TSTP Solution File: GEO083+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO083+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 : n025.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 23:21:19 EDT 2023

% Result   : Theorem 7.73s 1.76s
% Output   : Proof 10.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.34  % CPULimit : 300
% 0.20/0.34  % WCLimit  : 300
% 0.20/0.34  % DateTime : Wed Aug 30 00:22:55 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.05/1.09  Prover 4: Preprocessing ...
% 3.05/1.09  Prover 1: Preprocessing ...
% 3.05/1.12  Prover 5: Preprocessing ...
% 3.05/1.12  Prover 3: Preprocessing ...
% 3.05/1.12  Prover 2: Preprocessing ...
% 3.05/1.12  Prover 6: Preprocessing ...
% 3.05/1.12  Prover 0: Preprocessing ...
% 5.98/1.50  Prover 2: Proving ...
% 5.98/1.51  Prover 5: Proving ...
% 5.98/1.53  Prover 3: Warning: ignoring some quantifiers
% 5.98/1.55  Prover 6: Proving ...
% 5.98/1.55  Prover 3: Constructing countermodel ...
% 6.63/1.57  Prover 1: Warning: ignoring some quantifiers
% 6.80/1.59  Prover 1: Constructing countermodel ...
% 7.73/1.76  Prover 3: proved (1111ms)
% 7.73/1.76  
% 7.73/1.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.73/1.76  
% 7.73/1.76  Prover 2: stopped
% 7.73/1.76  Prover 5: stopped
% 8.20/1.78  Prover 6: stopped
% 8.20/1.78  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.20/1.78  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.20/1.78  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.20/1.81  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.20/1.83  Prover 8: Preprocessing ...
% 8.20/1.83  Prover 7: Preprocessing ...
% 8.20/1.86  Prover 10: Preprocessing ...
% 8.20/1.86  Prover 11: Preprocessing ...
% 8.96/1.90  Prover 1: Found proof (size 41)
% 8.96/1.90  Prover 1: proved (1266ms)
% 8.96/1.91  Prover 10: Warning: ignoring some quantifiers
% 8.96/1.92  Prover 7: Warning: ignoring some quantifiers
% 8.96/1.92  Prover 10: Constructing countermodel ...
% 9.24/1.92  Prover 10: stopped
% 9.24/1.93  Prover 7: Constructing countermodel ...
% 9.24/1.93  Prover 11: stopped
% 9.24/1.93  Prover 7: stopped
% 9.24/1.95  Prover 8: Warning: ignoring some quantifiers
% 9.24/1.97  Prover 8: Constructing countermodel ...
% 9.24/1.97  Prover 8: stopped
% 9.24/1.98  Prover 4: Warning: ignoring some quantifiers
% 9.24/2.02  Prover 4: Constructing countermodel ...
% 9.79/2.03  Prover 4: stopped
% 9.79/2.07  Prover 0: Proving ...
% 9.79/2.07  Prover 0: stopped
% 9.79/2.07  
% 9.79/2.07  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.79/2.07  
% 9.79/2.08  % SZS output start Proof for theBenchmark
% 9.79/2.08  Assumptions after simplification:
% 9.79/2.08  ---------------------------------
% 9.79/2.08  
% 9.79/2.08    (corollary_2_6_1)
% 10.31/2.11     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 10.31/2.11      $i] :  ? [v6: int] : ( ~ (v6 = 0) & meet(v3, v0, v2) = 0 & meet(v3, v0, v1)
% 10.31/2.11      = 0 & sum(v0, v2) = v5 & sum(v0, v1) = v4 & part_of(v4, v5) = v6 &
% 10.31/2.11      part_of(v1, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.31/2.11  
% 10.31/2.11    (part_of_defn)
% 10.31/2.11     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (part_of(v1, v0) = v2)
% 10.31/2.11      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 10.31/2.11        incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) &  ! [v0: $i]
% 10.31/2.11    :  ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2:
% 10.31/2.11        $i] :  ! [v3: int] : (v3 = 0 |  ~ (incident_c(v2, v0) = v3) |  ~ $i(v2) | 
% 10.31/2.11        ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)))
% 10.31/2.11  
% 10.31/2.11    (sum_defn)
% 10.31/2.12     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~ (sum(v1,
% 10.31/2.12          v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: $i] :  ? [v5:
% 10.31/2.12        any] :  ? [v6: any] :  ? [v7: any] : (incident_c(v4, v2) = v7 &
% 10.31/2.12        incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0)
% 10.31/2.12          | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) &  ! [v0:
% 10.31/2.12      $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sum(v1, v2) = v0) |  ~ $i(v2) |  ~
% 10.31/2.12      $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4: int] : (v4 = 0 |  ~
% 10.31/2.12          (incident_c(v3, v0) = v4) |  ~ $i(v3) |  ? [v5: int] :  ? [v6: int] : (
% 10.31/2.12            ~ (v6 = 0) &  ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3,
% 10.31/2.12              v1) = v5)) &  ! [v3: $i] : ( ~ (incident_c(v3, v0) = 0) |  ~ $i(v3)
% 10.31/2.12          |  ? [v4: any] :  ? [v5: any] : (incident_c(v3, v2) = v5 &
% 10.31/2.12            incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 10.31/2.12  
% 10.31/2.12    (function-axioms)
% 10.31/2.13     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 10.31/2.13    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (meet(v4, v3, v2) = v1) |  ~ (meet(v4,
% 10.31/2.13          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 10.31/2.13    :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (inner_point(v3, v2) = v1) |  ~
% 10.31/2.13      (inner_point(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.31/2.13      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.31/2.13      (end_point(v3, v2) = v1) |  ~ (end_point(v3, v2) = v0)) &  ! [v0: $i] :  !
% 10.31/2.13    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~
% 10.31/2.13      (sum(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.31/2.13      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (part_of(v3,
% 10.31/2.13          v2) = v1) |  ~ (part_of(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 10.31/2.13    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.31/2.13      (incident_c(v3, v2) = v1) |  ~ (incident_c(v3, v2) = v0)) &  ! [v0:
% 10.31/2.13      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 10.31/2.13      ~ (open(v2) = v1) |  ~ (open(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 10.31/2.13    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (closed(v2) = v1) |  ~
% 10.31/2.13      (closed(v2) = v0))
% 10.31/2.13  
% 10.31/2.13  Further assumptions not needed in the proof:
% 10.31/2.13  --------------------------------------------
% 10.31/2.13  c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 10.31/2.13  inner_point_defn, meet_defn, open_defn
% 10.31/2.13  
% 10.31/2.13  Those formulas are unsatisfiable:
% 10.31/2.13  ---------------------------------
% 10.31/2.13  
% 10.31/2.13  Begin of proof
% 10.31/2.13  | 
% 10.31/2.13  | ALPHA: (part_of_defn) implies:
% 10.31/2.13  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) |  ~ $i(v1) |  ~
% 10.31/2.13  |          $i(v0) |  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (incident_c(v2,
% 10.31/2.13  |                v0) = v3) |  ~ $i(v2) |  ? [v4: int] : ( ~ (v4 = 0) &
% 10.31/2.13  |              incident_c(v2, v1) = v4)))
% 10.31/2.14  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (part_of(v1,
% 10.31/2.14  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] :
% 10.31/2.14  |          ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 &
% 10.31/2.14  |            $i(v3)))
% 10.31/2.14  | 
% 10.31/2.14  | ALPHA: (sum_defn) implies:
% 10.31/2.14  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sum(v1, v2) = v0) |  ~
% 10.31/2.14  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4: int] : (v4 =
% 10.31/2.14  |              0 |  ~ (incident_c(v3, v0) = v4) |  ~ $i(v3) |  ? [v5: int] :  ?
% 10.31/2.14  |              [v6: int] : ( ~ (v6 = 0) &  ~ (v5 = 0) & incident_c(v3, v2) = v6
% 10.31/2.14  |                & incident_c(v3, v1) = v5)) &  ! [v3: $i] : ( ~ (incident_c(v3,
% 10.31/2.14  |                  v0) = 0) |  ~ $i(v3) |  ? [v4: any] :  ? [v5: any] :
% 10.31/2.14  |              (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4
% 10.31/2.14  |                  = 0)))))
% 10.31/2.14  | 
% 10.31/2.14  | ALPHA: (function-axioms) implies:
% 10.31/2.14  |   (4)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 10.31/2.14  |         ! [v3: $i] : (v1 = v0 |  ~ (incident_c(v3, v2) = v1) |  ~
% 10.31/2.14  |          (incident_c(v3, v2) = v0))
% 10.31/2.14  | 
% 10.31/2.14  | DELTA: instantiating (corollary_2_6_1) with fresh symbols all_19_0, all_19_1,
% 10.31/2.14  |        all_19_2, all_19_3, all_19_4, all_19_5, all_19_6 gives:
% 10.31/2.14  |   (5)   ~ (all_19_0 = 0) & meet(all_19_3, all_19_6, all_19_4) = 0 &
% 10.31/2.14  |        meet(all_19_3, all_19_6, all_19_5) = 0 & sum(all_19_6, all_19_4) =
% 10.31/2.14  |        all_19_1 & sum(all_19_6, all_19_5) = all_19_2 & part_of(all_19_2,
% 10.31/2.14  |          all_19_1) = all_19_0 & part_of(all_19_5, all_19_4) = 0 & $i(all_19_1)
% 10.31/2.14  |        & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) & $i(all_19_5) &
% 10.31/2.14  |        $i(all_19_6)
% 10.31/2.14  | 
% 10.31/2.14  | ALPHA: (5) implies:
% 10.31/2.14  |   (6)   ~ (all_19_0 = 0)
% 10.31/2.14  |   (7)  $i(all_19_6)
% 10.31/2.14  |   (8)  $i(all_19_5)
% 10.31/2.14  |   (9)  $i(all_19_4)
% 10.31/2.15  |   (10)  $i(all_19_2)
% 10.31/2.15  |   (11)  $i(all_19_1)
% 10.31/2.15  |   (12)  part_of(all_19_5, all_19_4) = 0
% 10.31/2.15  |   (13)  part_of(all_19_2, all_19_1) = all_19_0
% 10.31/2.15  |   (14)  sum(all_19_6, all_19_5) = all_19_2
% 10.31/2.15  |   (15)  sum(all_19_6, all_19_4) = all_19_1
% 10.31/2.15  | 
% 10.31/2.15  | GROUND_INST: instantiating (1) with all_19_4, all_19_5, simplifying with (8),
% 10.31/2.15  |              (9), (12) gives:
% 10.31/2.15  |   (16)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (incident_c(v0, all_19_4) =
% 10.31/2.15  |             v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 10.31/2.15  |               all_19_5) = v2))
% 10.31/2.15  | 
% 10.31/2.15  | GROUND_INST: instantiating (2) with all_19_1, all_19_2, all_19_0, simplifying
% 10.31/2.15  |              with (10), (11), (13) gives:
% 10.31/2.15  |   (17)  all_19_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 10.31/2.15  |           incident_c(v0, all_19_1) = v1 & incident_c(v0, all_19_2) = 0 &
% 10.31/2.15  |           $i(v0))
% 10.31/2.15  | 
% 10.31/2.15  | GROUND_INST: instantiating (3) with all_19_2, all_19_6, all_19_5, simplifying
% 10.31/2.15  |              with (7), (8), (10), (14) gives:
% 10.31/2.15  |   (18)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (incident_c(v0, all_19_2) =
% 10.31/2.15  |             v1) |  ~ $i(v0) |  ? [v2: int] :  ? [v3: int] : ( ~ (v3 = 0) &  ~
% 10.31/2.15  |             (v2 = 0) & incident_c(v0, all_19_5) = v3 & incident_c(v0,
% 10.31/2.15  |               all_19_6) = v2)) &  ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) =
% 10.31/2.15  |             0) |  ~ $i(v0) |  ? [v1: any] :  ? [v2: any] : (incident_c(v0,
% 10.31/2.15  |               all_19_5) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 =
% 10.31/2.15  |               0)))
% 10.31/2.15  | 
% 10.31/2.15  | ALPHA: (18) implies:
% 10.31/2.15  |   (19)   ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) = 0) |  ~ $i(v0) |  ? [v1:
% 10.31/2.15  |             any] :  ? [v2: any] : (incident_c(v0, all_19_5) = v2 &
% 10.31/2.15  |             incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 = 0)))
% 10.31/2.15  | 
% 10.31/2.15  | GROUND_INST: instantiating (3) with all_19_1, all_19_6, all_19_4, simplifying
% 10.31/2.15  |              with (7), (9), (11), (15) gives:
% 10.31/2.15  |   (20)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (incident_c(v0, all_19_1) =
% 10.31/2.15  |             v1) |  ~ $i(v0) |  ? [v2: int] :  ? [v3: int] : ( ~ (v3 = 0) &  ~
% 10.31/2.15  |             (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0,
% 10.31/2.15  |               all_19_6) = v2)) &  ! [v0: $i] : ( ~ (incident_c(v0, all_19_1) =
% 10.31/2.15  |             0) |  ~ $i(v0) |  ? [v1: any] :  ? [v2: any] : (incident_c(v0,
% 10.31/2.15  |               all_19_4) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 =
% 10.31/2.15  |               0)))
% 10.31/2.15  | 
% 10.31/2.15  | ALPHA: (20) implies:
% 10.31/2.16  |   (21)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (incident_c(v0, all_19_1) =
% 10.31/2.16  |             v1) |  ~ $i(v0) |  ? [v2: int] :  ? [v3: int] : ( ~ (v3 = 0) &  ~
% 10.31/2.16  |             (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0,
% 10.31/2.16  |               all_19_6) = v2))
% 10.31/2.16  | 
% 10.31/2.16  | BETA: splitting (17) gives:
% 10.31/2.16  | 
% 10.31/2.16  | Case 1:
% 10.31/2.16  | | 
% 10.31/2.16  | |   (22)  all_19_0 = 0
% 10.31/2.16  | | 
% 10.31/2.16  | | REDUCE: (6), (22) imply:
% 10.31/2.16  | |   (23)  $false
% 10.31/2.16  | | 
% 10.31/2.16  | | CLOSE: (23) is inconsistent.
% 10.31/2.16  | | 
% 10.31/2.16  | Case 2:
% 10.31/2.16  | | 
% 10.31/2.16  | |   (24)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_19_1)
% 10.31/2.16  | |           = v1 & incident_c(v0, all_19_2) = 0 & $i(v0))
% 10.31/2.16  | | 
% 10.31/2.16  | | DELTA: instantiating (24) with fresh symbols all_38_0, all_38_1 gives:
% 10.31/2.16  | |   (25)   ~ (all_38_0 = 0) & incident_c(all_38_1, all_19_1) = all_38_0 &
% 10.31/2.16  | |         incident_c(all_38_1, all_19_2) = 0 & $i(all_38_1)
% 10.31/2.16  | | 
% 10.31/2.16  | | ALPHA: (25) implies:
% 10.31/2.16  | |   (26)   ~ (all_38_0 = 0)
% 10.31/2.16  | |   (27)  $i(all_38_1)
% 10.31/2.16  | |   (28)  incident_c(all_38_1, all_19_2) = 0
% 10.31/2.16  | |   (29)  incident_c(all_38_1, all_19_1) = all_38_0
% 10.31/2.16  | | 
% 10.31/2.16  | | GROUND_INST: instantiating (19) with all_38_1, simplifying with (27), (28)
% 10.31/2.16  | |              gives:
% 10.31/2.16  | |   (30)   ? [v0: any] :  ? [v1: any] : (incident_c(all_38_1, all_19_5) = v1 &
% 10.31/2.16  | |           incident_c(all_38_1, all_19_6) = v0 & (v1 = 0 | v0 = 0))
% 10.31/2.16  | | 
% 10.31/2.16  | | GROUND_INST: instantiating (21) with all_38_1, all_38_0, simplifying with
% 10.31/2.16  | |              (27), (29) gives:
% 10.31/2.16  | |   (31)  all_38_0 = 0 |  ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 =
% 10.31/2.16  | |             0) & incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1,
% 10.31/2.16  | |             all_19_6) = v0)
% 10.31/2.16  | | 
% 10.31/2.16  | | DELTA: instantiating (30) with fresh symbols all_45_0, all_45_1 gives:
% 10.31/2.16  | |   (32)  incident_c(all_38_1, all_19_5) = all_45_0 & incident_c(all_38_1,
% 10.31/2.16  | |           all_19_6) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0)
% 10.31/2.16  | | 
% 10.31/2.16  | | ALPHA: (32) implies:
% 10.31/2.16  | |   (33)  incident_c(all_38_1, all_19_6) = all_45_1
% 10.31/2.16  | |   (34)  incident_c(all_38_1, all_19_5) = all_45_0
% 10.31/2.16  | |   (35)  all_45_0 = 0 | all_45_1 = 0
% 10.31/2.16  | | 
% 10.31/2.16  | | BETA: splitting (31) gives:
% 10.31/2.16  | | 
% 10.31/2.16  | | Case 1:
% 10.31/2.16  | | | 
% 10.31/2.16  | | |   (36)  all_38_0 = 0
% 10.31/2.16  | | | 
% 10.31/2.16  | | | REDUCE: (26), (36) imply:
% 10.31/2.16  | | |   (37)  $false
% 10.31/2.16  | | | 
% 10.31/2.16  | | | CLOSE: (37) is inconsistent.
% 10.31/2.16  | | | 
% 10.31/2.16  | | Case 2:
% 10.31/2.16  | | | 
% 10.31/2.16  | | |   (38)   ? [v0: int] :  ? [v1: int] : ( ~ (v1 = 0) &  ~ (v0 = 0) &
% 10.31/2.16  | | |           incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1,
% 10.31/2.16  | | |             all_19_6) = v0)
% 10.31/2.16  | | | 
% 10.31/2.16  | | | DELTA: instantiating (38) with fresh symbols all_51_0, all_51_1 gives:
% 10.31/2.17  | | |   (39)   ~ (all_51_0 = 0) &  ~ (all_51_1 = 0) & incident_c(all_38_1,
% 10.31/2.17  | | |           all_19_4) = all_51_0 & incident_c(all_38_1, all_19_6) = all_51_1
% 10.31/2.17  | | | 
% 10.31/2.17  | | | ALPHA: (39) implies:
% 10.31/2.17  | | |   (40)   ~ (all_51_1 = 0)
% 10.31/2.17  | | |   (41)   ~ (all_51_0 = 0)
% 10.31/2.17  | | |   (42)  incident_c(all_38_1, all_19_6) = all_51_1
% 10.31/2.17  | | |   (43)  incident_c(all_38_1, all_19_4) = all_51_0
% 10.31/2.17  | | | 
% 10.31/2.17  | | | GROUND_INST: instantiating (4) with all_45_1, all_51_1, all_19_6,
% 10.31/2.17  | | |              all_38_1, simplifying with (33), (42) gives:
% 10.31/2.17  | | |   (44)  all_51_1 = all_45_1
% 10.31/2.17  | | | 
% 10.31/2.17  | | | REDUCE: (40), (44) imply:
% 10.31/2.17  | | |   (45)   ~ (all_45_1 = 0)
% 10.31/2.17  | | | 
% 10.31/2.17  | | | BETA: splitting (35) gives:
% 10.31/2.17  | | | 
% 10.31/2.17  | | | Case 1:
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | |   (46)  all_45_0 = 0
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | REDUCE: (34), (46) imply:
% 10.31/2.17  | | | |   (47)  incident_c(all_38_1, all_19_5) = 0
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | GROUND_INST: instantiating (16) with all_38_1, all_51_0, simplifying
% 10.31/2.17  | | | |              with (27), (43) gives:
% 10.31/2.17  | | | |   (48)  all_51_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 10.31/2.17  | | | |           incident_c(all_38_1, all_19_5) = v0)
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | BETA: splitting (48) gives:
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | Case 1:
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | |   (49)  all_51_0 = 0
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | REDUCE: (41), (49) imply:
% 10.31/2.17  | | | | |   (50)  $false
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | CLOSE: (50) is inconsistent.
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | Case 2:
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | |   (51)   ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_38_1, all_19_5) =
% 10.31/2.17  | | | | |           v0)
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | DELTA: instantiating (51) with fresh symbol all_74_0 gives:
% 10.31/2.17  | | | | |   (52)   ~ (all_74_0 = 0) & incident_c(all_38_1, all_19_5) = all_74_0
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | ALPHA: (52) implies:
% 10.31/2.17  | | | | |   (53)   ~ (all_74_0 = 0)
% 10.31/2.17  | | | | |   (54)  incident_c(all_38_1, all_19_5) = all_74_0
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | GROUND_INST: instantiating (4) with 0, all_74_0, all_19_5, all_38_1,
% 10.31/2.17  | | | | |              simplifying with (47), (54) gives:
% 10.31/2.17  | | | | |   (55)  all_74_0 = 0
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | REDUCE: (53), (55) imply:
% 10.31/2.17  | | | | |   (56)  $false
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | | CLOSE: (56) is inconsistent.
% 10.31/2.17  | | | | | 
% 10.31/2.17  | | | | End of split
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | Case 2:
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | |   (57)  all_45_1 = 0
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | REDUCE: (45), (57) imply:
% 10.31/2.17  | | | |   (58)  $false
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | | CLOSE: (58) is inconsistent.
% 10.31/2.17  | | | | 
% 10.31/2.17  | | | End of split
% 10.31/2.17  | | | 
% 10.31/2.17  | | End of split
% 10.31/2.17  | | 
% 10.31/2.17  | End of split
% 10.31/2.17  | 
% 10.31/2.17  End of proof
% 10.65/2.17  % SZS output end Proof for theBenchmark
% 10.65/2.17  
% 10.65/2.17  1558ms
%------------------------------------------------------------------------------