TSTP Solution File: GEO204+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO204+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n015.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 23:22:16 EDT 2023

% Result   : Theorem 6.43s 1.65s
% Output   : Proof 8.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : GEO204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 22:29:56 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.65  ________       _____
% 0.21/0.65  ___  __ \_________(_)________________________________
% 0.21/0.65  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.65  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.65  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.65  
% 0.21/0.65  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.65  (2023-06-19)
% 0.21/0.65  
% 0.21/0.65  (c) Philipp Rümmer, 2009-2023
% 0.21/0.65  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.65                Amanda Stjerna.
% 0.21/0.65  Free software under BSD-3-Clause.
% 0.21/0.65  
% 0.21/0.65  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.65  
% 0.21/0.66  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.67  Running up to 7 provers in parallel.
% 0.21/0.70  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.70  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.69/1.11  Prover 4: Preprocessing ...
% 2.69/1.11  Prover 1: Preprocessing ...
% 2.69/1.15  Prover 6: Preprocessing ...
% 2.69/1.15  Prover 2: Preprocessing ...
% 2.69/1.15  Prover 0: Preprocessing ...
% 2.69/1.15  Prover 5: Preprocessing ...
% 2.69/1.15  Prover 3: Preprocessing ...
% 3.76/1.39  Prover 5: Proving ...
% 3.76/1.40  Prover 2: Proving ...
% 3.76/1.41  Prover 1: Constructing countermodel ...
% 3.76/1.43  Prover 6: Constructing countermodel ...
% 3.76/1.43  Prover 3: Constructing countermodel ...
% 5.85/1.56  Prover 4: Constructing countermodel ...
% 6.01/1.60  Prover 0: Proving ...
% 6.43/1.64  Prover 6: proved (942ms)
% 6.43/1.64  
% 6.43/1.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.43/1.65  
% 6.68/1.66  Prover 0: stopped
% 6.68/1.66  Prover 2: stopped
% 6.68/1.66  Prover 3: stopped
% 6.68/1.66  Prover 5: stopped
% 6.68/1.67  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.68/1.67  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.68/1.67  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.68/1.67  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.68/1.67  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.68/1.70  Prover 10: Preprocessing ...
% 6.68/1.71  Prover 13: Preprocessing ...
% 6.68/1.71  Prover 8: Preprocessing ...
% 6.68/1.71  Prover 7: Preprocessing ...
% 6.68/1.73  Prover 11: Preprocessing ...
% 7.24/1.74  Prover 10: Warning: ignoring some quantifiers
% 7.24/1.75  Prover 7: Warning: ignoring some quantifiers
% 7.24/1.76  Prover 10: Constructing countermodel ...
% 7.24/1.76  Prover 7: Constructing countermodel ...
% 7.24/1.77  Prover 13: Warning: ignoring some quantifiers
% 7.58/1.79  Prover 13: Constructing countermodel ...
% 7.58/1.81  Prover 8: Warning: ignoring some quantifiers
% 7.58/1.82  Prover 10: gave up
% 7.58/1.82  Prover 7: gave up
% 7.58/1.82  Prover 8: Constructing countermodel ...
% 7.58/1.82  Prover 1: Found proof (size 67)
% 7.58/1.82  Prover 1: proved (1144ms)
% 7.58/1.83  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.58/1.83  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.58/1.83  Prover 4: stopped
% 7.58/1.83  Prover 13: stopped
% 7.58/1.84  Prover 8: stopped
% 8.02/1.85  Prover 16: Preprocessing ...
% 8.02/1.85  Prover 19: Preprocessing ...
% 8.16/1.86  Prover 16: stopped
% 8.50/1.92  Prover 11: Constructing countermodel ...
% 8.50/1.92  Prover 19: Warning: ignoring some quantifiers
% 8.50/1.93  Prover 11: stopped
% 8.50/1.93  Prover 19: Constructing countermodel ...
% 8.50/1.93  Prover 19: stopped
% 8.50/1.93  
% 8.50/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.50/1.93  
% 8.50/1.95  % SZS output start Proof for theBenchmark
% 8.50/1.95  Assumptions after simplification:
% 8.50/1.95  ---------------------------------
% 8.50/1.95  
% 8.50/1.95    (apart4)
% 8.50/1.99     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 8.50/1.99      (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) |  ~
% 8.50/1.99      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | distinct_points(v1, v2) = 0)
% 8.50/1.99  
% 8.50/1.99    (ceq1)
% 8.50/1.99     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 8.50/1.99      (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) |  ~
% 8.50/1.99      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | apart_point_and_line(v2, v1) = 0)
% 8.50/1.99  
% 8.50/1.99    (ci1)
% 8.50/2.00     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 8.50/2.00       ~ (apart_point_and_line(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 8.50/2.00      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 8.50/2.00  
% 8.50/2.00    (ci2)
% 8.50/2.00     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 8.50/2.00       ~ (apart_point_and_line(v1, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 8.50/2.00      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 8.50/2.00  
% 8.50/2.00    (con)
% 8.50/2.00     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] :  ? [v4: any] :  ?
% 8.50/2.00    [v5: $i] :  ? [v6: $i] :  ? [v7: any] : ( ~ (v3 = 0) & line_connecting(v0, v2)
% 8.50/2.00      = v6 & line_connecting(v0, v1) = v5 & distinct_lines(v5, v6) = v7 &
% 8.50/2.00      distinct_points(v1, v2) = v3 & distinct_points(v0, v2) = v4 &
% 8.50/2.00      distinct_points(v0, v1) = 0 & $i(v6) & $i(v5) & $i(v2) & $i(v1) & $i(v0) & (
% 8.50/2.00        ~ (v4 = 0) | v7 = 0))
% 8.50/2.00  
% 8.50/2.00    (cu1)
% 8.50/2.00     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.50/2.00      (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ~ $i(v3)
% 8.50/2.00      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :  ? [v6:
% 8.50/2.00        any] :  ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 8.50/2.00        apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 8.50/2.00        apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 8.50/2.00  
% 8.50/2.00    (function-axioms)
% 8.50/2.01     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.50/2.01      (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) & 
% 8.50/2.01    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.50/2.01      (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  !
% 8.50/2.01    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 8.50/2.01      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 8.50/2.01      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 8.50/2.01      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 8.50/2.01      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 8.50/2.01    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 8.50/2.01      $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3,
% 8.50/2.01          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 8.50/2.01    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 8.50/2.01      (distinct_points(v3, v2) = v0))
% 8.50/2.01  
% 8.50/2.01  Further assumptions not needed in the proof:
% 8.50/2.01  --------------------------------------------
% 8.50/2.01  apart1, apart2, apart3, apart5, ax6, ceq2, ceq3, ci3, ci4
% 8.50/2.01  
% 8.50/2.01  Those formulas are unsatisfiable:
% 8.50/2.01  ---------------------------------
% 8.50/2.01  
% 8.50/2.01  Begin of proof
% 8.50/2.01  | 
% 8.50/2.01  | ALPHA: (function-axioms) implies:
% 8.50/2.01  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.50/2.01  |         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 8.50/2.01  |          (distinct_points(v3, v2) = v0))
% 8.50/2.01  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 8.50/2.01  |         ! [v3: $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 8.50/2.01  |          (apart_point_and_line(v3, v2) = v0))
% 8.50/2.01  | 
% 8.50/2.01  | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 8.50/2.01  |        all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives:
% 8.50/2.01  |   (3)   ~ (all_17_4 = 0) & line_connecting(all_17_7, all_17_5) = all_17_1 &
% 8.50/2.01  |        line_connecting(all_17_7, all_17_6) = all_17_2 &
% 8.50/2.01  |        distinct_lines(all_17_2, all_17_1) = all_17_0 &
% 8.50/2.01  |        distinct_points(all_17_6, all_17_5) = all_17_4 &
% 8.50/2.01  |        distinct_points(all_17_7, all_17_5) = all_17_3 &
% 8.50/2.01  |        distinct_points(all_17_7, all_17_6) = 0 & $i(all_17_1) & $i(all_17_2) &
% 8.50/2.01  |        $i(all_17_5) & $i(all_17_6) & $i(all_17_7) & ( ~ (all_17_3 = 0) |
% 8.50/2.01  |          all_17_0 = 0)
% 8.50/2.01  | 
% 8.50/2.01  | ALPHA: (3) implies:
% 8.50/2.01  |   (4)   ~ (all_17_4 = 0)
% 8.50/2.01  |   (5)  $i(all_17_7)
% 8.50/2.01  |   (6)  $i(all_17_6)
% 8.50/2.01  |   (7)  $i(all_17_5)
% 8.50/2.01  |   (8)  $i(all_17_2)
% 8.50/2.01  |   (9)  $i(all_17_1)
% 8.50/2.02  |   (10)  distinct_points(all_17_7, all_17_6) = 0
% 8.50/2.02  |   (11)  distinct_points(all_17_7, all_17_5) = all_17_3
% 8.50/2.02  |   (12)  distinct_points(all_17_6, all_17_5) = all_17_4
% 8.50/2.02  |   (13)  distinct_lines(all_17_2, all_17_1) = all_17_0
% 8.50/2.02  |   (14)  line_connecting(all_17_7, all_17_6) = all_17_2
% 8.50/2.02  |   (15)  line_connecting(all_17_7, all_17_5) = all_17_1
% 8.50/2.02  |   (16)   ~ (all_17_3 = 0) | all_17_0 = 0
% 8.50/2.02  | 
% 8.50/2.02  | GROUND_INST: instantiating (apart4) with all_17_7, all_17_6, all_17_5,
% 8.50/2.02  |              all_17_3, simplifying with (5), (6), (7), (10), (11) gives:
% 8.50/2.02  |   (17)  all_17_3 = 0 | distinct_points(all_17_6, all_17_5) = 0
% 8.50/2.02  | 
% 8.50/2.02  | BETA: splitting (16) gives:
% 8.50/2.02  | 
% 8.50/2.02  | Case 1:
% 8.50/2.02  | | 
% 8.50/2.02  | |   (18)   ~ (all_17_3 = 0)
% 8.50/2.02  | | 
% 8.50/2.02  | | BETA: splitting (17) gives:
% 8.50/2.02  | | 
% 8.50/2.02  | | Case 1:
% 8.50/2.02  | | | 
% 8.50/2.02  | | |   (19)  distinct_points(all_17_6, all_17_5) = 0
% 8.50/2.02  | | | 
% 8.50/2.02  | | | GROUND_INST: instantiating (1) with all_17_4, 0, all_17_5, all_17_6,
% 8.50/2.02  | | |              simplifying with (12), (19) gives:
% 8.50/2.02  | | |   (20)  all_17_4 = 0
% 8.50/2.02  | | | 
% 8.50/2.02  | | | REDUCE: (4), (20) imply:
% 8.50/2.02  | | |   (21)  $false
% 8.50/2.02  | | | 
% 8.50/2.02  | | | CLOSE: (21) is inconsistent.
% 8.50/2.02  | | | 
% 8.50/2.02  | | Case 2:
% 8.50/2.02  | | | 
% 8.50/2.02  | | |   (22)  all_17_3 = 0
% 8.50/2.02  | | | 
% 8.50/2.02  | | | REDUCE: (18), (22) imply:
% 8.50/2.02  | | |   (23)  $false
% 8.50/2.02  | | | 
% 8.50/2.02  | | | CLOSE: (23) is inconsistent.
% 8.50/2.02  | | | 
% 8.50/2.02  | | End of split
% 8.50/2.02  | | 
% 8.50/2.02  | Case 2:
% 8.50/2.02  | | 
% 8.50/2.02  | |   (24)  all_17_3 = 0
% 8.50/2.02  | |   (25)  all_17_0 = 0
% 8.50/2.02  | | 
% 8.50/2.02  | | REDUCE: (13), (25) imply:
% 8.50/2.02  | |   (26)  distinct_lines(all_17_2, all_17_1) = 0
% 8.50/2.02  | | 
% 8.50/2.02  | | REDUCE: (11), (24) imply:
% 8.50/2.02  | |   (27)  distinct_points(all_17_7, all_17_5) = 0
% 8.50/2.02  | | 
% 8.50/2.02  | | GROUND_INST: instantiating (cu1) with all_17_7, all_17_6, all_17_2,
% 8.50/2.02  | |              all_17_1, simplifying with (5), (6), (8), (9), (10), (26)
% 8.50/2.02  | |              gives:
% 8.50/2.02  | |   (28)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 8.50/2.02  | |         (apart_point_and_line(all_17_6, all_17_1) = v3 &
% 8.50/2.02  | |           apart_point_and_line(all_17_6, all_17_2) = v2 &
% 8.50/2.02  | |           apart_point_and_line(all_17_7, all_17_1) = v1 &
% 8.50/2.02  | |           apart_point_and_line(all_17_7, all_17_2) = v0 & (v3 = 0 | v2 = 0 |
% 8.50/2.02  | |             v1 = 0 | v0 = 0))
% 8.50/2.02  | | 
% 8.50/2.02  | | GROUND_INST: instantiating (cu1) with all_17_7, all_17_5, all_17_2,
% 8.50/2.02  | |              all_17_1, simplifying with (5), (7), (8), (9), (26), (27)
% 8.50/2.02  | |              gives:
% 8.50/2.03  | |   (29)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 8.50/2.03  | |         (apart_point_and_line(all_17_5, all_17_1) = v3 &
% 8.50/2.03  | |           apart_point_and_line(all_17_5, all_17_2) = v2 &
% 8.50/2.03  | |           apart_point_and_line(all_17_7, all_17_1) = v1 &
% 8.50/2.03  | |           apart_point_and_line(all_17_7, all_17_2) = v0 & (v3 = 0 | v2 = 0 |
% 8.50/2.03  | |             v1 = 0 | v0 = 0))
% 8.50/2.03  | | 
% 8.50/2.03  | | DELTA: instantiating (29) with fresh symbols all_31_0, all_31_1, all_31_2,
% 8.50/2.03  | |        all_31_3 gives:
% 8.50/2.03  | |   (30)  apart_point_and_line(all_17_5, all_17_1) = all_31_0 &
% 8.50/2.03  | |         apart_point_and_line(all_17_5, all_17_2) = all_31_1 &
% 8.50/2.03  | |         apart_point_and_line(all_17_7, all_17_1) = all_31_2 &
% 8.50/2.03  | |         apart_point_and_line(all_17_7, all_17_2) = all_31_3 & (all_31_0 = 0
% 8.50/2.03  | |           | all_31_1 = 0 | all_31_2 = 0 | all_31_3 = 0)
% 8.50/2.03  | | 
% 8.50/2.03  | | ALPHA: (30) implies:
% 8.50/2.03  | |   (31)  apart_point_and_line(all_17_7, all_17_2) = all_31_3
% 8.50/2.03  | |   (32)  apart_point_and_line(all_17_7, all_17_1) = all_31_2
% 8.50/2.03  | | 
% 8.50/2.03  | | DELTA: instantiating (28) with fresh symbols all_33_0, all_33_1, all_33_2,
% 8.50/2.03  | |        all_33_3 gives:
% 8.50/2.03  | |   (33)  apart_point_and_line(all_17_6, all_17_1) = all_33_0 &
% 8.50/2.03  | |         apart_point_and_line(all_17_6, all_17_2) = all_33_1 &
% 8.50/2.03  | |         apart_point_and_line(all_17_7, all_17_1) = all_33_2 &
% 8.50/2.03  | |         apart_point_and_line(all_17_7, all_17_2) = all_33_3 & (all_33_0 = 0
% 8.50/2.03  | |           | all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0)
% 8.50/2.03  | | 
% 8.50/2.03  | | ALPHA: (33) implies:
% 8.50/2.03  | |   (34)  apart_point_and_line(all_17_7, all_17_2) = all_33_3
% 8.50/2.03  | |   (35)  apart_point_and_line(all_17_7, all_17_1) = all_33_2
% 8.50/2.03  | |   (36)  apart_point_and_line(all_17_6, all_17_2) = all_33_1
% 8.50/2.03  | |   (37)  apart_point_and_line(all_17_6, all_17_1) = all_33_0
% 8.50/2.03  | |   (38)  all_33_0 = 0 | all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0
% 8.50/2.03  | | 
% 8.50/2.03  | | GROUND_INST: instantiating (2) with all_31_3, all_33_3, all_17_2, all_17_7,
% 8.50/2.03  | |              simplifying with (31), (34) gives:
% 8.50/2.03  | |   (39)  all_33_3 = all_31_3
% 8.50/2.03  | | 
% 8.50/2.03  | | GROUND_INST: instantiating (2) with all_31_2, all_33_2, all_17_1, all_17_7,
% 8.50/2.03  | |              simplifying with (32), (35) gives:
% 8.50/2.03  | |   (40)  all_33_2 = all_31_2
% 8.50/2.03  | | 
% 8.50/2.03  | | BETA: splitting (38) gives:
% 8.50/2.03  | | 
% 8.50/2.03  | | Case 1:
% 8.50/2.03  | | | 
% 8.50/2.03  | | |   (41)  all_33_0 = 0
% 8.50/2.03  | | | 
% 8.50/2.03  | | | REDUCE: (37), (41) imply:
% 8.50/2.03  | | |   (42)  apart_point_and_line(all_17_6, all_17_1) = 0
% 8.50/2.03  | | | 
% 8.50/2.03  | | | GROUND_INST: instantiating (ceq1) with all_17_6, all_17_1, all_17_5,
% 8.50/2.03  | | |              all_17_4, simplifying with (6), (7), (9), (12), (42) gives:
% 8.50/2.03  | | |   (43)  all_17_4 = 0 | apart_point_and_line(all_17_5, all_17_1) = 0
% 8.50/2.03  | | | 
% 8.50/2.03  | | | BETA: splitting (43) gives:
% 8.50/2.03  | | | 
% 8.50/2.03  | | | Case 1:
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | |   (44)  apart_point_and_line(all_17_5, all_17_1) = 0
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | GROUND_INST: instantiating (ci2) with all_17_7, all_17_5, all_17_1,
% 8.50/2.03  | | | |              simplifying with (5), (7), (15), (44) gives:
% 8.50/2.03  | | | |   (45)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7,
% 8.50/2.03  | | | |             all_17_5) = v0)
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | DELTA: instantiating (45) with fresh symbol all_51_0 gives:
% 8.50/2.03  | | | |   (46)   ~ (all_51_0 = 0) & distinct_points(all_17_7, all_17_5) =
% 8.50/2.03  | | | |         all_51_0
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | ALPHA: (46) implies:
% 8.50/2.03  | | | |   (47)   ~ (all_51_0 = 0)
% 8.50/2.03  | | | |   (48)  distinct_points(all_17_7, all_17_5) = all_51_0
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | GROUND_INST: instantiating (1) with 0, all_51_0, all_17_5, all_17_7,
% 8.50/2.03  | | | |              simplifying with (27), (48) gives:
% 8.50/2.03  | | | |   (49)  all_51_0 = 0
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | REDUCE: (47), (49) imply:
% 8.50/2.03  | | | |   (50)  $false
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | CLOSE: (50) is inconsistent.
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | Case 2:
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | |   (51)  all_17_4 = 0
% 8.50/2.03  | | | | 
% 8.50/2.03  | | | | REDUCE: (4), (51) imply:
% 8.50/2.03  | | | |   (52)  $false
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | CLOSE: (52) is inconsistent.
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | End of split
% 8.50/2.04  | | | 
% 8.50/2.04  | | Case 2:
% 8.50/2.04  | | | 
% 8.50/2.04  | | |   (53)  all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0
% 8.50/2.04  | | | 
% 8.50/2.04  | | | BETA: splitting (53) gives:
% 8.50/2.04  | | | 
% 8.50/2.04  | | | Case 1:
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | |   (54)  all_33_1 = 0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | REDUCE: (36), (54) imply:
% 8.50/2.04  | | | |   (55)  apart_point_and_line(all_17_6, all_17_2) = 0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | GROUND_INST: instantiating (ci2) with all_17_7, all_17_6, all_17_2,
% 8.50/2.04  | | | |              simplifying with (5), (6), (14), (55) gives:
% 8.50/2.04  | | | |   (56)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7,
% 8.50/2.04  | | | |             all_17_6) = v0)
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | DELTA: instantiating (56) with fresh symbol all_72_0 gives:
% 8.50/2.04  | | | |   (57)   ~ (all_72_0 = 0) & distinct_points(all_17_7, all_17_6) =
% 8.50/2.04  | | | |         all_72_0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | ALPHA: (57) implies:
% 8.50/2.04  | | | |   (58)   ~ (all_72_0 = 0)
% 8.50/2.04  | | | |   (59)  distinct_points(all_17_7, all_17_6) = all_72_0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | GROUND_INST: instantiating (1) with 0, all_72_0, all_17_6, all_17_7,
% 8.50/2.04  | | | |              simplifying with (10), (59) gives:
% 8.50/2.04  | | | |   (60)  all_72_0 = 0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | REDUCE: (58), (60) imply:
% 8.50/2.04  | | | |   (61)  $false
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | CLOSE: (61) is inconsistent.
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | Case 2:
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | |   (62)  all_33_2 = 0 | all_33_3 = 0
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | BETA: splitting (62) gives:
% 8.50/2.04  | | | | 
% 8.50/2.04  | | | | Case 1:
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | |   (63)  all_33_2 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | COMBINE_EQS: (40), (63) imply:
% 8.50/2.04  | | | | |   (64)  all_31_2 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | REDUCE: (32), (64) imply:
% 8.50/2.04  | | | | |   (65)  apart_point_and_line(all_17_7, all_17_1) = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | GROUND_INST: instantiating (ci1) with all_17_7, all_17_5, all_17_1,
% 8.50/2.04  | | | | |              simplifying with (5), (7), (15), (65) gives:
% 8.50/2.04  | | | | |   (66)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7,
% 8.50/2.04  | | | | |             all_17_5) = v0)
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | DELTA: instantiating (66) with fresh symbol all_79_0 gives:
% 8.50/2.04  | | | | |   (67)   ~ (all_79_0 = 0) & distinct_points(all_17_7, all_17_5) =
% 8.50/2.04  | | | | |         all_79_0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | ALPHA: (67) implies:
% 8.50/2.04  | | | | |   (68)   ~ (all_79_0 = 0)
% 8.50/2.04  | | | | |   (69)  distinct_points(all_17_7, all_17_5) = all_79_0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | GROUND_INST: instantiating (1) with 0, all_79_0, all_17_5, all_17_7,
% 8.50/2.04  | | | | |              simplifying with (27), (69) gives:
% 8.50/2.04  | | | | |   (70)  all_79_0 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | REDUCE: (68), (70) imply:
% 8.50/2.04  | | | | |   (71)  $false
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | CLOSE: (71) is inconsistent.
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | Case 2:
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | |   (72)  all_33_3 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | COMBINE_EQS: (39), (72) imply:
% 8.50/2.04  | | | | |   (73)  all_31_3 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | SIMP: (73) implies:
% 8.50/2.04  | | | | |   (74)  all_31_3 = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | REDUCE: (31), (74) imply:
% 8.50/2.04  | | | | |   (75)  apart_point_and_line(all_17_7, all_17_2) = 0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | GROUND_INST: instantiating (ci1) with all_17_7, all_17_6, all_17_2,
% 8.50/2.04  | | | | |              simplifying with (5), (6), (14), (75) gives:
% 8.50/2.04  | | | | |   (76)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7,
% 8.50/2.04  | | | | |             all_17_6) = v0)
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | DELTA: instantiating (76) with fresh symbol all_79_0 gives:
% 8.50/2.04  | | | | |   (77)   ~ (all_79_0 = 0) & distinct_points(all_17_7, all_17_6) =
% 8.50/2.04  | | | | |         all_79_0
% 8.50/2.04  | | | | | 
% 8.50/2.04  | | | | | ALPHA: (77) implies:
% 8.50/2.04  | | | | |   (78)   ~ (all_79_0 = 0)
% 8.50/2.04  | | | | |   (79)  distinct_points(all_17_7, all_17_6) = all_79_0
% 8.50/2.04  | | | | | 
% 8.50/2.05  | | | | | GROUND_INST: instantiating (1) with 0, all_79_0, all_17_6, all_17_7,
% 8.50/2.05  | | | | |              simplifying with (10), (79) gives:
% 8.50/2.05  | | | | |   (80)  all_79_0 = 0
% 8.50/2.05  | | | | | 
% 8.50/2.05  | | | | | REDUCE: (78), (80) imply:
% 8.50/2.05  | | | | |   (81)  $false
% 8.50/2.05  | | | | | 
% 8.50/2.05  | | | | | CLOSE: (81) is inconsistent.
% 8.50/2.05  | | | | | 
% 8.50/2.05  | | | | End of split
% 8.50/2.05  | | | | 
% 8.50/2.05  | | | End of split
% 8.50/2.05  | | | 
% 8.50/2.05  | | End of split
% 8.50/2.05  | | 
% 8.50/2.05  | End of split
% 8.50/2.05  | 
% 8.50/2.05  End of proof
% 8.50/2.05  % SZS output end Proof for theBenchmark
% 8.50/2.05  
% 8.50/2.05  1390ms
%------------------------------------------------------------------------------