TSTP Solution File: GEO196+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO196+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 : n002.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 23:22:09 EDT 2023

% Result   : Theorem 7.49s 2.00s
% Output   : Proof 8.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : GEO196+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Tue Aug 29 21:39:20 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62  
% 0.21/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62  (2023-06-19)
% 0.21/0.62  
% 0.21/0.62  (c) Philipp Rümmer, 2009-2023
% 0.21/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62                Amanda Stjerna.
% 0.21/0.62  Free software under BSD-3-Clause.
% 0.21/0.62  
% 0.21/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.05/1.09  Prover 1: Preprocessing ...
% 2.05/1.09  Prover 4: Preprocessing ...
% 2.59/1.14  Prover 5: Preprocessing ...
% 2.59/1.14  Prover 3: Preprocessing ...
% 2.59/1.14  Prover 0: Preprocessing ...
% 2.59/1.14  Prover 6: Preprocessing ...
% 2.59/1.14  Prover 2: Preprocessing ...
% 4.31/1.45  Prover 5: Proving ...
% 4.31/1.45  Prover 2: Proving ...
% 4.31/1.48  Prover 3: Constructing countermodel ...
% 4.31/1.48  Prover 6: Constructing countermodel ...
% 4.31/1.50  Prover 1: Constructing countermodel ...
% 5.45/1.64  Prover 3: gave up
% 5.45/1.66  Prover 6: gave up
% 5.45/1.66  Prover 1: gave up
% 5.45/1.66  Prover 0: Proving ...
% 5.45/1.66  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.45/1.66  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.45/1.67  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.45/1.67  Prover 4: Constructing countermodel ...
% 6.08/1.71  Prover 8: Preprocessing ...
% 6.08/1.72  Prover 7: Preprocessing ...
% 6.08/1.72  Prover 9: Preprocessing ...
% 6.08/1.78  Prover 7: Warning: ignoring some quantifiers
% 6.08/1.79  Prover 7: Constructing countermodel ...
% 6.63/1.84  Prover 8: Warning: ignoring some quantifiers
% 6.63/1.88  Prover 8: Constructing countermodel ...
% 6.63/1.95  Prover 8: gave up
% 6.63/1.96  Prover 9: Constructing countermodel ...
% 6.63/1.96  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.49/2.00  Prover 2: proved (1344ms)
% 7.49/2.00  
% 7.49/2.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.49/2.00  
% 7.49/2.01  Prover 0: stopped
% 7.49/2.02  Prover 5: stopped
% 7.49/2.02  Prover 9: stopped
% 7.49/2.03  Prover 10: Preprocessing ...
% 7.49/2.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.49/2.03  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.49/2.03  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.49/2.03  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.49/2.06  Prover 10: Warning: ignoring some quantifiers
% 7.49/2.06  Prover 10: Constructing countermodel ...
% 7.49/2.07  Prover 16: Preprocessing ...
% 7.49/2.07  Prover 11: Preprocessing ...
% 7.49/2.08  Prover 19: Preprocessing ...
% 8.20/2.08  Prover 13: Preprocessing ...
% 8.33/2.11  Prover 7: Found proof (size 25)
% 8.33/2.11  Prover 7: proved (450ms)
% 8.33/2.11  Prover 4: stopped
% 8.41/2.12  Prover 16: Warning: ignoring some quantifiers
% 8.41/2.12  Prover 10: stopped
% 8.41/2.12  Prover 13: stopped
% 8.41/2.12  Prover 16: Constructing countermodel ...
% 8.41/2.13  Prover 11: stopped
% 8.41/2.13  Prover 16: stopped
% 8.41/2.15  Prover 19: Warning: ignoring some quantifiers
% 8.41/2.15  Prover 19: Constructing countermodel ...
% 8.41/2.16  Prover 19: stopped
% 8.41/2.16  
% 8.41/2.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.41/2.16  
% 8.41/2.16  % SZS output start Proof for theBenchmark
% 8.41/2.17  Assumptions after simplification:
% 8.41/2.17  ---------------------------------
% 8.41/2.17  
% 8.41/2.17    (apart1)
% 8.41/2.17     ! [v0: $i] : ( ~ $i(v0) |  ~ distinct_points(v0, v0))
% 8.41/2.17  
% 8.41/2.17    (ceq3)
% 8.41/2.17     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ convergent_lines(v0,
% 8.41/2.17        v1) | distinct_lines(v0, v1))
% 8.41/2.17  
% 8.41/2.17    (con)
% 8.87/2.21     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 8.87/2.21      $i] : (intersection_point(v2, v3) = v5 & intersection_point(v0, v1) = v4 &
% 8.87/2.21      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & convergent_lines(v2,
% 8.87/2.21        v3) & convergent_lines(v0, v1) &  ~ apart_point_and_line(v4, v3) &  ~
% 8.87/2.21      apart_point_and_line(v4, v2) & (apart_point_and_line(v5, v1) |
% 8.87/2.22        apart_point_and_line(v5, v0)))
% 8.87/2.22  
% 8.87/2.22    (con2)
% 8.87/2.22     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.87/2.22      (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 8.87/2.22      apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) |
% 8.87/2.22      distinct_points(v2, v3)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 8.87/2.22      $i] : ( ~ (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 8.87/2.22      $i(v0) |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) |
% 8.87/2.22      distinct_points(v2, v3))
% 8.87/2.22  
% 8.87/2.22    (cu1)
% 8.87/2.22     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 8.87/2.22      |  ~ $i(v1) |  ~ $i(v0) |  ~ distinct_lines(v2, v3) |  ~ distinct_points(v0,
% 8.87/2.22        v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) |
% 8.87/2.22      apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 8.87/2.22  
% 8.87/2.22  Further assumptions not needed in the proof:
% 8.87/2.22  --------------------------------------------
% 8.87/2.22  apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, con1
% 8.87/2.22  
% 8.87/2.22  Those formulas are unsatisfiable:
% 8.87/2.22  ---------------------------------
% 8.87/2.22  
% 8.87/2.22  Begin of proof
% 8.87/2.22  | 
% 8.87/2.22  | ALPHA: (con2) implies:
% 8.87/2.23  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.87/2.23  |          (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.87/2.23  |          |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) |
% 8.87/2.23  |          distinct_points(v2, v3))
% 8.87/2.23  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.87/2.23  |          (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.87/2.23  |          |  ~ apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) |
% 8.87/2.23  |          distinct_points(v2, v3))
% 8.87/2.23  | 
% 8.87/2.23  | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 8.87/2.23  |        all_20_3, all_20_4, all_20_5 gives:
% 8.87/2.23  |   (3)  intersection_point(all_20_3, all_20_2) = all_20_0 &
% 8.87/2.23  |        intersection_point(all_20_5, all_20_4) = all_20_1 & $i(all_20_0) &
% 8.87/2.23  |        $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 8.87/2.23  |        $i(all_20_5) & convergent_lines(all_20_3, all_20_2) &
% 8.87/2.23  |        convergent_lines(all_20_5, all_20_4) &  ~
% 8.87/2.23  |        apart_point_and_line(all_20_1, all_20_2) &  ~
% 8.87/2.23  |        apart_point_and_line(all_20_1, all_20_3) &
% 8.87/2.23  |        (apart_point_and_line(all_20_0, all_20_4) |
% 8.87/2.23  |          apart_point_and_line(all_20_0, all_20_5))
% 8.87/2.23  | 
% 8.87/2.23  | ALPHA: (3) implies:
% 8.87/2.23  |   (4)   ~ apart_point_and_line(all_20_1, all_20_3)
% 8.87/2.23  |   (5)   ~ apart_point_and_line(all_20_1, all_20_2)
% 8.87/2.23  |   (6)  convergent_lines(all_20_5, all_20_4)
% 8.87/2.23  |   (7)  convergent_lines(all_20_3, all_20_2)
% 8.87/2.23  |   (8)  $i(all_20_5)
% 8.87/2.23  |   (9)  $i(all_20_4)
% 8.87/2.23  |   (10)  $i(all_20_3)
% 8.87/2.23  |   (11)  $i(all_20_2)
% 8.87/2.23  |   (12)  $i(all_20_1)
% 8.87/2.23  |   (13)  $i(all_20_0)
% 8.87/2.23  |   (14)  intersection_point(all_20_5, all_20_4) = all_20_1
% 8.87/2.23  |   (15)  intersection_point(all_20_3, all_20_2) = all_20_0
% 8.87/2.23  |   (16)  apart_point_and_line(all_20_0, all_20_4) |
% 8.87/2.23  |         apart_point_and_line(all_20_0, all_20_5)
% 8.87/2.23  | 
% 8.87/2.24  | GROUND_INST: instantiating (ceq3) with all_20_3, all_20_2, simplifying with
% 8.87/2.24  |              (7), (10), (11) gives:
% 8.87/2.24  |   (17)  distinct_lines(all_20_3, all_20_2)
% 8.87/2.24  | 
% 8.87/2.24  | BETA: splitting (16) gives:
% 8.87/2.24  | 
% 8.87/2.24  | Case 1:
% 8.87/2.24  | | 
% 8.87/2.24  | |   (18)  apart_point_and_line(all_20_0, all_20_4)
% 8.87/2.24  | | 
% 8.87/2.24  | | GROUND_INST: instantiating (2) with all_20_5, all_20_4, all_20_0, all_20_1,
% 8.87/2.24  | |              simplifying with (6), (8), (9), (13), (14), (18) gives:
% 8.87/2.24  | |   (19)  distinct_points(all_20_0, all_20_1)
% 8.87/2.24  | | 
% 8.87/2.24  | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (11), (12), (13), (15), (17),
% 8.87/2.24  | |            (19), (apart1), (cu1) are inconsistent by sub-proof #1.
% 8.87/2.24  | | 
% 8.87/2.24  | Case 2:
% 8.87/2.24  | | 
% 8.87/2.24  | |   (20)  apart_point_and_line(all_20_0, all_20_5)
% 8.87/2.24  | | 
% 8.87/2.24  | | GROUND_INST: instantiating (1) with all_20_5, all_20_4, all_20_0, all_20_1,
% 8.87/2.24  | |              simplifying with (6), (8), (9), (13), (14), (20) gives:
% 8.87/2.24  | |   (21)  distinct_points(all_20_0, all_20_1)
% 8.87/2.24  | | 
% 8.87/2.24  | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (11), (12), (13), (15), (17),
% 8.87/2.24  | |            (21), (apart1), (cu1) are inconsistent by sub-proof #1.
% 8.87/2.24  | | 
% 8.87/2.24  | End of split
% 8.87/2.24  | 
% 8.87/2.24  End of proof
% 8.87/2.24  
% 8.87/2.24  Sub-proof #1 shows that the following formulas are inconsistent:
% 8.87/2.24  ----------------------------------------------------------------
% 8.87/2.24    (1)   ~ apart_point_and_line(all_20_1, all_20_2)
% 8.87/2.24    (2)  $i(all_20_3)
% 8.87/2.24    (3)   ~ apart_point_and_line(all_20_1, all_20_3)
% 8.87/2.24    (4)  convergent_lines(all_20_3, all_20_2)
% 8.87/2.24    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.87/2.24           (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 8.87/2.24            ~ apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) |
% 8.87/2.24           distinct_points(v2, v3))
% 8.87/2.24    (6)  distinct_lines(all_20_3, all_20_2)
% 8.87/2.25    (7)  $i(all_20_1)
% 8.87/2.25    (8)  $i(all_20_2)
% 8.87/2.25    (9)   ! [v0: $i] : ( ~ $i(v0) |  ~ distinct_points(v0, v0))
% 8.87/2.25    (10)  intersection_point(all_20_3, all_20_2) = all_20_0
% 8.87/2.25    (11)  distinct_points(all_20_0, all_20_1)
% 8.87/2.25    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 8.87/2.25            (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 8.87/2.25            |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) |
% 8.87/2.25            distinct_points(v2, v3))
% 8.87/2.25    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~
% 8.87/2.25            $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ distinct_lines(v2, v3) |  ~
% 8.87/2.25            distinct_points(v0, v1) | apart_point_and_line(v1, v3) |
% 8.87/2.25            apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) |
% 8.87/2.25            apart_point_and_line(v0, v2))
% 8.87/2.25    (14)  $i(all_20_0)
% 8.87/2.25  
% 8.87/2.25  Begin of proof
% 8.87/2.25  | 
% 8.87/2.25  | GROUND_INST: instantiating (13) with all_20_0, all_20_1, all_20_3, all_20_2,
% 8.87/2.25  |              simplifying with (1), (2), (3), (6), (7), (8), (11), (14) gives:
% 8.87/2.25  |   (15)  apart_point_and_line(all_20_0, all_20_2) |
% 8.87/2.25  |         apart_point_and_line(all_20_0, all_20_3)
% 8.87/2.25  | 
% 8.87/2.25  | BETA: splitting (15) gives:
% 8.87/2.25  | 
% 8.87/2.25  | Case 1:
% 8.87/2.25  | | 
% 8.87/2.25  | |   (16)  apart_point_and_line(all_20_0, all_20_2)
% 8.87/2.25  | | 
% 8.87/2.25  | | GROUND_INST: instantiating (5) with all_20_3, all_20_2, all_20_0, all_20_0,
% 8.87/2.25  | |              simplifying with (2), (4), (8), (10), (14), (16) gives:
% 8.87/2.25  | |   (17)  distinct_points(all_20_0, all_20_0)
% 8.87/2.25  | | 
% 8.87/2.25  | | GROUND_INST: instantiating (9) with all_20_0, simplifying with (14), (17)
% 8.87/2.25  | |              gives:
% 8.87/2.25  | |   (18)  $false
% 8.87/2.25  | | 
% 8.87/2.25  | | CLOSE: (18) is inconsistent.
% 8.87/2.25  | | 
% 8.87/2.25  | Case 2:
% 8.87/2.25  | | 
% 8.87/2.25  | |   (19)  apart_point_and_line(all_20_0, all_20_3)
% 8.87/2.25  | | 
% 8.87/2.25  | | GROUND_INST: instantiating (12) with all_20_3, all_20_2, all_20_0, all_20_0,
% 8.87/2.25  | |              simplifying with (2), (4), (8), (10), (14), (19) gives:
% 8.87/2.25  | |   (20)  distinct_points(all_20_0, all_20_0)
% 8.87/2.25  | | 
% 8.87/2.25  | | GROUND_INST: instantiating (9) with all_20_0, simplifying with (14), (20)
% 8.87/2.25  | |              gives:
% 8.87/2.25  | |   (21)  $false
% 8.87/2.25  | | 
% 8.87/2.25  | | CLOSE: (21) is inconsistent.
% 8.87/2.25  | | 
% 8.87/2.25  | End of split
% 8.87/2.25  | 
% 8.87/2.25  End of proof
% 8.87/2.25  % SZS output end Proof for theBenchmark
% 8.87/2.25  
% 8.87/2.25  1635ms
%------------------------------------------------------------------------------