TSTP Solution File: GEO125+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO125+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 23:21:33 EDT 2023

% Result   : Theorem 10.06s 2.16s
% Output   : Proof 15.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO125+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Aug 29 19:59:14 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59  ________       _____
% 0.19/0.59  ___  __ \_________(_)________________________________
% 0.19/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59  (2023-06-19)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2023
% 0.19/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59                Amanda Stjerna.
% 0.19/0.59  Free software under BSD-3-Clause.
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.03/1.15  Prover 4: Preprocessing ...
% 3.03/1.16  Prover 1: Preprocessing ...
% 3.27/1.21  Prover 5: Preprocessing ...
% 3.27/1.21  Prover 2: Preprocessing ...
% 3.27/1.21  Prover 6: Preprocessing ...
% 3.27/1.21  Prover 3: Preprocessing ...
% 3.27/1.21  Prover 0: Preprocessing ...
% 7.49/1.80  Prover 2: Proving ...
% 7.49/1.81  Prover 5: Proving ...
% 8.16/1.91  Prover 6: Proving ...
% 8.16/1.92  Prover 1: Warning: ignoring some quantifiers
% 8.16/1.94  Prover 3: Warning: ignoring some quantifiers
% 8.16/1.96  Prover 3: Constructing countermodel ...
% 8.16/1.97  Prover 1: Constructing countermodel ...
% 10.06/2.15  Prover 2: proved (1532ms)
% 10.06/2.16  
% 10.06/2.16  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.06/2.16  
% 10.06/2.16  Prover 6: stopped
% 10.51/2.17  Prover 3: stopped
% 10.51/2.17  Prover 5: stopped
% 10.51/2.19  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.51/2.19  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.51/2.19  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.51/2.19  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.51/2.23  Prover 10: Preprocessing ...
% 10.51/2.23  Prover 8: Preprocessing ...
% 10.51/2.25  Prover 7: Preprocessing ...
% 10.51/2.25  Prover 11: Preprocessing ...
% 11.85/2.35  Prover 7: Warning: ignoring some quantifiers
% 11.85/2.35  Prover 4: Warning: ignoring some quantifiers
% 11.85/2.36  Prover 10: Warning: ignoring some quantifiers
% 11.85/2.37  Prover 7: Constructing countermodel ...
% 11.85/2.39  Prover 10: Constructing countermodel ...
% 12.36/2.45  Prover 4: Constructing countermodel ...
% 12.82/2.46  Prover 8: Warning: ignoring some quantifiers
% 12.82/2.49  Prover 8: Constructing countermodel ...
% 12.82/2.57  Prover 0: Proving ...
% 12.82/2.59  Prover 0: stopped
% 12.82/2.60  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.82/2.63  Prover 10: Found proof (size 23)
% 12.82/2.63  Prover 10: proved (457ms)
% 12.82/2.63  Prover 4: stopped
% 12.82/2.63  Prover 1: stopped
% 12.82/2.63  Prover 8: stopped
% 12.82/2.63  Prover 7: stopped
% 12.82/2.64  Prover 13: Preprocessing ...
% 13.87/2.66  Prover 13: stopped
% 14.92/2.83  Prover 11: Warning: ignoring some quantifiers
% 14.92/2.86  Prover 11: Constructing countermodel ...
% 14.92/2.87  Prover 11: stopped
% 14.92/2.87  
% 14.92/2.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.92/2.87  
% 14.92/2.87  % SZS output start Proof for theBenchmark
% 14.92/2.87  Assumptions after simplification:
% 14.92/2.87  ---------------------------------
% 14.92/2.87  
% 14.92/2.88    (between_c_defn)
% 15.19/2.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v3 = v1
% 15.19/2.88      |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.88      inner_point(v2, v4) |  ~ end_point(v3, v4) |  ~ end_point(v1, v4) |  ~
% 15.19/2.88      part_of(v4, v0) | between_c(v0, v1, v2, v3)) &  ! [v0: $i] :  ! [v1: $i] : 
% 15.19/2.88    ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.88      between_c(v0, v1, v2, v3) |  ? [v4: $i] : ($i(v4) & inner_point(v2, v4) &
% 15.19/2.88        end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) &  ! [v0: $i] : 
% 15.19/2.88    ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.88      between_c(v0, v1, v2, v1))
% 15.19/2.88  
% 15.19/2.88    (between_o_defn)
% 15.19/2.89     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 15.19/2.89      |  ~ $i(v1) |  ~ $i(v0) |  ~ ordered_by(v0, v3, v2) |  ~ ordered_by(v0, v2,
% 15.19/2.89        v1) | between_o(v0, v1, v2, v3)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 15.19/2.89    :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.89      ordered_by(v0, v2, v3) |  ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2,
% 15.19/2.89        v3)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3)
% 15.19/2.89      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ between_o(v0, v1, v2, v3) |
% 15.19/2.89      ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) &  ! [v0: $i] :  ! [v1: $i]
% 15.19/2.89    :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 15.19/2.89       ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1,
% 15.19/2.89        v2)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3)
% 15.19/2.89      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ between_o(v0, v1, v2, v3) |
% 15.19/2.89      ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) &  ! [v0: $i] :  ! [v1: $i]
% 15.19/2.89    :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 15.19/2.89       ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1,
% 15.19/2.89        v2))
% 15.19/2.89  
% 15.19/2.89    (corollary_4_10_2)
% 15.19/2.89     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = v1) & $i(v2) & $i(v1) &
% 15.19/2.89      $i(v0) & finish_point(v2, v0) & finish_point(v1, v0))
% 15.19/2.89  
% 15.19/2.89    (finish_point_defn)
% 15.19/2.89     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ $i(v2) |  ~ $i(v1) | 
% 15.19/2.89      ~ $i(v0) |  ~ finish_point(v0, v1) |  ~ incident_o(v2, v1) | ordered_by(v1,
% 15.19/2.89        v2, v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.89      finish_point(v0, v1) | incident_o(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 15.19/2.89      $i(v1) |  ~ $i(v0) |  ~ incident_o(v0, v1) | finish_point(v0, v1) |  ? [v2:
% 15.19/2.89        $i] : ( ~ (v2 = v0) & $i(v2) & incident_o(v2, v1) &  ~ ordered_by(v1, v2,
% 15.19/2.89          v0)))
% 15.19/2.89  
% 15.19/2.89    (o3)
% 15.19/2.90     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 15.19/2.90      $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ between_c(v4,
% 15.19/2.90        v1, v2, v3) | between_o(v0, v1, v2, v3) |  ? [v5: $i] : ($i(v5) & ( ~
% 15.19/2.90          incident_o(v5, v0) |  ~ incident_c(v5, v4)) & (incident_o(v5, v0) |
% 15.19/2.90          incident_c(v5, v4)))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 15.19/2.90    [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ between_o(v3,
% 15.19/2.90        v0, v1, v2) |  ? [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) &  ! [v5:
% 15.19/2.90          $i] : ( ~ $i(v5) |  ~ incident_o(v5, v3) | incident_c(v5, v4)) &  ! [v5:
% 15.19/2.90          $i] : ( ~ $i(v5) |  ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 15.19/2.90  
% 15.19/2.90  Further assumptions not needed in the proof:
% 15.19/2.90  --------------------------------------------
% 15.19/2.90  c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 15.19/2.90  inner_point_defn, meet_defn, o1, o2, o4, o5, o6, open_defn, part_of_defn,
% 15.19/2.90  start_point_defn, sum_defn, underlying_curve_defn
% 15.19/2.90  
% 15.19/2.90  Those formulas are unsatisfiable:
% 15.19/2.90  ---------------------------------
% 15.19/2.90  
% 15.19/2.90  Begin of proof
% 15.19/2.90  | 
% 15.19/2.90  | ALPHA: (between_c_defn) implies:
% 15.19/2.90  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 15.19/2.90  |          $i(v0) |  ~ between_c(v0, v1, v2, v1))
% 15.19/2.90  | 
% 15.19/2.90  | ALPHA: (between_o_defn) implies:
% 15.19/2.90  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~
% 15.19/2.90  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ ordered_by(v0, v3, v2) |  ~
% 15.19/2.90  |          ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3))
% 15.19/2.90  | 
% 15.19/2.90  | ALPHA: (finish_point_defn) implies:
% 15.19/2.90  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 15.19/2.90  |          finish_point(v0, v1) | incident_o(v0, v1))
% 15.19/2.90  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ $i(v2) |  ~
% 15.19/2.90  |          $i(v1) |  ~ $i(v0) |  ~ finish_point(v0, v1) |  ~ incident_o(v2, v1)
% 15.19/2.90  |          | ordered_by(v1, v2, v0))
% 15.19/2.90  | 
% 15.19/2.90  | ALPHA: (o3) implies:
% 15.19/2.90  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~
% 15.19/2.90  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ between_o(v3, v0, v1, v2) |  ?
% 15.19/2.90  |          [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) &  ! [v5: $i] : ( ~
% 15.19/2.90  |              $i(v5) |  ~ incident_o(v5, v3) | incident_c(v5, v4)) &  ! [v5:
% 15.19/2.90  |              $i] : ( ~ $i(v5) |  ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 15.19/2.90  | 
% 15.19/2.90  | DELTA: instantiating (corollary_4_10_2) with fresh symbols all_29_0, all_29_1,
% 15.19/2.90  |        all_29_2 gives:
% 15.19/2.91  |   (6)   ~ (all_29_0 = all_29_1) & $i(all_29_0) & $i(all_29_1) & $i(all_29_2) &
% 15.19/2.91  |        finish_point(all_29_0, all_29_2) & finish_point(all_29_1, all_29_2)
% 15.19/2.91  | 
% 15.19/2.91  | ALPHA: (6) implies:
% 15.19/2.91  |   (7)   ~ (all_29_0 = all_29_1)
% 15.19/2.91  |   (8)  finish_point(all_29_1, all_29_2)
% 15.19/2.91  |   (9)  finish_point(all_29_0, all_29_2)
% 15.19/2.91  |   (10)  $i(all_29_2)
% 15.19/2.91  |   (11)  $i(all_29_1)
% 15.19/2.91  |   (12)  $i(all_29_0)
% 15.19/2.91  | 
% 15.19/2.91  | GROUND_INST: instantiating (3) with all_29_1, all_29_2, simplifying with (8),
% 15.19/2.91  |              (10), (11) gives:
% 15.19/2.91  |   (13)  incident_o(all_29_1, all_29_2)
% 15.19/2.91  | 
% 15.19/2.91  | GROUND_INST: instantiating (3) with all_29_0, all_29_2, simplifying with (9),
% 15.19/2.91  |              (10), (12) gives:
% 15.19/2.91  |   (14)  incident_o(all_29_0, all_29_2)
% 15.19/2.91  | 
% 15.19/2.91  | GROUND_INST: instantiating (4) with all_29_0, all_29_2, all_29_1, simplifying
% 15.19/2.91  |              with (9), (10), (11), (12), (13) gives:
% 15.19/2.91  |   (15)  all_29_0 = all_29_1 | ordered_by(all_29_2, all_29_1, all_29_0)
% 15.19/2.91  | 
% 15.19/2.91  | GROUND_INST: instantiating (4) with all_29_1, all_29_2, all_29_0, simplifying
% 15.19/2.91  |              with (8), (10), (11), (12), (14) gives:
% 15.19/2.91  |   (16)  all_29_0 = all_29_1 | ordered_by(all_29_2, all_29_0, all_29_1)
% 15.19/2.91  | 
% 15.19/2.91  | BETA: splitting (15) gives:
% 15.19/2.91  | 
% 15.19/2.91  | Case 1:
% 15.19/2.91  | | 
% 15.19/2.91  | |   (17)  ordered_by(all_29_2, all_29_1, all_29_0)
% 15.19/2.91  | | 
% 15.19/2.91  | | BETA: splitting (16) gives:
% 15.19/2.91  | | 
% 15.19/2.91  | | Case 1:
% 15.19/2.91  | | | 
% 15.19/2.91  | | |   (18)  ordered_by(all_29_2, all_29_0, all_29_1)
% 15.19/2.91  | | | 
% 15.19/2.91  | | | GROUND_INST: instantiating (2) with all_29_2, all_29_1, all_29_0,
% 15.19/2.91  | | |              all_29_1, simplifying with (10), (11), (12), (17), (18)
% 15.19/2.91  | | |              gives:
% 15.19/2.91  | | |   (19)  between_o(all_29_2, all_29_1, all_29_0, all_29_1)
% 15.19/2.91  | | | 
% 15.19/2.91  | | | GROUND_INST: instantiating (5) with all_29_1, all_29_0, all_29_1,
% 15.19/2.91  | | |              all_29_2, simplifying with (10), (11), (12), (19) gives:
% 15.19/2.91  | | |   (20)   ? [v0: $i] : ($i(v0) & between_c(v0, all_29_1, all_29_0,
% 15.19/2.91  | | |             all_29_1) &  ! [v1: $i] : ( ~ $i(v1) |  ~ incident_o(v1,
% 15.19/2.91  | | |               all_29_2) | incident_c(v1, v0)) &  ! [v1: $i] : ( ~ $i(v1) |
% 15.19/2.91  | | |              ~ incident_c(v1, v0) | incident_o(v1, all_29_2)))
% 15.19/2.91  | | | 
% 15.19/2.91  | | | DELTA: instantiating (20) with fresh symbol all_76_0 gives:
% 15.19/2.92  | | |   (21)  $i(all_76_0) & between_c(all_76_0, all_29_1, all_29_0, all_29_1) &
% 15.19/2.92  | | |          ! [v0: $i] : ( ~ $i(v0) |  ~ incident_o(v0, all_29_2) |
% 15.19/2.92  | | |           incident_c(v0, all_76_0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 15.19/2.92  | | |           incident_c(v0, all_76_0) | incident_o(v0, all_29_2))
% 15.19/2.92  | | | 
% 15.19/2.92  | | | ALPHA: (21) implies:
% 15.19/2.92  | | |   (22)  between_c(all_76_0, all_29_1, all_29_0, all_29_1)
% 15.19/2.92  | | |   (23)  $i(all_76_0)
% 15.19/2.92  | | | 
% 15.19/2.92  | | | GROUND_INST: instantiating (1) with all_76_0, all_29_1, all_29_0,
% 15.19/2.92  | | |              simplifying with (11), (12), (22), (23) gives:
% 15.19/2.92  | | |   (24)  $false
% 15.19/2.92  | | | 
% 15.19/2.92  | | | CLOSE: (24) is inconsistent.
% 15.19/2.92  | | | 
% 15.19/2.92  | | Case 2:
% 15.19/2.92  | | | 
% 15.19/2.92  | | |   (25)  all_29_0 = all_29_1
% 15.19/2.92  | | | 
% 15.19/2.92  | | | REDUCE: (7), (25) imply:
% 15.19/2.92  | | |   (26)  $false
% 15.19/2.92  | | | 
% 15.19/2.92  | | | CLOSE: (26) is inconsistent.
% 15.19/2.92  | | | 
% 15.19/2.92  | | End of split
% 15.19/2.92  | | 
% 15.19/2.92  | Case 2:
% 15.19/2.92  | | 
% 15.19/2.92  | |   (27)  all_29_0 = all_29_1
% 15.19/2.92  | | 
% 15.19/2.92  | | REDUCE: (7), (27) imply:
% 15.19/2.92  | |   (28)  $false
% 15.19/2.92  | | 
% 15.19/2.92  | | CLOSE: (28) is inconsistent.
% 15.19/2.92  | | 
% 15.19/2.92  | End of split
% 15.19/2.92  | 
% 15.19/2.92  End of proof
% 15.19/2.92  % SZS output end Proof for theBenchmark
% 15.19/2.92  
% 15.19/2.92  2325ms
%------------------------------------------------------------------------------