%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO233+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n008.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 23:22:37 EDT 2023

% Result   : Theorem 48.00s 7.35s
% Output   : Proof 52.91s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO233+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34  % Computer : n008.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Aug 29 19:21:47 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.01/1.13  Prover 1: Preprocessing ...
% 3.01/1.13  Prover 4: Preprocessing ...
% 3.01/1.17  Prover 5: Preprocessing ...
% 3.01/1.17  Prover 0: Preprocessing ...
% 3.01/1.17  Prover 6: Preprocessing ...
% 3.01/1.17  Prover 2: Preprocessing ...
% 3.01/1.18  Prover 3: Preprocessing ...
% 6.13/1.69  Prover 5: Proving ...
% 7.35/1.80  Prover 2: Proving ...
% 7.35/1.80  Prover 6: Constructing countermodel ...
% 7.99/1.84  Prover 1: Constructing countermodel ...
% 7.99/1.85  Prover 3: Constructing countermodel ...
% 8.50/1.93  Prover 6: gave up
% 8.50/1.95  Prover 3: gave up
% 8.50/1.96  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.50/1.96  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.14/1.99  Prover 1: gave up
% 9.14/1.99  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.41/2.02  Prover 8: Preprocessing ...
% 9.41/2.02  Prover 7: Preprocessing ...
% 9.55/2.04  Prover 9: Preprocessing ...
% 10.22/2.16  Prover 7: Warning: ignoring some quantifiers
% 10.72/2.21  Prover 7: Constructing countermodel ...
% 10.72/2.21  Prover 4: Constructing countermodel ...
% 10.72/2.24  Prover 8: Warning: ignoring some quantifiers
% 10.72/2.26  Prover 8: Constructing countermodel ...
% 10.72/2.32  Prover 0: Proving ...
% 12.03/2.42  Prover 8: gave up
% 12.49/2.45  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.76/2.50  Prover 10: Preprocessing ...
% 12.76/2.50  Prover 9: Constructing countermodel ...
% 13.47/2.58  Prover 10: Warning: ignoring some quantifiers
% 13.47/2.58  Prover 7: gave up
% 13.47/2.59  Prover 10: Constructing countermodel ...
% 13.47/2.60  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.14/2.66  Prover 10: gave up
% 14.14/2.68  Prover 12: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 14.14/2.69  Prover 11: Preprocessing ...
% 14.14/2.72  Prover 12: Preprocessing ...
% 15.71/2.95  Prover 12: Proving ...
% 15.71/3.09  Prover 11: Constructing countermodel ...
% 35.78/5.55  Prover 12: stopped
% 35.78/5.55  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.78/5.57  Prover 13: Preprocessing ...
% 36.46/5.67  Prover 13: Warning: ignoring some quantifiers
% 37.04/5.72  Prover 13: Constructing countermodel ...
% 41.04/6.22  Prover 13: gave up
% 41.04/6.23  Prover 14: Options:  -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 41.28/6.27  Prover 14: Preprocessing ...
% 43.94/6.66  Prover 14: Proving ...
% 48.00/7.35  Prover 14: proved (1128ms)
% 48.00/7.35  
% 48.00/7.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.08/7.35  
% 49.08/7.35  Prover 9: stopped
% 49.08/7.35  Prover 5: stopped
% 49.08/7.35  Prover 0: stopped
% 49.08/7.35  Prover 2: stopped
% 49.08/7.35  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 49.08/7.35  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 49.08/7.38  Prover 16: Preprocessing ...
% 49.08/7.38  Prover 19: Preprocessing ...
% 49.08/7.42  Prover 16: Warning: ignoring some quantifiers
% 49.08/7.43  Prover 16: Constructing countermodel ...
% 50.49/7.46  Prover 19: Warning: ignoring some quantifiers
% 50.49/7.47  Prover 19: Constructing countermodel ...
% 51.30/7.63  Prover 16: gave up
% 51.30/7.63  Prover 19: gave up
% 52.36/7.78  Prover 11: Found proof (size 203)
% 52.36/7.78  Prover 11: proved (5176ms)
% 52.36/7.78  Prover 4: stopped
% 52.36/7.78  
% 52.36/7.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.36/7.78  
% 52.36/7.79  % SZS output start Proof for theBenchmark
% 52.36/7.79  Assumptions after simplification:
% 52.36/7.79  ---------------------------------
% 52.36/7.79  
% 52.36/7.79    (a1_defns)
% 52.66/7.82     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 52.66/7.82      (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ~
% 52.66/7.82      $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) &
% 52.66/7.82        unequally_directed_opposite_lines(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1:
% 52.66/7.82      $i] :  ! [v2: int] : (v2 = 0 |  ~ (unequally_directed_opposite_lines(v0, v1)
% 52.66/7.82        = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0)
% 52.66/7.82        & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 52.66/7.82    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (reverse_line(v1) = v2) |  ~
% 52.66/7.82      (unequally_directed_lines(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 52.66/7.82      unequally_directed_opposite_lines(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] :
% 52.66/7.82    ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 52.66/7.82      ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 52.66/7.82        $i(v2)))
% 52.66/7.82  
% 52.66/7.82    (a2_defns)
% 52.66/7.83     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 52.66/7.83      (left_apart_point(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ~ $i(v1) | 
% 52.66/7.83      ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & 
% 52.66/7.83    ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (right_apart_point(v0,
% 52.66/7.83          v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4
% 52.66/7.83          = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3 & $i(v3)))
% 52.66/7.83    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0)
% 52.66/7.83      |  ~ (reverse_line(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | right_apart_point(v0,
% 52.66/7.83        v1) = 0) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0)
% 52.66/7.83      |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] : (left_apart_point(v0, v2) = 0 &
% 52.66/7.83        reverse_line(v1) = v2 & $i(v2)))
% 52.66/7.83  
% 52.66/7.83    (a4_defns)
% 52.66/7.83     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.66/7.83      (equally_directed_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 52.66/7.83      unequally_directed_lines(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 52.66/7.83      int] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) = v2) |  ~ $i(v1) |  ~
% 52.66/7.83      $i(v0) | equally_directed_lines(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] : (
% 52.66/7.83      ~ (equally_directed_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2:
% 52.66/7.83        int] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) &  ! [v0:
% 52.66/7.83      $i] :  ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ~ $i(v1) |
% 52.66/7.83       ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) =
% 52.66/7.83        v2))
% 52.66/7.83  
% 52.66/7.83    (a6_defns)
% 52.66/7.83     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.66/7.83      (apart_point_and_line(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] :
% 52.66/7.83       ? [v4: int] : ( ~ (v4 = 0) &  ~ (v3 = 0) & left_apart_point(v0, v1) = v3 &
% 52.66/7.83        right_apart_point(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 52.66/7.83      int] : (v2 = 0 |  ~ (left_apart_point(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 52.66/7.83      |  ? [v3: int] :  ? [v4: int] : ((v4 = 0 & right_apart_point(v0, v1) = 0) |
% 52.66/7.83        ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) &  ! [v0: $i] :  !
% 52.66/7.83    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (right_apart_point(v0, v1) = v2) |  ~
% 52.66/7.83      $i(v1) |  ~ $i(v0) |  ? [v3: int] :  ? [v4: int] : ((v4 = 0 &
% 52.66/7.83          left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0,
% 52.66/7.83            v1) = v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~
% 52.66/7.83      (left_apart_point(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] :  ?
% 52.66/7.83      [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) &  ~
% 52.66/7.83          (v2 = 0) & right_apart_point(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1: $i]
% 52.66/7.83    :  ! [v2: any] : ( ~ (right_apart_point(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 52.66/7.83      |  ? [v3: int] :  ? [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0)
% 52.66/7.83        | ( ~ (v3 = 0) &  ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) &  ! [v0:
% 52.66/7.83      $i] :  ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ~ $i(v1) |  ~
% 52.66/7.83      $i(v0) |  ? [v2: int] :  ? [v3: int] : ((v3 = 0 & right_apart_point(v0, v1)
% 52.66/7.83          = 0) | (v2 = 0 & left_apart_point(v0, v1) = 0)))
% 52.66/7.83  
% 52.66/7.83    (a7_defns)
% 52.66/7.84     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (convergent_lines(v0,
% 52.66/7.84          v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] :  ? [v4: int] : (( ~
% 52.66/7.84          (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4) | ( ~ (v3 =
% 52.66/7.84            0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1:
% 52.66/7.84      $i] :  ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) |  ~ $i(v1)
% 52.66/7.84      |  ~ $i(v0) |  ? [v3: int] :  ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 52.66/7.84          unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 52.66/7.84          convergent_lines(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 52.66/7.84      any] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) |  ~ $i(v1) |  ~
% 52.66/7.84      $i(v0) |  ? [v3: int] :  ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 52.66/7.84          unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 52.66/7.84          convergent_lines(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 52.66/7.84      (convergent_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 52.66/7.84      (unequally_directed_lines(v0, v1) = 0 &
% 52.66/7.84        unequally_directed_opposite_lines(v0, v1) = 0)) &  ! [v0: $i] :  ! [v1:
% 52.66/7.84      $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 52.66/7.84      ? [v2: int] :  ? [v3: int] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~
% 52.66/7.84          (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) &  ! [v0:
% 52.66/7.84      $i] :  ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ~
% 52.66/7.84      $i(v1) |  ~ $i(v0) |  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 52.66/7.84          convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) &
% 52.66/7.84          unequally_directed_lines(v0, v1) = v2)))
% 52.66/7.84  
% 52.66/7.84    (ax11_basics)
% 52.66/7.84     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) =
% 52.66/7.84        0) |  ~ (reverse_line(v1) = v2) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] : 
% 52.66/7.84    ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0))
% 52.66/7.84  
% 52.66/7.84    (ax1_uniq_cons)
% 52.91/7.87     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 52.91/7.87      int] :  ! [v6: $i] :  ! [v7: int] : (v7 = 0 | v5 = 0 |  ~
% 52.91/7.87      (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v6) = v7) |  ~
% 52.91/7.87      (left_apart_point(v1, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~
% 52.91/7.87      (reverse_line(v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.87      [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ? [v12: int] : 
% 52.91/7.87      ? [v13: int] :  ? [v14: int] : ((v14 = 0 & left_apart_point(v0, v6) = 0) |
% 52.91/7.87        (v13 = 0 & left_apart_point(v0, v4) = 0) | (v12 = 0 & left_apart_point(v1,
% 52.91/7.87            v3) = 0) | (v11 = 0 & left_apart_point(v0, v3) = 0) | (v10 = 0 &
% 52.91/7.87          left_apart_point(v1, v2) = 0) | (v9 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.87        | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.87      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: int] :  ! [v6: $i] :
% 52.91/7.87     ! [v7: int] : (v7 = 0 | v5 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~
% 52.91/7.87      (left_apart_point(v0, v6) = v7) |  ~ (left_apart_point(v0, v4) = v5) |  ~
% 52.91/7.87      (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ~ $i(v3) |  ~ $i(v2)
% 52.91/7.87      |  ~ $i(v1) |  ~ $i(v0) |  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ?
% 52.91/7.87      [v11: int] :  ? [v12: int] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 &
% 52.91/7.87          left_apart_point(v1, v6) = 0) | (v13 = 0 & left_apart_point(v1, v4) = 0)
% 52.91/7.87        | (v12 = 0 & left_apart_point(v1, v3) = 0) | (v11 = 0 &
% 52.91/7.87          left_apart_point(v0, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0)
% 52.91/7.87        | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) &
% 52.91/7.87          distinct_lines(v2, v3) = v8))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 52.91/7.87    :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: int] :  ! [v6: $i] :  ! [v7: int] : (v7
% 52.91/7.87      = 0 | v5 = 0 |  ~ (left_apart_point(v1, v6) = v7) |  ~ (left_apart_point(v0,
% 52.91/7.87          v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ~
% 52.91/7.87      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v8: int] :  ? [v9: int] : 
% 52.91/7.87      ? [v10: int] :  ? [v11: int] :  ? [v12: int] :  ? [v13: int] :  ? [v14: int]
% 52.91/7.87      :  ? [v15: int] : ((v15 = 0 & left_apart_point(v0, v6) = 0) | (v14 = 0 &
% 52.91/7.87          left_apart_point(v1, v4) = 0) | (v13 = 0 & left_apart_point(v1, v3) = 0)
% 52.91/7.87        | (v12 = 0 & left_apart_point(v0, v3) = 0) | (v11 = 0 &
% 52.91/7.87          left_apart_point(v1, v2) = 0) | (v10 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.87        | ( ~ (v9 = 0) & distinct_lines(v2, v3) = v9) | ( ~ (v8 = 0) &
% 52.91/7.87          distinct_points(v0, v1) = v8))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 52.91/7.87      $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: int] :  ! [v6: $i] :  ! [v7: int]
% 52.91/7.87    : (v7 = 0 | v5 = 0 |  ~ (left_apart_point(v1, v4) = v5) |  ~
% 52.91/7.87      (left_apart_point(v0, v6) = v7) |  ~ (reverse_line(v3) = v6) |  ~
% 52.91/7.87      (reverse_line(v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.87      [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ? [v12: int] : 
% 52.91/7.87      ? [v13: int] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.87          left_apart_point(v1, v6) = 0) | (v14 = 0 & left_apart_point(v0, v4) = 0)
% 52.91/7.87        | (v13 = 0 & left_apart_point(v1, v3) = 0) | (v12 = 0 &
% 52.91/7.87          left_apart_point(v0, v3) = 0) | (v11 = 0 & left_apart_point(v1, v2) = 0)
% 52.91/7.87        | (v10 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v9 = 0) &
% 52.91/7.87          distinct_lines(v2, v3) = v9) | ( ~ (v8 = 0) & distinct_points(v0, v1) =
% 52.91/7.87          v8))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.87      $i] :  ! [v5: int] :  ! [v6: int] : (v6 = 0 | v5 = 0 |  ~
% 52.91/7.87      (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v4) = v6) |  ~
% 52.91/7.87      (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v4) |  ~ $i(v3) | 
% 52.91/7.87      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.87        int] :  ? [v10: int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ?
% 52.91/7.87      [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v2) =
% 52.91/7.87          v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 &
% 52.91/7.87          reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v3)
% 52.91/7.87          = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 &
% 52.91/7.87          left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.87        | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.87      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: int] :  ! [v6: int]
% 52.91/7.87    : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~
% 52.91/7.87      (left_apart_point(v1, v4) = v6) |  ~ (left_apart_point(v0, v4) = v5) |  ~
% 52.91/7.87      (reverse_line(v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.87      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.87      [v12: $i] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 & left_apart_point(v1,
% 52.91/7.87            v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 &
% 52.91/7.87          left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11
% 52.91/7.87          = 0 & left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0,
% 52.91/7.87            v3) = 0) | (v9 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 &
% 52.91/7.87          left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.87          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.87      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.87      (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~
% 52.91/7.87      (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v3) = v5) |  ~ $i(v3) | 
% 52.91/7.87      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.87        int] :  ? [v10: int] :  ? [v11: $i] :  ? [v12: int] :  ? [v13: int] :  ?
% 52.91/7.87      [v14: int] : ((v14 = 0 & left_apart_point(v0, v5) = 0) | (v13 = 0 &
% 52.91/7.87          left_apart_point(v1, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v12
% 52.91/7.87          = 0 & left_apart_point(v0, v11) = 0 & reverse_line(v2) = v11 & $i(v11))
% 52.91/7.87        | (v10 = 0 & left_apart_point(v1, v3) = 0) | (v9 = 0 &
% 52.91/7.87          left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.87        | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.87      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int]
% 52.91/7.87    : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~
% 52.91/7.88      (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~
% 52.91/7.88      (reverse_line(v2) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: $i] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 & left_apart_point(v1,
% 52.91/7.88            v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 &
% 52.91/7.88          left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11
% 52.91/7.88          = 0 & left_apart_point(v0, v5) = 0) | (v10 = 0 & left_apart_point(v1,
% 52.91/7.88            v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 &
% 52.91/7.88          left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.88      (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v3) = v4) |  ~
% 52.91/7.88      (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v3) = v5) |  ~ $i(v3) | 
% 52.91/7.88      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.88        int] :  ? [v10: int] :  ? [v11: $i] :  ? [v12: int] :  ? [v13: int] :  ?
% 52.91/7.88      [v14: int] : ((v14 = 0 & left_apart_point(v1, v5) = 0) | (v13 = 0 &
% 52.91/7.88          left_apart_point(v1, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v12
% 52.91/7.88          = 0 & left_apart_point(v0, v11) = 0 & reverse_line(v2) = v11 & $i(v11))
% 52.91/7.88        | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 &
% 52.91/7.88          left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.88        | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.88      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int]
% 52.91/7.88    : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~
% 52.91/7.88      (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~
% 52.91/7.88      (reverse_line(v2) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: $i] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 & left_apart_point(v1,
% 52.91/7.88            v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 &
% 52.91/7.88          left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11
% 52.91/7.88          = 0 & left_apart_point(v1, v5) = 0) | (v10 = 0 & left_apart_point(v1,
% 52.91/7.88            v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 &
% 52.91/7.88          left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.88      (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~
% 52.91/7.88      (left_apart_point(v1, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ~ $i(v3) | 
% 52.91/7.88      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.88        int] :  ? [v10: int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ?
% 52.91/7.88      [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) =
% 52.91/7.88          v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 &
% 52.91/7.88          reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v0, v5)
% 52.91/7.88          = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 &
% 52.91/7.88          left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.88        | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.88      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int]
% 52.91/7.88    : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~
% 52.91/7.88      (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v1, v2) = v4) |  ~
% 52.91/7.88      (reverse_line(v3) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: $i] :  ?
% 52.91/7.88      [v12: int] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 &
% 52.91/7.88          left_apart_point(v0, v5) = 0) | (v13 = 0 & left_apart_point(v1, v11) = 0
% 52.91/7.88          & reverse_line(v2) = v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0,
% 52.91/7.88            v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v10 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 52.91/7.88    :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |
% 52.91/7.88       ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v5) = v6) |  ~
% 52.91/7.88      (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ~ $i(v3) | 
% 52.91/7.88      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.88        int] :  ? [v10: int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ?
% 52.91/7.88      [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) =
% 52.91/7.88          v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 &
% 52.91/7.88          reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v5)
% 52.91/7.88          = 0) | (v10 = 0 & left_apart_point(v1, v3) = 0) | (v9 = 0 &
% 52.91/7.88          left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0)
% 52.91/7.88        | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.88      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int]
% 52.91/7.88    : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~
% 52.91/7.88      (left_apart_point(v0, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~
% 52.91/7.88      (reverse_line(v3) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: $i] :  ?
% 52.91/7.88      [v12: int] :  ? [v13: int] :  ? [v14: int] : ((v14 = 0 &
% 52.91/7.88          left_apart_point(v1, v5) = 0) | (v13 = 0 & left_apart_point(v1, v11) = 0
% 52.91/7.88          & reverse_line(v2) = v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0,
% 52.91/7.88            v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v10 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | (v8 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 52.91/7.88    :  ! [v3: $i] :  ! [v4: int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |
% 52.91/7.88       ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~
% 52.91/7.88      (reverse_line(v2) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: int] :  ? [v13: $i] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14
% 52.91/7.88          = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13))
% 52.91/7.88        | (v12 = 0 & left_apart_point(v0, v5) = 0) | (v11 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0)
% 52.91/7.88        | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.88      (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~
% 52.91/7.88      (reverse_line(v3) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: $i] :  ? [v13: int] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v0, v5) = 0) | (v14 = 0 & left_apart_point(v1, v12) = 0
% 52.91/7.88          & reverse_line(v2) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0,
% 52.91/7.88            v12) = 0 & reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | (v9 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v8 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.88      (left_apart_point(v1, v3) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~
% 52.91/7.88      (reverse_line(v2) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: int] :  ? [v13: $i] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14
% 52.91/7.88          = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13))
% 52.91/7.88        | (v12 = 0 & left_apart_point(v1, v5) = 0) | (v11 = 0 &
% 52.91/7.88          left_apart_point(v0, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0)
% 52.91/7.88        | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.88      (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~
% 52.91/7.88      (reverse_line(v3) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: int] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: $i] :  ? [v13: int] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v1, v5) = 0) | (v14 = 0 & left_apart_point(v1, v12) = 0
% 52.91/7.88          & reverse_line(v2) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0,
% 52.91/7.88            v12) = 0 & reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) =
% 52.91/7.88          v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 52.91/7.88      int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) | 
% 52.91/7.88      ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v3) = v4) |  ~
% 52.91/7.88      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] : 
% 52.91/7.88      ? [v8: int] :  ? [v9: $i] :  ? [v10: int] :  ? [v11: int] :  ? [v12: $i] : 
% 52.91/7.88      ? [v13: int] :  ? [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 &
% 52.91/7.88          reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12)
% 52.91/7.88          = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 &
% 52.91/7.88          left_apart_point(v1, v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v10 =
% 52.91/7.88          0 & left_apart_point(v0, v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v8
% 52.91/7.88          = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2)
% 52.91/7.88          = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0: $i] :  !
% 52.91/7.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 |
% 52.91/7.88      v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v2) =
% 52.91/7.88        v5) |  ~ (left_apart_point(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 52.91/7.88      $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9:
% 52.91/7.88        $i] :  ? [v10: int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ?
% 52.91/7.88      [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) =
% 52.91/7.88          v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 &
% 52.91/7.88          reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9)
% 52.91/7.88          = 0 & reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0,
% 52.91/7.88            v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0: $i] :  ! [v1:
% 52.91/7.88      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4
% 52.91/7.88      = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v3) = v5)
% 52.91/7.88      |  ~ (left_apart_point(v1, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 52.91/7.88      ~ $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: $i] :  ?
% 52.91/7.88      [v10: int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ? [v14: int] :
% 52.91/7.88      ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = v12 &
% 52.91/7.88          $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & reverse_line(v3) =
% 52.91/7.88          v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9) = 0 &
% 52.91/7.88          reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0, v9) =
% 52.91/7.88          0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 & left_apart_point(v0, v3)
% 52.91/7.88          = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v6))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 52.91/7.88    :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~
% 52.91/7.88      (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v3) = v5) |  ~
% 52.91/7.88      (left_apart_point(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 52.91/7.88      $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: $i] :  ? [v10:
% 52.91/7.88        int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ? [v14: int] :
% 52.91/7.88      ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = v12 &
% 52.91/7.88          $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & reverse_line(v3) =
% 52.91/7.88          v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9) = 0 &
% 52.91/7.88          reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0, v9) =
% 52.91/7.88          0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 & left_apart_point(v1, v3)
% 52.91/7.88          = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) &
% 52.91/7.88          distinct_lines(v2, v3) = v6))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 52.91/7.88    :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~
% 52.91/7.88      (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ~
% 52.91/7.88      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] : 
% 52.91/7.88      ? [v8: int] :  ? [v9: int] :  ? [v10: $i] :  ? [v11: int] :  ? [v12: int] : 
% 52.91/7.88      ? [v13: $i] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14
% 52.91/7.88          = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13))
% 52.91/7.88        | (v12 = 0 & left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 &
% 52.91/7.88          $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 & reverse_line(v2) =
% 52.91/7.88          v10 & $i(v10)) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 &
% 52.91/7.88          left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) =
% 52.91/7.88          v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0: $i] :  !
% 52.91/7.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int] : (v5 = 0 |
% 52.91/7.88      v4 = 0 |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v3) =
% 52.91/7.88        v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ?
% 52.91/7.88      [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10: $i] :  ? [v11: int] :  ?
% 52.91/7.88      [v12: int] :  ? [v13: $i] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.88          left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14
% 52.91/7.88          = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13))
% 52.91/7.88        | (v12 = 0 & left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 &
% 52.91/7.88          $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 & reverse_line(v2) =
% 52.91/7.88          v10 & $i(v10)) | (v9 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 &
% 52.91/7.88          left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) =
% 52.91/7.88          v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0: $i] :  !
% 52.91/7.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |  ~
% 52.91/7.88      (distinct_points(v0, v1) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 52.91/7.88      $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8:
% 52.91/7.88        $i] :  ? [v9: int] :  ? [v10: int] :  ? [v11: $i] :  ? [v12: int] :  ?
% 52.91/7.88      [v13: int] : ((v13 = 0 & left_apart_point(v1, v11) = 0 & reverse_line(v3) =
% 52.91/7.88          v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0, v11) = 0 &
% 52.91/7.88          reverse_line(v3) = v11 & $i(v11)) | (v10 = 0 & left_apart_point(v1, v8)
% 52.91/7.88          = 0 & reverse_line(v2) = v8 & $i(v8)) | (v9 = 0 & left_apart_point(v0,
% 52.91/7.88            v8) = 0 & reverse_line(v2) = v8 & $i(v8)) | (v7 = 0 &
% 52.91/7.88          left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0)
% 52.91/7.88        | (v5 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0,
% 52.91/7.88            v2) = 0)))
% 52.91/7.88  
% 52.91/7.88    (ax6_basics)
% 52.91/7.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 52.91/7.88      0 | v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~
% 52.91/7.88      (unequally_directed_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 52.91/7.88      |  ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) &  !
% 52.91/7.88    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 52.91/7.88      (unequally_directed_lines(v1, v2) = v3) |  ~ (unequally_directed_lines(v0,
% 52.91/7.88          v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 52.91/7.88      unequally_directed_lines(v0, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 52.91/7.88      $i] :  ! [v3: int] : (v3 = 0 |  ~ (unequally_directed_lines(v0, v2) = v3) | 
% 52.91/7.88      ~ (unequally_directed_lines(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 52.91/7.88      | unequally_directed_lines(v1, v2) = 0)
% 52.91/7.88  
% 52.91/7.88    (ax6_cons_objs)
% 52.91/7.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 52.91/7.88        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] :  ? [v4: $i] :  ? [v5: int] : 
% 52.91/7.88      ? [v6: int] :  ? [v7: int] : (( ~ (v7 = 0) &  ~ (v6 = 0) &
% 52.91/7.88          apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6) |
% 52.91/7.88        ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) =
% 52.91/7.88          v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &
% 52.91/7.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (reverse_line(v1) = v2) |  ~
% 52.91/7.88      (unequally_directed_lines(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 52.91/7.88        int] :  ? [v4: $i] :  ? [v5: int] :  ? [v6: int] : (( ~ (v6 = 0) &  ~ (v5
% 52.91/7.88            = 0) & intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1)
% 52.91/7.88          = v6 & apart_point_and_line(v4, v0) = v5 & $i(v4)) | ( ~ (v3 = 0) &
% 52.91/7.88          unequally_directed_lines(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1: $i] : (
% 52.91/7.88      ~ (unequally_directed_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2:
% 52.91/7.88        $i] :  ? [v3: int] :  ? [v4: $i] :  ? [v5: int] :  ? [v6: int] : (( ~ (v6
% 52.91/7.88            = 0) &  ~ (v5 = 0) & intersection_point(v0, v1) = v4 &
% 52.91/7.88          apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 &
% 52.91/7.88          $i(v4)) | ( ~ (v3 = 0) & reverse_line(v1) = v2 &
% 52.91/7.88          unequally_directed_lines(v0, v2) = v3 & $i(v2))))
% 52.91/7.88  
% 52.91/7.88    (ax8_basics)
% 52.91/7.89     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 52.91/7.89      (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ~
% 52.91/7.89      $i(v1) |  ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) &  ! [v0: $i] : 
% 52.91/7.89    ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) =
% 52.91/7.89        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] : (reverse_line(v1) = v3 &
% 52.91/7.89        unequally_directed_lines(v0, v3) = 0 & $i(v3)))
% 52.91/7.89  
% 52.91/7.89    (ax9_basics)
% 52.91/7.89     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 52.91/7.89      (left_convergent_lines(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ~
% 52.91/7.89      $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int] : ((v6 = 0 &
% 52.91/7.89          left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) &
% 52.91/7.89          unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) &
% 52.91/7.89          unequally_directed_lines(v0, v1) = v4))) &  ! [v0: $i] :  ! [v1: $i] : 
% 52.91/7.89    ! [v2: int] : (v2 = 0 |  ~ (left_convergent_lines(v0, v1) = v2) |  ~ $i(v1) | 
% 52.91/7.89      ~ $i(v0) |  ? [v3: int] :  ? [v4: $i] :  ? [v5: int] :  ? [v6: int] : ((v6 =
% 52.91/7.89          0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4))
% 52.91/7.89        | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4)
% 52.91/7.89          = v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 52.91/7.89    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (reverse_line(v1) = v2) |  ~
% 52.91/7.89      (unequally_directed_lines(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 52.91/7.89        int] :  ? [v4: int] :  ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0,
% 52.91/7.89            v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0)
% 52.91/7.89          & unequally_directed_lines(v0, v1) = v3))) &  ! [v0: $i] :  ! [v1: $i] :
% 52.91/7.89    ( ~ (unequally_directed_lines(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2:
% 52.91/7.89        $i] :  ? [v3: int] :  ? [v4: int] :  ? [v5: int] : ((v5 = 0 &
% 52.91/7.89          left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) |
% 52.91/7.89        (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 52.91/7.89          reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 &
% 52.91/7.89          $i(v2))))
% 52.91/7.89  
% 52.91/7.89    (con)
% 52.91/7.89     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 52.91/7.89      equally_directed_lines(v2, v0) = v3 & reverse_line(v1) = v2 &
% 52.91/7.89      reverse_line(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 52.91/7.89  
% 52.91/7.89    (function-axioms)
% 52.91/7.89     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 52.91/7.89    [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v1 = v0 |  ~ (between_on_line(v5, v4,
% 52.91/7.89          v3, v2) = v1) |  ~ (between_on_line(v5, v4, v3, v2) = v0)) &  ! [v0:
% 52.91/7.89      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 52.91/7.89    :  ! [v4: $i] : (v1 = v0 |  ~ (before_on_line(v4, v3, v2) = v1) |  ~
% 52.91/7.89      (before_on_line(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 52.91/7.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~
% 52.91/7.89      (divides_points(v4, v3, v2) = v1) |  ~ (divides_points(v4, v3, v2) = v0)) & 
% 52.91/7.89    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) =
% 52.91/7.89        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 52.91/7.89      ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 52.91/7.89    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 52.91/7.89    [v3: $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~
% 52.91/7.89      (distinct_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 52.91/7.89    ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 52.91/7.89      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 52.91/7.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  !
% 52.91/7.89    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 52.91/7.89      $i] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~
% 52.91/7.89      (incident_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 52.91/7.89    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 52.91/7.89    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 52.91/7.89      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 52.91/7.89      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 52.91/7.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (equally_directed_opposite_lines(v3, v2) = v1) |  ~
% 52.91/7.89      (equally_directed_opposite_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool]
% 52.91/7.89    :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (equally_directed_lines(v3, v2) = v1) |  ~ (equally_directed_lines(v3, v2) =
% 52.91/7.89        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 52.91/7.89      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (left_convergent_lines(v3, v2) = v1) |  ~
% 52.91/7.89      (left_convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 52.91/7.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (right_convergent_lines(v3, v2) = v1) |  ~ (right_convergent_lines(v3, v2) =
% 52.91/7.89        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 52.91/7.89      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (left_apart_point(v3, v2) = v1) |  ~
% 52.91/7.89      (left_apart_point(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 52.91/7.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (right_apart_point(v3, v2) = v1) |  ~ (right_apart_point(v3, v2) = v0)) &  !
% 52.91/7.89    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 52.91/7.89      $i] : (v1 = v0 |  ~ (unequally_directed_lines(v3, v2) = v1) |  ~
% 52.91/7.89      (unequally_directed_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 52.91/7.89    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 52.91/7.89      (unequally_directed_opposite_lines(v3, v2) = v1) |  ~
% 52.91/7.89      (unequally_directed_opposite_lines(v3, v2) = v0)) &  ! [v0:
% 52.91/7.89      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 52.91/7.89      ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 52.91/7.89    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (line(v2) = v1) |  ~
% 52.91/7.89      (line(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 52.91/7.89      (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 52.91/7.89  
% 52.91/7.89  Further assumptions not needed in the proof:
% 52.91/7.89  --------------------------------------------
% 52.91/7.89  a3_defns, a5_defns, a8_defns, a9_defns, ax10_basics, ax10_cons_objs, ax1_basics,
% 52.91/7.89  ax1_cons_objs, ax1_subs, ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons,
% 52.91/7.89  ax3_basics, ax3_cons_objs, ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns,
% 52.91/7.89  ax5_basics, ax5_cons_objs, ax7_basics, ax7_cons_objs, ax8_cons_objs,
% 52.91/7.89  ax9_cons_objs
% 52.91/7.89  
% 52.91/7.89  Those formulas are unsatisfiable:
% 52.91/7.89  ---------------------------------
% 52.91/7.89  
% 52.91/7.89  Begin of proof
% 52.91/7.89  | 
% 52.91/7.90  | ALPHA: (a1_defns) implies:
% 52.91/7.90  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0,
% 52.91/7.90  |              v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] :
% 52.91/7.90  |          (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 52.91/7.90  |            $i(v2)))
% 52.91/7.90  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.91/7.90  |          (unequally_directed_opposite_lines(v0, v1) = v2) |  ~ $i(v1) |  ~
% 52.91/7.90  |          $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & reverse_line(v1)
% 52.91/7.90  |            = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (a2_defns) implies:
% 52.91/7.90  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.91/7.90  |          (right_apart_point(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 52.91/7.90  |            $i] :  ? [v4: int] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 &
% 52.91/7.90  |            reverse_line(v1) = v3 & $i(v3)))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (a4_defns) implies:
% 52.91/7.90  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.91/7.90  |          (equally_directed_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 52.91/7.90  |          unequally_directed_lines(v0, v1) = 0)
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (a6_defns) implies:
% 52.91/7.90  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.91/7.90  |          (apart_point_and_line(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 52.91/7.90  |            int] :  ? [v4: int] : ( ~ (v4 = 0) &  ~ (v3 = 0) &
% 52.91/7.90  |            left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (a7_defns) implies:
% 52.91/7.90  |   (6)   ! [v0: $i] :  ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0)
% 52.91/7.90  |          |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: int] :  ? [v3: int] : ((v3 = 0 &
% 52.91/7.90  |              convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) &
% 52.91/7.90  |              unequally_directed_opposite_lines(v0, v1) = v2)))
% 52.91/7.90  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~
% 52.91/7.90  |          (unequally_directed_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.90  |          [v3: int] :  ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 52.91/7.90  |              unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 52.91/7.90  |              convergent_lines(v0, v1) = v3)))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax6_basics) implies:
% 52.91/7.90  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] :
% 52.91/7.90  |        (v4 = 0 | v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~
% 52.91/7.90  |          (unequally_directed_lines(v0, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 52.91/7.90  |          $i(v0) |  ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0,
% 52.91/7.90  |              v1) = v5))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax8_basics) implies:
% 52.91/7.90  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 52.91/7.90  |          (unequally_directed_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 52.91/7.90  |          [v3: $i] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3)
% 52.91/7.90  |            = 0 & $i(v3)))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax9_basics) implies:
% 52.91/7.90  |   (10)   ! [v0: $i] :  ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0)
% 52.91/7.90  |           |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3: int] :  ? [v4: int]
% 52.91/7.90  |           :  ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0, v2) = 0 &
% 52.91/7.90  |               reverse_line(v1) = v2 & $i(v2)) | (v4 = 0 &
% 52.91/7.90  |               left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 52.91/7.90  |               reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 &
% 52.91/7.90  |               $i(v2))))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax11_basics) implies:
% 52.91/7.90  |   (11)   ! [v0: $i] :  ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | 
% 52.91/7.90  |           ~ $i(v1) |  ~ $i(v0))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax6_cons_objs) implies:
% 52.91/7.90  |   (12)   ! [v0: $i] :  ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0)
% 52.91/7.90  |           |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3: int] :  ? [v4: $i] :
% 52.91/7.90  |            ? [v5: int] :  ? [v6: int] : (( ~ (v6 = 0) &  ~ (v5 = 0) &
% 52.91/7.90  |               intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) =
% 52.91/7.90  |               v6 & apart_point_and_line(v4, v0) = v5 & $i(v4)) | ( ~ (v3 = 0)
% 52.91/7.90  |               & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3
% 52.91/7.90  |               & $i(v2))))
% 52.91/7.90  | 
% 52.91/7.90  | ALPHA: (ax1_uniq_cons) implies:
% 52.91/7.91  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 52.91/7.91  |          ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v3) = v5) |
% 52.91/7.91  |            ~ (left_apart_point(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 52.91/7.91  |           $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ?
% 52.91/7.91  |           [v9: int] :  ? [v10: $i] :  ? [v11: int] :  ? [v12: int] :  ? [v13:
% 52.91/7.91  |             $i] :  ? [v14: int] :  ? [v15: int] : ((v15 = 0 &
% 52.91/7.91  |               left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 &
% 52.91/7.91  |               $i(v13)) | (v14 = 0 & left_apart_point(v0, v13) = 0 &
% 52.91/7.91  |               reverse_line(v3) = v13 & $i(v13)) | (v12 = 0 &
% 52.91/7.91  |               left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 &
% 52.91/7.91  |               $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 &
% 52.91/7.91  |               reverse_line(v2) = v10 & $i(v10)) | (v9 = 0 &
% 52.91/7.91  |               left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v1,
% 52.91/7.91  |                 v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~
% 52.91/7.91  |               (v6 = 0) & distinct_points(v0, v1) = v6)))
% 52.91/7.91  |   (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :
% 52.91/7.91  |          ! [v5: $i] :  ! [v6: int] : (v6 = 0 | v4 = 0 |  ~
% 52.91/7.91  |           (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4)
% 52.91/7.91  |           |  ~ (reverse_line(v3) = v5) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 52.91/7.91  |           ~ $i(v0) |  ? [v7: int] :  ? [v8: int] :  ? [v9: int] :  ? [v10:
% 52.91/7.91  |             int] :  ? [v11: int] :  ? [v12: $i] :  ? [v13: int] :  ? [v14:
% 52.91/7.91  |             int] :  ? [v15: int] : ((v15 = 0 & left_apart_point(v0, v5) = 0) |
% 52.91/7.91  |             (v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v2) = v12
% 52.91/7.91  |               & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 &
% 52.91/7.91  |               reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 &
% 52.91/7.91  |               left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0,
% 52.91/7.91  |                 v3) = 0) | (v9 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v8 =
% 52.91/7.91  |                 0) & distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) &
% 52.91/7.91  |               distinct_points(v0, v1) = v7)))
% 52.91/7.91  | 
% 52.91/7.91  | ALPHA: (function-axioms) implies:
% 52.91/7.91  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 52.91/7.91  |           (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 52.91/7.91  |   (16)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 52.91/7.91  |         :  ! [v3: $i] : (v1 = v0 |  ~ (unequally_directed_lines(v3, v2) = v1)
% 52.91/7.91  |           |  ~ (unequally_directed_lines(v3, v2) = v0))
% 52.91/7.91  |   (17)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 52.91/7.91  |         :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 52.91/7.91  |           (convergent_lines(v3, v2) = v0))
% 52.91/7.91  | 
% 52.91/7.91  | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2,
% 52.91/7.91  |        all_39_3 gives:
% 52.91/7.91  |   (18)   ~ (all_39_0 = 0) & equally_directed_lines(all_39_1, all_39_3) =
% 52.91/7.91  |         all_39_0 & reverse_line(all_39_2) = all_39_1 & reverse_line(all_39_3)
% 52.91/7.91  |         = all_39_2 & $i(all_39_1) & $i(all_39_2) & $i(all_39_3)
% 52.91/7.91  | 
% 52.91/7.91  | ALPHA: (18) implies:
% 52.91/7.91  |   (19)   ~ (all_39_0 = 0)
% 52.91/7.91  |   (20)  $i(all_39_3)
% 52.91/7.91  |   (21)  $i(all_39_2)
% 52.91/7.91  |   (22)  $i(all_39_1)
% 52.91/7.91  |   (23)  reverse_line(all_39_3) = all_39_2
% 52.91/7.91  |   (24)  reverse_line(all_39_2) = all_39_1
% 52.91/7.91  |   (25)  equally_directed_lines(all_39_1, all_39_3) = all_39_0
% 52.91/7.91  | 
% 52.91/7.91  | GROUND_INST: instantiating (4) with all_39_1, all_39_3, all_39_0, simplifying
% 52.91/7.91  |              with (20), (22), (25) gives:
% 52.91/7.91  |   (26)  all_39_0 = 0 | unequally_directed_lines(all_39_1, all_39_3) = 0
% 52.91/7.91  | 
% 52.91/7.91  | BETA: splitting (26) gives:
% 52.91/7.91  | 
% 52.91/7.91  | Case 1:
% 52.91/7.91  | | 
% 52.91/7.91  | |   (27)  unequally_directed_lines(all_39_1, all_39_3) = 0
% 52.91/7.91  | | 
% 52.91/7.91  | | GROUND_INST: instantiating (12) with all_39_1, all_39_3, simplifying with
% 52.91/7.91  | |              (20), (22), (27) gives:
% 52.91/7.91  | |   (28)   ? [v0: $i] :  ? [v1: int] :  ? [v2: $i] :  ? [v3: int] :  ? [v4:
% 52.91/7.91  | |           int] : (( ~ (v4 = 0) &  ~ (v3 = 0) & intersection_point(all_39_1,
% 52.91/7.91  | |               all_39_3) = v2 & apart_point_and_line(v2, all_39_1) = v3 &
% 52.91/7.91  | |             apart_point_and_line(v2, all_39_3) = v4 & $i(v2)) | ( ~ (v1 = 0)
% 52.91/7.91  | |             & reverse_line(all_39_3) = v0 &
% 52.91/7.91  | |             unequally_directed_lines(all_39_1, v0) = v1 & $i(v0)))
% 52.91/7.91  | | 
% 52.91/7.91  | | GROUND_INST: instantiating (10) with all_39_1, all_39_3, simplifying with
% 52.91/7.91  | |              (20), (22), (27) gives:
% 52.91/7.91  | |   (29)   ? [v0: $i] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 = 0
% 52.91/7.91  | |             & left_convergent_lines(all_39_1, v0) = 0 &
% 52.91/7.91  | |             reverse_line(all_39_3) = v0 & $i(v0)) | (v2 = 0 &
% 52.91/7.91  | |             left_convergent_lines(all_39_1, all_39_3) = 0) | ( ~ (v1 = 0) &
% 52.91/7.91  | |             reverse_line(all_39_3) = v0 & unequally_directed_lines(all_39_1,
% 52.91/7.91  | |               v0) = v1 & $i(v0)))
% 52.91/7.91  | | 
% 52.91/7.91  | | GROUND_INST: instantiating (6) with all_39_1, all_39_3, simplifying with
% 52.91/7.91  | |              (20), (22), (27) gives:
% 52.91/7.91  | |   (30)   ? [v0: int] :  ? [v1: int] : ((v1 = 0 & convergent_lines(all_39_1,
% 52.91/7.91  | |               all_39_3) = 0) | ( ~ (v0 = 0) &
% 52.91/7.91  | |             unequally_directed_opposite_lines(all_39_1, all_39_3) = v0))
% 52.91/7.91  | | 
% 52.91/7.91  | | GROUND_INST: instantiating (7) with all_39_1, all_39_3, 0, simplifying with
% 52.91/7.91  | |              (20), (22), (27) gives:
% 52.91/7.91  | |   (31)   ? [v0: int] :  ? [v1: int] : ((v1 = 0 &
% 52.91/7.91  | |             unequally_directed_opposite_lines(all_39_1, all_39_3) = 0) | ( ~
% 52.91/7.91  | |             (v0 = 0) & convergent_lines(all_39_1, all_39_3) = v0))
% 52.91/7.91  | | 
% 52.91/7.91  | | DELTA: instantiating (31) with fresh symbols all_61_0, all_61_1 gives:
% 52.91/7.91  | |   (32)  (all_61_0 = 0 & unequally_directed_opposite_lines(all_39_1,
% 52.91/7.91  | |             all_39_3) = 0) | ( ~ (all_61_1 = 0) & convergent_lines(all_39_1,
% 52.91/7.91  | |             all_39_3) = all_61_1)
% 52.91/7.91  | | 
% 52.91/7.91  | | DELTA: instantiating (30) with fresh symbols all_62_0, all_62_1 gives:
% 52.91/7.92  | |   (33)  (all_62_0 = 0 & convergent_lines(all_39_1, all_39_3) = 0) | ( ~
% 52.91/7.92  | |           (all_62_1 = 0) & unequally_directed_opposite_lines(all_39_1,
% 52.91/7.92  | |             all_39_3) = all_62_1)
% 52.91/7.92  | | 
% 52.91/7.92  | | DELTA: instantiating (28) with fresh symbols all_63_0, all_63_1, all_63_2,
% 52.91/7.92  | |        all_63_3, all_63_4 gives:
% 52.91/7.92  | |   (34)  ( ~ (all_63_0 = 0) &  ~ (all_63_1 = 0) &
% 52.91/7.92  | |           intersection_point(all_39_1, all_39_3) = all_63_2 &
% 52.91/7.92  | |           apart_point_and_line(all_63_2, all_39_1) = all_63_1 &
% 52.91/7.92  | |           apart_point_and_line(all_63_2, all_39_3) = all_63_0 &
% 52.91/7.92  | |           $i(all_63_2)) | ( ~ (all_63_3 = 0) & reverse_line(all_39_3) =
% 52.91/7.92  | |           all_63_4 & unequally_directed_lines(all_39_1, all_63_4) = all_63_3
% 52.91/7.92  | |           & $i(all_63_4))
% 52.91/7.92  | | 
% 52.91/7.92  | | DELTA: instantiating (29) with fresh symbols all_64_0, all_64_1, all_64_2,
% 52.91/7.92  | |        all_64_3 gives:
% 52.91/7.92  | |   (35)  (all_64_0 = 0 & left_convergent_lines(all_39_1, all_64_3) = 0 &
% 52.91/7.92  | |           reverse_line(all_39_3) = all_64_3 & $i(all_64_3)) | (all_64_1 = 0
% 52.91/7.92  | |           & left_convergent_lines(all_39_1, all_39_3) = 0) | ( ~ (all_64_2 =
% 52.91/7.92  | |             0) & reverse_line(all_39_3) = all_64_3 &
% 52.91/7.92  | |           unequally_directed_lines(all_39_1, all_64_3) = all_64_2 &
% 52.91/7.92  | |           $i(all_64_3))
% 52.91/7.92  | | 
% 52.91/7.92  | | BETA: splitting (34) gives:
% 52.91/7.92  | | 
% 52.91/7.92  | | Case 1:
% 52.91/7.92  | | | 
% 52.91/7.92  | | |   (36)   ~ (all_63_0 = 0) &  ~ (all_63_1 = 0) &
% 52.91/7.92  | | |         intersection_point(all_39_1, all_39_3) = all_63_2 &
% 52.91/7.92  | | |         apart_point_and_line(all_63_2, all_39_1) = all_63_1 &
% 52.91/7.92  | | |         apart_point_and_line(all_63_2, all_39_3) = all_63_0 & $i(all_63_2)
% 52.91/7.92  | | | 
% 52.91/7.92  | | | ALPHA: (36) implies:
% 52.91/7.92  | | |   (37)   ~ (all_63_1 = 0)
% 52.91/7.92  | | |   (38)   ~ (all_63_0 = 0)
% 52.91/7.92  | | |   (39)  $i(all_63_2)
% 52.91/7.92  | | |   (40)  apart_point_and_line(all_63_2, all_39_3) = all_63_0
% 52.91/7.92  | | |   (41)  apart_point_and_line(all_63_2, all_39_1) = all_63_1
% 52.91/7.92  | | | 
% 52.91/7.92  | | | GROUND_INST: instantiating (5) with all_63_2, all_39_3, all_63_0,
% 52.91/7.92  | | |              simplifying with (20), (39), (40) gives:
% 52.91/7.92  | | |   (42)  all_63_0 = 0 |  ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0
% 52.91/7.92  | | |             = 0) & left_apart_point(all_63_2, all_39_3) = v0 &
% 52.91/7.92  | | |           right_apart_point(all_63_2, all_39_3) = v1)
% 52.91/7.92  | | | 
% 52.91/7.92  | | | GROUND_INST: instantiating (5) with all_63_2, all_39_1, all_63_1,
% 52.91/7.92  | | |              simplifying with (22), (39), (41) gives:
% 52.91/7.92  | | |   (43)  all_63_1 = 0 |  ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0
% 52.91/7.92  | | |             = 0) & left_apart_point(all_63_2, all_39_1) = v0 &
% 52.91/7.92  | | |           right_apart_point(all_63_2, all_39_1) = v1)
% 52.91/7.92  | | | 
% 52.91/7.92  | | | BETA: splitting (32) gives:
% 52.91/7.92  | | | 
% 52.91/7.92  | | | Case 1:
% 52.91/7.92  | | | | 
% 52.91/7.92  | | | |   (44)  all_61_0 = 0 & unequally_directed_opposite_lines(all_39_1,
% 52.91/7.92  | | | |           all_39_3) = 0
% 52.91/7.92  | | | | 
% 52.91/7.92  | | | | ALPHA: (44) implies:
% 52.91/7.92  | | | |   (45)  unequally_directed_opposite_lines(all_39_1, all_39_3) = 0
% 52.91/7.92  | | | | 
% 52.91/7.92  | | | | BETA: splitting (43) gives:
% 52.91/7.92  | | | | 
% 52.91/7.92  | | | | Case 1:
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | |   (46)  all_63_1 = 0
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | REDUCE: (37), (46) imply:
% 52.91/7.92  | | | | |   (47)  $false
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | CLOSE: (47) is inconsistent.
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | Case 2:
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | |   (48)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 = 0) &
% 52.91/7.92  | | | | |           left_apart_point(all_63_2, all_39_1) = v0 &
% 52.91/7.92  | | | | |           right_apart_point(all_63_2, all_39_1) = v1)
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | DELTA: instantiating (48) with fresh symbols all_122_0, all_122_1
% 52.91/7.92  | | | | |        gives:
% 52.91/7.92  | | | | |   (49)   ~ (all_122_0 = 0) &  ~ (all_122_1 = 0) &
% 52.91/7.92  | | | | |         left_apart_point(all_63_2, all_39_1) = all_122_1 &
% 52.91/7.92  | | | | |         right_apart_point(all_63_2, all_39_1) = all_122_0
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | ALPHA: (49) implies:
% 52.91/7.92  | | | | |   (50)   ~ (all_122_1 = 0)
% 52.91/7.92  | | | | |   (51)  left_apart_point(all_63_2, all_39_1) = all_122_1
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | BETA: splitting (42) gives:
% 52.91/7.92  | | | | | 
% 52.91/7.92  | | | | | Case 1:
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | |   (52)  all_63_0 = 0
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | REDUCE: (38), (52) imply:
% 52.91/7.92  | | | | | |   (53)  $false
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | CLOSE: (53) is inconsistent.
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | Case 2:
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | |   (54)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 = 0) &
% 52.91/7.92  | | | | | |           left_apart_point(all_63_2, all_39_3) = v0 &
% 52.91/7.92  | | | | | |           right_apart_point(all_63_2, all_39_3) = v1)
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | DELTA: instantiating (54) with fresh symbols all_127_0, all_127_1
% 52.91/7.92  | | | | | |        gives:
% 52.91/7.92  | | | | | |   (55)   ~ (all_127_0 = 0) &  ~ (all_127_1 = 0) &
% 52.91/7.92  | | | | | |         left_apart_point(all_63_2, all_39_3) = all_127_1 &
% 52.91/7.92  | | | | | |         right_apart_point(all_63_2, all_39_3) = all_127_0
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | ALPHA: (55) implies:
% 52.91/7.92  | | | | | |   (56)   ~ (all_127_1 = 0)
% 52.91/7.92  | | | | | |   (57)   ~ (all_127_0 = 0)
% 52.91/7.92  | | | | | |   (58)  right_apart_point(all_63_2, all_39_3) = all_127_0
% 52.91/7.92  | | | | | |   (59)  left_apart_point(all_63_2, all_39_3) = all_127_1
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | GROUND_INST: instantiating (1) with all_39_1, all_39_3, simplifying
% 52.91/7.92  | | | | | |              with (20), (22), (45) gives:
% 52.91/7.92  | | | | | |   (60)   ? [v0: $i] : (reverse_line(all_39_3) = v0 &
% 52.91/7.92  | | | | | |           unequally_directed_lines(all_39_1, v0) = 0 & $i(v0))
% 52.91/7.92  | | | | | | 
% 52.91/7.92  | | | | | | GROUND_INST: instantiating (3) with all_63_2, all_39_3, all_127_0,
% 52.91/7.92  | | | | | |              simplifying with (20), (39), (58) gives:
% 52.91/7.92  | | | | | |   (61)  all_127_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 52.91/7.92  | | | | | |           left_apart_point(all_63_2, v0) = v1 &
% 52.91/7.92  | | | | | |           reverse_line(all_39_3) = v0 & $i(v0))
% 52.91/7.92  | | | | | | 
% 52.91/7.93  | | | | | | GROUND_INST: instantiating (14) with all_63_2, all_63_2, all_39_3,
% 52.91/7.93  | | | | | |              all_39_2, all_127_1, all_39_1, all_122_1, simplifying
% 52.91/7.93  | | | | | |              with (20), (21), (24), (39), (51), (59) gives:
% 52.91/7.93  | | | | | |   (62)  all_127_1 = 0 | all_122_1 = 0 |  ? [v0: int] :  ? [v1: int]
% 52.91/7.93  | | | | | |         :  ? [v2: int] :  ? [v3: int] :  ? [v4: int] :  ? [v5: $i] :
% 52.91/7.93  | | | | | |          ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, all_39_1) = 0) | (v7 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, v5) = 0 &
% 52.91/7.93  | | | | | |             reverse_line(all_39_3) = v5 & $i(v5)) | (v6 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, v5) = 0 &
% 52.91/7.93  | | | | | |             reverse_line(all_39_3) = v5 & $i(v5)) | (v4 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, all_39_2) = 0) | (v3 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, all_39_2) = 0) | (v2 = 0 &
% 52.91/7.93  | | | | | |             left_apart_point(all_63_2, all_39_3) = 0) | ( ~ (v1 = 0)
% 52.91/7.93  | | | | | |             & distinct_lines(all_39_3, all_39_2) = v1) | ( ~ (v0 =
% 52.91/7.93  | | | | | |               0) & distinct_points(all_63_2, all_63_2) = v0))
% 52.91/7.93  | | | | | | 
% 52.91/7.93  | | | | | | DELTA: instantiating (60) with fresh symbol all_136_0 gives:
% 52.91/7.93  | | | | | |   (63)  reverse_line(all_39_3) = all_136_0 &
% 52.91/7.93  | | | | | |         unequally_directed_lines(all_39_1, all_136_0) = 0 &
% 52.91/7.93  | | | | | |         $i(all_136_0)
% 52.91/7.93  | | | | | | 
% 52.91/7.93  | | | | | | ALPHA: (63) implies:
% 52.91/7.93  | | | | | |   (64)  unequally_directed_lines(all_39_1, all_136_0) = 0
% 52.91/7.93  | | | | | |   (65)  reverse_line(all_39_3) = all_136_0
% 52.91/7.93  | | | | | | 
% 52.91/7.93  | | | | | | BETA: splitting (61) gives:
% 52.91/7.93  | | | | | | 
% 52.91/7.93  | | | | | | Case 1:
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | |   (66)  all_127_0 = 0
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | REDUCE: (57), (66) imply:
% 52.91/7.93  | | | | | | |   (67)  $false
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | CLOSE: (67) is inconsistent.
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | Case 2:
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | |   (68)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 52.91/7.93  | | | | | | |           left_apart_point(all_63_2, v0) = v1 &
% 52.91/7.93  | | | | | | |           reverse_line(all_39_3) = v0 & $i(v0))
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | DELTA: instantiating (68) with fresh symbols all_142_0, all_142_1
% 52.91/7.93  | | | | | | |        gives:
% 52.91/7.93  | | | | | | |   (69)   ~ (all_142_0 = 0) & left_apart_point(all_63_2, all_142_1)
% 52.91/7.93  | | | | | | |         = all_142_0 & reverse_line(all_39_3) = all_142_1 &
% 52.91/7.93  | | | | | | |         $i(all_142_1)
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | ALPHA: (69) implies:
% 52.91/7.93  | | | | | | |   (70)  reverse_line(all_39_3) = all_142_1
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | BETA: splitting (62) gives:
% 52.91/7.93  | | | | | | | 
% 52.91/7.93  | | | | | | | Case 1:
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | |   (71)  all_127_1 = 0
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | | REDUCE: (56), (71) imply:
% 52.91/7.93  | | | | | | | |   (72)  $false
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | | CLOSE: (72) is inconsistent.
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | Case 2:
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | |   (73)  all_122_1 = 0 |  ? [v0: int] :  ? [v1: int] :  ? [v2:
% 52.91/7.93  | | | | | | | |           int] :  ? [v3: int] :  ? [v4: int] :  ? [v5: $i] :  ?
% 52.91/7.93  | | | | | | | |         [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 &
% 52.91/7.93  | | | | | | | |             left_apart_point(all_63_2, all_39_1) = 0) | (v7 = 0
% 52.91/7.93  | | | | | | | |             & left_apart_point(all_63_2, v5) = 0 &
% 52.91/7.93  | | | | | | | |             reverse_line(all_39_3) = v5 & $i(v5)) | (v6 = 0 &
% 52.91/7.93  | | | | | | | |             left_apart_point(all_63_2, v5) = 0 &
% 52.91/7.93  | | | | | | | |             reverse_line(all_39_3) = v5 & $i(v5)) | (v4 = 0 &
% 52.91/7.93  | | | | | | | |             left_apart_point(all_63_2, all_39_2) = 0) | (v3 = 0
% 52.91/7.93  | | | | | | | |             & left_apart_point(all_63_2, all_39_2) = 0) | (v2 =
% 52.91/7.93  | | | | | | | |             0 & left_apart_point(all_63_2, all_39_3) = 0) | ( ~
% 52.91/7.93  | | | | | | | |             (v1 = 0) & distinct_lines(all_39_3, all_39_2) = v1)
% 52.91/7.93  | | | | | | | |           | ( ~ (v0 = 0) & distinct_points(all_63_2, all_63_2) =
% 52.91/7.93  | | | | | | | |             v0))
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | | BETA: splitting (73) gives:
% 52.91/7.93  | | | | | | | | 
% 52.91/7.93  | | | | | | | | Case 1:
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | |   (74)  all_122_1 = 0
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | REDUCE: (50), (74) imply:
% 52.91/7.93  | | | | | | | | |   (75)  $false
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | CLOSE: (75) is inconsistent.
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | Case 2:
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_142_1,
% 52.91/7.93  | | | | | | | | |              all_39_3, simplifying with (23), (70) gives:
% 52.91/7.93  | | | | | | | | |   (76)  all_142_1 = all_39_2
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | GROUND_INST: instantiating (15) with all_136_0, all_142_1,
% 52.91/7.93  | | | | | | | | |              all_39_3, simplifying with (65), (70) gives:
% 52.91/7.93  | | | | | | | | |   (77)  all_142_1 = all_136_0
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | COMBINE_EQS: (76), (77) imply:
% 52.91/7.93  | | | | | | | | |   (78)  all_136_0 = all_39_2
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | REDUCE: (64), (78) imply:
% 52.91/7.93  | | | | | | | | |   (79)  unequally_directed_lines(all_39_1, all_39_2) = 0
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | BETA: splitting (35) gives:
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | Case 1:
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | |   (80)  all_64_0 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.93  | | | | | | | | | |           all_64_3) = 0 & reverse_line(all_39_3) = all_64_3
% 52.91/7.93  | | | | | | | | | |         & $i(all_64_3)
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | ALPHA: (80) implies:
% 52.91/7.93  | | | | | | | | | |   (81)  $i(all_64_3)
% 52.91/7.93  | | | | | | | | | |   (82)  reverse_line(all_39_3) = all_64_3
% 52.91/7.93  | | | | | | | | | |   (83)  left_convergent_lines(all_39_1, all_64_3) = 0
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_64_3,
% 52.91/7.93  | | | | | | | | | |              all_39_3, simplifying with (23), (82) gives:
% 52.91/7.93  | | | | | | | | | |   (84)  all_64_3 = all_39_2
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | REDUCE: (83), (84) imply:
% 52.91/7.93  | | | | | | | | | |   (85)  left_convergent_lines(all_39_1, all_39_2) = 0
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_2,
% 52.91/7.93  | | | | | | | | | |              simplifying with (21), (22), (85) gives:
% 52.91/7.93  | | | | | | | | | |   (86)  $false
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | CLOSE: (86) is inconsistent.
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | Case 2:
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | |   (87)  (all_64_1 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.93  | | | | | | | | | |             all_39_3) = 0) | ( ~ (all_64_2 = 0) &
% 52.91/7.93  | | | | | | | | | |           reverse_line(all_39_3) = all_64_3 &
% 52.91/7.93  | | | | | | | | | |           unequally_directed_lines(all_39_1, all_64_3) =
% 52.91/7.93  | | | | | | | | | |           all_64_2 & $i(all_64_3))
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | BETA: splitting (87) gives:
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | Case 1:
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | |   (88)  all_64_1 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.93  | | | | | | | | | | |           all_39_3) = 0
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | ALPHA: (88) implies:
% 52.91/7.93  | | | | | | | | | | |   (89)  left_convergent_lines(all_39_1, all_39_3) = 0
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_3,
% 52.91/7.93  | | | | | | | | | | |              simplifying with (20), (22), (89) gives:
% 52.91/7.93  | | | | | | | | | | |   (90)  $false
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | CLOSE: (90) is inconsistent.
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | Case 2:
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | |   (91)   ~ (all_64_2 = 0) & reverse_line(all_39_3) =
% 52.91/7.93  | | | | | | | | | | |         all_64_3 & unequally_directed_lines(all_39_1,
% 52.91/7.93  | | | | | | | | | | |           all_64_3) = all_64_2 & $i(all_64_3)
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | ALPHA: (91) implies:
% 52.91/7.93  | | | | | | | | | | |   (92)   ~ (all_64_2 = 0)
% 52.91/7.93  | | | | | | | | | | |   (93)  unequally_directed_lines(all_39_1, all_64_3) =
% 52.91/7.93  | | | | | | | | | | |         all_64_2
% 52.91/7.93  | | | | | | | | | | |   (94)  reverse_line(all_39_3) = all_64_3
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_64_3,
% 52.91/7.93  | | | | | | | | | | |              all_39_3, simplifying with (23), (94) gives:
% 52.91/7.93  | | | | | | | | | | |   (95)  all_64_3 = all_39_2
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | REDUCE: (93), (95) imply:
% 52.91/7.93  | | | | | | | | | | |   (96)  unequally_directed_lines(all_39_1, all_39_2) =
% 52.91/7.93  | | | | | | | | | | |         all_64_2
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | GROUND_INST: instantiating (16) with all_64_2, 0, all_39_2,
% 52.91/7.93  | | | | | | | | | | |              all_39_1, simplifying with (79), (96) gives:
% 52.91/7.93  | | | | | | | | | | |   (97)  all_64_2 = 0
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | REDUCE: (92), (97) imply:
% 52.91/7.93  | | | | | | | | | | |   (98)  $false
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | | CLOSE: (98) is inconsistent.
% 52.91/7.93  | | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | | End of split
% 52.91/7.93  | | | | | | | | | | 
% 52.91/7.93  | | | | | | | | | End of split
% 52.91/7.93  | | | | | | | | | 
% 52.91/7.93  | | | | | | | | End of split
% 52.91/7.94  | | | | | | | | 
% 52.91/7.94  | | | | | | | End of split
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | End of split
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | End of split
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | End of split
% 52.91/7.94  | | | | 
% 52.91/7.94  | | | Case 2:
% 52.91/7.94  | | | | 
% 52.91/7.94  | | | |   (99)   ~ (all_61_1 = 0) & convergent_lines(all_39_1, all_39_3) =
% 52.91/7.94  | | | |         all_61_1
% 52.91/7.94  | | | | 
% 52.91/7.94  | | | | ALPHA: (99) implies:
% 52.91/7.94  | | | |   (100)   ~ (all_61_1 = 0)
% 52.91/7.94  | | | |   (101)  convergent_lines(all_39_1, all_39_3) = all_61_1
% 52.91/7.94  | | | | 
% 52.91/7.94  | | | | BETA: splitting (33) gives:
% 52.91/7.94  | | | | 
% 52.91/7.94  | | | | Case 1:
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | |   (102)  all_62_0 = 0 & convergent_lines(all_39_1, all_39_3) = 0
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | ALPHA: (102) implies:
% 52.91/7.94  | | | | |   (103)  convergent_lines(all_39_1, all_39_3) = 0
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | GROUND_INST: instantiating (17) with 0, all_61_1, all_39_3, all_39_1,
% 52.91/7.94  | | | | |              simplifying with (101), (103) gives:
% 52.91/7.94  | | | | |   (104)  all_61_1 = 0
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | REDUCE: (100), (104) imply:
% 52.91/7.94  | | | | |   (105)  $false
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | CLOSE: (105) is inconsistent.
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | Case 2:
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | |   (106)   ~ (all_62_1 = 0) &
% 52.91/7.94  | | | | |          unequally_directed_opposite_lines(all_39_1, all_39_3) =
% 52.91/7.94  | | | | |          all_62_1
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | ALPHA: (106) implies:
% 52.91/7.94  | | | | |   (107)   ~ (all_62_1 = 0)
% 52.91/7.94  | | | | |   (108)  unequally_directed_opposite_lines(all_39_1, all_39_3) =
% 52.91/7.94  | | | | |          all_62_1
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | BETA: splitting (43) gives:
% 52.91/7.94  | | | | | 
% 52.91/7.94  | | | | | Case 1:
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | |   (109)  all_63_1 = 0
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | REDUCE: (37), (109) imply:
% 52.91/7.94  | | | | | |   (110)  $false
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | CLOSE: (110) is inconsistent.
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | Case 2:
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | |   (111)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 = 0) &
% 52.91/7.94  | | | | | |            left_apart_point(all_63_2, all_39_1) = v0 &
% 52.91/7.94  | | | | | |            right_apart_point(all_63_2, all_39_1) = v1)
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | DELTA: instantiating (111) with fresh symbols all_122_0, all_122_1
% 52.91/7.94  | | | | | |        gives:
% 52.91/7.94  | | | | | |   (112)   ~ (all_122_0 = 0) &  ~ (all_122_1 = 0) &
% 52.91/7.94  | | | | | |          left_apart_point(all_63_2, all_39_1) = all_122_1 &
% 52.91/7.94  | | | | | |          right_apart_point(all_63_2, all_39_1) = all_122_0
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | ALPHA: (112) implies:
% 52.91/7.94  | | | | | |   (113)   ~ (all_122_1 = 0)
% 52.91/7.94  | | | | | |   (114)  left_apart_point(all_63_2, all_39_1) = all_122_1
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | BETA: splitting (42) gives:
% 52.91/7.94  | | | | | | 
% 52.91/7.94  | | | | | | Case 1:
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | |   (115)  all_63_0 = 0
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | REDUCE: (38), (115) imply:
% 52.91/7.94  | | | | | | |   (116)  $false
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | CLOSE: (116) is inconsistent.
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | Case 2:
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | |   (117)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 = 0)
% 52.91/7.94  | | | | | | |            & left_apart_point(all_63_2, all_39_3) = v0 &
% 52.91/7.94  | | | | | | |            right_apart_point(all_63_2, all_39_3) = v1)
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | DELTA: instantiating (117) with fresh symbols all_127_0, all_127_1
% 52.91/7.94  | | | | | | |        gives:
% 52.91/7.94  | | | | | | |   (118)   ~ (all_127_0 = 0) &  ~ (all_127_1 = 0) &
% 52.91/7.94  | | | | | | |          left_apart_point(all_63_2, all_39_3) = all_127_1 &
% 52.91/7.94  | | | | | | |          right_apart_point(all_63_2, all_39_3) = all_127_0
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | ALPHA: (118) implies:
% 52.91/7.94  | | | | | | |   (119)   ~ (all_127_1 = 0)
% 52.91/7.94  | | | | | | |   (120)   ~ (all_127_0 = 0)
% 52.91/7.94  | | | | | | |   (121)  right_apart_point(all_63_2, all_39_3) = all_127_0
% 52.91/7.94  | | | | | | |   (122)  left_apart_point(all_63_2, all_39_3) = all_127_1
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | GROUND_INST: instantiating (2) with all_39_1, all_39_3, all_62_1,
% 52.91/7.94  | | | | | | |              simplifying with (20), (22), (108) gives:
% 52.91/7.94  | | | | | | |   (123)  all_62_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0)
% 52.91/7.94  | | | | | | |            & reverse_line(all_39_3) = v0 &
% 52.91/7.94  | | | | | | |            unequally_directed_lines(all_39_1, v0) = v1 & $i(v0))
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | GROUND_INST: instantiating (3) with all_63_2, all_39_3, all_127_0,
% 52.91/7.94  | | | | | | |              simplifying with (20), (39), (121) gives:
% 52.91/7.94  | | | | | | |   (124)  all_127_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0)
% 52.91/7.94  | | | | | | |            & left_apart_point(all_63_2, v0) = v1 &
% 52.91/7.94  | | | | | | |            reverse_line(all_39_3) = v0 & $i(v0))
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | GROUND_INST: instantiating (13) with all_63_2, all_63_2, all_39_1,
% 52.91/7.94  | | | | | | |              all_39_3, all_122_1, all_127_1, simplifying with
% 52.91/7.94  | | | | | | |              (20), (22), (39), (114), (122) gives:
% 52.91/7.94  | | | | | | |   (125)  all_127_1 = 0 | all_122_1 = 0 |  ? [v0: int] :  ? [v1:
% 52.91/7.94  | | | | | | |            int] :  ? [v2: int] :  ? [v3: int] :  ? [v4: $i] :  ?
% 52.91/7.94  | | | | | | |          [v5: int] :  ? [v6: int] :  ? [v7: $i] :  ? [v8: int] : 
% 52.91/7.94  | | | | | | |          ? [v9: int] : ((v9 = 0 & left_apart_point(all_63_2, v7) =
% 52.91/7.94  | | | | | | |              0 & reverse_line(all_39_3) = v7 & $i(v7)) | (v8 = 0 &
% 52.91/7.94  | | | | | | |              left_apart_point(all_63_2, v7) = 0 &
% 52.91/7.94  | | | | | | |              reverse_line(all_39_3) = v7 & $i(v7)) | (v6 = 0 &
% 52.91/7.94  | | | | | | |              left_apart_point(all_63_2, v4) = 0 &
% 52.91/7.94  | | | | | | |              reverse_line(all_39_1) = v4 & $i(v4)) | (v5 = 0 &
% 52.91/7.94  | | | | | | |              left_apart_point(all_63_2, v4) = 0 &
% 52.91/7.94  | | | | | | |              reverse_line(all_39_1) = v4 & $i(v4)) | (v3 = 0 &
% 52.91/7.94  | | | | | | |              left_apart_point(all_63_2, all_39_3) = 0) | (v2 = 0 &
% 52.91/7.94  | | | | | | |              left_apart_point(all_63_2, all_39_1) = 0) | ( ~ (v1 =
% 52.91/7.94  | | | | | | |                0) & distinct_lines(all_39_1, all_39_3) = v1) | ( ~
% 52.91/7.94  | | | | | | |              (v0 = 0) & distinct_points(all_63_2, all_63_2) = v0))
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | BETA: splitting (35) gives:
% 52.91/7.94  | | | | | | | 
% 52.91/7.94  | | | | | | | Case 1:
% 52.91/7.94  | | | | | | | | 
% 52.91/7.94  | | | | | | | |   (126)  all_64_0 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.94  | | | | | | | |            all_64_3) = 0 & reverse_line(all_39_3) = all_64_3 &
% 52.91/7.94  | | | | | | | |          $i(all_64_3)
% 52.91/7.94  | | | | | | | | 
% 52.91/7.94  | | | | | | | | ALPHA: (126) implies:
% 52.91/7.94  | | | | | | | |   (127)  $i(all_64_3)
% 52.91/7.94  | | | | | | | |   (128)  reverse_line(all_39_3) = all_64_3
% 52.91/7.94  | | | | | | | |   (129)  left_convergent_lines(all_39_1, all_64_3) = 0
% 52.91/7.94  | | | | | | | | 
% 52.91/7.94  | | | | | | | | BETA: splitting (123) gives:
% 52.91/7.94  | | | | | | | | 
% 52.91/7.94  | | | | | | | | Case 1:
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | |   (130)  all_62_1 = 0
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | REDUCE: (107), (130) imply:
% 52.91/7.94  | | | | | | | | |   (131)  $false
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | CLOSE: (131) is inconsistent.
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | Case 2:
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | |   (132)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 52.91/7.94  | | | | | | | | |            reverse_line(all_39_3) = v0 &
% 52.91/7.94  | | | | | | | | |            unequally_directed_lines(all_39_1, v0) = v1 &
% 52.91/7.94  | | | | | | | | |            $i(v0))
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_143_0,
% 52.91/7.94  | | | | | | | | |        all_143_1 gives:
% 52.91/7.94  | | | | | | | | |   (133)   ~ (all_143_0 = 0) & reverse_line(all_39_3) =
% 52.91/7.94  | | | | | | | | |          all_143_1 & unequally_directed_lines(all_39_1,
% 52.91/7.94  | | | | | | | | |            all_143_1) = all_143_0 & $i(all_143_1)
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | ALPHA: (133) implies:
% 52.91/7.94  | | | | | | | | |   (134)  reverse_line(all_39_3) = all_143_1
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | BETA: splitting (125) gives:
% 52.91/7.94  | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | Case 1:
% 52.91/7.94  | | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | |   (135)  all_127_1 = 0
% 52.91/7.94  | | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | | REDUCE: (119), (135) imply:
% 52.91/7.94  | | | | | | | | | |   (136)  $false
% 52.91/7.94  | | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | | CLOSE: (136) is inconsistent.
% 52.91/7.94  | | | | | | | | | | 
% 52.91/7.94  | | | | | | | | | Case 2:
% 52.91/7.94  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | |   (137)  all_122_1 = 0 |  ? [v0: int] :  ? [v1: int] :  ?
% 52.91/7.95  | | | | | | | | | |          [v2: int] :  ? [v3: int] :  ? [v4: $i] :  ? [v5:
% 52.91/7.95  | | | | | | | | | |            int] :  ? [v6: int] :  ? [v7: $i] :  ? [v8: int]
% 52.91/7.95  | | | | | | | | | |          :  ? [v9: int] : ((v9 = 0 &
% 52.91/7.95  | | | | | | | | | |              left_apart_point(all_63_2, v7) = 0 &
% 52.91/7.95  | | | | | | | | | |              reverse_line(all_39_3) = v7 & $i(v7)) | (v8 = 0
% 52.91/7.95  | | | | | | | | | |              & left_apart_point(all_63_2, v7) = 0 &
% 52.91/7.95  | | | | | | | | | |              reverse_line(all_39_3) = v7 & $i(v7)) | (v6 = 0
% 52.91/7.95  | | | | | | | | | |              & left_apart_point(all_63_2, v4) = 0 &
% 52.91/7.95  | | | | | | | | | |              reverse_line(all_39_1) = v4 & $i(v4)) | (v5 = 0
% 52.91/7.95  | | | | | | | | | |              & left_apart_point(all_63_2, v4) = 0 &
% 52.91/7.95  | | | | | | | | | |              reverse_line(all_39_1) = v4 & $i(v4)) | (v3 = 0
% 52.91/7.95  | | | | | | | | | |              & left_apart_point(all_63_2, all_39_3) = 0) |
% 52.91/7.95  | | | | | | | | | |            (v2 = 0 & left_apart_point(all_63_2, all_39_1) =
% 52.91/7.95  | | | | | | | | | |              0) | ( ~ (v1 = 0) & distinct_lines(all_39_1,
% 52.91/7.95  | | | | | | | | | |                all_39_3) = v1) | ( ~ (v0 = 0) &
% 52.91/7.95  | | | | | | | | | |              distinct_points(all_63_2, all_63_2) = v0))
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | BETA: splitting (124) gives:
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | |   (138)  all_127_0 = 0
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | REDUCE: (120), (138) imply:
% 52.91/7.95  | | | | | | | | | | |   (139)  $false
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | |   (140)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 52.91/7.95  | | | | | | | | | | |            left_apart_point(all_63_2, v0) = v1 &
% 52.91/7.95  | | | | | | | | | | |            reverse_line(all_39_3) = v0 & $i(v0))
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | DELTA: instantiating (140) with fresh symbols all_189_0,
% 52.91/7.95  | | | | | | | | | | |        all_189_1 gives:
% 52.91/7.95  | | | | | | | | | | |   (141)   ~ (all_189_0 = 0) & left_apart_point(all_63_2,
% 52.91/7.95  | | | | | | | | | | |            all_189_1) = all_189_0 & reverse_line(all_39_3)
% 52.91/7.95  | | | | | | | | | | |          = all_189_1 & $i(all_189_1)
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | ALPHA: (141) implies:
% 52.91/7.95  | | | | | | | | | | |   (142)  reverse_line(all_39_3) = all_189_1
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | BETA: splitting (137) gives:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | |   (143)  all_122_1 = 0
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | REDUCE: (113), (143) imply:
% 52.91/7.95  | | | | | | | | | | | |   (144)  $false
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_143_1,
% 52.91/7.95  | | | | | | | | | | | |              all_39_3, simplifying with (23), (134) gives:
% 52.91/7.95  | | | | | | | | | | | |   (145)  all_143_1 = all_39_2
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_143_1, all_189_1,
% 52.91/7.95  | | | | | | | | | | | |              all_39_3, simplifying with (134), (142) gives:
% 52.91/7.95  | | | | | | | | | | | |   (146)  all_189_1 = all_143_1
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_64_3, all_189_1,
% 52.91/7.95  | | | | | | | | | | | |              all_39_3, simplifying with (128), (142) gives:
% 52.91/7.95  | | | | | | | | | | | |   (147)  all_189_1 = all_64_3
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | COMBINE_EQS: (146), (147) imply:
% 52.91/7.95  | | | | | | | | | | | |   (148)  all_143_1 = all_64_3
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | SIMP: (148) implies:
% 52.91/7.95  | | | | | | | | | | | |   (149)  all_143_1 = all_64_3
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | COMBINE_EQS: (145), (149) imply:
% 52.91/7.95  | | | | | | | | | | | |   (150)  all_64_3 = all_39_2
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | SIMP: (150) implies:
% 52.91/7.95  | | | | | | | | | | | |   (151)  all_64_3 = all_39_2
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | REDUCE: (129), (151) imply:
% 52.91/7.95  | | | | | | | | | | | |   (152)  left_convergent_lines(all_39_1, all_39_2) = 0
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_2,
% 52.91/7.95  | | | | | | | | | | | |              simplifying with (21), (22), (152) gives:
% 52.91/7.95  | | | | | | | | | | | |   (153)  $false
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | End of split
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | End of split
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | End of split
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | End of split
% 52.91/7.95  | | | | | | | | 
% 52.91/7.95  | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | 
% 52.91/7.95  | | | | | | | |   (154)  (all_64_1 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.95  | | | | | | | |              all_39_3) = 0) | ( ~ (all_64_2 = 0) &
% 52.91/7.95  | | | | | | | |            reverse_line(all_39_3) = all_64_3 &
% 52.91/7.95  | | | | | | | |            unequally_directed_lines(all_39_1, all_64_3) =
% 52.91/7.95  | | | | | | | |            all_64_2 & $i(all_64_3))
% 52.91/7.95  | | | | | | | | 
% 52.91/7.95  | | | | | | | | BETA: splitting (154) gives:
% 52.91/7.95  | | | | | | | | 
% 52.91/7.95  | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | |   (155)  all_64_1 = 0 & left_convergent_lines(all_39_1,
% 52.91/7.95  | | | | | | | | |            all_39_3) = 0
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | ALPHA: (155) implies:
% 52.91/7.95  | | | | | | | | |   (156)  left_convergent_lines(all_39_1, all_39_3) = 0
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_3,
% 52.91/7.95  | | | | | | | | |              simplifying with (20), (22), (156) gives:
% 52.91/7.95  | | | | | | | | |   (157)  $false
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | CLOSE: (157) is inconsistent.
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | |   (158)   ~ (all_64_2 = 0) & reverse_line(all_39_3) = all_64_3
% 52.91/7.95  | | | | | | | | |          & unequally_directed_lines(all_39_1, all_64_3) =
% 52.91/7.95  | | | | | | | | |          all_64_2 & $i(all_64_3)
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | ALPHA: (158) implies:
% 52.91/7.95  | | | | | | | | |   (159)   ~ (all_64_2 = 0)
% 52.91/7.95  | | | | | | | | |   (160)  $i(all_64_3)
% 52.91/7.95  | | | | | | | | |   (161)  unequally_directed_lines(all_39_1, all_64_3) =
% 52.91/7.95  | | | | | | | | |          all_64_2
% 52.91/7.95  | | | | | | | | |   (162)  reverse_line(all_39_3) = all_64_3
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | BETA: splitting (124) gives:
% 52.91/7.95  | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | |   (163)  all_127_0 = 0
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | REDUCE: (120), (163) imply:
% 52.91/7.95  | | | | | | | | | |   (164)  $false
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | CLOSE: (164) is inconsistent.
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | |   (165)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 52.91/7.95  | | | | | | | | | |            left_apart_point(all_63_2, v0) = v1 &
% 52.91/7.95  | | | | | | | | | |            reverse_line(all_39_3) = v0 & $i(v0))
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_184_0,
% 52.91/7.95  | | | | | | | | | |        all_184_1 gives:
% 52.91/7.95  | | | | | | | | | |   (166)   ~ (all_184_0 = 0) & left_apart_point(all_63_2,
% 52.91/7.95  | | | | | | | | | |            all_184_1) = all_184_0 & reverse_line(all_39_3) =
% 52.91/7.95  | | | | | | | | | |          all_184_1 & $i(all_184_1)
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | ALPHA: (166) implies:
% 52.91/7.95  | | | | | | | | | |   (167)  reverse_line(all_39_3) = all_184_1
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_184_1,
% 52.91/7.95  | | | | | | | | | |              all_39_3, simplifying with (23), (167) gives:
% 52.91/7.95  | | | | | | | | | |   (168)  all_184_1 = all_39_2
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | GROUND_INST: instantiating (15) with all_64_3, all_184_1,
% 52.91/7.95  | | | | | | | | | |              all_39_3, simplifying with (162), (167) gives:
% 52.91/7.95  | | | | | | | | | |   (169)  all_184_1 = all_64_3
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | COMBINE_EQS: (168), (169) imply:
% 52.91/7.95  | | | | | | | | | |   (170)  all_64_3 = all_39_2
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | REDUCE: (161), (170) imply:
% 52.91/7.95  | | | | | | | | | |   (171)  unequally_directed_lines(all_39_1, all_39_2) =
% 52.91/7.95  | | | | | | | | | |          all_64_2
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | GROUND_INST: instantiating (8) with all_39_1, all_39_1,
% 52.91/7.95  | | | | | | | | | |              all_39_2, all_64_2, all_64_2, simplifying with
% 52.91/7.95  | | | | | | | | | |              (21), (22), (171) gives:
% 52.91/7.95  | | | | | | | | | |   (172)  all_64_2 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 52.91/7.95  | | | | | | | | | |            unequally_directed_lines(all_39_1, all_39_1) =
% 52.91/7.95  | | | | | | | | | |            v0)
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | GROUND_INST: instantiating (9) with all_39_1, all_39_2,
% 52.91/7.95  | | | | | | | | | |              all_64_2, simplifying with (21), (22), (171)
% 52.91/7.95  | | | | | | | | | |              gives:
% 52.91/7.95  | | | | | | | | | |   (173)  all_64_2 = 0 |  ? [v0: $i] :
% 52.91/7.95  | | | | | | | | | |          (reverse_line(all_39_2) = v0 &
% 52.91/7.95  | | | | | | | | | |            unequally_directed_lines(all_39_1, v0) = 0 &
% 52.91/7.95  | | | | | | | | | |            $i(v0))
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | BETA: splitting (173) gives:
% 52.91/7.95  | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | |   (174)  all_64_2 = 0
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | REDUCE: (159), (174) imply:
% 52.91/7.95  | | | | | | | | | | |   (175)  $false
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | |   (176)   ? [v0: $i] : (reverse_line(all_39_2) = v0 &
% 52.91/7.95  | | | | | | | | | | |            unequally_directed_lines(all_39_1, v0) = 0 &
% 52.91/7.95  | | | | | | | | | | |            $i(v0))
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | DELTA: instantiating (176) with fresh symbol all_244_0
% 52.91/7.95  | | | | | | | | | | |        gives:
% 52.91/7.95  | | | | | | | | | | |   (177)  reverse_line(all_39_2) = all_244_0 &
% 52.91/7.95  | | | | | | | | | | |          unequally_directed_lines(all_39_1, all_244_0) = 0
% 52.91/7.95  | | | | | | | | | | |          & $i(all_244_0)
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | ALPHA: (177) implies:
% 52.91/7.95  | | | | | | | | | | |   (178)  unequally_directed_lines(all_39_1, all_244_0) = 0
% 52.91/7.95  | | | | | | | | | | |   (179)  reverse_line(all_39_2) = all_244_0
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | BETA: splitting (172) gives:
% 52.91/7.95  | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | Case 1:
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | |   (180)  all_64_2 = 0
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | REDUCE: (159), (180) imply:
% 52.91/7.95  | | | | | | | | | | | |   (181)  $false
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | Case 2:
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | |   (182)   ? [v0: int] : ( ~ (v0 = 0) &
% 52.91/7.95  | | | | | | | | | | | |            unequally_directed_lines(all_39_1, all_39_1) =
% 52.91/7.95  | | | | | | | | | | | |            v0)
% 52.91/7.95  | | | | | | | | | | | | 
% 52.91/7.95  | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_339_0
% 52.91/7.95  | | | | | | | | | | | |        gives:
% 52.91/7.96  | | | | | | | | | | | |   (183)   ~ (all_339_0 = 0) &
% 52.91/7.96  | | | | | | | | | | | |          unequally_directed_lines(all_39_1, all_39_1) =
% 52.91/7.96  | | | | | | | | | | | |          all_339_0
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | ALPHA: (183) implies:
% 52.91/7.96  | | | | | | | | | | | |   (184)   ~ (all_339_0 = 0)
% 52.91/7.96  | | | | | | | | | | | |   (185)  unequally_directed_lines(all_39_1, all_39_1) =
% 52.91/7.96  | | | | | | | | | | | |          all_339_0
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_1, all_244_0,
% 52.91/7.96  | | | | | | | | | | | |              all_39_2, simplifying with (24), (179) gives:
% 52.91/7.96  | | | | | | | | | | | |   (186)  all_244_0 = all_39_1
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | REDUCE: (178), (186) imply:
% 52.91/7.96  | | | | | | | | | | | |   (187)  unequally_directed_lines(all_39_1, all_39_1) = 0
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_339_0, 0, all_39_1,
% 52.91/7.96  | | | | | | | | | | | |              all_39_1, simplifying with (185), (187) gives:
% 52.91/7.96  | | | | | | | | | | | |   (188)  all_339_0 = 0
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | REDUCE: (184), (188) imply:
% 52.91/7.96  | | | | | | | | | | | |   (189)  $false
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 52.91/7.96  | | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | | End of split
% 52.91/7.96  | | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | | End of split
% 52.91/7.96  | | | | | | | | | | 
% 52.91/7.96  | | | | | | | | | End of split
% 52.91/7.96  | | | | | | | | | 
% 52.91/7.96  | | | | | | | | End of split
% 52.91/7.96  | | | | | | | | 
% 52.91/7.96  | | | | | | | End of split
% 52.91/7.96  | | | | | | | 
% 52.91/7.96  | | | | | | End of split
% 52.91/7.96  | | | | | | 
% 52.91/7.96  | | | | | End of split
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | End of split
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | End of split
% 52.91/7.96  | | | 
% 52.91/7.96  | | Case 2:
% 52.91/7.96  | | | 
% 52.91/7.96  | | |   (190)   ~ (all_63_3 = 0) & reverse_line(all_39_3) = all_63_4 &
% 52.91/7.96  | | |          unequally_directed_lines(all_39_1, all_63_4) = all_63_3 &
% 52.91/7.96  | | |          $i(all_63_4)
% 52.91/7.96  | | | 
% 52.91/7.96  | | | ALPHA: (190) implies:
% 52.91/7.96  | | |   (191)   ~ (all_63_3 = 0)
% 52.91/7.96  | | |   (192)  $i(all_63_4)
% 52.91/7.96  | | |   (193)  unequally_directed_lines(all_39_1, all_63_4) = all_63_3
% 52.91/7.96  | | |   (194)  reverse_line(all_39_3) = all_63_4
% 52.91/7.96  | | | 
% 52.91/7.96  | | | GROUND_INST: instantiating (15) with all_39_2, all_63_4, all_39_3,
% 52.91/7.96  | | |              simplifying with (23), (194) gives:
% 52.91/7.96  | | |   (195)  all_63_4 = all_39_2
% 52.91/7.96  | | | 
% 52.91/7.96  | | | REDUCE: (193), (195) imply:
% 52.91/7.96  | | |   (196)  unequally_directed_lines(all_39_1, all_39_2) = all_63_3
% 52.91/7.96  | | | 
% 52.91/7.96  | | | GROUND_INST: instantiating (8) with all_39_1, all_39_1, all_39_2,
% 52.91/7.96  | | |              all_63_3, all_63_3, simplifying with (21), (22), (196) gives:
% 52.91/7.96  | | |   (197)  all_63_3 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 52.91/7.96  | | |            unequally_directed_lines(all_39_1, all_39_1) = v0)
% 52.91/7.96  | | | 
% 52.91/7.96  | | | GROUND_INST: instantiating (9) with all_39_1, all_39_2, all_63_3,
% 52.91/7.96  | | |              simplifying with (21), (22), (196) gives:
% 52.91/7.96  | | |   (198)  all_63_3 = 0 |  ? [v0: $i] : (reverse_line(all_39_2) = v0 &
% 52.91/7.96  | | |            unequally_directed_lines(all_39_1, v0) = 0 & $i(v0))
% 52.91/7.96  | | | 
% 52.91/7.96  | | | BETA: splitting (198) gives:
% 52.91/7.96  | | | 
% 52.91/7.96  | | | Case 1:
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | |   (199)  all_63_3 = 0
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | REDUCE: (191), (199) imply:
% 52.91/7.96  | | | |   (200)  $false
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | CLOSE: (200) is inconsistent.
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | Case 2:
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | |   (201)   ? [v0: $i] : (reverse_line(all_39_2) = v0 &
% 52.91/7.96  | | | |            unequally_directed_lines(all_39_1, v0) = 0 & $i(v0))
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | DELTA: instantiating (201) with fresh symbol all_135_0 gives:
% 52.91/7.96  | | | |   (202)  reverse_line(all_39_2) = all_135_0 &
% 52.91/7.96  | | | |          unequally_directed_lines(all_39_1, all_135_0) = 0 &
% 52.91/7.96  | | | |          $i(all_135_0)
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | ALPHA: (202) implies:
% 52.91/7.96  | | | |   (203)  unequally_directed_lines(all_39_1, all_135_0) = 0
% 52.91/7.96  | | | |   (204)  reverse_line(all_39_2) = all_135_0
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | BETA: splitting (197) gives:
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | | Case 1:
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | |   (205)  all_63_3 = 0
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | REDUCE: (191), (205) imply:
% 52.91/7.96  | | | | |   (206)  $false
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | CLOSE: (206) is inconsistent.
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | Case 2:
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | |   (207)   ? [v0: int] : ( ~ (v0 = 0) &
% 52.91/7.96  | | | | |            unequally_directed_lines(all_39_1, all_39_1) = v0)
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | DELTA: instantiating (207) with fresh symbol all_144_0 gives:
% 52.91/7.96  | | | | |   (208)   ~ (all_144_0 = 0) & unequally_directed_lines(all_39_1,
% 52.91/7.96  | | | | |            all_39_1) = all_144_0
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | ALPHA: (208) implies:
% 52.91/7.96  | | | | |   (209)   ~ (all_144_0 = 0)
% 52.91/7.96  | | | | |   (210)  unequally_directed_lines(all_39_1, all_39_1) = all_144_0
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | GROUND_INST: instantiating (15) with all_39_1, all_135_0, all_39_2,
% 52.91/7.96  | | | | |              simplifying with (24), (204) gives:
% 52.91/7.96  | | | | |   (211)  all_135_0 = all_39_1
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | REDUCE: (203), (211) imply:
% 52.91/7.96  | | | | |   (212)  unequally_directed_lines(all_39_1, all_39_1) = 0
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | GROUND_INST: instantiating (16) with all_144_0, 0, all_39_1, all_39_1,
% 52.91/7.96  | | | | |              simplifying with (210), (212) gives:
% 52.91/7.96  | | | | |   (213)  all_144_0 = 0
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | REDUCE: (209), (213) imply:
% 52.91/7.96  | | | | |   (214)  $false
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | | CLOSE: (214) is inconsistent.
% 52.91/7.96  | | | | | 
% 52.91/7.96  | | | | End of split
% 52.91/7.96  | | | | 
% 52.91/7.96  | | | End of split
% 52.91/7.96  | | | 
% 52.91/7.96  | | End of split
% 52.91/7.96  | | 
% 52.91/7.96  | Case 2:
% 52.91/7.96  | | 
% 52.91/7.96  | |   (215)  all_39_0 = 0
% 52.91/7.96  | | 
% 52.91/7.96  | | REDUCE: (19), (215) imply:
% 52.91/7.96  | |   (216)  $false
% 52.91/7.96  | | 
% 52.91/7.96  | | CLOSE: (216) is inconsistent.
% 52.91/7.96  | | 
% 52.91/7.96  | End of split
% 52.91/7.96  | 
% 52.91/7.96  End of proof
% 52.91/7.96  % SZS output end Proof for theBenchmark
% 52.91/7.96  
% 52.91/7.96  7362ms
%------------------------------------------------------------------------------