%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO188+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n021.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 23:22:01 EDT 2023

% Result   : Theorem 15.91s 2.87s
% Output   : Proof 26.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO188+1 : 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 : n021.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 22:40:14 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.59  ________       _____
% 0.20/0.59  ___  __ \_________(_)________________________________
% 0.20/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59  (2023-06-19)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2023
% 0.20/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59                Amanda Stjerna.
% 0.20/0.59  Free software under BSD-3-Clause.
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.34/1.06  Prover 4: Preprocessing ...
% 2.34/1.07  Prover 1: Preprocessing ...
% 2.86/1.10  Prover 0: Preprocessing ...
% 2.86/1.10  Prover 5: Preprocessing ...
% 2.86/1.10  Prover 3: Preprocessing ...
% 2.86/1.10  Prover 6: Preprocessing ...
% 2.86/1.10  Prover 2: Preprocessing ...
% 4.28/1.34  Prover 2: Proving ...
% 4.28/1.34  Prover 5: Proving ...
% 4.28/1.36  Prover 6: Constructing countermodel ...
% 4.28/1.36  Prover 3: Constructing countermodel ...
% 4.28/1.36  Prover 1: Constructing countermodel ...
% 5.25/1.47  Prover 3: gave up
% 5.25/1.47  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.25/1.47  Prover 1: gave up
% 5.25/1.48  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.25/1.48  Prover 4: Constructing countermodel ...
% 5.25/1.50  Prover 7: Preprocessing ...
% 5.93/1.51  Prover 6: gave up
% 5.93/1.52  Prover 8: Preprocessing ...
% 5.93/1.52  Prover 0: Proving ...
% 5.93/1.53  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.93/1.54  Prover 7: Warning: ignoring some quantifiers
% 5.93/1.55  Prover 7: Constructing countermodel ...
% 5.93/1.55  Prover 9: Preprocessing ...
% 6.49/1.60  Prover 8: Warning: ignoring some quantifiers
% 6.49/1.62  Prover 8: Constructing countermodel ...
% 7.16/1.68  Prover 8: gave up
% 7.23/1.69  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.38/1.71  Prover 10: Preprocessing ...
% 7.38/1.72  Prover 7: gave up
% 7.38/1.72  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.38/1.73  Prover 9: Constructing countermodel ...
% 7.38/1.74  Prover 11: Preprocessing ...
% 7.38/1.76  Prover 10: Warning: ignoring some quantifiers
% 7.38/1.76  Prover 10: Constructing countermodel ...
% 7.75/1.83  Prover 10: gave up
% 7.75/1.83  Prover 12: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 7.75/1.87  Prover 12: Preprocessing ...
% 8.63/1.91  Prover 11: Constructing countermodel ...
% 9.29/2.02  Prover 12: Proving ...
% 15.91/2.86  Prover 9: proved (1337ms)
% 15.91/2.86  
% 15.91/2.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.91/2.87  
% 15.91/2.87  Prover 12: stopped
% 15.91/2.87  Prover 0: stopped
% 15.91/2.87  Prover 2: stopped
% 15.91/2.87  Prover 5: stopped
% 15.91/2.87  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.91/2.87  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.91/2.87  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 15.91/2.88  Prover 16: Preprocessing ...
% 15.91/2.88  Prover 13: Preprocessing ...
% 15.91/2.89  Prover 19: Preprocessing ...
% 15.91/2.91  Prover 16: Warning: ignoring some quantifiers
% 15.91/2.91  Prover 13: Warning: ignoring some quantifiers
% 15.91/2.91  Prover 16: Constructing countermodel ...
% 15.91/2.91  Prover 13: Constructing countermodel ...
% 16.48/2.95  Prover 19: Warning: ignoring some quantifiers
% 16.48/2.96  Prover 19: Constructing countermodel ...
% 16.48/2.99  Prover 19: gave up
% 16.48/3.00  Prover 13: gave up
% 17.08/3.08  Prover 16: gave up
% 25.68/4.62  Prover 4: Found proof (size 580)
% 25.68/4.62  Prover 4: proved (3999ms)
% 25.68/4.63  Prover 11: stopped
% 25.68/4.63  
% 25.68/4.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.68/4.63  
% 25.90/4.68  % SZS output start Proof for theBenchmark
% 25.90/4.69  Assumptions after simplification:
% 25.90/4.69  ---------------------------------
% 25.90/4.69  
% 25.90/4.69    (apart1)
% 26.24/4.75     ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) |  ~ $i(v0))
% 26.24/4.75  
% 26.24/4.75    (apart4)
% 26.24/4.76     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 26.24/4.76      0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2)
% 26.24/4.76        = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 = 0) &
% 26.24/4.76        distinct_points(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 26.24/4.76     ! [v3: int] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~
% 26.24/4.76      (distinct_points(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 26.24/4.76      distinct_points(v0, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 26.24/4.77    [v3: int] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~
% 26.24/4.77      (distinct_points(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 26.24/4.77      distinct_points(v1, v2) = 0)
% 26.24/4.77  
% 26.24/4.77    (ceq2)
% 26.24/4.77     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 26.24/4.77      0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1,
% 26.24/4.77          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 =
% 26.24/4.77          0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] : 
% 26.24/4.77    ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |
% 26.24/4.77       ~ (apart_point_and_line(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 26.24/4.77      distinct_lines(v1, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 26.24/4.77    [v3: int] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~
% 26.24/4.77      (distinct_lines(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 26.24/4.77      apart_point_and_line(v0, v2) = 0)
% 26.24/4.77  
% 26.24/4.77    (ci1)
% 26.24/4.78     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 26.24/4.78       ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 26.24/4.78      (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 26.24/4.78            = 0) |  ~ (v3 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 26.24/4.78      (distinct_points(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ?
% 26.24/4.78      [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 26.24/4.78        apart_point_and_line(v0, v2) = v3 & $i(v2)))
% 26.24/4.78  
% 26.24/4.78    (ci2)
% 26.24/4.78     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 26.24/4.78       ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 26.24/4.78      (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 26.24/4.78            = 0) |  ~ (v3 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 26.24/4.78      (distinct_points(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ?
% 26.24/4.78      [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 26.24/4.78        apart_point_and_line(v1, v2) = v3 & $i(v2)))
% 26.24/4.78  
% 26.37/4.78    (con)
% 26.37/4.79     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] :  ? [v5:
% 26.37/4.79      $i] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1)
% 26.37/4.79      = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, v5) = 0
% 26.37/4.79      & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 &
% 26.37/4.79      distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 26.37/4.79  
% 26.37/4.79    (cu1)
% 26.37/4.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5:
% 26.37/4.80      int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~
% 26.37/4.80      (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ~
% 26.37/4.80      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: any] : 
% 26.37/4.80      ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 26.37/4.80          v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 26.37/4.80          0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 26.37/4.80      int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) =
% 26.37/4.80        v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3)
% 26.37/4.80        = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ?
% 26.37/4.80      [v7: any] :  ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 26.37/4.80        apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 26.37/4.80            = 0) | v8 = 0 | v7 = 0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 26.37/4.80    ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~
% 26.37/4.80      (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4)
% 26.37/4.80      |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7:
% 26.37/4.80        any] :  ? [v8: any] :  ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 26.37/4.80        apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 26.37/4.80        distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 =
% 26.37/4.80          0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 26.37/4.80      int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) =
% 26.37/4.80        v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 26.37/4.80      $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: any] :  ? [v8: any] :  ? [v9:
% 26.37/4.80        any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 26.37/4.80        v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 26.37/4.80            = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [v0: $i] :  ! [v1: $i] : 
% 26.37/4.80    ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~
% 26.37/4.80      (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4)
% 26.37/4.80      |  ~ (distinct_lines(v2, v3) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 26.37/4.80      $i(v0) |  ? [v6: any] :  ? [v7: any] :  ? [v8: any] :
% 26.37/4.80      (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 26.37/4.80        distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0:
% 26.37/4.80      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int]
% 26.37/4.80    : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~
% 26.37/4.80      (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ~
% 26.37/4.80      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: any] : 
% 26.37/4.80      ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 26.37/4.80          v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 26.37/4.80          0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 26.37/4.80      (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ~ $i(v3)
% 26.37/4.80      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :  ? [v6:
% 26.37/4.80        any] :  ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 26.37/4.80        apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 26.37/4.80        apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 26.37/4.80  
% 26.37/4.80    (function-axioms)
% 26.37/4.80     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 26.37/4.80      (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) & 
% 26.37/4.80    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 26.37/4.80      (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  !
% 26.37/4.80    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 26.37/4.80      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 26.37/4.80      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 26.37/4.80      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 26.37/4.80      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 26.37/4.80    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 26.37/4.80      $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3,
% 26.37/4.80          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 26.37/4.80    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 26.37/4.80      (distinct_points(v3, v2) = v0))
% 26.37/4.80  
% 26.37/4.80  Further assumptions not needed in the proof:
% 26.37/4.80  --------------------------------------------
% 26.37/4.80  apart2, apart3, apart5, ax6, ceq1, ceq3, ci3, ci4
% 26.37/4.80  
% 26.37/4.80  Those formulas are unsatisfiable:
% 26.37/4.80  ---------------------------------
% 26.37/4.80  
% 26.37/4.80  Begin of proof
% 26.37/4.80  | 
% 26.37/4.80  | ALPHA: (apart4) implies:
% 26.37/4.80  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 26.37/4.80  |          (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | 
% 26.37/4.80  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | distinct_points(v0, v2) = 0)
% 26.37/4.80  | 
% 26.37/4.80  | ALPHA: (ci1) implies:
% 26.37/4.80  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) |  ~
% 26.37/4.81  |          $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 26.37/4.81  |            line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 26.37/4.81  |            $i(v2)))
% 26.37/4.81  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 26.37/4.81  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 26.37/4.81  |          (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 26.37/4.81  |              ~ (v4 = 0) |  ~ (v3 = 0))))
% 26.37/4.81  | 
% 26.37/4.81  | ALPHA: (ci2) implies:
% 26.37/4.81  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) |  ~
% 26.37/4.81  |          $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 26.37/4.81  |            line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 26.37/4.81  |            $i(v2)))
% 26.37/4.81  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 26.37/4.81  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 26.37/4.81  |          (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 26.37/4.81  |              ~ (v4 = 0) |  ~ (v3 = 0))))
% 26.37/4.81  | 
% 26.37/4.81  | ALPHA: (cu1) implies:
% 26.37/4.81  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : 
% 26.37/4.81  |        ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5)
% 26.37/4.81  |          |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0,
% 26.37/4.81  |              v1) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 26.37/4.81  |          [v6: any] :  ? [v7: any] :  ? [v8: any] : (apart_point_and_line(v1,
% 26.37/4.81  |              v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2,
% 26.37/4.81  |              v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 26.37/4.81  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : 
% 26.37/4.81  |        ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5)
% 26.37/4.81  |          |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 26.37/4.81  |          $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: any] :  ? [v8: any] :  ?
% 26.37/4.81  |          [v9: any] : (apart_point_and_line(v1, v3) = v9 &
% 26.37/4.81  |            apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 &
% 26.37/4.81  |            distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0
% 26.37/4.81  |              | v8 = 0)))
% 26.37/4.81  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : 
% 26.37/4.81  |        ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5)
% 26.37/4.81  |          |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 26.37/4.81  |          $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: any] :  ? [v8: any] :  ?
% 26.37/4.81  |          [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 26.37/4.81  |            apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 26.37/4.81  |            distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0
% 26.37/4.81  |              | v8 = 0)))
% 26.37/4.82  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : 
% 26.37/4.82  |        ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5)
% 26.37/4.82  |          |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0,
% 26.37/4.82  |              v1) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 26.37/4.82  |          [v6: any] :  ? [v7: any] :  ? [v8: any] : (apart_point_and_line(v0,
% 26.37/4.82  |              v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2,
% 26.37/4.82  |              v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 26.37/4.82  | 
% 26.37/4.82  | ALPHA: (ceq2) implies:
% 26.37/4.82  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 26.37/4.82  |           (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0,
% 26.37/4.82  |               v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 26.37/4.82  |           distinct_lines(v1, v2) = 0)
% 26.37/4.82  | 
% 26.37/4.82  | ALPHA: (function-axioms) implies:
% 26.37/4.82  |   (11)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 26.37/4.82  |         :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 26.37/4.82  |           (distinct_points(v3, v2) = v0))
% 26.37/4.82  |   (12)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 26.37/4.82  |         :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~
% 26.37/4.82  |           (distinct_lines(v3, v2) = v0))
% 26.37/4.82  |   (13)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 26.37/4.82  |         :  ! [v3: $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 26.37/4.82  |           (apart_point_and_line(v3, v2) = v0))
% 26.37/4.82  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 26.37/4.82  |           (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 26.37/4.82  | 
% 26.37/4.82  | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 26.37/4.82  |        all_17_3, all_17_4, all_17_5 gives:
% 26.37/4.82  |   (15)   ~ (all_17_1 = 0) & line_connecting(all_17_3, all_17_4) = all_17_0 &
% 26.37/4.82  |         line_connecting(all_17_5, all_17_4) = all_17_2 &
% 26.37/4.82  |         apart_point_and_line(all_17_3, all_17_2) = all_17_1 &
% 26.37/4.82  |         apart_point_and_line(all_17_5, all_17_0) = 0 &
% 26.37/4.82  |         distinct_points(all_17_4, all_17_3) = 0 & distinct_points(all_17_5,
% 26.37/4.82  |           all_17_3) = 0 & distinct_points(all_17_5, all_17_4) = 0 &
% 26.37/4.82  |         $i(all_17_0) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) &
% 26.37/4.82  |         $i(all_17_5)
% 26.37/4.82  | 
% 26.37/4.82  | ALPHA: (15) implies:
% 26.37/4.82  |   (16)   ~ (all_17_1 = 0)
% 26.37/4.82  |   (17)  $i(all_17_5)
% 26.37/4.82  |   (18)  $i(all_17_4)
% 26.37/4.82  |   (19)  $i(all_17_3)
% 26.37/4.82  |   (20)  $i(all_17_2)
% 26.37/4.82  |   (21)  $i(all_17_0)
% 26.37/4.82  |   (22)  distinct_points(all_17_5, all_17_4) = 0
% 26.37/4.82  |   (23)  distinct_points(all_17_5, all_17_3) = 0
% 26.37/4.82  |   (24)  distinct_points(all_17_4, all_17_3) = 0
% 26.37/4.82  |   (25)  apart_point_and_line(all_17_5, all_17_0) = 0
% 26.37/4.82  |   (26)  apart_point_and_line(all_17_3, all_17_2) = all_17_1
% 26.37/4.82  |   (27)  line_connecting(all_17_5, all_17_4) = all_17_2
% 26.37/4.82  |   (28)  line_connecting(all_17_3, all_17_4) = all_17_0
% 26.37/4.82  | 
% 26.37/4.82  | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (17),
% 26.37/4.82  |              (18), (22) gives:
% 26.37/4.82  |   (29)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 26.37/4.82  |             all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0))
% 26.37/4.82  | 
% 26.37/4.83  | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (17),
% 26.37/4.83  |              (18), (22) gives:
% 26.37/4.83  |   (30)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 26.37/4.83  |             all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (4) with all_17_5, all_17_3, simplifying with (17),
% 26.37/4.83  |              (19), (23) gives:
% 26.37/4.83  |   (31)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 26.37/4.83  |             all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (2) with all_17_5, all_17_3, simplifying with (17),
% 26.37/4.83  |              (19), (23) gives:
% 26.37/4.83  |   (32)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 26.37/4.83  |             all_17_3) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (4) with all_17_4, all_17_3, simplifying with (18),
% 26.37/4.83  |              (19), (24) gives:
% 26.37/4.83  |   (33)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4,
% 26.37/4.83  |             all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (2) with all_17_4, all_17_3, simplifying with (18),
% 26.37/4.83  |              (19), (24) gives:
% 26.37/4.83  |   (34)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4,
% 26.37/4.83  |             all_17_3) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (9) with all_17_4, all_17_3, all_17_2, all_17_2,
% 26.37/4.83  |              all_17_1, all_17_1, simplifying with (18), (19), (20), (24), (26)
% 26.37/4.83  |              gives:
% 26.37/4.83  |   (35)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.37/4.83  |         (apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.37/4.83  |           apart_point_and_line(all_17_4, all_17_2) = v1 &
% 26.37/4.83  |           distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 26.37/4.83  |             = 0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (9) with all_17_5, all_17_3, all_17_2, all_17_2,
% 26.37/4.83  |              all_17_1, all_17_1, simplifying with (17), (19), (20), (23), (26)
% 26.37/4.83  |              gives:
% 26.37/4.83  |   (36)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.37/4.83  |         (apart_point_and_line(all_17_5, all_17_2) = v2 &
% 26.37/4.83  |           apart_point_and_line(all_17_5, all_17_2) = v1 &
% 26.37/4.83  |           distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 26.37/4.83  |             = 0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (8) with all_17_3, all_17_3, all_17_2, all_17_2,
% 26.37/4.83  |              all_17_1, all_17_1, simplifying with (19), (20), (26) gives:
% 26.37/4.83  |   (37)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3:
% 26.37/4.83  |           any] : (apart_point_and_line(all_17_3, all_17_2) = v3 &
% 26.37/4.83  |           apart_point_and_line(all_17_3, all_17_2) = v2 &
% 26.37/4.83  |           distinct_lines(all_17_2, all_17_2) = v1 & distinct_points(all_17_3,
% 26.37/4.83  |             all_17_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying
% 26.37/4.83  |              with (17), (18), (27) gives:
% 26.37/4.83  |   (38)   ? [v0: any] :  ? [v1: any] : (apart_point_and_line(all_17_4,
% 26.37/4.83  |             all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~
% 26.37/4.83  |             (v1 = 0) |  ~ (v0 = 0)))
% 26.37/4.83  | 
% 26.37/4.83  | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying
% 26.37/4.84  |              with (17), (18), (27) gives:
% 26.37/4.84  |   (39)   ? [v0: any] :  ? [v1: any] : (apart_point_and_line(all_17_5,
% 26.37/4.84  |             all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~
% 26.37/4.84  |             (v1 = 0) |  ~ (v0 = 0)))
% 26.37/4.84  | 
% 26.37/4.84  | GROUND_INST: instantiating (5) with all_17_3, all_17_4, all_17_0, simplifying
% 26.37/4.84  |              with (18), (19), (28) gives:
% 26.37/4.84  |   (40)   ? [v0: any] :  ? [v1: any] : (apart_point_and_line(all_17_4,
% 26.37/4.84  |             all_17_0) = v1 & distinct_points(all_17_3, all_17_4) = v0 & ( ~
% 26.37/4.84  |             (v1 = 0) |  ~ (v0 = 0)))
% 26.37/4.84  | 
% 26.37/4.84  | GROUND_INST: instantiating (3) with all_17_3, all_17_4, all_17_0, simplifying
% 26.37/4.84  |              with (18), (19), (28) gives:
% 26.37/4.84  |   (41)   ? [v0: any] :  ? [v1: any] : (apart_point_and_line(all_17_3,
% 26.37/4.84  |             all_17_0) = v1 & distinct_points(all_17_3, all_17_4) = v0 & ( ~
% 26.37/4.84  |             (v1 = 0) |  ~ (v0 = 0)))
% 26.37/4.84  | 
% 26.37/4.84  | DELTA: instantiating (41) with fresh symbols all_24_0, all_24_1 gives:
% 26.62/4.84  |   (42)  apart_point_and_line(all_17_3, all_17_0) = all_24_0 &
% 26.62/4.84  |         distinct_points(all_17_3, all_17_4) = all_24_1 & ( ~ (all_24_0 = 0) | 
% 26.62/4.84  |           ~ (all_24_1 = 0))
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (42) implies:
% 26.62/4.84  |   (43)  distinct_points(all_17_3, all_17_4) = all_24_1
% 26.62/4.84  |   (44)  apart_point_and_line(all_17_3, all_17_0) = all_24_0
% 26.62/4.84  |   (45)   ~ (all_24_0 = 0) |  ~ (all_24_1 = 0)
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (34) with fresh symbols all_26_0, all_26_1 gives:
% 26.62/4.84  |   (46)   ~ (all_26_0 = 0) & line_connecting(all_17_4, all_17_3) = all_26_1 &
% 26.62/4.84  |         apart_point_and_line(all_17_4, all_26_1) = all_26_0 & $i(all_26_1)
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (46) implies:
% 26.62/4.84  |   (47)   ~ (all_26_0 = 0)
% 26.62/4.84  |   (48)  apart_point_and_line(all_17_4, all_26_1) = all_26_0
% 26.62/4.84  |   (49)  line_connecting(all_17_4, all_17_3) = all_26_1
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (40) with fresh symbols all_28_0, all_28_1 gives:
% 26.62/4.84  |   (50)  apart_point_and_line(all_17_4, all_17_0) = all_28_0 &
% 26.62/4.84  |         distinct_points(all_17_3, all_17_4) = all_28_1 & ( ~ (all_28_0 = 0) | 
% 26.62/4.84  |           ~ (all_28_1 = 0))
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (50) implies:
% 26.62/4.84  |   (51)  distinct_points(all_17_3, all_17_4) = all_28_1
% 26.62/4.84  |   (52)  apart_point_and_line(all_17_4, all_17_0) = all_28_0
% 26.62/4.84  |   (53)   ~ (all_28_0 = 0) |  ~ (all_28_1 = 0)
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (39) with fresh symbols all_30_0, all_30_1 gives:
% 26.62/4.84  |   (54)  apart_point_and_line(all_17_5, all_17_2) = all_30_0 &
% 26.62/4.84  |         distinct_points(all_17_5, all_17_4) = all_30_1 & ( ~ (all_30_0 = 0) | 
% 26.62/4.84  |           ~ (all_30_1 = 0))
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (54) implies:
% 26.62/4.84  |   (55)  apart_point_and_line(all_17_5, all_17_2) = all_30_0
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (33) with fresh symbols all_32_0, all_32_1 gives:
% 26.62/4.84  |   (56)   ~ (all_32_0 = 0) & line_connecting(all_17_4, all_17_3) = all_32_1 &
% 26.62/4.84  |         apart_point_and_line(all_17_3, all_32_1) = all_32_0 & $i(all_32_1)
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (56) implies:
% 26.62/4.84  |   (57)   ~ (all_32_0 = 0)
% 26.62/4.84  |   (58)  $i(all_32_1)
% 26.62/4.84  |   (59)  apart_point_and_line(all_17_3, all_32_1) = all_32_0
% 26.62/4.84  |   (60)  line_connecting(all_17_4, all_17_3) = all_32_1
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1 gives:
% 26.62/4.84  |   (61)   ~ (all_34_0 = 0) & line_connecting(all_17_5, all_17_3) = all_34_1 &
% 26.62/4.84  |         apart_point_and_line(all_17_5, all_34_1) = all_34_0 & $i(all_34_1)
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (61) implies:
% 26.62/4.84  |   (62)  line_connecting(all_17_5, all_17_3) = all_34_1
% 26.62/4.84  | 
% 26.62/4.84  | DELTA: instantiating (30) with fresh symbols all_36_0, all_36_1 gives:
% 26.62/4.84  |   (63)   ~ (all_36_0 = 0) & line_connecting(all_17_5, all_17_4) = all_36_1 &
% 26.62/4.84  |         apart_point_and_line(all_17_5, all_36_1) = all_36_0 & $i(all_36_1)
% 26.62/4.84  | 
% 26.62/4.84  | ALPHA: (63) implies:
% 26.62/4.84  |   (64)   ~ (all_36_0 = 0)
% 26.62/4.84  |   (65)  $i(all_36_1)
% 26.62/4.84  |   (66)  apart_point_and_line(all_17_5, all_36_1) = all_36_0
% 26.62/4.85  |   (67)  line_connecting(all_17_5, all_17_4) = all_36_1
% 26.62/4.85  | 
% 26.62/4.85  | DELTA: instantiating (38) with fresh symbols all_38_0, all_38_1 gives:
% 26.62/4.85  |   (68)  apart_point_and_line(all_17_4, all_17_2) = all_38_0 &
% 26.62/4.85  |         distinct_points(all_17_5, all_17_4) = all_38_1 & ( ~ (all_38_0 = 0) | 
% 26.62/4.85  |           ~ (all_38_1 = 0))
% 26.62/4.85  | 
% 26.62/4.85  | ALPHA: (68) implies:
% 26.62/4.85  |   (69)  apart_point_and_line(all_17_4, all_17_2) = all_38_0
% 26.62/4.85  | 
% 26.62/4.85  | DELTA: instantiating (29) with fresh symbols all_40_0, all_40_1 gives:
% 26.62/4.85  |   (70)   ~ (all_40_0 = 0) & line_connecting(all_17_5, all_17_4) = all_40_1 &
% 26.62/4.85  |         apart_point_and_line(all_17_4, all_40_1) = all_40_0 & $i(all_40_1)
% 26.62/4.85  | 
% 26.62/4.85  | ALPHA: (70) implies:
% 26.62/4.85  |   (71)   ~ (all_40_0 = 0)
% 26.62/4.85  |   (72)  apart_point_and_line(all_17_4, all_40_1) = all_40_0
% 26.62/4.85  |   (73)  line_connecting(all_17_5, all_17_4) = all_40_1
% 26.62/4.85  | 
% 26.62/4.85  | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives:
% 26.62/4.85  |   (74)   ~ (all_42_0 = 0) & line_connecting(all_17_5, all_17_3) = all_42_1 &
% 26.62/4.85  |         apart_point_and_line(all_17_3, all_42_1) = all_42_0 & $i(all_42_1)
% 26.62/4.85  | 
% 26.62/4.85  | ALPHA: (74) implies:
% 26.62/4.85  |   (75)   ~ (all_42_0 = 0)
% 26.62/4.85  |   (76)  $i(all_42_1)
% 26.62/4.85  |   (77)  apart_point_and_line(all_17_3, all_42_1) = all_42_0
% 26.62/4.85  |   (78)  line_connecting(all_17_5, all_17_3) = all_42_1
% 26.62/4.85  | 
% 26.62/4.85  | BETA: splitting (36) gives:
% 26.62/4.85  | 
% 26.62/4.85  | Case 1:
% 26.62/4.85  | | 
% 26.62/4.85  | |   (79)  all_17_1 = 0
% 26.62/4.85  | | 
% 26.62/4.85  | | REDUCE: (16), (79) imply:
% 26.62/4.85  | |   (80)  $false
% 26.62/4.85  | | 
% 26.62/4.85  | | CLOSE: (80) is inconsistent.
% 26.62/4.85  | | 
% 26.62/4.85  | Case 2:
% 26.62/4.85  | | 
% 26.62/4.85  | |   (81)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.62/4.85  | |         (apart_point_and_line(all_17_5, all_17_2) = v2 &
% 26.62/4.85  | |           apart_point_and_line(all_17_5, all_17_2) = v1 &
% 26.62/4.85  | |           distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 |
% 26.62/4.85  | |             v1 = 0))
% 26.62/4.85  | | 
% 26.62/4.85  | | DELTA: instantiating (81) with fresh symbols all_48_0, all_48_1, all_48_2
% 26.62/4.85  | |        gives:
% 26.62/4.85  | |   (82)  apart_point_and_line(all_17_5, all_17_2) = all_48_0 &
% 26.62/4.85  | |         apart_point_and_line(all_17_5, all_17_2) = all_48_1 &
% 26.62/4.85  | |         distinct_lines(all_17_2, all_17_2) = all_48_2 & ( ~ (all_48_2 = 0) |
% 26.62/4.85  | |           all_48_0 = 0 | all_48_1 = 0)
% 26.62/4.85  | | 
% 26.62/4.85  | | ALPHA: (82) implies:
% 26.62/4.85  | |   (83)  apart_point_and_line(all_17_5, all_17_2) = all_48_1
% 26.62/4.85  | |   (84)  apart_point_and_line(all_17_5, all_17_2) = all_48_0
% 26.62/4.85  | | 
% 26.62/4.85  | | BETA: splitting (35) gives:
% 26.62/4.85  | | 
% 26.62/4.85  | | Case 1:
% 26.62/4.85  | | | 
% 26.62/4.85  | | |   (85)  all_17_1 = 0
% 26.62/4.86  | | | 
% 26.62/4.86  | | | REDUCE: (16), (85) imply:
% 26.62/4.86  | | |   (86)  $false
% 26.62/4.86  | | | 
% 26.62/4.86  | | | CLOSE: (86) is inconsistent.
% 26.62/4.86  | | | 
% 26.62/4.86  | | Case 2:
% 26.62/4.86  | | | 
% 26.62/4.86  | | |   (87)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.62/4.86  | | |         (apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.62/4.86  | | |           apart_point_and_line(all_17_4, all_17_2) = v1 &
% 26.62/4.86  | | |           distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0
% 26.62/4.86  | | |             | v1 = 0))
% 26.62/4.86  | | | 
% 26.62/4.86  | | | DELTA: instantiating (87) with fresh symbols all_53_0, all_53_1, all_53_2
% 26.62/4.86  | | |        gives:
% 26.62/4.86  | | |   (88)  apart_point_and_line(all_17_4, all_17_2) = all_53_0 &
% 26.62/4.86  | | |         apart_point_and_line(all_17_4, all_17_2) = all_53_1 &
% 26.62/4.86  | | |         distinct_lines(all_17_2, all_17_2) = all_53_2 & ( ~ (all_53_2 = 0)
% 26.62/4.86  | | |           | all_53_0 = 0 | all_53_1 = 0)
% 26.62/4.86  | | | 
% 26.62/4.86  | | | ALPHA: (88) implies:
% 26.62/4.86  | | |   (89)  apart_point_and_line(all_17_4, all_17_2) = all_53_1
% 26.62/4.86  | | |   (90)  apart_point_and_line(all_17_4, all_17_2) = all_53_0
% 26.62/4.86  | | | 
% 26.62/4.86  | | | BETA: splitting (37) gives:
% 26.62/4.86  | | | 
% 26.62/4.86  | | | Case 1:
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | |   (91)  all_17_1 = 0
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | REDUCE: (16), (91) imply:
% 26.62/4.86  | | | |   (92)  $false
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | CLOSE: (92) is inconsistent.
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | Case 2:
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | |   (93)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 26.62/4.86  | | | |         (apart_point_and_line(all_17_3, all_17_2) = v3 &
% 26.62/4.86  | | | |           apart_point_and_line(all_17_3, all_17_2) = v2 &
% 26.62/4.86  | | | |           distinct_lines(all_17_2, all_17_2) = v1 &
% 26.62/4.86  | | | |           distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.86  | | | |             (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | DELTA: instantiating (93) with fresh symbols all_58_0, all_58_1,
% 26.62/4.86  | | | |        all_58_2, all_58_3 gives:
% 26.62/4.86  | | | |   (94)  apart_point_and_line(all_17_3, all_17_2) = all_58_0 &
% 26.62/4.86  | | | |         apart_point_and_line(all_17_3, all_17_2) = all_58_1 &
% 26.62/4.86  | | | |         distinct_lines(all_17_2, all_17_2) = all_58_2 &
% 26.62/4.86  | | | |         distinct_points(all_17_3, all_17_3) = all_58_3 & ( ~ (all_58_2 =
% 26.62/4.86  | | | |             0) |  ~ (all_58_3 = 0) | all_58_0 = 0 | all_58_1 = 0)
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | ALPHA: (94) implies:
% 26.62/4.86  | | | |   (95)  apart_point_and_line(all_17_3, all_17_2) = all_58_1
% 26.62/4.86  | | | |   (96)  apart_point_and_line(all_17_3, all_17_2) = all_58_0
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (11) with all_24_1, all_28_1, all_17_4,
% 26.62/4.86  | | | |              all_17_3, simplifying with (43), (51) gives:
% 26.62/4.86  | | | |   (97)  all_28_1 = all_24_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_48_1, all_48_0, all_17_2,
% 26.62/4.86  | | | |              all_17_5, simplifying with (83), (84) gives:
% 26.62/4.86  | | | |   (98)  all_48_0 = all_48_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_30_0, all_48_0, all_17_2,
% 26.62/4.86  | | | |              all_17_5, simplifying with (55), (84) gives:
% 26.62/4.86  | | | |   (99)  all_48_0 = all_30_0
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_53_1, all_53_0, all_17_2,
% 26.62/4.86  | | | |              all_17_4, simplifying with (89), (90) gives:
% 26.62/4.86  | | | |   (100)  all_53_0 = all_53_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_38_0, all_53_0, all_17_2,
% 26.62/4.86  | | | |              all_17_4, simplifying with (69), (90) gives:
% 26.62/4.86  | | | |   (101)  all_53_0 = all_38_0
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_17_1, all_58_0, all_17_2,
% 26.62/4.86  | | | |              all_17_3, simplifying with (26), (96) gives:
% 26.62/4.86  | | | |   (102)  all_58_0 = all_17_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (13) with all_58_1, all_58_0, all_17_2,
% 26.62/4.86  | | | |              all_17_3, simplifying with (95), (96) gives:
% 26.62/4.86  | | | |   (103)  all_58_0 = all_58_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (14) with all_17_2, all_40_1, all_17_4,
% 26.62/4.86  | | | |              all_17_5, simplifying with (27), (73) gives:
% 26.62/4.86  | | | |   (104)  all_40_1 = all_17_2
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (14) with all_36_1, all_40_1, all_17_4,
% 26.62/4.86  | | | |              all_17_5, simplifying with (67), (73) gives:
% 26.62/4.86  | | | |   (105)  all_40_1 = all_36_1
% 26.62/4.86  | | | | 
% 26.62/4.86  | | | | GROUND_INST: instantiating (14) with all_34_1, all_42_1, all_17_3,
% 26.62/4.86  | | | |              all_17_5, simplifying with (62), (78) gives:
% 26.62/4.87  | | | |   (106)  all_42_1 = all_34_1
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (14) with all_26_1, all_32_1, all_17_3,
% 26.62/4.87  | | | |              all_17_4, simplifying with (49), (60) gives:
% 26.62/4.87  | | | |   (107)  all_32_1 = all_26_1
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | COMBINE_EQS: (102), (103) imply:
% 26.62/4.87  | | | |   (108)  all_58_1 = all_17_1
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | COMBINE_EQS: (100), (101) imply:
% 26.62/4.87  | | | |   (109)  all_53_1 = all_38_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | COMBINE_EQS: (98), (99) imply:
% 26.62/4.87  | | | |   (110)  all_48_1 = all_30_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | COMBINE_EQS: (104), (105) imply:
% 26.62/4.87  | | | |   (111)  all_36_1 = all_17_2
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | SIMP: (111) implies:
% 26.62/4.87  | | | |   (112)  all_36_1 = all_17_2
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (77), (106) imply:
% 26.62/4.87  | | | |   (113)  apart_point_and_line(all_17_3, all_34_1) = all_42_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (59), (107) imply:
% 26.62/4.87  | | | |   (114)  apart_point_and_line(all_17_3, all_26_1) = all_32_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (72), (104) imply:
% 26.62/4.87  | | | |   (115)  apart_point_and_line(all_17_4, all_17_2) = all_40_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (66), (112) imply:
% 26.62/4.87  | | | |   (116)  apart_point_and_line(all_17_5, all_17_2) = all_36_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (76), (106) imply:
% 26.62/4.87  | | | |   (117)  $i(all_34_1)
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (58), (107) imply:
% 26.62/4.87  | | | |   (118)  $i(all_26_1)
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (13) with all_30_0, all_36_0, all_17_2,
% 26.62/4.87  | | | |              all_17_5, simplifying with (55), (116) gives:
% 26.62/4.87  | | | |   (119)  all_36_0 = all_30_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (13) with all_38_0, all_40_0, all_17_2,
% 26.62/4.87  | | | |              all_17_4, simplifying with (69), (115) gives:
% 26.62/4.87  | | | |   (120)  all_40_0 = all_38_0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (71), (120) imply:
% 26.62/4.87  | | | |   (121)   ~ (all_38_0 = 0)
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | REDUCE: (64), (119) imply:
% 26.62/4.87  | | | |   (122)   ~ (all_30_0 = 0)
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (1) with all_17_4, all_17_3, all_17_4,
% 26.62/4.87  | | | |              all_24_1, simplifying with (18), (19), (24), (43) gives:
% 26.62/4.87  | | | |   (123)  all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (10) with all_17_5, all_17_0, all_17_2,
% 26.62/4.87  | | | |              all_30_0, simplifying with (17), (20), (21), (25), (55)
% 26.62/4.87  | | | |              gives:
% 26.62/4.87  | | | |   (124)  all_30_0 = 0 | distinct_lines(all_17_0, all_17_2) = 0
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_5, all_17_2,
% 26.62/4.87  | | | |              all_17_2, all_38_0, all_30_0, simplifying with (17), (18),
% 26.62/4.87  | | | |              (20), (55), (69) gives:
% 26.62/4.87  | | | |   (125)  all_38_0 = 0 | all_30_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.87  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_4,
% 26.62/4.87  | | | |              all_17_2) = v2 & apart_point_and_line(all_17_5, all_17_2) =
% 26.62/4.87  | | | |            v3 & distinct_lines(all_17_2, all_17_2) = v1 &
% 26.62/4.87  | | | |            distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.87  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (8) with all_17_3, all_17_4, all_17_2,
% 26.62/4.87  | | | |              all_17_0, all_17_1, all_28_0, simplifying with (18), (19),
% 26.62/4.87  | | | |              (20), (21), (26), (52) gives:
% 26.62/4.87  | | | |   (126)  all_28_0 = 0 | all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.87  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.87  | | | |              all_17_0) = v2 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.87  | | | |            v3 & distinct_lines(all_17_2, all_17_0) = v1 &
% 26.62/4.87  | | | |            distinct_points(all_17_3, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.87  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.87  | | | | 
% 26.62/4.87  | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_0,
% 26.62/4.87  | | | |              all_17_2, all_28_0, all_17_1, simplifying with (18), (19),
% 26.62/4.87  | | | |              (20), (21), (26), (52) gives:
% 26.62/4.88  | | | |   (127)  all_28_0 = 0 | all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.88  | | | |              all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v2 & distinct_lines(all_17_0, all_17_2) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_3, all_17_2,
% 26.62/4.88  | | | |              all_17_0, all_28_0, all_17_1, simplifying with (18), (19),
% 26.62/4.88  | | | |              (20), (21), (26), (52) gives:
% 26.62/4.88  | | | |   (128)  all_28_0 = 0 | all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.88  | | | |              all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v2 & distinct_lines(all_17_2, all_17_0) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (6) with all_17_4, all_17_3, all_17_0,
% 26.62/4.88  | | | |              all_17_0, all_28_0, all_28_0, simplifying with (18), (19),
% 26.62/4.88  | | | |              (21), (24), (52) gives:
% 26.62/4.88  | | | |   (129)  all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.62/4.88  | | | |          (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.88  | | | |            apart_point_and_line(all_17_3, all_17_0) = v1 &
% 26.62/4.88  | | | |            distinct_lines(all_17_0, all_17_0) = v0 & ( ~ (v0 = 0) | v2 =
% 26.62/4.88  | | | |              0 | v1 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (6) with all_17_4, all_17_3, all_17_2,
% 26.62/4.88  | | | |              all_17_0, all_38_0, all_28_0, simplifying with (18), (19),
% 26.62/4.88  | | | |              (20), (21), (24), (52), (69) gives:
% 26.62/4.88  | | | |   (130)  all_38_0 = 0 | all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] : (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.88  | | | |            apart_point_and_line(all_17_3, all_17_2) = v1 &
% 26.62/4.88  | | | |            distinct_lines(all_17_2, all_17_0) = v0 & ( ~ (v0 = 0) | v2 =
% 26.62/4.88  | | | |              0 | v1 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_17_2,
% 26.62/4.88  | | | |              all_17_0, all_38_0, all_28_0, simplifying with (18), (20),
% 26.62/4.88  | | | |              (21), (52), (69) gives:
% 26.62/4.88  | | | |   (131)  all_38_0 = 0 | all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_4,
% 26.62/4.88  | | | |              all_17_0) = v2 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v3 & distinct_lines(all_17_2, all_17_0) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_4, all_17_2,
% 26.62/4.88  | | | |              all_17_0, all_28_0, all_38_0, simplifying with (18), (20),
% 26.62/4.88  | | | |              (21), (52), (69) gives:
% 26.62/4.88  | | | |   (132)  all_38_0 = 0 | all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_4,
% 26.62/4.88  | | | |              all_17_0) = v3 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v2 & distinct_lines(all_17_2, all_17_0) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_4, all_26_1,
% 26.62/4.88  | | | |              all_17_2, all_26_0, all_38_0, simplifying with (18), (20),
% 26.62/4.88  | | | |              (48), (69), (118) gives:
% 26.62/4.88  | | | |   (133)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_4,
% 26.62/4.88  | | | |              all_26_1) = v3 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v2 & distinct_lines(all_26_1, all_17_2) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_4, all_26_1,
% 26.62/4.88  | | | |              all_17_2, all_38_0, all_26_0, simplifying with (18), (20),
% 26.62/4.88  | | | |              (48), (69), (118) gives:
% 26.62/4.88  | | | |   (134)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.88  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_4,
% 26.62/4.88  | | | |              all_26_1) = v2 & apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.88  | | | |            v3 & distinct_lines(all_26_1, all_17_2) = v1 &
% 26.62/4.88  | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.88  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.88  | | | | 
% 26.62/4.88  | | | | GROUND_INST: instantiating (8) with all_17_3, all_17_3, all_17_0,
% 26.62/4.88  | | | |              all_26_1, all_24_0, all_32_0, simplifying with (19), (21),
% 26.62/4.88  | | | |              (44), (114), (118) gives:
% 26.62/4.89  | | | |   (135)  all_32_0 = 0 | all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_26_1) = v2 & apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.89  | | | |            v3 & distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_26_1,
% 26.62/4.89  | | | |              all_17_0, all_24_0, all_32_0, simplifying with (19), (21),
% 26.62/4.89  | | | |              (44), (114), (118) gives:
% 26.62/4.89  | | | |   (136)  all_32_0 = 0 | all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_26_1) = v2 & apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.89  | | | |            v3 & distinct_lines(all_26_1, all_17_0) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_17_0,
% 26.62/4.89  | | | |              all_26_1, all_32_0, all_24_0, simplifying with (19), (21),
% 26.62/4.89  | | | |              (44), (114), (118) gives:
% 26.62/4.89  | | | |   (137)  all_32_0 = 0 | all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_26_1) = v3 & apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.89  | | | |            v2 & distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_2,
% 26.62/4.89  | | | |              all_26_1, all_38_0, all_32_0, simplifying with (18), (19),
% 26.62/4.89  | | | |              (20), (69), (114), (118) gives:
% 26.62/4.89  | | | |   (138)  all_38_0 = 0 | all_32_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_17_2) = v3 & apart_point_and_line(all_17_4, all_26_1) =
% 26.62/4.89  | | | |            v2 & distinct_lines(all_17_2, all_26_1) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (9) with all_17_4, all_17_3, all_17_2,
% 26.62/4.89  | | | |              all_34_1, all_17_1, all_42_0, simplifying with (18), (19),
% 26.62/4.89  | | | |              (20), (24), (26), (113), (117) gives:
% 26.62/4.89  | | | |   (139)  all_42_0 = 0 | all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] : (apart_point_and_line(all_17_4, all_34_1) = v2 &
% 26.62/4.89  | | | |            apart_point_and_line(all_17_4, all_17_2) = v1 &
% 26.62/4.89  | | | |            distinct_lines(all_17_2, all_34_1) = v0 & ( ~ (v0 = 0) | v2 =
% 26.62/4.89  | | | |              0 | v1 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_34_1,
% 26.62/4.89  | | | |              all_17_0, all_24_0, all_42_0, simplifying with (19), (21),
% 26.62/4.89  | | | |              (44), (113), (117) gives:
% 26.62/4.89  | | | |   (140)  all_42_0 = 0 | all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_34_1) = v2 & apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.89  | | | |            v3 & distinct_lines(all_34_1, all_17_0) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | GROUND_INST: instantiating (7) with all_17_4, all_17_3, all_34_1,
% 26.62/4.89  | | | |              all_26_1, all_26_0, all_42_0, simplifying with (18), (19),
% 26.62/4.89  | | | |              (48), (113), (117), (118) gives:
% 26.62/4.89  | | | |   (141)  all_42_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.89  | | | |          [v2: any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | |              all_26_1) = v3 & apart_point_and_line(all_17_4, all_34_1) =
% 26.62/4.89  | | | |            v2 & distinct_lines(all_34_1, all_26_1) = v1 &
% 26.62/4.89  | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1 = 0) |  ~
% 26.62/4.89  | | | |              (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | BETA: splitting (45) gives:
% 26.62/4.89  | | | | 
% 26.62/4.89  | | | | Case 1:
% 26.62/4.89  | | | | | 
% 26.62/4.89  | | | | |   (142)   ~ (all_24_0 = 0)
% 26.62/4.89  | | | | | 
% 26.62/4.89  | | | | | BETA: splitting (124) gives:
% 26.62/4.89  | | | | | 
% 26.62/4.89  | | | | | Case 1:
% 26.62/4.89  | | | | | | 
% 26.62/4.89  | | | | | |   (143)  distinct_lines(all_17_0, all_17_2) = 0
% 26.62/4.89  | | | | | | 
% 26.62/4.89  | | | | | | BETA: splitting (127) gives:
% 26.62/4.89  | | | | | | 
% 26.62/4.89  | | | | | | Case 1:
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | |   (144)  all_28_0 = 0
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.62/4.89  | | | | | | |            (134), (144), (apart1) are inconsistent by sub-proof
% 26.62/4.89  | | | | | | |            #1.
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | Case 2:
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | |   (145)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any]
% 26.62/4.89  | | | | | | |          :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.89  | | | | | | |              all_17_0) = v3 & apart_point_and_line(all_17_4,
% 26.62/4.89  | | | | | | |              all_17_2) = v2 & distinct_lines(all_17_0, all_17_2) =
% 26.62/4.89  | | | | | | |            v1 & distinct_points(all_17_4, all_17_3) = v0 & ( ~ (v1
% 26.62/4.89  | | | | | | |                = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | | BETA: splitting (138) gives:
% 26.62/4.89  | | | | | | | 
% 26.62/4.89  | | | | | | | Case 1:
% 26.62/4.89  | | | | | | | | 
% 26.62/4.89  | | | | | | | |   (146)  all_38_0 = 0
% 26.62/4.89  | | | | | | | | 
% 26.62/4.89  | | | | | | | | REDUCE: (121), (146) imply:
% 26.62/4.90  | | | | | | | |   (147)  $false
% 26.62/4.90  | | | | | | | | 
% 26.62/4.90  | | | | | | | | CLOSE: (147) is inconsistent.
% 26.62/4.90  | | | | | | | | 
% 26.62/4.90  | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | 
% 26.62/4.90  | | | | | | | |   (148)  all_32_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2:
% 26.62/4.90  | | | | | | | |            any] :  ? [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.90  | | | | | | | |              all_17_2) = v3 & apart_point_and_line(all_17_4,
% 26.62/4.90  | | | | | | | |              all_26_1) = v2 & distinct_lines(all_17_2, all_26_1)
% 26.62/4.90  | | | | | | | |            = v1 & distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | 
% 26.62/4.90  | | | | | | | | BETA: splitting (125) gives:
% 26.62/4.90  | | | | | | | | 
% 26.62/4.90  | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | |   (149)  all_38_0 = 0
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | REDUCE: (121), (149) imply:
% 26.62/4.90  | | | | | | | | |   (150)  $false
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | CLOSE: (150) is inconsistent.
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | |   (151)  all_30_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2:
% 26.62/4.90  | | | | | | | | |            any] :  ? [v3: any] :
% 26.62/4.90  | | | | | | | | |          (apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.62/4.90  | | | | | | | | |            apart_point_and_line(all_17_5, all_17_2) = v3 &
% 26.62/4.90  | | | | | | | | |            distinct_lines(all_17_2, all_17_2) = v1 &
% 26.62/4.90  | | | | | | | | |            distinct_points(all_17_4, all_17_5) = v0 & ( ~ (v1
% 26.62/4.90  | | | | | | | | |                = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | BETA: splitting (137) gives:
% 26.62/4.90  | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | |   (152)  all_32_0 = 0
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | REDUCE: (57), (152) imply:
% 26.62/4.90  | | | | | | | | | |   (153)  $false
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | CLOSE: (153) is inconsistent.
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | |   (154)  all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.90  | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.90  | | | | | | | | | |          (apart_point_and_line(all_17_3, all_26_1) = v3 &
% 26.62/4.90  | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.90  | | | | | | | | | |            distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.90  | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | BETA: splitting (140) gives:
% 26.62/4.90  | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | |   (155)  all_42_0 = 0
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | REDUCE: (75), (155) imply:
% 26.62/4.90  | | | | | | | | | | |   (156)  $false
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | |   (157)  all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.90  | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.90  | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_34_1) = v2 &
% 26.62/4.90  | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.90  | | | | | | | | | | |            distinct_lines(all_34_1, all_17_0) = v1 &
% 26.62/4.90  | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | BETA: splitting (135) gives:
% 26.62/4.90  | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | |   (158)  all_32_0 = 0
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | REDUCE: (57), (158) imply:
% 26.62/4.90  | | | | | | | | | | | |   (159)  $false
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | |   (160)  all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.90  | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.90  | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_26_1) = v2 &
% 26.62/4.90  | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.90  | | | | | | | | | | | |            distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.90  | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | BETA: splitting (136) gives:
% 26.62/4.90  | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | |   (161)  all_32_0 = 0
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | REDUCE: (57), (161) imply:
% 26.62/4.90  | | | | | | | | | | | | |   (162)  $false
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | |   (163)  all_24_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.90  | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.90  | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_26_1) = v2 &
% 26.62/4.90  | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.90  | | | | | | | | | | | | |            distinct_lines(all_26_1, all_17_0) = v1 &
% 26.62/4.90  | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | BETA: splitting (139) gives:
% 26.62/4.90  | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | |   (164)  all_42_0 = 0
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | REDUCE: (75), (164) imply:
% 26.62/4.90  | | | | | | | | | | | | | |   (165)  $false
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | |   (166)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.90  | | | | | | | | | | | | | |          [v2: any] : (apart_point_and_line(all_17_4,
% 26.62/4.90  | | | | | | | | | | | | | |              all_34_1) = v2 &
% 26.62/4.90  | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v1 &
% 26.62/4.90  | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_34_1) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | | | | | |              (v0 = 0) | v2 = 0 | v1 = 0))
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 26.62/4.90  | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | Case 1:
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | |   (167)  all_17_1 = 0
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | | REDUCE: (16), (167) imply:
% 26.62/4.90  | | | | | | | | | | | | | | |   (168)  $false
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | Case 2:
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | |   (169)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.62/4.90  | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.90  | | | | | | | | | | | | | | |              all_17_0) = v3 &
% 26.62/4.90  | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.62/4.90  | | | | | | | | | | | | | | |            distinct_lines(all_17_0, all_17_2) = v1 &
% 26.62/4.90  | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.62/4.90  | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_263_0,
% 26.62/4.90  | | | | | | | | | | | | | | |        all_263_1, all_263_2, all_263_3 gives:
% 26.62/4.90  | | | | | | | | | | | | | | |   (170)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.90  | | | | | | | | | | | | | | |          all_263_0 & apart_point_and_line(all_17_4,
% 26.62/4.90  | | | | | | | | | | | | | | |            all_17_2) = all_263_1 & distinct_lines(all_17_0,
% 26.62/4.90  | | | | | | | | | | | | | | |            all_17_2) = all_263_2 &
% 26.62/4.90  | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_3) = all_263_3 &
% 26.62/4.90  | | | | | | | | | | | | | | |          ( ~ (all_263_2 = 0) |  ~ (all_263_3 = 0) |
% 26.62/4.90  | | | | | | | | | | | | | | |            all_263_0 = 0 | all_263_1 = 0)
% 26.62/4.90  | | | | | | | | | | | | | | | 
% 26.62/4.90  | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 26.62/4.90  | | | | | | | | | | | | | | |   (171)  distinct_points(all_17_4, all_17_3) = all_263_3
% 26.62/4.90  | | | | | | | | | | | | | | |   (172)  distinct_lines(all_17_0, all_17_2) = all_263_2
% 26.62/4.90  | | | | | | | | | | | | | | |   (173)  apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.90  | | | | | | | | | | | | | | |          all_263_1
% 26.62/4.91  | | | | | | | | | | | | | | |   (174)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | |          all_263_0
% 26.62/4.91  | | | | | | | | | | | | | | |   (175)   ~ (all_263_2 = 0) |  ~ (all_263_3 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | |          all_263_0 = 0 | all_263_1 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | |   (176)  all_28_0 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.62/4.91  | | | | | | | | | | | | | | | |            (134), (176), (apart1) are inconsistent by
% 26.62/4.91  | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | |   (177)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.91  | | | | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.91  | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.62/4.91  | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_4) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | |   (178)  all_24_0 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | REDUCE: (142), (178) imply:
% 26.62/4.91  | | | | | | | | | | | | | | | | |   (179)  $false
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | |   (180)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.62/4.91  | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | |              all_34_1) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | |            distinct_lines(all_34_1, all_17_0) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbols all_319_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | |        all_319_1, all_319_2, all_319_3 gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | |   (181)  apart_point_and_line(all_17_3, all_34_1) =
% 26.62/4.91  | | | | | | | | | | | | | | | | |          all_319_1 & apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | |            all_17_0) = all_319_0 & distinct_lines(all_34_1,
% 26.62/4.91  | | | | | | | | | | | | | | | | |            all_17_0) = all_319_2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | |          distinct_points(all_17_3, all_17_3) = all_319_3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | |          ( ~ (all_319_2 = 0) |  ~ (all_319_3 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | | | |            all_319_0 = 0 | all_319_1 = 0)
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 26.62/4.91  | | | | | | | | | | | | | | | | |   (182)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | | | |          all_319_0
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | |   (183)  all_24_0 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | REDUCE: (142), (183) imply:
% 26.62/4.91  | | | | | | | | | | | | | | | | | |   (184)  $false
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | |   (185)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.62/4.91  | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | | |              all_26_1) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            distinct_lines(all_26_1, all_17_0) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_324_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | |        all_324_1, all_324_2, all_324_3 gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | |   (186)  apart_point_and_line(all_17_3, all_26_1) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | |          all_324_1 & apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            all_17_0) = all_324_0 & distinct_lines(all_26_1,
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            all_17_0) = all_324_2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | |          distinct_points(all_17_3, all_17_3) = all_324_3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | |          ( ~ (all_324_2 = 0) |  ~ (all_324_3 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | | | | |            all_324_0 = 0 | all_324_1 = 0)
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 26.62/4.91  | | | | | | | | | | | | | | | | | |   (187)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | |          all_324_0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |   (188)  all_17_1 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | REDUCE: (16), (188) imply:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |   (189)  $false
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |   (190)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_4, all_34_1) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_34_1) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |              (v0 = 0) | v2 = 0 | v1 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_334_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |        all_334_1, all_334_2 gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |   (191)  apart_point_and_line(all_17_4, all_34_1) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |          all_334_0 & apart_point_and_line(all_17_4,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |            all_17_2) = all_334_1 & distinct_lines(all_17_2,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |            all_34_1) = all_334_2 & ( ~ (all_334_2 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |            all_334_0 = 0 | all_334_1 = 0)
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |   (192)  apart_point_and_line(all_17_4, all_17_2) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | |          all_334_1
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |   (193)  all_28_0 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            (134), (193), (apart1) are inconsistent by
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |   (194)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_0, all_17_0) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |              (v0 = 0) | v2 = 0 | v1 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (194) with fresh symbols all_355_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |        all_355_1, all_355_2 gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |   (195)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |          all_355_0 & apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_355_1 & distinct_lines(all_17_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_355_2 & ( ~ (all_355_2 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |            all_355_0 = 0 | all_355_1 = 0)
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |   (196)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |          all_355_1
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |   (197)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | |          all_355_0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |   (198)  all_24_0 = 0
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (198) imply:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |   (199)  $false
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |   (200)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |              all_26_1) = v3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (200) with fresh symbols all_368_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |        all_368_1, all_368_2, all_368_3 gives:
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |   (201)  apart_point_and_line(all_17_3, all_26_1) =
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |          all_368_0 & apart_point_and_line(all_17_3,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_368_1 & distinct_lines(all_17_0,
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            all_26_1) = all_368_2 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_3, all_17_3) = all_368_3 &
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_368_2 = 0) |  ~ (all_368_3 = 0) |
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | |            all_368_0 = 0 | all_368_1 = 0)
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | |   (202)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | |          all_368_1
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |   (203)  all_24_0 = 0
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (203) imply:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |   (204)  $false
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |   (205)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |              all_26_1) = v2 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_0, all_26_1) = v1 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_373_0,
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |        all_373_1, all_373_2, all_373_3 gives:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |   (206)  apart_point_and_line(all_17_3, all_26_1) =
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |          all_373_1 & apart_point_and_line(all_17_3,
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_373_0 & distinct_lines(all_17_0,
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            all_26_1) = all_373_2 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_3, all_17_3) = all_373_3 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_373_2 = 0) |  ~ (all_373_3 = 0) |
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |            all_373_0 = 0 | all_373_1 = 0)
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |   (207)  apart_point_and_line(all_17_3, all_17_0) =
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | |          all_373_0
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_38_0 = 0
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (208) imply:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |   (209)  $false
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |          [v2: any] : (apart_point_and_line(all_17_3,
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |              all_17_0) = v2 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_2) = v1 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v0 & ( ~
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | |              (v0 = 0) | v2 = 0 | v1 = 0))
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_42_0 = 0
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (211) imply:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |   (212)  $false
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_26_1) = v3 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_34_1) = v2 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_34_1, all_26_1) = v1 &
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_28_0 = 0
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (214), (apart1) are inconsistent by
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.62/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_17_1 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_17_0) = v3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_38_0 = 0
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (216) imply:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  $false
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_4, all_17_0) = v3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_38_0 = 0
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (219) imply:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  $false
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent.
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_28_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ?
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v2: any] :  ? [v3: any] :
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_4, all_17_0) = v2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_32_0 = 0
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (222) imply:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  $false
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2) = v3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_26_1) = v2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_26_1) = v1 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (224) with fresh symbols all_418_0,
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_418_1, all_418_2, all_418_3 gives:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  apart_point_and_line(all_17_3, all_17_2) =
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_418_0 & apart_point_and_line(all_17_4,
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_26_1) = all_418_1 & distinct_lines(all_17_2,
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_26_1) = all_418_2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_3) = all_418_3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_418_2 = 0) |  ~ (all_418_3 = 0) |
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_418_0 = 0 | all_418_1 = 0)
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  distinct_points(all_17_4, all_17_3) = all_418_3
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_30_0 = 0
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (227) imply:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  $false
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_4,
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2) = v2 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_5, all_17_2) = v3 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_2) = v1 &
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_5) = v0 & ( ~
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_478_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_478_1, all_478_2, all_478_3 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  apart_point_and_line(all_17_4, all_17_2) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_478_1 & apart_point_and_line(all_17_5,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_478_0 & distinct_lines(all_17_2,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_478_2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_5) = all_478_3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_478_2 = 0) |  ~ (all_478_3 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_478_0 = 0 | all_478_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  apart_point_and_line(all_17_4, all_17_2) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_478_1
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_17_1 = 0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (232) imply:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  $false
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0) = v2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_3, all_17_4) = v0 & ( ~
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_498_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_498_1, all_498_2, all_498_3 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_498_1 & apart_point_and_line(all_17_4,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_498_0 & distinct_lines(all_17_2,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_498_2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_3, all_17_4) = all_498_3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_498_2 = 0) |  ~ (all_498_3 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_498_0 = 0 | all_498_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  apart_point_and_line(all_17_4, all_17_2) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_498_0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_498_1
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_28_0 = 0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (238), (apart1) are inconsistent by
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_3, all_17_2) = v1 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v0 & ( ~
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v0 = 0) | v2 = 0 | v1 = 0))
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (239) with fresh symbols all_523_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_523_1, all_523_2 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_523_0 & apart_point_and_line(all_17_3,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_523_1 & distinct_lines(all_17_2,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_523_2 & ( ~ (all_523_2 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_523_0 = 0 | all_523_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_523_0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_26_0 = 0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (242) imply:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  $false
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1) = v3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_34_1) = v2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_34_1, all_26_1) = v1 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (244) with fresh symbols all_533_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_533_1, all_533_2, all_533_3 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  apart_point_and_line(all_17_3, all_26_1) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_533_0 & apart_point_and_line(all_17_4,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_34_1) = all_533_1 & distinct_lines(all_34_1,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_26_1) = all_533_2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_3) = all_533_3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_533_2 = 0) |  ~ (all_533_3 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_533_0 = 0 | all_533_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  distinct_points(all_17_4, all_17_3) = all_533_3
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_17_1 = 0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (247) imply:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  $false
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_3,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0) = v3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_3) = v0 & ( ~
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_543_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_543_1, all_543_2, all_543_3 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_543_0 & apart_point_and_line(all_17_4,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_543_1 & distinct_lines(all_17_2,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_543_2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_3) = all_543_3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_543_2 = 0) |  ~ (all_543_3 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_543_0 = 0 | all_543_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  distinct_points(all_17_4, all_17_3) = all_543_3
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  apart_point_and_line(all_17_3, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_543_0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_28_0 = 0
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (253), (apart1) are inconsistent by
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_4,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0) = v3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_553_0,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_553_1, all_553_2, all_553_3 gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  apart_point_and_line(all_17_4, all_17_0) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_553_0 & apart_point_and_line(all_17_4,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_553_1 & distinct_lines(all_17_2,
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_553_2 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_4) = all_553_3 &
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_553_2 = 0) |  ~ (all_553_3 = 0) |
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_553_0 = 0 | all_553_1 = 0)
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  apart_point_and_line(all_17_4, all_17_2) =
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_553_1
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_28_0 = 0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (47), (53), (97), (121), (123), (133),
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (257), (apart1) are inconsistent by
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          [v3: any] : (apart_point_and_line(all_17_4,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0) = v2 &
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_lines(all_17_2, all_17_0) = v1 &
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            distinct_points(all_17_4, all_17_4) = v0 & ( ~
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_558_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |        all_558_1, all_558_2, all_558_3 gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  apart_point_and_line(all_17_4, all_17_0) =
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_558_1 & apart_point_and_line(all_17_4,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_2) = all_558_0 & distinct_lines(all_17_2,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_17_0) = all_558_2 &
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          distinct_points(all_17_4, all_17_4) = all_558_3 &
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ( ~ (all_558_2 = 0) |  ~ (all_558_3 = 0) |
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_558_0 = 0 | all_558_1 = 0)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  apart_point_and_line(all_17_4, all_17_2) =
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_558_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_418_3, all_17_3,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_4, simplifying with (24), (226) gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_418_3 = 0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_418_3, all_533_3,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_3, all_17_4, simplifying with (226), (246)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_533_3 = all_418_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_533_3, all_543_3,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_3, all_17_4, simplifying with (246), (251)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_543_3 = all_533_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_263_3, all_543_3,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_3, all_17_4, simplifying with (171), (251)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_543_3 = all_263_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_263_2, all_17_2,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, simplifying with (143), (172) gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_263_2 = 0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_263_1, all_478_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (173), (231)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_478_1 = all_263_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_38_0, all_553_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (69), (256)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_553_1 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_498_0, all_553_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (236), (256)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_553_1 = all_498_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_498_0, all_558_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (236), (260)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_558_0 = all_498_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_478_1, all_558_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (231), (260)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_558_0 = all_478_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_334_1, all_558_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_2, all_17_4, simplifying with (192), (260)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_558_0 = all_334_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_355_1, all_355_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (196), (197)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_355_0 = all_355_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_263_0, all_355_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (174), (197)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_355_0 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_355_1, all_368_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (196), (202)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_368_1 = all_355_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_24_0, all_498_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (44), (237)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_498_1 = all_24_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_368_1, all_498_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (202), (237)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_498_1 = all_368_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_319_0, all_498_1,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (182), (237)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_498_1 = all_319_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_368_1, all_523_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (202), (241)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_523_0 = all_368_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_324_0, all_523_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (187), (241)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_523_0 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_523_0, all_543_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (241), (252)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_543_0 = all_523_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_373_0, all_543_0,
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_17_0, all_17_3, simplifying with (207), (252)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_543_0 = all_373_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_478_1 = all_334_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_478_1 = all_334_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (271) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_498_0 = all_334_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_498_0 = all_334_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (268) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_498_0 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_498_0 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_523_0 = all_373_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_523_0 = all_373_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (264) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_533_3 = all_263_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (290) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_533_3 = all_263_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (291) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_418_3 = all_263_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_418_3 = all_263_3
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (289) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_373_0 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (289) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_373_0 = all_368_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (287) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_334_1 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_334_1 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (277) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_319_0 = all_24_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (277) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_368_1 = all_319_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (299) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_368_1 = all_319_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (283) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_334_1 = all_263_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_334_1 = all_263_1
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (293) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_263_3 = 0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (295) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_368_1 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (304) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_368_1 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (305) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_355_1 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_355_1 = all_324_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (305) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_324_0 = all_319_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (273) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_355_1 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_355_1 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (310) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_324_0 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_324_0 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (302) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_263_1 = all_38_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (312) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_319_0 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_319_0 = all_263_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (315) imply:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_263_0 = all_24_0
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)   ~ (all_263_2 = 0)
% 26.86/4.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (265), (317) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  $false
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent.
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)   ~ (all_263_3 = 0) | all_263_0 = 0 | all_263_1 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)   ~ (all_263_3 = 0)
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (320) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  $false
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_263_0 = 0 | all_263_1 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_263_0 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (323) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_24_0 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (324) implies:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_24_0 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (325) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  $false
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (326) is inconsistent.
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_263_1 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (327) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_38_0 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (328) implies:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_38_0 = 0
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (329) imply:
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  $false
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent.
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | | 
% 26.86/4.95  | | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | | 
% 26.86/4.95  | | | | | | | | End of split
% 26.86/4.95  | | | | | | | | 
% 26.86/4.95  | | | | | | | End of split
% 26.86/4.95  | | | | | | | 
% 26.86/4.95  | | | | | | End of split
% 26.86/4.95  | | | | | | 
% 26.86/4.95  | | | | | Case 2:
% 26.86/4.95  | | | | | | 
% 26.86/4.95  | | | | | |   (331)  all_30_0 = 0
% 26.86/4.95  | | | | | | 
% 26.86/4.95  | | | | | | REDUCE: (122), (331) imply:
% 26.86/4.95  | | | | | |   (332)  $false
% 26.86/4.95  | | | | | | 
% 26.86/4.95  | | | | | | CLOSE: (332) is inconsistent.
% 26.86/4.95  | | | | | | 
% 26.86/4.95  | | | | | End of split
% 26.86/4.95  | | | | | 
% 26.86/4.95  | | | | Case 2:
% 26.86/4.95  | | | | | 
% 26.86/4.95  | | | | |   (333)   ~ (all_24_1 = 0)
% 26.86/4.95  | | | | | 
% 26.86/4.95  | | | | | REF_CLOSE: (11), (18), (47), (121), (123), (133), (134), (333),
% 26.86/4.95  | | | | |            (apart1) are inconsistent by sub-proof #2.
% 26.86/4.95  | | | | | 
% 26.86/4.95  | | | | End of split
% 26.86/4.95  | | | | 
% 26.86/4.95  | | | End of split
% 26.86/4.95  | | | 
% 26.86/4.95  | | End of split
% 26.86/4.95  | | 
% 26.86/4.95  | End of split
% 26.86/4.95  | 
% 26.86/4.95  End of proof
% 26.86/4.95  
% 26.86/4.95  Sub-proof #1 shows that the following formulas are inconsistent:
% 26.86/4.95  ----------------------------------------------------------------
% 26.86/4.95    (1)   ~ (all_38_0 = 0)
% 26.86/4.95    (2)  all_28_0 = 0
% 26.86/4.95    (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 26.86/4.95         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 26.86/4.95           (distinct_points(v3, v2) = v0))
% 26.86/4.95    (4)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any]
% 26.86/4.95         :  ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 &
% 26.86/4.95           apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.95           distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4,
% 26.86/4.95             all_17_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.95    (5)  all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0
% 26.86/4.95    (6)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any]
% 26.86/4.95         :  ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 &
% 26.86/4.95           apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.95           distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4,
% 26.86/4.95             all_17_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.95    (7)   ~ (all_28_0 = 0) |  ~ (all_28_1 = 0)
% 26.86/4.95    (8)  $i(all_17_4)
% 26.86/4.95    (9)   ~ (all_26_0 = 0)
% 26.86/4.95    (10)   ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) |  ~ $i(v0))
% 26.86/4.95    (11)  all_28_1 = all_24_1
% 26.86/4.95  
% 26.86/4.95  Begin of proof
% 26.86/4.95  | 
% 26.86/4.95  | BETA: splitting (7) gives:
% 26.86/4.95  | 
% 26.86/4.95  | Case 1:
% 26.86/4.95  | | 
% 26.86/4.95  | |   (12)   ~ (all_28_0 = 0)
% 26.86/4.95  | | 
% 26.86/4.95  | | REDUCE: (2), (12) imply:
% 26.86/4.95  | |   (13)  $false
% 26.86/4.95  | | 
% 26.86/4.95  | | CLOSE: (13) is inconsistent.
% 26.86/4.95  | | 
% 26.86/4.95  | Case 2:
% 26.86/4.95  | | 
% 26.86/4.95  | |   (14)   ~ (all_28_1 = 0)
% 26.86/4.95  | | 
% 26.86/4.95  | | REDUCE: (11), (14) imply:
% 26.86/4.95  | |   (15)   ~ (all_24_1 = 0)
% 26.86/4.95  | | 
% 26.86/4.95  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (15) are inconsistent by
% 26.86/4.95  | |            sub-proof #2.
% 26.86/4.95  | | 
% 26.86/4.95  | End of split
% 26.86/4.95  | 
% 26.86/4.95  End of proof
% 26.86/4.95  
% 26.86/4.95  Sub-proof #2 shows that the following formulas are inconsistent:
% 26.86/4.95  ----------------------------------------------------------------
% 26.86/4.95    (1)   ~ (all_38_0 = 0)
% 26.86/4.95    (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 26.86/4.95         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 26.86/4.95           (distinct_points(v3, v2) = v0))
% 26.86/4.95    (3)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any]
% 26.86/4.95         :  ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 &
% 26.86/4.95           apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.95           distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4,
% 26.86/4.95             all_17_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.95    (4)  all_24_1 = 0 | distinct_points(all_17_4, all_17_4) = 0
% 26.86/4.95    (5)  all_38_0 = 0 | all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any]
% 26.86/4.95         :  ? [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 &
% 26.86/4.95           apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.95           distinct_lines(all_26_1, all_17_2) = v1 & distinct_points(all_17_4,
% 26.86/4.95             all_17_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.95    (6)  $i(all_17_4)
% 26.86/4.96    (7)   ~ (all_26_0 = 0)
% 26.86/4.96    (8)   ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) |  ~ $i(v0))
% 26.86/4.96    (9)   ~ (all_24_1 = 0)
% 26.86/4.96  
% 26.86/4.96  Begin of proof
% 26.86/4.96  | 
% 26.86/4.96  | BETA: splitting (4) gives:
% 26.86/4.96  | 
% 26.86/4.96  | Case 1:
% 26.86/4.96  | | 
% 26.86/4.96  | |   (10)  distinct_points(all_17_4, all_17_4) = 0
% 26.86/4.96  | | 
% 26.86/4.96  | | BETA: splitting (3) gives:
% 26.86/4.96  | | 
% 26.86/4.96  | | Case 1:
% 26.86/4.96  | | | 
% 26.86/4.96  | | |   (11)  all_38_0 = 0
% 26.86/4.96  | | | 
% 26.86/4.96  | | | REDUCE: (1), (11) imply:
% 26.86/4.96  | | |   (12)  $false
% 26.86/4.96  | | | 
% 26.86/4.96  | | | CLOSE: (12) is inconsistent.
% 26.86/4.96  | | | 
% 26.86/4.96  | | Case 2:
% 26.86/4.96  | | | 
% 26.86/4.96  | | |   (13)  all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.96  | | |         [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v3 &
% 26.86/4.96  | | |           apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.96  | | |           distinct_lines(all_26_1, all_17_2) = v1 &
% 26.86/4.96  | | |           distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~ (v0
% 26.86/4.96  | | |               = 0) | v3 = 0 | v2 = 0))
% 26.86/4.96  | | | 
% 26.86/4.96  | | | BETA: splitting (5) gives:
% 26.86/4.96  | | | 
% 26.86/4.96  | | | Case 1:
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | |   (14)  all_38_0 = 0
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | | REDUCE: (1), (14) imply:
% 26.86/4.96  | | | |   (15)  $false
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | | CLOSE: (15) is inconsistent.
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | Case 2:
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | |   (16)  all_26_0 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ?
% 26.86/4.96  | | | |         [v3: any] : (apart_point_and_line(all_17_4, all_26_1) = v2 &
% 26.86/4.96  | | | |           apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.96  | | | |           distinct_lines(all_26_1, all_17_2) = v1 &
% 26.86/4.96  | | | |           distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.86/4.96  | | | |             (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | | BETA: splitting (13) gives:
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | | Case 1:
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | |   (17)  all_26_0 = 0
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | REDUCE: (7), (17) imply:
% 26.86/4.96  | | | | |   (18)  $false
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | CLOSE: (18) is inconsistent.
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | Case 2:
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | |   (19)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 26.86/4.96  | | | | |         (apart_point_and_line(all_17_4, all_26_1) = v3 &
% 26.86/4.96  | | | | |           apart_point_and_line(all_17_4, all_17_2) = v2 &
% 26.86/4.96  | | | | |           distinct_lines(all_26_1, all_17_2) = v1 &
% 26.86/4.96  | | | | |           distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) |  ~
% 26.86/4.96  | | | | |             (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | DELTA: instantiating (19) with fresh symbols all_839_0, all_839_1,
% 26.86/4.96  | | | | |        all_839_2, all_839_3 gives:
% 26.86/4.96  | | | | |   (20)  apart_point_and_line(all_17_4, all_26_1) = all_839_0 &
% 26.86/4.96  | | | | |         apart_point_and_line(all_17_4, all_17_2) = all_839_1 &
% 26.86/4.96  | | | | |         distinct_lines(all_26_1, all_17_2) = all_839_2 &
% 26.86/4.96  | | | | |         distinct_points(all_17_4, all_17_4) = all_839_3 & ( ~
% 26.86/4.96  | | | | |           (all_839_2 = 0) |  ~ (all_839_3 = 0) | all_839_0 = 0 |
% 26.86/4.96  | | | | |           all_839_1 = 0)
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | ALPHA: (20) implies:
% 26.86/4.96  | | | | |   (21)  distinct_points(all_17_4, all_17_4) = all_839_3
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | BETA: splitting (16) gives:
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | | Case 1:
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | |   (22)  all_26_0 = 0
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | REDUCE: (7), (22) imply:
% 26.86/4.96  | | | | | |   (23)  $false
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | CLOSE: (23) is inconsistent.
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | Case 2:
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | |   (24)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 26.86/4.96  | | | | | |         (apart_point_and_line(all_17_4, all_26_1) = v2 &
% 26.86/4.96  | | | | | |           apart_point_and_line(all_17_4, all_17_2) = v3 &
% 26.86/4.96  | | | | | |           distinct_lines(all_26_1, all_17_2) = v1 &
% 26.86/4.96  | | | | | |           distinct_points(all_17_4, all_17_4) = v0 & ( ~ (v1 = 0) | 
% 26.86/4.96  | | | | | |             ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | DELTA: instantiating (24) with fresh symbols all_861_0, all_861_1,
% 26.86/4.96  | | | | | |        all_861_2, all_861_3 gives:
% 26.86/4.96  | | | | | |   (25)  apart_point_and_line(all_17_4, all_26_1) = all_861_1 &
% 26.86/4.96  | | | | | |         apart_point_and_line(all_17_4, all_17_2) = all_861_0 &
% 26.86/4.96  | | | | | |         distinct_lines(all_26_1, all_17_2) = all_861_2 &
% 26.86/4.96  | | | | | |         distinct_points(all_17_4, all_17_4) = all_861_3 & ( ~
% 26.86/4.96  | | | | | |           (all_861_2 = 0) |  ~ (all_861_3 = 0) | all_861_0 = 0 |
% 26.86/4.96  | | | | | |           all_861_1 = 0)
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | ALPHA: (25) implies:
% 26.86/4.96  | | | | | |   (26)  distinct_points(all_17_4, all_17_4) = all_861_3
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | GROUND_INST: instantiating (2) with 0, all_861_3, all_17_4,
% 26.86/4.96  | | | | | |              all_17_4, simplifying with (10), (26) gives:
% 26.86/4.96  | | | | | |   (27)  all_861_3 = 0
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | GROUND_INST: instantiating (2) with all_839_3, all_861_3, all_17_4,
% 26.86/4.96  | | | | | |              all_17_4, simplifying with (21), (26) gives:
% 26.86/4.96  | | | | | |   (28)  all_861_3 = all_839_3
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | COMBINE_EQS: (27), (28) imply:
% 26.86/4.96  | | | | | |   (29)  all_839_3 = 0
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | GROUND_INST: instantiating (8) with all_17_4, simplifying with (6),
% 26.86/4.96  | | | | | |              (10) gives:
% 26.86/4.96  | | | | | |   (30)  $false
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | | CLOSE: (30) is inconsistent.
% 26.86/4.96  | | | | | | 
% 26.86/4.96  | | | | | End of split
% 26.86/4.96  | | | | | 
% 26.86/4.96  | | | | End of split
% 26.86/4.96  | | | | 
% 26.86/4.96  | | | End of split
% 26.86/4.96  | | | 
% 26.86/4.96  | | End of split
% 26.86/4.96  | | 
% 26.86/4.96  | Case 2:
% 26.86/4.96  | | 
% 26.86/4.96  | |   (31)  all_24_1 = 0
% 26.86/4.96  | | 
% 26.86/4.96  | | REDUCE: (9), (31) imply:
% 26.86/4.96  | |   (32)  $false
% 26.86/4.96  | | 
% 26.86/4.96  | | CLOSE: (32) is inconsistent.
% 26.86/4.96  | | 
% 26.86/4.96  | End of split
% 26.86/4.96  | 
% 26.86/4.96  End of proof
% 26.86/4.96  % SZS output end Proof for theBenchmark
% 26.86/4.96  
% 26.86/4.96  4367ms
%------------------------------------------------------------------------------