TSTP Solution File: GEO190+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO190+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n031.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 23:22:03 EDT 2023

% Result   : Theorem 14.09s 2.58s
% Output   : Proof 14.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO190+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n031.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Aug 29 22:18:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.54/0.60  ________       _____
% 0.54/0.60  ___  __ \_________(_)________________________________
% 0.54/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.54/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.54/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.54/0.60  
% 0.54/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.60  (2023-06-19)
% 0.54/0.60  
% 0.54/0.60  (c) Philipp Rümmer, 2009-2023
% 0.54/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.60                Amanda Stjerna.
% 0.54/0.60  Free software under BSD-3-Clause.
% 0.54/0.60  
% 0.54/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.60  
% 0.54/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.61  Running up to 7 provers in parallel.
% 0.72/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.72/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.43/1.02  Prover 1: Preprocessing ...
% 2.43/1.02  Prover 4: Preprocessing ...
% 2.43/1.05  Prover 6: Preprocessing ...
% 2.43/1.05  Prover 2: Preprocessing ...
% 2.43/1.05  Prover 3: Preprocessing ...
% 2.43/1.05  Prover 5: Preprocessing ...
% 2.43/1.05  Prover 0: Preprocessing ...
% 4.44/1.26  Prover 5: Proving ...
% 4.44/1.26  Prover 2: Proving ...
% 4.44/1.27  Prover 6: Constructing countermodel ...
% 4.60/1.29  Prover 1: Constructing countermodel ...
% 4.60/1.29  Prover 3: Constructing countermodel ...
% 5.05/1.37  Prover 4: Constructing countermodel ...
% 5.05/1.41  Prover 0: Proving ...
% 5.63/1.44  Prover 3: gave up
% 5.63/1.46  Prover 6: gave up
% 5.63/1.46  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.63/1.46  Prover 1: gave up
% 5.63/1.46  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.63/1.46  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.08/1.49  Prover 7: Preprocessing ...
% 6.08/1.50  Prover 8: Preprocessing ...
% 6.08/1.51  Prover 9: Preprocessing ...
% 6.84/1.58  Prover 7: Warning: ignoring some quantifiers
% 6.84/1.59  Prover 7: Constructing countermodel ...
% 6.84/1.62  Prover 8: Warning: ignoring some quantifiers
% 7.16/1.62  Prover 8: Constructing countermodel ...
% 7.38/1.69  Prover 9: Constructing countermodel ...
% 7.38/1.72  Prover 7: gave up
% 7.38/1.72  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.09/1.75  Prover 8: gave up
% 8.09/1.75  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.09/1.76  Prover 10: Preprocessing ...
% 8.09/1.78  Prover 11: Preprocessing ...
% 8.54/1.80  Prover 10: Warning: ignoring some quantifiers
% 8.54/1.81  Prover 10: Constructing countermodel ...
% 8.98/1.87  Prover 10: gave up
% 8.98/1.89  Prover 12: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.98/1.91  Prover 12: Preprocessing ...
% 8.98/1.92  Prover 11: Constructing countermodel ...
% 10.00/2.00  Prover 12: Proving ...
% 14.09/2.58  Prover 11: Found proof (size 81)
% 14.09/2.58  Prover 11: proved (830ms)
% 14.09/2.58  Prover 9: stopped
% 14.09/2.58  Prover 12: stopped
% 14.09/2.58  Prover 2: stopped
% 14.09/2.58  Prover 5: stopped
% 14.09/2.58  Prover 0: stopped
% 14.09/2.58  Prover 4: stopped
% 14.09/2.58  
% 14.09/2.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.09/2.58  
% 14.09/2.59  % SZS output start Proof for theBenchmark
% 14.58/2.59  Assumptions after simplification:
% 14.58/2.59  ---------------------------------
% 14.58/2.59  
% 14.58/2.59    (apart1)
% 14.58/2.62     ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) |  ~ $i(v0))
% 14.58/2.62  
% 14.58/2.62    (apart4)
% 14.58/2.62     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 14.58/2.62      0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2)
% 14.58/2.62        = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 = 0) &
% 14.58/2.62        distinct_points(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 14.58/2.62     ! [v3: int] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~
% 14.58/2.62      (distinct_points(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 14.58/2.62      distinct_points(v0, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 14.58/2.62    [v3: int] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~
% 14.58/2.62      (distinct_points(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 14.58/2.62      distinct_points(v1, v2) = 0)
% 14.58/2.62  
% 14.58/2.62    (ceq2)
% 14.58/2.62     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 14.58/2.62      0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1,
% 14.58/2.62          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: int] : ( ~ (v5 =
% 14.58/2.62          0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0: $i] :  ! [v1: $i] : 
% 14.58/2.62    ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |
% 14.58/2.62       ~ (apart_point_and_line(v0, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 14.58/2.62      distinct_lines(v1, v2) = 0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 14.58/2.62    [v3: int] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~
% 14.58/2.62      (distinct_lines(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 14.58/2.62      apart_point_and_line(v0, v2) = 0)
% 14.58/2.62  
% 14.58/2.62    (con)
% 14.58/2.63     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] :  ? [v5:
% 14.58/2.63      $i] : ( ~ (v4 = 0) & line_connecting(v1, v0) = v5 & line_connecting(v0, v1)
% 14.58/2.63      = v3 & apart_point_and_line(v2, v5) = 0 & apart_point_and_line(v2, v3) = v4
% 14.58/2.63      & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 &
% 14.58/2.63      distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.58/2.63  
% 14.58/2.63    (con1)
% 14.58/2.63     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 14.58/2.63      (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ~
% 14.58/2.63      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int]
% 14.58/2.63      : ((v6 = 0 & v5 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0)
% 14.58/2.63          = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 14.58/2.63  
% 14.58/2.63    (cu1)
% 14.58/2.63     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5:
% 14.58/2.63      int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~
% 14.58/2.63      (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ~
% 14.58/2.63      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] : 
% 14.58/2.63      ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 14.58/2.64          apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 14.58/2.64            v3) = v6))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : 
% 14.58/2.64    ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1,
% 14.58/2.64          v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~
% 14.58/2.64      (distinct_lines(v2, v3) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 14.58/2.64      |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 &
% 14.58/2.64          apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 14.58/2.64            v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0:
% 14.58/2.64      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int]
% 14.58/2.64    : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~
% 14.58/2.64      (apart_point_and_line(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 14.58/2.64      $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ((v9 =
% 14.58/2.64          0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 14.58/2.64          apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 14.58/2.64            v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0:
% 14.58/2.64      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int]
% 14.58/2.64    : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~
% 14.58/2.64      (apart_point_and_line(v0, v3) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 14.58/2.64      $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ((v9 =
% 14.58/2.64          0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 14.58/2.64          apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 14.58/2.64            v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0:
% 14.58/2.64      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] :  ! [v5: int]
% 14.58/2.64    : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~
% 14.58/2.64      (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ~
% 14.58/2.64      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] : 
% 14.58/2.64      ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 14.58/2.64          apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 14.58/2.64            v1) = v6))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : 
% 14.58/2.64    ! [v4: int] :  ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0,
% 14.58/2.64          v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~
% 14.58/2.64      (distinct_points(v0, v1) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 14.58/2.64      $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] : ((v8 = 0 &
% 14.58/2.64          apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 14.58/2.64            v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0: $i]
% 14.58/2.64    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 14.58/2.64       ~ (distinct_points(v0, v1) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 14.58/2.64      $i(v0) |  ? [v4: int] :  ? [v5: int] :  ? [v6: int] :  ? [v7: int] : ((v7 =
% 14.58/2.64          0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 14.58/2.64          apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 14.58/2.64            v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 14.58/2.64  
% 14.58/2.64    (function-axioms)
% 14.58/2.64     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.58/2.64      (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) & 
% 14.58/2.64    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.58/2.64      (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  !
% 14.58/2.64    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.58/2.64      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 14.58/2.64      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 14.58/2.64      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 14.58/2.64      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 14.58/2.64    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 14.58/2.64      $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3,
% 14.58/2.64          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 14.58/2.64    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 14.58/2.64      (distinct_points(v3, v2) = v0))
% 14.58/2.64  
% 14.58/2.64  Further assumptions not needed in the proof:
% 14.58/2.64  --------------------------------------------
% 14.58/2.64  apart2, apart3, apart5, apart6, ceq1, ceq3, con2
% 14.58/2.64  
% 14.58/2.64  Those formulas are unsatisfiable:
% 14.58/2.64  ---------------------------------
% 14.58/2.64  
% 14.58/2.64  Begin of proof
% 14.58/2.64  | 
% 14.58/2.64  | ALPHA: (apart4) implies:
% 14.58/2.64  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 14.58/2.64  |          (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | 
% 14.58/2.64  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | distinct_points(v0, v2) = 0)
% 14.58/2.64  | 
% 14.58/2.64  | ALPHA: (cu1) implies:
% 14.58/2.64  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 14.58/2.64  |          (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ~
% 14.58/2.64  |          $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5:
% 14.58/2.64  |            int] :  ? [v6: int] :  ? [v7: int] : ((v7 = 0 &
% 14.58/2.64  |              apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 14.58/2.64  |              apart_point_and_line(v1, v2) = 0) | (v5 = 0 &
% 14.58/2.64  |              apart_point_and_line(v0, v3) = 0) | (v4 = 0 &
% 14.58/2.64  |              apart_point_and_line(v0, v2) = 0)))
% 14.58/2.64  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : 
% 14.58/2.64  |        ! [v5: int] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5)
% 14.58/2.64  |          |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 14.58/2.64  |          $i(v1) |  ~ $i(v0) |  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ?
% 14.58/2.64  |          [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 14.58/2.64  |              apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) &
% 14.58/2.64  |              distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 14.58/2.64  |                v1) = v6)))
% 14.58/2.64  | 
% 14.58/2.64  | ALPHA: (ceq2) implies:
% 14.58/2.64  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 14.58/2.64  |          (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0,
% 14.58/2.64  |              v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | distinct_lines(v1,
% 14.58/2.64  |            v2) = 0)
% 14.58/2.64  | 
% 14.58/2.64  | ALPHA: (function-axioms) implies:
% 14.58/2.65  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 14.58/2.65  |         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 14.58/2.65  |          (distinct_points(v3, v2) = v0))
% 14.58/2.65  | 
% 14.58/2.65  | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 14.58/2.65  |        all_15_3, all_15_4, all_15_5 gives:
% 14.58/2.65  |   (6)   ~ (all_15_1 = 0) & line_connecting(all_15_4, all_15_5) = all_15_0 &
% 14.58/2.65  |        line_connecting(all_15_5, all_15_4) = all_15_2 &
% 14.58/2.65  |        apart_point_and_line(all_15_3, all_15_0) = 0 &
% 14.58/2.65  |        apart_point_and_line(all_15_3, all_15_2) = all_15_1 &
% 14.58/2.65  |        distinct_points(all_15_4, all_15_3) = 0 & distinct_points(all_15_5,
% 14.58/2.65  |          all_15_3) = 0 & distinct_points(all_15_5, all_15_4) = 0 &
% 14.58/2.65  |        $i(all_15_0) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 14.58/2.65  |        $i(all_15_5)
% 14.58/2.65  | 
% 14.58/2.65  | ALPHA: (6) implies:
% 14.58/2.65  |   (7)   ~ (all_15_1 = 0)
% 14.58/2.65  |   (8)  $i(all_15_5)
% 14.58/2.65  |   (9)  $i(all_15_4)
% 14.58/2.65  |   (10)  $i(all_15_3)
% 14.58/2.65  |   (11)  $i(all_15_2)
% 14.58/2.65  |   (12)  $i(all_15_0)
% 14.58/2.65  |   (13)  distinct_points(all_15_5, all_15_4) = 0
% 14.58/2.65  |   (14)  apart_point_and_line(all_15_3, all_15_2) = all_15_1
% 14.58/2.65  |   (15)  apart_point_and_line(all_15_3, all_15_0) = 0
% 14.58/2.65  |   (16)  line_connecting(all_15_5, all_15_4) = all_15_2
% 14.58/2.65  |   (17)  line_connecting(all_15_4, all_15_5) = all_15_0
% 14.58/2.65  | 
% 14.58/2.65  | GROUND_INST: instantiating (3) with all_15_3, all_15_3, all_15_2, all_15_2,
% 14.58/2.65  |              all_15_1, all_15_1, simplifying with (10), (11), (14) gives:
% 14.58/2.65  |   (18)  all_15_1 = 0 |  ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3:
% 14.58/2.65  |           int] : ((v3 = 0 & apart_point_and_line(all_15_3, all_15_2) = 0) |
% 14.58/2.65  |           (v2 = 0 & apart_point_and_line(all_15_3, all_15_2) = 0) | ( ~ (v1 =
% 14.58/2.65  |               0) & distinct_lines(all_15_2, all_15_2) = v1) | ( ~ (v0 = 0) &
% 14.58/2.65  |             distinct_points(all_15_3, all_15_3) = v0))
% 14.58/2.65  | 
% 14.58/2.65  | GROUND_INST: instantiating (4) with all_15_3, all_15_0, all_15_2, all_15_1,
% 14.58/2.65  |              simplifying with (10), (11), (12), (14), (15) gives:
% 14.58/2.65  |   (19)  all_15_1 = 0 | distinct_lines(all_15_0, all_15_2) = 0
% 14.58/2.65  | 
% 14.58/2.65  | BETA: splitting (19) gives:
% 14.58/2.65  | 
% 14.58/2.65  | Case 1:
% 14.58/2.65  | | 
% 14.58/2.65  | |   (20)  distinct_lines(all_15_0, all_15_2) = 0
% 14.58/2.65  | | 
% 14.58/2.65  | | BETA: splitting (18) gives:
% 14.58/2.65  | | 
% 14.58/2.65  | | Case 1:
% 14.58/2.65  | | | 
% 14.58/2.65  | | |   (21)  all_15_1 = 0
% 14.58/2.65  | | | 
% 14.58/2.65  | | | REDUCE: (7), (21) imply:
% 14.58/2.65  | | |   (22)  $false
% 14.58/2.65  | | | 
% 14.58/2.65  | | | CLOSE: (22) is inconsistent.
% 14.58/2.65  | | | 
% 14.58/2.65  | | Case 2:
% 14.58/2.65  | | | 
% 14.58/2.65  | | | 
% 14.58/2.65  | | | GROUND_INST: instantiating (2) with all_15_5, all_15_4, all_15_0,
% 14.58/2.65  | | |              all_15_2, simplifying with (8), (9), (11), (12), (13), (20)
% 14.58/2.65  | | |              gives:
% 14.58/2.65  | | |   (23)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] : ((v3 =
% 14.58/2.65  | | |             0 & apart_point_and_line(all_15_4, all_15_2) = 0) | (v2 = 0 &
% 14.58/2.65  | | |             apart_point_and_line(all_15_4, all_15_0) = 0) | (v1 = 0 &
% 14.58/2.65  | | |             apart_point_and_line(all_15_5, all_15_2) = 0) | (v0 = 0 &
% 14.58/2.65  | | |             apart_point_and_line(all_15_5, all_15_0) = 0))
% 14.58/2.65  | | | 
% 14.58/2.65  | | | DELTA: instantiating (23) with fresh symbols all_43_0, all_43_1, all_43_2,
% 14.58/2.65  | | |        all_43_3 gives:
% 14.58/2.66  | | |   (24)  (all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0) |
% 14.58/2.66  | | |         (all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0) |
% 14.58/2.66  | | |         (all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0) |
% 14.58/2.66  | | |         (all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0)
% 14.58/2.66  | | | 
% 14.58/2.66  | | | BETA: splitting (24) gives:
% 14.58/2.66  | | | 
% 14.58/2.66  | | | Case 1:
% 14.58/2.66  | | | | 
% 14.58/2.66  | | | |   (25)  (all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0) |
% 14.58/2.66  | | | |         (all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0)
% 14.58/2.66  | | | | 
% 14.58/2.66  | | | | BETA: splitting (25) gives:
% 14.58/2.66  | | | | 
% 14.58/2.66  | | | | Case 1:
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | |   (26)  all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | ALPHA: (26) implies:
% 14.58/2.66  | | | | |   (27)  apart_point_and_line(all_15_4, all_15_2) = 0
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_4,
% 14.58/2.66  | | | | |              all_15_2, simplifying with (8), (9), (16), (27) gives:
% 14.58/2.66  | | | | |   (28)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.58/2.66  | | | | |             & distinct_points(all_15_4, all_15_4) = 0 &
% 14.58/2.66  | | | | |             distinct_points(all_15_4, all_15_5) = 0) | ( ~ (v0 = 0) &
% 14.58/2.66  | | | | |             distinct_points(all_15_5, all_15_4) = v0))
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | DELTA: instantiating (28) with fresh symbols all_118_0, all_118_1,
% 14.58/2.66  | | | | |        all_118_2 gives:
% 14.58/2.66  | | | | |   (29)  (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4,
% 14.58/2.66  | | | | |             all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0) |
% 14.58/2.66  | | | | |         ( ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) =
% 14.58/2.66  | | | | |           all_118_2)
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | BETA: splitting (29) gives:
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | Case 1:
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | |   (30)  all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4,
% 14.58/2.66  | | | | | |           all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | ALPHA: (30) implies:
% 14.58/2.66  | | | | | |   (31)  distinct_points(all_15_4, all_15_4) = 0
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying with
% 14.58/2.66  | | | | | |              (9), (31) gives:
% 14.58/2.66  | | | | | |   (32)  $false
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | CLOSE: (32) is inconsistent.
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | Case 2:
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | |   (33)   ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) =
% 14.58/2.66  | | | | | |         all_118_2
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | ALPHA: (33) implies:
% 14.58/2.66  | | | | | |   (34)   ~ (all_118_2 = 0)
% 14.58/2.66  | | | | | |   (35)  distinct_points(all_15_5, all_15_4) = all_118_2
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | GROUND_INST: instantiating (5) with 0, all_118_2, all_15_4,
% 14.58/2.66  | | | | | |              all_15_5, simplifying with (13), (35) gives:
% 14.58/2.66  | | | | | |   (36)  all_118_2 = 0
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | REDUCE: (34), (36) imply:
% 14.58/2.66  | | | | | |   (37)  $false
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | | CLOSE: (37) is inconsistent.
% 14.58/2.66  | | | | | | 
% 14.58/2.66  | | | | | End of split
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | Case 2:
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | |   (38)  all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0
% 14.58/2.66  | | | | | 
% 14.58/2.66  | | | | | ALPHA: (38) implies:
% 14.58/2.66  | | | | |   (39)  apart_point_and_line(all_15_4, all_15_0) = 0
% 14.58/2.66  | | | | | 
% 14.92/2.66  | | | | | GROUND_INST: instantiating (con1) with all_15_4, all_15_5, all_15_4,
% 14.92/2.66  | | | | |              all_15_0, simplifying with (8), (9), (17), (39) gives:
% 14.92/2.66  | | | | |   (40)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.92/2.66  | | | | |             & distinct_points(all_15_4, all_15_4) = 0 &
% 14.92/2.66  | | | | |             distinct_points(all_15_4, all_15_5) = 0) | ( ~ (v0 = 0) &
% 14.92/2.66  | | | | |             distinct_points(all_15_4, all_15_5) = v0))
% 14.92/2.66  | | | | | 
% 14.92/2.66  | | | | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1,
% 14.92/2.66  | | | | |        all_118_2 gives:
% 14.92/2.66  | | | | |   (41)  (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4,
% 14.92/2.66  | | | | |             all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0) |
% 14.92/2.66  | | | | |         ( ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) =
% 14.92/2.66  | | | | |           all_118_2)
% 14.92/2.66  | | | | | 
% 14.92/2.66  | | | | | BETA: splitting (41) gives:
% 14.92/2.66  | | | | | 
% 14.92/2.66  | | | | | Case 1:
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | |   (42)  all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4,
% 14.92/2.66  | | | | | |           all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | | ALPHA: (42) implies:
% 14.92/2.66  | | | | | |   (43)  distinct_points(all_15_4, all_15_4) = 0
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying with
% 14.92/2.66  | | | | | |              (9), (43) gives:
% 14.92/2.66  | | | | | |   (44)  $false
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | | CLOSE: (44) is inconsistent.
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | Case 2:
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | |   (45)   ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) =
% 14.92/2.66  | | | | | |         all_118_2
% 14.92/2.66  | | | | | | 
% 14.92/2.66  | | | | | | ALPHA: (45) implies:
% 14.92/2.66  | | | | | |   (46)   ~ (all_118_2 = 0)
% 14.92/2.66  | | | | | |   (47)  distinct_points(all_15_4, all_15_5) = all_118_2
% 14.92/2.66  | | | | | | 
% 14.92/2.67  | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_4, all_15_5,
% 14.92/2.67  | | | | | |              all_118_2, simplifying with (8), (9), (13), (47) gives:
% 14.93/2.67  | | | | | |   (48)  all_118_2 = 0 | distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | BETA: splitting (48) gives:
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | Case 1:
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | |   (49)  distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying
% 14.93/2.67  | | | | | | |              with (8), (49) gives:
% 14.93/2.67  | | | | | | |   (50)  $false
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | | CLOSE: (50) is inconsistent.
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | Case 2:
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | |   (51)  all_118_2 = 0
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | | REDUCE: (46), (51) imply:
% 14.93/2.67  | | | | | | |   (52)  $false
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | | CLOSE: (52) is inconsistent.
% 14.93/2.67  | | | | | | | 
% 14.93/2.67  | | | | | | End of split
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | End of split
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | End of split
% 14.93/2.67  | | | | 
% 14.93/2.67  | | | Case 2:
% 14.93/2.67  | | | | 
% 14.93/2.67  | | | |   (53)  (all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0) |
% 14.93/2.67  | | | |         (all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0)
% 14.93/2.67  | | | | 
% 14.93/2.67  | | | | BETA: splitting (53) gives:
% 14.93/2.67  | | | | 
% 14.93/2.67  | | | | Case 1:
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | |   (54)  all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | ALPHA: (54) implies:
% 14.93/2.67  | | | | |   (55)  apart_point_and_line(all_15_5, all_15_2) = 0
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_5,
% 14.93/2.67  | | | | |              all_15_2, simplifying with (8), (9), (16), (55) gives:
% 14.93/2.67  | | | | |   (56)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.93/2.67  | | | | |             & distinct_points(all_15_5, all_15_4) = 0 &
% 14.93/2.67  | | | | |             distinct_points(all_15_5, all_15_5) = 0) | ( ~ (v0 = 0) &
% 14.93/2.67  | | | | |             distinct_points(all_15_5, all_15_4) = v0))
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | DELTA: instantiating (56) with fresh symbols all_118_0, all_118_1,
% 14.93/2.67  | | | | |        all_118_2 gives:
% 14.93/2.67  | | | | |   (57)  (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5,
% 14.93/2.67  | | | | |             all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0) |
% 14.93/2.67  | | | | |         ( ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) =
% 14.93/2.67  | | | | |           all_118_2)
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | BETA: splitting (57) gives:
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | Case 1:
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | |   (58)  all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5,
% 14.93/2.67  | | | | | |           all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | ALPHA: (58) implies:
% 14.93/2.67  | | | | | |   (59)  distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with
% 14.93/2.67  | | | | | |              (8), (59) gives:
% 14.93/2.67  | | | | | |   (60)  $false
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | CLOSE: (60) is inconsistent.
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | Case 2:
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | |   (61)   ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) =
% 14.93/2.67  | | | | | |         all_118_2
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | ALPHA: (61) implies:
% 14.93/2.67  | | | | | |   (62)   ~ (all_118_2 = 0)
% 14.93/2.67  | | | | | |   (63)  distinct_points(all_15_5, all_15_4) = all_118_2
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | GROUND_INST: instantiating (5) with 0, all_118_2, all_15_4,
% 14.93/2.67  | | | | | |              all_15_5, simplifying with (13), (63) gives:
% 14.93/2.67  | | | | | |   (64)  all_118_2 = 0
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | REDUCE: (62), (64) imply:
% 14.93/2.67  | | | | | |   (65)  $false
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | | CLOSE: (65) is inconsistent.
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | End of split
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | Case 2:
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | |   (66)  all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | ALPHA: (66) implies:
% 14.93/2.67  | | | | |   (67)  apart_point_and_line(all_15_5, all_15_0) = 0
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | GROUND_INST: instantiating (con1) with all_15_4, all_15_5, all_15_5,
% 14.93/2.67  | | | | |              all_15_0, simplifying with (8), (9), (17), (67) gives:
% 14.93/2.67  | | | | |   (68)   ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.93/2.67  | | | | |             & distinct_points(all_15_5, all_15_4) = 0 &
% 14.93/2.67  | | | | |             distinct_points(all_15_5, all_15_5) = 0) | ( ~ (v0 = 0) &
% 14.93/2.67  | | | | |             distinct_points(all_15_4, all_15_5) = v0))
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | DELTA: instantiating (68) with fresh symbols all_118_0, all_118_1,
% 14.93/2.67  | | | | |        all_118_2 gives:
% 14.93/2.67  | | | | |   (69)  (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5,
% 14.93/2.67  | | | | |             all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0) |
% 14.93/2.67  | | | | |         ( ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) =
% 14.93/2.67  | | | | |           all_118_2)
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | BETA: splitting (69) gives:
% 14.93/2.67  | | | | | 
% 14.93/2.67  | | | | | Case 1:
% 14.93/2.67  | | | | | | 
% 14.93/2.67  | | | | | |   (70)  all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5,
% 14.93/2.67  | | | | | |           all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | ALPHA: (70) implies:
% 14.93/2.68  | | | | | |   (71)  distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with
% 14.93/2.68  | | | | | |              (8), (71) gives:
% 14.93/2.68  | | | | | |   (72)  $false
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | CLOSE: (72) is inconsistent.
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | Case 2:
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | |   (73)   ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) =
% 14.93/2.68  | | | | | |         all_118_2
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | ALPHA: (73) implies:
% 14.93/2.68  | | | | | |   (74)   ~ (all_118_2 = 0)
% 14.93/2.68  | | | | | |   (75)  distinct_points(all_15_4, all_15_5) = all_118_2
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_4, all_15_5,
% 14.93/2.68  | | | | | |              all_118_2, simplifying with (8), (9), (13), (75) gives:
% 14.93/2.68  | | | | | |   (76)  all_118_2 = 0 | distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | BETA: splitting (76) gives:
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | | Case 1:
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | |   (77)  distinct_points(all_15_5, all_15_5) = 0
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying
% 14.93/2.68  | | | | | | |              with (8), (77) gives:
% 14.93/2.68  | | | | | | |   (78)  $false
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | | CLOSE: (78) is inconsistent.
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | Case 2:
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | |   (79)  all_118_2 = 0
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | | REDUCE: (74), (79) imply:
% 14.93/2.68  | | | | | | |   (80)  $false
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | | CLOSE: (80) is inconsistent.
% 14.93/2.68  | | | | | | | 
% 14.93/2.68  | | | | | | End of split
% 14.93/2.68  | | | | | | 
% 14.93/2.68  | | | | | End of split
% 14.93/2.68  | | | | | 
% 14.93/2.68  | | | | End of split
% 14.93/2.68  | | | | 
% 14.93/2.68  | | | End of split
% 14.93/2.68  | | | 
% 14.93/2.68  | | End of split
% 14.93/2.68  | | 
% 14.93/2.68  | Case 2:
% 14.93/2.68  | | 
% 14.93/2.68  | |   (81)  all_15_1 = 0
% 14.93/2.68  | | 
% 14.93/2.68  | | REDUCE: (7), (81) imply:
% 14.93/2.68  | |   (82)  $false
% 14.93/2.68  | | 
% 14.93/2.68  | | CLOSE: (82) is inconsistent.
% 14.93/2.68  | | 
% 14.93/2.68  | End of split
% 14.93/2.68  | 
% 14.93/2.68  End of proof
% 14.93/2.68  % SZS output end Proof for theBenchmark
% 14.93/2.68  
% 14.93/2.68  2078ms
%------------------------------------------------------------------------------