & convergent_lines(all_23_3, all_23_3) = 0) | (all_30_2 = 0 &
% 20.36/3.93  |           convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_30_3 = 0) &
% 20.36/3.93  |           convergent_lines(all_23_4, all_23_3) = all_30_3)
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (30) with fresh symbols all_31_0, all_31_1, all_31_2,
% 20.36/3.93  |        all_31_3 gives:
% 20.36/3.93  |   (39)  (all_31_0 = 0 & convergent_lines(all_23_4, all_23_3) = 0) | (all_31_1
% 20.36/3.93  |           = 0 & convergent_lines(all_23_4, all_23_3) = 0) | ( ~ (all_31_2 = 0)
% 20.36/3.93  |           & unorthogonal_lines(all_23_4, all_23_4) = all_31_2) | ( ~ (all_31_3
% 20.36/3.93  |             = 0) & convergent_lines(all_23_4, all_23_4) = all_31_3)
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2,
% 20.36/3.93  |        all_32_3 gives:
% 20.36/3.93  |   (40)  (all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_23_3, all_23_2)
% 20.36/3.93  |           = 0 & convergent_lines(all_23_3, all_23_2) = 0) | (all_32_2 = 0 &
% 20.36/3.93  |           all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.93  |           (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_32_3)
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (34) with fresh symbols all_33_0, all_33_1, all_33_2,
% 20.36/3.93  |        all_33_3 gives:
% 20.36/3.93  |   (41)  (all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.36/3.93  |           0) | (all_33_1 = 0 & all_33_2 = 0 & unorthogonal_lines(all_23_4,
% 20.36/3.93  |             all_23_2) = 0 & convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 20.36/3.93  |           (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3) = all_33_3)
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (33) with fresh symbols all_34_0, all_34_1, all_34_2,
% 20.36/3.93  |        all_34_3 gives:
% 20.36/3.93  |   (42)  (all_34_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 20.36/3.93  |           0) | (all_34_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 20.36/3.93  |             all_23_2) = 0) | ( ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 20.36/3.93  |             all_23_3) = all_34_2) | ( ~ (all_34_3 = 0) &
% 20.36/3.93  |           convergent_lines(all_23_3, all_23_3) = all_34_3)
% 20.36/3.93  | 
% 20.36/3.93  | DELTA: instantiating (28) with fresh symbols all_35_0, all_35_1, all_35_2,
% 20.36/3.93  |        all_35_3 gives:
% 21.03/3.93  |   (43)  (all_35_0 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2)
% 21.03/3.93  |           = 0) | (all_35_1 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.93  |             all_23_2) = 0) | ( ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.03/3.93  |             all_23_4) = all_35_2) | ( ~ (all_35_3 = 0) &
% 21.03/3.93  |           convergent_lines(all_23_4, all_23_4) = all_35_3)
% 21.03/3.93  | 
% 21.03/3.93  | DELTA: instantiating (36) with fresh symbols all_36_0, all_36_1, all_36_2,
% 21.03/3.93  |        all_36_3 gives:
% 21.03/3.93  |   (44)  (all_36_0 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4, all_23_2)
% 21.03/3.93  |           = 0) | (all_36_1 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 21.03/3.93  |             all_23_2) = 0) | ( ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.03/3.93  |             all_23_4) = all_36_2) | ( ~ (all_36_3 = 0) &
% 21.03/3.93  |           convergent_lines(all_23_3, all_23_4) = all_36_3)
% 21.03/3.93  | 
% 21.03/3.93  | DELTA: instantiating (35) with fresh symbols all_37_0, all_37_1, all_37_2,
% 21.03/3.93  |        all_37_3 gives:
% 21.03/3.93  |   (45)  (all_37_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 21.03/3.93  |           0) | (all_37_1 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.93  |             all_23_2) = 0) | ( ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.03/3.93  |             all_23_3) = all_37_2) | ( ~ (all_37_3 = 0) &
% 21.03/3.93  |           convergent_lines(all_23_4, all_23_3) = all_37_3)
% 21.03/3.93  | 
% 21.03/3.93  | BETA: splitting (29) gives:
% 21.03/3.93  | 
% 21.03/3.93  | Case 1:
% 21.03/3.93  | | 
% 21.03/3.93  | |   (46)  unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.03/3.93  | | 
% 21.03/3.93  | | BETA: splitting (37) gives:
% 21.03/3.93  | | 
% 21.03/3.93  | | Case 1:
% 21.03/3.93  | | | 
% 21.03/3.93  | | |   (47)  convergent_lines(all_23_3, all_23_2) = 0
% 21.03/3.93  | | | 
% 21.03/3.93  | | | BETA: splitting (40) gives:
% 21.03/3.93  | | | 
% 21.03/3.93  | | | Case 1:
% 21.03/3.93  | | | | 
% 21.03/3.93  | | | |   (48)  all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_23_3,
% 21.03/3.93  | | | |           all_23_2) = 0 & convergent_lines(all_23_3, all_23_2) = 0
% 21.03/3.93  | | | | 
% 21.03/3.93  | | | | ALPHA: (48) implies:
% 21.03/3.93  | | | |   (49)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.03/3.94  | | | | 
% 21.03/3.94  | | | | REF_CLOSE: (17), (20), (26), (49) are inconsistent by sub-proof #6.
% 21.03/3.94  | | | | 
% 21.03/3.94  | | | Case 2:
% 21.03/3.94  | | | | 
% 21.03/3.94  | | | |   (50)  (all_32_2 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.94  | | | |             all_23_2) = 0) | ( ~ (all_32_3 = 0) &
% 21.03/3.94  | | | |           convergent_lines(all_23_4, all_23_3) = all_32_3)
% 21.03/3.94  | | | | 
% 21.03/3.94  | | | | BETA: splitting (50) gives:
% 21.03/3.94  | | | | 
% 21.03/3.94  | | | | Case 1:
% 21.03/3.94  | | | | | 
% 21.03/3.94  | | | | |   (51)  all_32_2 = 0 & all_23_1 = 0 & unorthogonal_lines(all_23_4,
% 21.03/3.94  | | | | |           all_23_2) = 0
% 21.03/3.94  | | | | | 
% 21.03/3.94  | | | | | ALPHA: (51) implies:
% 21.03/3.94  | | | | |   (52)  all_23_1 = 0
% 21.03/3.94  | | | | | 
% 21.03/3.94  | | | | | REDUCE: (19), (52) imply:
% 21.03/3.94  | | | | |   (53)  $false
% 21.03/3.94  | | | | | 
% 21.03/3.94  | | | | | CLOSE: (53) is inconsistent.
% 21.03/3.94  | | | | | 
% 21.03/3.94  | | | | Case 2:
% 21.03/3.94  | | | | | 
% 21.07/3.94  | | | | |   (54)   ~ (all_32_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 21.07/3.94  | | | | |         all_32_3
% 21.07/3.94  | | | | | 
% 21.07/3.94  | | | | | ALPHA: (54) implies:
% 21.07/3.94  | | | | |   (55)  convergent_lines(all_23_4, all_23_3) = all_32_3
% 21.07/3.94  | | | | | 
% 21.07/3.94  | | | | | BETA: splitting (27) gives:
% 21.07/3.94  | | | | | 
% 21.07/3.94  | | | | | Case 1:
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | |   (56)  all_23_1 = 0
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | REDUCE: (19), (56) imply:
% 21.07/3.94  | | | | | |   (57)  $false
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | CLOSE: (57) is inconsistent.
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | Case 2:
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | |   (58)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.07/3.94  | | | | | |             all_23_4) = v0)
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | DELTA: instantiating (58) with fresh symbol all_51_0 gives:
% 21.07/3.94  | | | | | |   (59)   ~ (all_51_0 = 0) & convergent_lines(all_23_4, all_23_4) =
% 21.07/3.94  | | | | | |         all_51_0
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | ALPHA: (59) implies:
% 21.07/3.94  | | | | | |   (60)   ~ (all_51_0 = 0)
% 21.07/3.94  | | | | | |   (61)  convergent_lines(all_23_4, all_23_4) = all_51_0
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | BETA: splitting (41) gives:
% 21.07/3.94  | | | | | | 
% 21.07/3.94  | | | | | | Case 1:
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | |   (62)  all_33_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3,
% 21.07/3.94  | | | | | | |           all_23_2) = 0
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | | ALPHA: (62) implies:
% 21.07/3.94  | | | | | | |   (63)  all_23_0 = 0
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | | REDUCE: (20), (63) imply:
% 21.07/3.94  | | | | | | |   (64)  $false
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | | CLOSE: (64) is inconsistent.
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | Case 2:
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | |   (65)  (all_33_1 = 0 & all_33_2 = 0 &
% 21.07/3.94  | | | | | | |           unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 21.07/3.94  | | | | | | |           convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.07/3.94  | | | | | | |           (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3) =
% 21.07/3.94  | | | | | | |           all_33_3)
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | | BETA: splitting (65) gives:
% 21.07/3.94  | | | | | | | 
% 21.07/3.94  | | | | | | | Case 1:
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | |   (66)  all_33_1 = 0 & all_33_2 = 0 &
% 21.07/3.94  | | | | | | | |         unorthogonal_lines(all_23_4, all_23_2) = 0 &
% 21.07/3.94  | | | | | | | |         convergent_lines(all_23_4, all_23_2) = 0
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | | ALPHA: (66) implies:
% 21.07/3.94  | | | | | | | |   (67)  convergent_lines(all_23_4, all_23_2) = 0
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | | REF_CLOSE: (16), (19), (24), (67) are inconsistent by sub-proof
% 21.07/3.94  | | | | | | | |            #5.
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | Case 2:
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | |   (68)   ~ (all_33_3 = 0) & convergent_lines(all_23_4, all_23_3)
% 21.07/3.94  | | | | | | | |         = all_33_3
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | | ALPHA: (68) implies:
% 21.07/3.94  | | | | | | | |   (69)   ~ (all_33_3 = 0)
% 21.07/3.94  | | | | | | | |   (70)  convergent_lines(all_23_4, all_23_3) = all_33_3
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | | BETA: splitting (45) gives:
% 21.07/3.94  | | | | | | | | 
% 21.07/3.94  | | | | | | | | Case 1:
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | |   (71)  (all_37_0 = 0 & all_23_0 = 0 &
% 21.07/3.94  | | | | | | | | |           convergent_lines(all_23_3, all_23_2) = 0) |
% 21.07/3.94  | | | | | | | | |         (all_37_1 = 0 & all_23_1 = 0 &
% 21.07/3.94  | | | | | | | | |           unorthogonal_lines(all_23_4, all_23_2) = 0)
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | BETA: splitting (71) gives:
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | Case 1:
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | |   (72)  all_37_0 = 0 & all_23_0 = 0 &
% 21.07/3.94  | | | | | | | | | |         convergent_lines(all_23_3, all_23_2) = 0
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | ALPHA: (72) implies:
% 21.07/3.94  | | | | | | | | | |   (73)  all_23_0 = 0
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | REDUCE: (20), (73) imply:
% 21.07/3.94  | | | | | | | | | |   (74)  $false
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | CLOSE: (74) is inconsistent.
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | Case 2:
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | |   (75)  all_37_1 = 0 & all_23_1 = 0 &
% 21.07/3.94  | | | | | | | | | |         unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | ALPHA: (75) implies:
% 21.07/3.94  | | | | | | | | | |   (76)  all_23_1 = 0
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | REDUCE: (19), (76) imply:
% 21.07/3.94  | | | | | | | | | |   (77)  $false
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | CLOSE: (77) is inconsistent.
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | End of split
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | Case 2:
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | |   (78)  ( ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.94  | | | | | | | | |             all_23_3) = all_37_2) | ( ~ (all_37_3 = 0) &
% 21.07/3.94  | | | | | | | | |           convergent_lines(all_23_4, all_23_3) = all_37_3)
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | BETA: splitting (78) gives:
% 21.07/3.94  | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | Case 1:
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | |   (79)   ~ (all_37_2 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.94  | | | | | | | | | |           all_23_3) = all_37_2
% 21.07/3.94  | | | | | | | | | | 
% 21.07/3.94  | | | | | | | | | | ALPHA: (79) implies:
% 21.07/3.94  | | | | | | | | | |   (80)   ~ (all_37_2 = 0)
% 21.07/3.95  | | | | | | | | | |   (81)  unorthogonal_lines(all_23_4, all_23_3) = all_37_2
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_37_2, all_23_3,
% 21.07/3.95  | | | | | | | | | |              all_23_4, simplifying with (25), (81) gives:
% 21.07/3.95  | | | | | | | | | |   (82)  all_37_2 = 0
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | REDUCE: (80), (82) imply:
% 21.07/3.95  | | | | | | | | | |   (83)  $false
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | CLOSE: (83) is inconsistent.
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | Case 2:
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | |   (84)   ~ (all_37_3 = 0) & convergent_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |           all_23_3) = all_37_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | ALPHA: (84) implies:
% 21.07/3.95  | | | | | | | | | |   (85)  convergent_lines(all_23_4, all_23_3) = all_37_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (16) with all_33_3, all_37_3,
% 21.07/3.95  | | | | | | | | | |              all_23_3, all_23_4, simplifying with (70), (85)
% 21.07/3.95  | | | | | | | | | |              gives:
% 21.07/3.95  | | | | | | | | | |   (86)  all_37_3 = all_33_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_37_3,
% 21.07/3.95  | | | | | | | | | |              all_23_3, all_23_4, simplifying with (55), (85)
% 21.07/3.95  | | | | | | | | | |              gives:
% 21.07/3.95  | | | | | | | | | |   (87)  all_37_3 = all_32_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | COMBINE_EQS: (86), (87) imply:
% 21.07/3.95  | | | | | | | | | |   (88)  all_33_3 = all_32_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | SIMP: (88) implies:
% 21.07/3.95  | | | | | | | | | |   (89)  all_33_3 = all_32_3
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | REDUCE: (69), (89) imply:
% 21.07/3.95  | | | | | | | | | |   (90)   ~ (all_32_3 = 0)
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_4, all_23_4,
% 21.07/3.95  | | | | | | | | | |              all_23_4, all_51_0, all_51_0, simplifying with
% 21.07/3.95  | | | | | | | | | |              (21), (61) gives:
% 21.07/3.95  | | | | | | | | | |   (91)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & all_51_0 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.07/3.95  | | | | | | | | | |           (v2 = 0 & all_51_0 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.07/3.95  | | | | | | | | | |             ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_3,
% 21.07/3.95  | | | | | | | | | |              all_23_4, all_51_0, simplifying with (21), (22),
% 21.07/3.95  | | | | | | | | | |              (25), (61) gives:
% 21.07/3.95  | | | | | | | | | |   (92)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_3, all_23_4) = 0) | (v1
% 21.07/3.95  | | | | | | | | | |             = 0 & all_51_0 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.07/3.95  | | | | | | | | | |             ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_3) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_4, all_23_4,
% 21.07/3.95  | | | | | | | | | |              all_51_0, simplifying with (21), (61) gives:
% 21.07/3.95  | | | | | | | | | |   (93)  all_51_0 = 0 | unorthogonal_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |           all_23_4) = 0
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_4, all_23_4,
% 21.07/3.95  | | | | | | | | | |              all_23_3, all_32_3, all_32_3, simplifying with
% 21.07/3.95  | | | | | | | | | |              (21), (22), (55) gives:
% 21.07/3.95  | | | | | | | | | |   (94)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & all_32_3 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.07/3.95  | | | | | | | | | |           (v2 = 0 & all_32_3 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.07/3.95  | | | | | | | | | |             ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4,
% 21.07/3.95  | | | | | | | | | |              all_23_3, all_32_3, 0, simplifying with (21),
% 21.07/3.95  | | | | | | | | | |              (22), (25), (55) gives:
% 21.07/3.95  | | | | | | | | | |   (95)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_3) = 0) | (v2 = 0 & all_32_3 = 0) | ( ~
% 21.07/3.95  | | | | | | | | | |             (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4,
% 21.07/3.95  | | | | | | | | | |              all_23_3, 0, all_32_3, simplifying with (21),
% 21.07/3.95  | | | | | | | | | |              (22), (25), (55) gives:
% 21.07/3.95  | | | | | | | | | |   (96)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & all_32_3 = 0) | (v2 = 0 &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.07/3.95  | | | | | | | | | |             (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.95  | | | | | | | | | |               all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_3,
% 21.07/3.95  | | | | | | | | | |              all_23_3, all_32_3, simplifying with (21), (22),
% 21.07/3.95  | | | | | | | | | |              (25), (55) gives:
% 21.07/3.95  | | | | | | | | | |   (97)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.95  | | | | | | | | | |           int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.95  | | | | | | | | | |             unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_3, all_23_3) = 0) | (v1
% 21.07/3.95  | | | | | | | | | |             = 0 & all_32_3 = 0) | ( ~ (v0 = 0) &
% 21.07/3.95  | | | | | | | | | |             convergent_lines(all_23_4, all_23_3) = v0))
% 21.07/3.95  | | | | | | | | | | 
% 21.07/3.95  | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_3, all_23_3,
% 21.07/3.95  | | | | | | | | | |              all_23_2, 0, 0, simplifying with (22), (23), (47)
% 21.07/3.95  | | | | | | | | | |              gives:
% 21.07/3.96  | | | | | | | | | |   (98)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.96  | | | | | | | | | |           int] : ((v3 = 0 & unorthogonal_lines(all_23_3,
% 21.07/3.96  | | | | | | | | | |               all_23_2) = 0) | (v2 = 0 &
% 21.07/3.96  | | | | | | | | | |             unorthogonal_lines(all_23_3, all_23_2) = 0) | (
% 21.07/3.96  | | | | | | | | | |             ~ (v1 = 0) & unorthogonal_lines(all_23_3,
% 21.07/3.96  | | | | | | | | | |               all_23_3) = v1) | ( ~ (v0 = 0) &
% 21.07/3.96  | | | | | | | | | |             convergent_lines(all_23_3, all_23_3) = v0))
% 21.07/3.96  | | | | | | | | | | 
% 21.07/3.96  | | | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_23_2,
% 21.07/3.96  | | | | | | | | | |              all_23_2, 0, simplifying with (22), (23), (47)
% 21.07/3.96  | | | | | | | | | |              gives:
% 21.07/3.96  | | | | | | | | | |   (99)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 21.07/3.96  | | | | | | | | | |           int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.96  | | | | | | | | | |             unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.07/3.96  | | | | | | | | | |             convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.07/3.96  | | | | | | | | | |             = 0 & unorthogonal_lines(all_23_3, all_23_2) =
% 21.07/3.96  | | | | | | | | | |             0) | ( ~ (v0 = 0) & unorthogonal_lines(all_23_3,
% 21.07/3.96  | | | | | | | | | |               all_23_2) = v0))
% 21.07/3.96  | | | | | | | | | | 
% 21.07/3.96  | | | | | | | | | | GROUND_INST: instantiating (8) with all_23_3, all_23_2,
% 21.07/3.96  | | | | | | | | | |              all_23_2, all_23_0, simplifying with (22), (23),
% 21.07/3.96  | | | | | | | | | |              (26), (47) gives:
% 21.07/3.96  | | | | | | | | | |   (100)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.07/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.07/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.07/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.07/3.96  | | | | | | | | | |              = 0 & all_23_0 = 0) | ( ~ (v0 = 0) &
% 21.07/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_3, all_23_2) = v0))
% 21.07/3.96  | | | | | | | | | | 
% 21.07/3.96  | | | | | | | | | | GROUND_INST: instantiating (15) with all_23_4, all_23_4,
% 21.07/3.96  | | | | | | | | | |              all_23_2, 0, 0, simplifying with (21), (23), (46)
% 21.07/3.96  | | | | | | | | | |              gives:
% 21.07/3.96  | | | | | | | | | |   (101)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.07/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.07/3.96  | | | | | | | | | |                all_23_2) = 0) | (v2 = 0 &
% 21.07/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.07/3.96  | | | | | | | | | |              (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.07/3.96  | | | | | | | | | |                all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.07/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_4) = v0))
% 21.07/3.96  | | | | | | | | | | 
% 21.07/3.96  | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 21.07/3.96  | | | | | | | | | |              all_23_2, 0, simplifying with (21), (23), (46)
% 21.07/3.96  | | | | | | | | | |              gives:
% 21.18/3.96  | | | | | | | | | |   (102)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.18/3.96  | | | | | | | | | |              = 0 & convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/3.96  | | | | | | | | | |            | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_2) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_4, all_23_4,
% 21.18/3.96  | | | | | | | | | |              all_23_2, all_23_1, 0, simplifying with (21),
% 21.18/3.96  | | | | | | | | | |              (23), (24), (46) gives:
% 21.18/3.96  | | | | | | | | | |   (103)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_2) = 0) | (v2 = 0 & all_23_1 = 0) | (
% 21.18/3.96  | | | | | | | | | |              ~ (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_4) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (13) with all_23_4, all_23_4,
% 21.18/3.96  | | | | | | | | | |              all_23_2, 0, all_23_1, simplifying with (21),
% 21.18/3.96  | | | | | | | | | |              (23), (24), (46) gives:
% 21.18/3.96  | | | | | | | | | |   (104)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & all_23_1 = 0) | (v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.96  | | | | | | | | | |              (v1 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_4) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_2,
% 21.18/3.96  | | | | | | | | | |              all_23_3, 0, simplifying with (21), (22), (23),
% 21.18/3.96  | | | | | | | | | |              (25), (46) gives:
% 21.18/3.96  | | | | | | | | | |   (105)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_3) = 0) | (v1
% 21.18/3.96  | | | | | | | | | |              = 0 & convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.96  | | | | | | | | | |            | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_2) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96  | | | | | | | | | |              all_23_2, all_23_1, simplifying with (21), (23),
% 21.18/3.96  | | | | | | | | | |              (24), (46) gives:
% 21.18/3.96  | | | | | | | | | |   (106)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_2) = 0) | (v1
% 21.18/3.96  | | | | | | | | | |              = 0 & all_23_1 = 0) | ( ~ (v0 = 0) &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_4, all_23_2) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96  | | | | | | | | | |              all_23_3, all_32_3, simplifying with (21), (22),
% 21.18/3.96  | | | | | | | | | |              (23), (46), (55) gives:
% 21.18/3.96  | | | | | | | | | |   (107)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_3) = 0) | (v1
% 21.18/3.96  | | | | | | | | | |              = 0 & all_32_3 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.18/3.96  | | | | | | | | | |              ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_2) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | GROUND_INST: instantiating (7) with all_23_4, all_23_2,
% 21.18/3.96  | | | | | | | | | |              all_23_4, all_51_0, simplifying with (21), (23),
% 21.18/3.96  | | | | | | | | | |              (46), (61) gives:
% 21.18/3.96  | | | | | | | | | |   (108)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/3.96  | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.18/3.96  | | | | | | | | | |              convergent_lines(all_23_2, all_23_4) = 0) | (v1
% 21.18/3.96  | | | | | | | | | |              = 0 & all_51_0 = 0 &
% 21.18/3.96  | | | | | | | | | |              unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.18/3.96  | | | | | | | | | |              ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/3.96  | | | | | | | | | |                all_23_2) = v0))
% 21.18/3.96  | | | | | | | | | | 
% 21.18/3.96  | | | | | | | | | | DELTA: instantiating (100) with fresh symbols all_71_0,
% 21.18/3.96  | | | | | | | | | |        all_71_1, all_71_2, all_71_3 gives:
% 21.18/3.97  | | | | | | | | | |   (109)  (all_71_0 = 0 & all_71_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_71_2 = 0 & all_23_0 = 0) | ( ~ (all_71_3 = 0)
% 21.18/3.97  | | | | | | | | | |            & unorthogonal_lines(all_23_3, all_23_2) =
% 21.18/3.97  | | | | | | | | | |            all_71_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_72_0,
% 21.18/3.97  | | | | | | | | | |        all_72_1, all_72_2, all_72_3 gives:
% 21.18/3.97  | | | | | | | | | |   (110)  (all_72_0 = 0 & all_72_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_3, all_23_3) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_72_2 = 0 & all_32_3 = 0) | ( ~ (all_72_3 = 0)
% 21.18/3.97  | | | | | | | | | |            & convergent_lines(all_23_4, all_23_3) =
% 21.18/3.97  | | | | | | | | | |            all_72_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (96) with fresh symbols all_73_0,
% 21.18/3.97  | | | | | | | | | |        all_73_1, all_73_2, all_73_3 gives:
% 21.18/3.97  | | | | | | | | | |   (111)  (all_73_0 = 0 & all_32_3 = 0) | (all_73_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_73_2) | ( ~ (all_73_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_73_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (95) with fresh symbols all_74_0,
% 21.18/3.97  | | | | | | | | | |        all_74_1, all_74_2, all_74_3 gives:
% 21.18/3.97  | | | | | | | | | |   (112)  (all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_3) = 0) | (all_74_1 = 0 & all_32_3 = 0)
% 21.18/3.97  | | | | | | | | | |          | ( ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_74_2) | ( ~ (all_74_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_74_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (106) with fresh symbols all_77_0,
% 21.18/3.97  | | | | | | | | | |        all_77_1, all_77_2, all_77_3 gives:
% 21.18/3.97  | | | | | | | | | |   (113)  (all_77_0 = 0 & all_77_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_77_2 = 0 & all_23_1 = 0) | ( ~ (all_77_3 = 0)
% 21.18/3.97  | | | | | | | | | |            & convergent_lines(all_23_4, all_23_2) =
% 21.18/3.97  | | | | | | | | | |            all_77_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_78_0,
% 21.18/3.97  | | | | | | | | | |        all_78_1, all_78_2, all_78_3 gives:
% 21.18/3.97  | | | | | | | | | |   (114)  (all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = 0) | (all_78_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_78_2) | ( ~ (all_78_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_78_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (105) with fresh symbols all_79_0,
% 21.18/3.97  | | | | | | | | | |        all_79_1, all_79_2, all_79_3 gives:
% 21.18/3.97  | | | | | | | | | |   (115)  (all_79_0 = 0 & all_79_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_3) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_79_2 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_79_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_79_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (99) with fresh symbols all_80_0,
% 21.18/3.97  | | | | | | | | | |        all_80_1, all_80_2, all_80_3 gives:
% 21.18/3.97  | | | | | | | | | |   (116)  (all_80_0 = 0 & all_80_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_80_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_2) =
% 21.18/3.97  | | | | | | | | | |            all_80_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_82_0,
% 21.18/3.97  | | | | | | | | | |        all_82_1, all_82_2, all_82_3 gives:
% 21.18/3.97  | | | | | | | | | |   (117)  (all_82_0 = 0 & all_23_1 = 0) | (all_82_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_82_2) | ( ~ (all_82_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_82_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_83_0,
% 21.18/3.97  | | | | | | | | | |        all_83_1, all_83_2, all_83_3 gives:
% 21.18/3.97  | | | | | | | | | |   (118)  (all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = 0) | (all_83_1 = 0 & all_23_1 = 0)
% 21.18/3.97  | | | | | | | | | |          | ( ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_83_2) | ( ~ (all_83_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_83_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_84_0,
% 21.18/3.97  | | | | | | | | | |        all_84_1, all_84_2, all_84_3 gives:
% 21.18/3.97  | | | | | | | | | |   (119)  (all_84_0 = 0 & all_84_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_84_2 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_84_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_84_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_85_0,
% 21.18/3.97  | | | | | | | | | |        all_85_1, all_85_2, all_85_3 gives:
% 21.18/3.97  | | | | | | | | | |   (120)  (all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = 0) | (all_85_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_2) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/3.97  | | | | | | | | | |              all_23_3) = all_85_2) | ( ~ (all_85_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_3, all_23_3) = all_85_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (92) with fresh symbols all_88_0,
% 21.18/3.97  | | | | | | | | | |        all_88_1, all_88_2, all_88_3 gives:
% 21.18/3.97  | | | | | | | | | |   (121)  (all_88_0 = 0 & all_88_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_88_2 = 0 & all_51_0 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_3) = all_88_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_89_0,
% 21.18/3.97  | | | | | | | | | |        all_89_1, all_89_2, all_89_3 gives:
% 21.18/3.97  | | | | | | | | | |   (122)  (all_89_0 = 0 & all_89_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_89_2 = 0 & all_51_0 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = all_89_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (107) with fresh symbols all_90_0,
% 21.18/3.97  | | | | | | | | | |        all_90_1, all_90_2, all_90_3 gives:
% 21.18/3.97  | | | | | | | | | |   (123)  (all_90_0 = 0 & all_90_1 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_2, all_23_3) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_90_2 = 0 & all_32_3 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_2) = all_90_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (94) with fresh symbols all_91_0,
% 21.18/3.97  | | | | | | | | | |        all_91_1, all_91_2, all_91_3 gives:
% 21.18/3.97  | | | | | | | | | |   (124)  (all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_91_2) | ( ~ (all_91_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_91_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_92_0,
% 21.18/3.97  | | | | | | | | | |        all_92_1, all_92_2, all_92_3 gives:
% 21.18/3.97  | | | | | | | | | |   (125)  (all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.18/3.97  | | | | | | | | | |          (all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.97  | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | ( ~
% 21.18/3.97  | | | | | | | | | |            (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | |              all_23_4) = all_92_2) | ( ~ (all_92_3 = 0) &
% 21.18/3.97  | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_92_3)
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | BETA: splitting (93) gives:
% 21.18/3.97  | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | Case 1:
% 21.18/3.97  | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | |   (126)  unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.97  | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | | BETA: splitting (112) gives:
% 21.18/3.97  | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | | Case 1:
% 21.18/3.97  | | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | | |   (127)  (all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.97  | | | | | | | | | | | |              all_23_3) = 0) | (all_74_1 = 0 & all_32_3 = 0)
% 21.18/3.97  | | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | | | BETA: splitting (127) gives:
% 21.18/3.97  | | | | | | | | | | | | 
% 21.18/3.97  | | | | | | | | | | | | Case 1:
% 21.18/3.97  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | |   (128)  all_74_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | ALPHA: (128) implies:
% 21.18/3.98  | | | | | | | | | | | | |   (129)  convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (129) are inconsistent by
% 21.18/3.98  | | | | | | | | | | | | |            sub-proof #4.
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | |   (130)  all_74_1 = 0 & all_32_3 = 0
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | ALPHA: (130) implies:
% 21.18/3.98  | | | | | | | | | | | | |   (131)  all_32_3 = 0
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | REDUCE: (90), (131) imply:
% 21.18/3.98  | | | | | | | | | | | | |   (132)  $false
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | End of split
% 21.18/3.98  | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | |   (133)  ( ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | |              all_23_4) = all_74_2) | ( ~ (all_74_3 = 0) &
% 21.18/3.98  | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_74_3)
% 21.18/3.98  | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | BETA: splitting (133) gives:
% 21.18/3.98  | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | |   (134)   ~ (all_74_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | |            all_23_4) = all_74_2
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | ALPHA: (134) implies:
% 21.18/3.98  | | | | | | | | | | | | |   (135)   ~ (all_74_2 = 0)
% 21.18/3.98  | | | | | | | | | | | | |   (136)  unorthogonal_lines(all_23_4, all_23_4) = all_74_2
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_74_2, all_23_4,
% 21.18/3.98  | | | | | | | | | | | | |              all_23_4, simplifying with (126), (136) gives:
% 21.18/3.98  | | | | | | | | | | | | |   (137)  all_74_2 = 0
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | REDUCE: (135), (137) imply:
% 21.18/3.98  | | | | | | | | | | | | |   (138)  $false
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | |   (139)   ~ (all_74_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | |            all_23_4) = all_74_3
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | ALPHA: (139) implies:
% 21.18/3.98  | | | | | | | | | | | | |   (140)  convergent_lines(all_23_4, all_23_4) = all_74_3
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | BETA: splitting (111) gives:
% 21.18/3.98  | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | |   (141)  (all_73_0 = 0 & all_32_3 = 0) | (all_73_1 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | |   (142)  all_73_0 = 0 & all_32_3 = 0
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 21.18/3.98  | | | | | | | | | | | | | | |   (143)  all_32_3 = 0
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | REDUCE: (90), (143) imply:
% 21.18/3.98  | | | | | | | | | | | | | | |   (144)  $false
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | |   (145)  all_73_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 21.18/3.98  | | | | | | | | | | | | | | |   (146)  convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (146) are inconsistent by
% 21.18/3.98  | | | | | | | | | | | | | | |            sub-proof #4.
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | End of split
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | |   (147)  ( ~ (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | |              all_23_4) = all_73_2) | ( ~ (all_73_3 = 0) &
% 21.18/3.98  | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_73_3)
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 21.18/3.98  | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | |   (148)   ~ (all_73_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | |            all_23_4) = all_73_2
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 21.18/3.98  | | | | | | | | | | | | | | |   (149)   ~ (all_73_2 = 0)
% 21.18/3.98  | | | | | | | | | | | | | | |   (150)  unorthogonal_lines(all_23_4, all_23_4) = all_73_2
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_73_2, all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (150) gives:
% 21.18/3.98  | | | | | | | | | | | | | | |   (151)  all_73_2 = 0
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | REDUCE: (149), (151) imply:
% 21.18/3.98  | | | | | | | | | | | | | | |   (152)  $false
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | |   (153)   ~ (all_73_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | |            all_23_4) = all_73_3
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 21.18/3.98  | | | | | | | | | | | | | | |   (154)  convergent_lines(all_23_4, all_23_4) = all_73_3
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | |   (155)  (all_31_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | |              all_23_3) = 0) | (all_31_1 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (156)  all_31_0 = 0 & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (157)  convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (157) are inconsistent by
% 21.18/3.98  | | | | | | | | | | | | | | | | |            sub-proof #4.
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (158)  all_31_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (159)  convergent_lines(all_23_4, all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (159) are inconsistent by
% 21.18/3.98  | | | | | | | | | | | | | | | | |            sub-proof #4.
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | End of split
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | |   (160)  ( ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | |              all_23_4) = all_31_2) | ( ~ (all_31_3 = 0) &
% 21.18/3.98  | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_31_3)
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (161)   ~ (all_31_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | | |            all_23_4) = all_31_2
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (162)   ~ (all_31_2 = 0)
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (163)  unorthogonal_lines(all_23_4, all_23_4) = all_31_2
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_31_2, all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (163) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (164)  all_31_2 = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | REDUCE: (162), (164) imply:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (165)  $false
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (166)   ~ (all_31_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.98  | | | | | | | | | | | | | | | | |            all_23_4) = all_31_3
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 21.18/3.98  | | | | | | | | | | | | | | | | |   (167)  convergent_lines(all_23_4, all_23_4) = all_31_3
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | |   (168)  (all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.18/3.98  | | | | | | | | | | | | | | | | | |          (all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0)
% 21.18/3.98  | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |   (169)  all_91_0 = 0 & all_32_3 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |   (170)  all_32_3 = 0
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | REDUCE: (90), (170) imply:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |   (171)  $false
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent.
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.98  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |   (172)  all_91_1 = 0 & all_32_3 = 0 &
% 21.18/3.98  | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (173)  all_32_3 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | REDUCE: (90), (173) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (174)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99  | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | |   (175)  ( ~ (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | |              all_23_4) = all_91_2) | ( ~ (all_91_3 = 0) &
% 21.18/3.99  | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_91_3)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (176)   ~ (all_91_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |            all_23_4) = all_91_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (177)   ~ (all_91_2 = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (178)  unorthogonal_lines(all_23_4, all_23_4) = all_91_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_91_2, all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (178) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (179)  all_91_2 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | REDUCE: (177), (179) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (180)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (181)   ~ (all_91_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |            all_23_4) = all_91_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | |   (182)  convergent_lines(all_23_4, all_23_4) = all_91_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |   (183)  (all_35_0 = 0 & all_23_1 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |          (all_35_1 = 0 & all_23_1 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (184)  all_35_0 = 0 & all_23_1 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (185)  all_23_1 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (185) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (186)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (187)  all_35_1 = 0 & all_23_1 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (188)  all_23_1 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (188) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (189)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |   (190)  ( ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_35_2) | ( ~ (all_35_3 = 0) &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_35_3)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (191)   ~ (all_35_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_35_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (192)   ~ (all_35_2 = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (193)  unorthogonal_lines(all_23_4, all_23_4) = all_35_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_35_2, all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (193) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (194)  all_35_2 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (194) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (195)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (196)   ~ (all_35_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_35_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (197)   ~ (all_35_3 = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | |   (198)  convergent_lines(all_23_4, all_23_4) = all_35_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_82_0 = 0 & all_23_1 = 0) | (all_82_1 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_82_0 = 0 & all_23_1 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_23_1 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (201) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (202)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_82_1 = 0 & convergent_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (204)  convergent_lines(all_23_4, all_23_2) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (204) are inconsistent by
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | |   (205)  ( ~ (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_82_2) | ( ~ (all_82_3 = 0) &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_82_3)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (206)   ~ (all_82_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_82_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (all_82_2 = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (208)  unorthogonal_lines(all_23_4, all_23_4) = all_82_2
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_82_2, all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (208) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_82_2 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (209) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (210)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (211)   ~ (all_82_3 = 0) & convergent_lines(all_23_4,
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_82_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | |   (212)  convergent_lines(all_23_4, all_23_4) = all_82_3
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | |   (213)  (all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) |
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | |          (all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0)
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_92_0 = 0 & all_51_0 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_51_0 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (215) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_92_1 = 0 & all_51_0 = 0 &
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_51_0 = 0
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (218) imply:
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  $false
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/3.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | |   (220)  ( ~ (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_92_2) | ( ~ (all_92_3 = 0) &
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_92_3)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (221)   ~ (all_92_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_92_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (222)   ~ (all_92_2 = 0)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  unorthogonal_lines(all_23_4, all_23_4) = all_92_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_92_2, all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (223) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  all_92_2 = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (224) imply:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  $false
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (226)   ~ (all_92_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_92_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  convergent_lines(all_23_4, all_23_4) = all_92_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  (all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_78_1 = 0 &
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = 0)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_78_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (230) are inconsistent by
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_78_1 = 0 & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (232) are inconsistent by
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  ( ~ (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_78_2) | ( ~ (all_78_3 = 0) &
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_78_3)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)   ~ (all_78_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_78_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)   ~ (all_78_2 = 0)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  unorthogonal_lines(all_23_4, all_23_4) = all_78_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_78_2, all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (236) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_78_2 = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (235), (237) imply:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  $false
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)   ~ (all_78_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_78_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  convergent_lines(all_23_4, all_23_4) = all_78_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  (all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_83_1 = 0 & all_23_1 = 0)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_83_0 = 0 & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  convergent_lines(all_23_4, all_23_2) = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (243) are inconsistent by
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_83_1 = 0 & all_23_1 = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_23_1 = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (245) imply:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  $false
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  ( ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_83_2) | ( ~ (all_83_3 = 0) &
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_4) = all_83_3)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (all_83_2 = 0) & unorthogonal_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_83_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)   ~ (all_83_2 = 0)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  unorthogonal_lines(all_23_4, all_23_4) = all_83_2
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_83_2, all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, simplifying with (126), (250) gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_83_2 = 0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (251) imply:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  $false
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)   ~ (all_83_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_83_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  convergent_lines(all_23_4, all_23_4) = all_83_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_51_0, all_73_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (61), (154)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_73_3 = all_51_0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_51_0, all_78_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (61), (240)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_78_3 = all_51_0
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_74_3, all_78_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (140), (240)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_78_3 = all_74_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_82_3, all_83_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (212), (254)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_83_3 = all_82_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_73_3, all_83_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (154), (254)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_83_3 = all_73_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_35_3, all_83_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (198), (254)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_83_3 = all_35_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_78_3, all_91_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (182), (240)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_91_3 = all_78_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_91_3, all_92_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (182), (227)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_92_3 = all_91_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_31_3, all_92_3,
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_4, simplifying with (167), (227)
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_92_3 = all_31_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (263) imply:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_91_3 = all_31_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (264) implies:
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_91_3 = all_31_3
% 21.18/4.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (265) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_78_3 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_78_3 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (259) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_82_3 = all_73_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (260) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_82_3 = all_35_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (269) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_73_3 = all_35_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_73_3 = all_35_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_74_3 = all_51_0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (267) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_74_3 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_51_0 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_51_0 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (271) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_51_0 = all_35_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (276) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_51_0 = all_35_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (277) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_35_3 = all_31_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (278) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)   ~ (all_31_3 = 0)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_4, all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, 0, simplifying with (21), (22), (25),
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (126) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & v2 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v1 = 0 & convergent_lines(all_23_4, all_23_4) =
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              0) | ( ~ (v0 = 0) & convergent_lines(all_23_4,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_3) = v0))
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (280) with fresh symbols all_142_0,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_142_1, all_142_2, all_142_3 gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  (all_142_0 = 0 & all_142_1 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = 0) |
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) =
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_142_3)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_30_0 = 0 & all_30_1 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (22), (283) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  (all_30_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_30_3 = 0) &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) = all_30_3)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_30_2 = 0 & convergent_lines(all_23_4,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  convergent_lines(all_23_4, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (287) are inconsistent by
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #4.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)   ~ (all_30_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_30_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  convergent_lines(all_23_4, all_23_3) = all_30_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_32_3, all_30_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (55), (289)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_32_3 = all_30_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (290) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)   ~ (all_30_3 = 0)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  (all_34_0 = 0 & all_23_0 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0) |
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_34_1 = 0 & all_23_0 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_34_0 = 0 & all_23_0 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_2) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_23_0 = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (294) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_34_1 = 0 & all_23_0 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_2) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_23_0 = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (297) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  ( ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_34_2) | ( ~ (all_34_3 = 0) &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_3) = all_34_3)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)   ~ (all_34_2 = 0) & unorthogonal_lines(all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_34_2
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)   ~ (all_34_2 = 0)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  unorthogonal_lines(all_23_3, all_23_3) = all_34_2
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_3, all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_2, simplifying with (22), (302) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_34_2 = 0 | convergent_lines(all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (22), (304) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_34_2 = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (306) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)   ~ (all_34_3 = 0) & convergent_lines(all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_34_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)   ~ (all_34_3 = 0)
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  convergent_lines(all_23_3, all_23_3) = all_34_3
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_72_0 = 0 & all_72_1 = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_3) = 0 &
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  convergent_lines(all_23_3, all_23_3) = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_34_3, all_23_3,
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (310), (312) gives:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_34_3 = 0
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (313) imply:
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  $false
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent.
% 21.18/4.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  (all_72_2 = 0 & all_32_3 = 0) | ( ~ (all_72_3 = 0)
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & convergent_lines(all_23_4, all_23_3) =
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_72_3)
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_72_2 = 0 & all_32_3 = 0
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_32_3 = 0
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (317) imply:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_30_3 = 0
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_30_3 = 0
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (319) imply:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  $false
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent.
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)   ~ (all_72_3 = 0) & convergent_lines(all_23_4,
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_72_3
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)   ~ (all_72_3 = 0)
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  convergent_lines(all_23_4, all_23_3) = all_72_3
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_30_3, all_72_3,
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (289), (323)
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_72_3 = all_30_3
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_3, all_23_2,
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_34_3, simplifying with (22), (23),
% 21.18/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (47), (310) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_34_3 = 0 | convergent_lines(all_23_2,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_23_3, all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_34_3, all_30_3, simplifying with
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21), (22), (289), (310) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_34_3 = 0 | all_30_3 = 0 |  ? [v0: int] : ( ~
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v0 = 0) & convergent_lines(all_23_3, all_23_4)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = v0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_3, all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_3, simplifying with (22), (310) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_34_3 = 0 | unorthogonal_lines(all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  (all_36_0 = 0 & all_23_1 = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_2) = 0) |
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_36_1 = 0 & all_23_0 = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_36_0 = 0 & all_23_1 = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_2) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_23_1 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (330) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_36_1 = 0 & all_23_0 = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_2) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  all_23_0 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (333) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  ( ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_36_2) | ( ~ (all_36_3 = 0) &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = all_36_3)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)   ~ (all_36_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_36_2
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)   ~ (all_36_2 = 0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  unorthogonal_lines(all_23_3, all_23_4) = all_36_2
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_34_3 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (339) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_30_3 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = v0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_30_3 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (342) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)   ? [v0: int] : ( ~ (v0 = 0) &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_4) = v0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (344) with fresh symbol all_193_0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)   ~ (all_193_0 = 0) & convergent_lines(all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_193_0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)   ~ (all_193_0 = 0)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  convergent_lines(all_23_3, all_23_4) = all_193_0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_142_0 = 0 & all_142_1 = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_36_2, all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (338), (349) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_36_2 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (350) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) =
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_142_3)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  convergent_lines(all_23_4, all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (167), (279), (354) are inconsistent by
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #3.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_23_3, all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_193_0, simplifying with (21), (22), (347)
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_193_0 = 0 | unorthogonal_lines(all_23_3,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  unorthogonal_lines(all_23_3, all_23_4) = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_36_2, all_23_4,
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (338), (356) gives:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_36_2 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (357) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_193_0 = 0
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (359) imply:
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  $false
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)   ~ (all_36_3 = 0) & convergent_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_36_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)   ~ (all_36_3 = 0)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  convergent_lines(all_23_3, all_23_4) = all_36_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_88_0 = 0 & all_88_1 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (362), (363), (366) are inconsistent by
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  (all_88_2 = 0 & all_51_0 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_88_3)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_88_2 = 0 & all_51_0 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  all_51_0 = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (369) imply:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  all_31_3 = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (370) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  all_31_3 = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (371) imply:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  $false
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)   ~ (all_88_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_88_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)   ~ (all_88_3 = 0)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)  convergent_lines(all_23_4, all_23_3) = all_88_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)  unorthogonal_lines(all_23_3, all_23_3) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)  all_142_0 = 0 & all_142_1 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_3, all_23_4) = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  convergent_lines(all_23_3, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (362), (363), (378) are inconsistent by
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  (all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = 0) | ( ~ (all_142_3 = 0) &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_3) =
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_142_3)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  all_142_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  convergent_lines(all_23_4, all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (167), (279), (381) are inconsistent by
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #3.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)   ~ (all_142_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_142_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  convergent_lines(all_23_4, all_23_3) = all_142_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  (all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | (all_85_1 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_2) = 0)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_85_0 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (386) are inconsistent by
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)  all_85_1 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (388) are inconsistent by
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)  ( ~ (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_85_2) | ( ~ (all_85_3 = 0) &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_3) = all_85_3)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (390)   ~ (all_85_2 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = all_85_2
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (391)   ~ (all_85_2 = 0)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (392)  unorthogonal_lines(all_23_3, all_23_3) = all_85_2
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_85_2, all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, simplifying with (376), (392) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (393)  all_85_2 = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (393) imply:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (394)  $false
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (394) is inconsistent.
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_30_3, all_142_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (289), (383)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (395)  all_142_3 = all_30_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_88_3, all_142_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, all_23_4, simplifying with (375), (383)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (396)  all_142_3 = all_88_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (396) imply:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (397)  all_88_3 = all_30_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (398)  all_88_3 = all_30_3
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_23_2, all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, 0, all_30_3, simplifying with (21),
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (22), (23), (289), (364) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (399)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & all_30_3 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v2 = 0 & unorthogonal_lines(all_23_2, all_23_3)
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = 0) | ( ~ (v1 = 0) &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_4) = v1) |
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ( ~ (v0 = 0) & convergent_lines(all_23_2,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_4) = v0))
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_23_2, all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3, 0, 0, simplifying with (21), (22), (23),
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (25), (364) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (400)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & convergent_lines(all_23_4,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_3) = 0) | (v2 = 0 &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = 0) |
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ( ~ (v1 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_4) = v1) | ( ~ (v0 = 0) &
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              convergent_lines(all_23_2, all_23_4) = v0))
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_36_3, simplifying with (21), (22),
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (23), (363), (364) gives:
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (401)  all_36_3 = 0 | convergent_lines(all_23_2,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = 0
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_23_2, all_23_3,
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_0, simplifying with (22), (23),
% 21.46/4.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (26), (364) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (402)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ?
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: int] : ((v3 = 0 & all_23_0 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              convergent_lines(all_23_3, all_23_2) = 0) |
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (v2 = 0 & v1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_2) = 0 & convergent_lines(all_23_2,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_23_2) = 0) | ( ~ (v0 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              unorthogonal_lines(all_23_2, all_23_3) = v0))
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (400) with fresh symbols all_223_0,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_223_1, all_223_2, all_223_3 gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (403)  (all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | (all_223_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0) | (
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_223_2) | ( ~ (all_223_3 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_223_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (402) with fresh symbols all_233_0,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_233_1, all_233_2, all_233_3 gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (404)  (all_233_0 = 0 & all_23_0 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_3, all_23_2) = 0) |
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_233_1 = 0 & all_233_2 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_233_3 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = all_233_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (399) with fresh symbols all_237_0,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_237_1, all_237_2, all_237_3 gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (405)  (all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_237_2 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_4) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_237_2) | ( ~ (all_237_3 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_237_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (406)  convergent_lines(all_23_2, all_23_4) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (407)  all_71_0 = 0 & all_71_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (408)  convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (408) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (409)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (409) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (410)  (all_71_2 = 0 & all_23_0 = 0) | ( ~ (all_71_3 = 0)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & unorthogonal_lines(all_23_3, all_23_2) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_71_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (411)  all_71_2 = 0 & all_23_0 = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (412)  all_23_0 = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (412) imply:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (413)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (414)   ~ (all_71_3 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_71_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (415)   ~ (all_71_3 = 0)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (416)  unorthogonal_lines(all_23_3, all_23_2) = all_71_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_23_0, all_71_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_3, simplifying with (26), (416)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (417)  all_71_3 = all_23_0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (418)  all_77_0 = 0 & all_77_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (419)  convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (419) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (420)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (421)  (all_77_2 = 0 & all_23_1 = 0) | ( ~ (all_77_3 = 0)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & convergent_lines(all_23_4, all_23_2) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_77_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (422)  all_77_2 = 0 & all_23_1 = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (423)  all_23_1 = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (423) imply:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (424)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (424) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (425)   ~ (all_77_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_77_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)  convergent_lines(all_23_4, all_23_2) = all_77_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_77_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (24), (426)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)  all_77_3 = all_23_1
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)  all_79_0 = 0 & all_79_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (428) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (429), (apart3) are
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  (all_79_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | ( ~ (all_79_3 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_79_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  all_79_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  convergent_lines(all_23_4, all_23_3) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (432) are inconsistent by
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #4.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)   ~ (all_79_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_79_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)   ~ (all_79_3 = 0)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  convergent_lines(all_23_4, all_23_2) = all_79_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_79_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (24), (435)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_79_3 = all_23_1
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  all_80_0 = 0 & all_80_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (438) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  (all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_80_3 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_3, all_23_2) =
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_80_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_80_2 = 0 & unorthogonal_lines(all_23_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (26), (442) are inconsistent by
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #6.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)   ~ (all_80_3 = 0) & unorthogonal_lines(all_23_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_80_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)   ~ (all_80_3 = 0)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  unorthogonal_lines(all_23_3, all_23_2) = all_80_3
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_23_0, all_80_3,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_3, simplifying with (26), (445)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_80_3 = all_23_0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_84_0 = 0 & all_84_1 = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_2) = 0 &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (448) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  $false
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent.
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  (all_84_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = 0) | ( ~ (all_84_3 = 0) &
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_4, all_23_2) = all_84_3)
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_84_2 = 0 & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  convergent_lines(all_23_4, all_23_2) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (24), (452) are inconsistent by
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #5.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)   ~ (all_84_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_84_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (453) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  convergent_lines(all_23_4, all_23_2) = all_84_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_84_3,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (24), (454)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  all_84_3 = all_23_1
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_89_0 = 0 & all_89_1 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_4) = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_4) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  unorthogonal_lines(all_23_2, all_23_4) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  (all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0) | (all_223_1 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_2, all_23_3) = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_223_0 = 0 & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  convergent_lines(all_23_4, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (55), (90), (460) are inconsistent by
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #4.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  all_223_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (461) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (462), (apart3) are
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  ( ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_223_2) | ( ~ (all_223_3 = 0) &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_223_3)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)   ~ (all_223_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_223_2
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)   ~ (all_223_2 = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  unorthogonal_lines(all_23_2, all_23_4) = all_223_2
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_223_2, all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, simplifying with (457), (466) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_223_2 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (465), (467) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_223_3 = 0) & convergent_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_223_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)   ~ (all_223_3 = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  convergent_lines(all_23_2, all_23_4) = all_223_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (405) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  (all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) |
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_3) = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  all_237_0 = 0 & all_30_3 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  all_30_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (474) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (475) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  all_237_1 = 0 & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (477), (apart3) are
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  ( ~ (all_237_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4) = all_237_2) | ( ~ (all_237_3 = 0) &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            convergent_lines(all_23_2, all_23_4) =
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_237_3)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)   ~ (all_237_2 = 0) & unorthogonal_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_237_2
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)   ~ (all_237_2 = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  unorthogonal_lines(all_23_2, all_23_4) = all_237_2
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_237_2, all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, simplifying with (457), (481) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_237_2 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (480), (482) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (483) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)   ~ (all_237_3 = 0) & convergent_lines(all_23_2,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_4) = all_237_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  convergent_lines(all_23_2, all_23_4) = all_237_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_237_3, all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, simplifying with (406), (485) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_237_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_223_3, all_237_3,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_4, all_23_2, simplifying with (471), (485)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_237_3 = all_223_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (486), (487) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_223_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (488) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (489) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  (all_89_2 = 0 & all_51_0 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_4) = 0) | (
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = all_89_3)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_89_2 = 0 & all_51_0 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_4) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_51_0 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (492) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_31_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_31_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (494) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (495) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)   ~ (all_89_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_89_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  convergent_lines(all_23_4, all_23_2) = all_89_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_89_3,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (24), (497)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_89_3 = all_23_1
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_90_0 = 0 & all_90_1 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_2, all_23_3) = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          convergent_lines(all_23_2, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (23), (404), (500), (apart3) are
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  (all_90_2 = 0 & all_32_3 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            unorthogonal_lines(all_23_4, all_23_3) = 0) | (
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2) = all_90_3)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_90_2 = 0 & all_32_3 = 0 &
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          unorthogonal_lines(all_23_4, all_23_3) = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_32_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (503) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  all_30_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_30_3 = 0
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (505) imply:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  $false
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)   ~ (all_90_3 = 0) & convergent_lines(all_23_4,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = all_90_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (507) implies:
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)   ~ (all_90_3 = 0)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  convergent_lines(all_23_4, all_23_2) = all_90_3
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_23_1, all_90_3,
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_4, simplifying with (24), (509)
% 21.46/4.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_90_3 = all_23_1
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_2, all_23_4,
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_23_2, all_23_1, simplifying with (21), (23),
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24), (406) gives:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  all_23_1 = 0 | convergent_lines(all_23_2,
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_23_2) = 0
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  convergent_lines(all_23_2, all_23_2) = 0
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_2, simplifying
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (23), (512) gives:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  $false
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (513) is inconsistent.
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_23_1 = 0
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.46/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (514) imply:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  $false
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent.
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  all_36_3 = 0
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (516) imply:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  $false
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (517) is inconsistent.
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_34_3 = 0
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (518) imply:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  $false
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_34_3 = 0
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (520) imply:
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  $false
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent.
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | Case 2:
% 21.64/4.06  | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | |   (522)  all_51_0 = 0
% 21.64/4.06  | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | REDUCE: (60), (522) imply:
% 21.64/4.06  | | | | | | | | | | |   (523)  $false
% 21.64/4.06  | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | | CLOSE: (523) is inconsistent.
% 21.64/4.06  | | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | | 
% 21.64/4.06  | | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | | 
% 21.64/4.06  | | | | | | | | End of split
% 21.64/4.06  | | | | | | | | 
% 21.64/4.06  | | | | | | | End of split
% 21.64/4.06  | | | | | | | 
% 21.64/4.06  | | | | | | End of split
% 21.64/4.06  | | | | | | 
% 21.64/4.06  | | | | | End of split
% 21.64/4.06  | | | | | 
% 21.64/4.06  | | | | End of split
% 21.64/4.06  | | | | 
% 21.64/4.06  | | | End of split
% 21.64/4.06  | | | 
% 21.64/4.06  | | Case 2:
% 21.64/4.06  | | | 
% 21.64/4.06  | | |   (524)  all_23_0 = 0
% 21.64/4.06  | | | 
% 21.64/4.06  | | | REDUCE: (20), (524) imply:
% 21.64/4.06  | | |   (525)  $false
% 21.64/4.06  | | | 
% 21.64/4.06  | | | CLOSE: (525) is inconsistent.
% 21.64/4.06  | | | 
% 21.64/4.06  | | End of split
% 21.64/4.06  | | 
% 21.64/4.06  | Case 2:
% 21.64/4.06  | | 
% 21.64/4.06  | |   (526)  all_23_1 = 0
% 21.64/4.06  | | 
% 21.64/4.06  | | REDUCE: (19), (526) imply:
% 21.64/4.06  | |   (527)  $false
% 21.64/4.06  | | 
% 21.64/4.06  | | CLOSE: (527) is inconsistent.
% 21.64/4.06  | | 
% 21.64/4.06  | End of split
% 21.64/4.06  | 
% 21.64/4.06  End of proof
% 21.64/4.06  
% 21.64/4.06  Sub-proof #1 shows that the following formulas are inconsistent:
% 21.64/4.06  ----------------------------------------------------------------
% 21.64/4.06    (1)  unorthogonal_lines(all_23_2, all_23_3) = 0
% 21.64/4.06    (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.06         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 21.64/4.06           (unorthogonal_lines(v3, v2) = v0))
% 21.64/4.06    (3)   ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) |  ~ $i(v0))
% 21.64/4.06    (4)  (all_233_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) = 0)
% 21.64/4.06         | (all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2, all_23_2)
% 21.64/4.06           = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~ (all_233_3 = 0) &
% 21.64/4.06           unorthogonal_lines(all_23_2, all_23_3) = all_233_3)
% 21.64/4.06    (5)   ~ (all_23_0 = 0)
% 21.64/4.06    (6)  $i(all_23_2)
% 21.64/4.06  
% 21.64/4.06  Begin of proof
% 21.64/4.06  | 
% 21.64/4.06  | BETA: splitting (4) gives:
% 21.64/4.06  | 
% 21.64/4.06  | Case 1:
% 21.64/4.06  | | 
% 21.64/4.06  | |   (7)  all_233_0 = 0 & all_23_0 = 0 & convergent_lines(all_23_3, all_23_2) =
% 21.64/4.06  | |        0
% 21.64/4.06  | | 
% 21.64/4.06  | | ALPHA: (7) implies:
% 21.64/4.06  | |   (8)  all_23_0 = 0
% 21.64/4.06  | | 
% 21.64/4.06  | | REDUCE: (5), (8) imply:
% 21.64/4.06  | |   (9)  $false
% 21.64/4.06  | | 
% 21.64/4.06  | | CLOSE: (9) is inconsistent.
% 21.64/4.06  | | 
% 21.64/4.06  | Case 2:
% 21.64/4.06  | | 
% 21.64/4.06  | |   (10)  (all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2,
% 21.64/4.06  | |             all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0) | ( ~
% 21.64/4.06  | |           (all_233_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 21.64/4.06  | |           all_233_3)
% 21.64/4.06  | | 
% 21.64/4.06  | | BETA: splitting (10) gives:
% 21.64/4.06  | | 
% 21.64/4.06  | | Case 1:
% 21.64/4.06  | | | 
% 21.64/4.06  | | |   (11)  all_233_1 = 0 & all_233_2 = 0 & unorthogonal_lines(all_23_2,
% 21.64/4.06  | | |           all_23_2) = 0 & convergent_lines(all_23_2, all_23_2) = 0
% 21.64/4.06  | | | 
% 21.64/4.06  | | | ALPHA: (11) implies:
% 21.64/4.06  | | |   (12)  convergent_lines(all_23_2, all_23_2) = 0
% 21.64/4.06  | | | 
% 21.64/4.06  | | | GROUND_INST: instantiating (3) with all_23_2, simplifying with (6), (12)
% 21.64/4.06  | | |              gives:
% 21.64/4.06  | | |   (13)  $false
% 21.64/4.06  | | | 
% 21.64/4.06  | | | CLOSE: (13) is inconsistent.
% 21.64/4.06  | | | 
% 21.64/4.06  | | Case 2:
% 21.64/4.06  | | | 
% 21.64/4.06  | | |   (14)   ~ (all_233_3 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 21.64/4.06  | | |         all_233_3
% 21.64/4.06  | | | 
% 21.64/4.06  | | | ALPHA: (14) implies:
% 21.64/4.06  | | |   (15)   ~ (all_233_3 = 0)
% 21.64/4.06  | | |   (16)  unorthogonal_lines(all_23_2, all_23_3) = all_233_3
% 21.64/4.06  | | | 
% 21.64/4.06  | | | GROUND_INST: instantiating (2) with 0, all_233_3, all_23_3, all_23_2,
% 21.64/4.06  | | |              simplifying with (1), (16) gives:
% 21.64/4.06  | | |   (17)  all_233_3 = 0
% 21.64/4.06  | | | 
% 21.64/4.06  | | | REDUCE: (15), (17) imply:
% 21.64/4.06  | | |   (18)  $false
% 21.64/4.06  | | | 
% 21.64/4.06  | | | CLOSE: (18) is inconsistent.
% 21.64/4.06  | | | 
% 21.64/4.06  | | End of split
% 21.64/4.06  | | 
% 21.64/4.06  | End of split
% 21.64/4.06  | 
% 21.64/4.06  End of proof
% 21.64/4.06  
% 21.64/4.06  Sub-proof #2 shows that the following formulas are inconsistent:
% 21.64/4.06  ----------------------------------------------------------------
% 21.64/4.06    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.06         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 21.64/4.06           (convergent_lines(v3, v2) = v0))
% 21.64/4.06    (2)  convergent_lines(all_23_3, all_23_4) = all_36_3
% 21.64/4.06    (3)  convergent_lines(all_23_3, all_23_4) = 0
% 21.64/4.06    (4)   ~ (all_36_3 = 0)
% 21.64/4.06  
% 21.64/4.06  Begin of proof
% 21.64/4.06  | 
% 21.64/4.06  | GROUND_INST: instantiating (1) with 0, all_36_3, all_23_4, all_23_3,
% 21.64/4.06  |              simplifying with (2), (3) gives:
% 21.64/4.06  |   (5)  all_36_3 = 0
% 21.64/4.06  | 
% 21.64/4.06  | REDUCE: (4), (5) imply:
% 21.64/4.06  |   (6)  $false
% 21.64/4.06  | 
% 21.64/4.06  | CLOSE: (6) is inconsistent.
% 21.64/4.06  | 
% 21.64/4.06  End of proof
% 21.64/4.06  
% 21.64/4.06  Sub-proof #3 shows that the following formulas are inconsistent:
% 21.64/4.06  ----------------------------------------------------------------
% 21.64/4.06    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.06         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 21.64/4.06           (convergent_lines(v3, v2) = v0))
% 21.64/4.06    (2)  convergent_lines(all_23_4, all_23_4) = all_31_3
% 21.64/4.06    (3)  convergent_lines(all_23_4, all_23_4) = 0
% 21.64/4.06    (4)   ~ (all_31_3 = 0)
% 21.64/4.06  
% 21.64/4.06  Begin of proof
% 21.64/4.06  | 
% 21.64/4.06  | GROUND_INST: instantiating (1) with all_31_3, 0, all_23_4, all_23_4,
% 21.64/4.06  |              simplifying with (2), (3) gives:
% 21.64/4.06  |   (5)  all_31_3 = 0
% 21.64/4.06  | 
% 21.64/4.06  | REDUCE: (4), (5) imply:
% 21.64/4.06  |   (6)  $false
% 21.64/4.06  | 
% 21.64/4.06  | CLOSE: (6) is inconsistent.
% 21.64/4.06  | 
% 21.64/4.06  End of proof
% 21.64/4.06  
% 21.64/4.06  Sub-proof #4 shows that the following formulas are inconsistent:
% 21.64/4.06  ----------------------------------------------------------------
% 21.64/4.06    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.06         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 21.64/4.06           (convergent_lines(v3, v2) = v0))
% 21.64/4.06    (2)  convergent_lines(all_23_4, all_23_3) = all_32_3
% 21.64/4.06    (3)  convergent_lines(all_23_4, all_23_3) = 0
% 21.64/4.06    (4)   ~ (all_32_3 = 0)
% 21.64/4.06  
% 21.64/4.06  Begin of proof
% 21.64/4.06  | 
% 21.64/4.06  | GROUND_INST: instantiating (1) with all_32_3, 0, all_23_3, all_23_4,
% 21.64/4.06  |              simplifying with (2), (3) gives:
% 21.64/4.06  |   (5)  all_32_3 = 0
% 21.64/4.07  | 
% 21.64/4.07  | REDUCE: (4), (5) imply:
% 21.64/4.07  |   (6)  $false
% 21.64/4.07  | 
% 21.64/4.07  | CLOSE: (6) is inconsistent.
% 21.64/4.07  | 
% 21.64/4.07  End of proof
% 21.64/4.07  
% 21.64/4.07  Sub-proof #5 shows that the following formulas are inconsistent:
% 21.64/4.07  ----------------------------------------------------------------
% 21.64/4.07    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.07         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 21.64/4.07           (convergent_lines(v3, v2) = v0))
% 21.64/4.07    (2)  convergent_lines(all_23_4, all_23_2) = all_23_1
% 21.64/4.07    (3)  convergent_lines(all_23_4, all_23_2) = 0
% 21.64/4.07    (4)   ~ (all_23_1 = 0)
% 21.64/4.07  
% 21.64/4.07  Begin of proof
% 21.64/4.07  | 
% 21.64/4.07  | GROUND_INST: instantiating (1) with all_23_1, 0, all_23_2, all_23_4,
% 21.64/4.07  |              simplifying with (2), (3) gives:
% 21.64/4.07  |   (5)  all_23_1 = 0
% 21.64/4.07  | 
% 21.64/4.07  | REDUCE: (4), (5) imply:
% 21.64/4.07  |   (6)  $false
% 21.64/4.07  | 
% 21.64/4.07  | CLOSE: (6) is inconsistent.
% 21.64/4.07  | 
% 21.64/4.07  End of proof
% 21.64/4.07  
% 21.64/4.07  Sub-proof #6 shows that the following formulas are inconsistent:
% 21.64/4.07  ----------------------------------------------------------------
% 21.64/4.07    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.64/4.07         ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~
% 21.64/4.07           (unorthogonal_lines(v3, v2) = v0))
% 21.64/4.07    (2)  unorthogonal_lines(all_23_3, all_23_2) = all_23_0
% 21.64/4.07    (3)  unorthogonal_lines(all_23_3, all_23_2) = 0
% 21.64/4.07    (4)   ~ (all_23_0 = 0)
% 21.64/4.07  
% 21.64/4.07  Begin of proof
% 21.64/4.07  | 
% 21.64/4.07  | GROUND_INST: instantiating (1) with all_23_0, 0, all_23_2, all_23_3,
% 21.64/4.07  |              simplifying with (2), (3) gives:
% 21.64/4.07  |   (5)  all_23_0 = 0
% 21.64/4.07  | 
% 21.64/4.07  | REDUCE: (4), (5) imply:
% 21.64/4.07  |   (6)  $false
% 21.64/4.07  | 
% 21.64/4.07  | CLOSE: (6) is inconsistent.
% 21.64/4.07  | 
% 21.64/4.07  End of proof
% 21.64/4.07  % SZS output end Proof for theBenchmark
% 21.64/4.07  
% 21.64/4.07  3451ms
%------------------------------------------------------------------------------