TSTP Solution File: PRO012+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : PRO012+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n027.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 : Thu Aug 31 13:08:49 EDT 2023

% Result   : Theorem 9.63s 2.15s
% Output   : Proof 19.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PRO012+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n027.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 : Mon Aug 28 19:53:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.61  ________       _____
% 0.19/0.61  ___  __ \_________(_)________________________________
% 0.19/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61  
% 0.19/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61  (2023-06-19)
% 0.19/0.61  
% 0.19/0.61  (c) Philipp Rümmer, 2009-2023
% 0.19/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61                Amanda Stjerna.
% 0.19/0.61  Free software under BSD-3-Clause.
% 0.19/0.61  
% 0.19/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61  
% 0.19/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.70/1.16  Prover 4: Preprocessing ...
% 2.70/1.16  Prover 1: Preprocessing ...
% 3.46/1.19  Prover 3: Preprocessing ...
% 3.46/1.19  Prover 6: Preprocessing ...
% 3.46/1.19  Prover 2: Preprocessing ...
% 3.46/1.19  Prover 0: Preprocessing ...
% 3.46/1.19  Prover 5: Preprocessing ...
% 5.93/1.63  Prover 2: Constructing countermodel ...
% 5.93/1.63  Prover 5: Proving ...
% 7.52/1.77  Prover 1: Constructing countermodel ...
% 7.52/1.77  Prover 6: Proving ...
% 7.52/1.80  Prover 3: Constructing countermodel ...
% 9.63/2.06  Prover 4: Constructing countermodel ...
% 9.63/2.13  Prover 5: proved (1490ms)
% 9.63/2.13  
% 9.63/2.15  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.63/2.15  
% 9.63/2.15  Prover 6: stopped
% 9.63/2.15  Prover 3: stopped
% 9.63/2.16  Prover 0: Proving ...
% 9.63/2.16  Prover 2: stopped
% 9.63/2.17  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.63/2.17  Prover 0: stopped
% 9.63/2.17  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.63/2.17  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.63/2.17  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.63/2.17  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.52/2.24  Prover 8: Preprocessing ...
% 10.52/2.25  Prover 11: Preprocessing ...
% 11.09/2.27  Prover 7: Preprocessing ...
% 11.09/2.28  Prover 10: Preprocessing ...
% 11.09/2.29  Prover 13: Preprocessing ...
% 11.60/2.37  Prover 7: Constructing countermodel ...
% 11.60/2.42  Prover 13: Constructing countermodel ...
% 12.29/2.43  Prover 10: Constructing countermodel ...
% 12.75/2.51  Prover 8: Warning: ignoring some quantifiers
% 12.75/2.55  Prover 8: Constructing countermodel ...
% 13.82/2.66  Prover 11: Constructing countermodel ...
% 18.88/3.38  Prover 7: Found proof (size 39)
% 18.88/3.38  Prover 7: proved (1221ms)
% 18.88/3.38  Prover 10: stopped
% 18.88/3.38  Prover 13: stopped
% 18.88/3.38  Prover 11: stopped
% 18.88/3.38  Prover 1: stopped
% 18.88/3.38  Prover 8: stopped
% 18.88/3.38  Prover 4: stopped
% 18.88/3.38  
% 18.88/3.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.88/3.38  
% 18.88/3.39  % SZS output start Proof for theBenchmark
% 18.88/3.39  Assumptions after simplification:
% 18.88/3.39  ---------------------------------
% 18.88/3.40  
% 18.88/3.40    (goals)
% 18.88/3.40    $i(tptp1) & $i(tptp2) & $i(tptp3) & $i(tptp0) &  ? [v0: $i] : ($i(v0) &
% 18.88/3.40      occurrence_of(v0, tptp0) &  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~
% 18.88/3.40        $i(v1) |  ~ root_occ(v1, v0) |  ~ occurrence_of(v2, tptp1) |  ~
% 18.88/3.40        occurrence_of(v1, tptp3) |  ~ min_precedes(v1, v2, tptp0)) &  ! [v1: $i] :
% 18.88/3.40       ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ root_occ(v1, v0) |  ~
% 18.88/3.40        occurrence_of(v2, tptp2) |  ~ occurrence_of(v1, tptp3) |  ~
% 18.88/3.40        min_precedes(v1, v2, tptp0)))
% 18.88/3.40  
% 18.88/3.40    (sos)
% 19.49/3.40     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 19.49/3.40      |  ~ $i(v1) |  ~ $i(v0) |  ~ min_precedes(v1, v2, v3) |  ~ min_precedes(v0,
% 19.49/3.40        v1, v3) | min_precedes(v0, v2, v3))
% 19.49/3.40  
% 19.49/3.40    (sos_02)
% 19.49/3.41     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ $i(v3) |
% 19.49/3.41       ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ root_occ(v1, v2) |  ~ root_occ(v0,
% 19.49/3.41        v2) |  ~ occurrence_of(v2, v3))
% 19.49/3.41  
% 19.49/3.41    (sos_10)
% 19.49/3.41     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 19.49/3.41       ~ subactivity_occurrence(v0, v1) |  ~ root(v0, v2) |  ~ occurrence_of(v1,
% 19.49/3.41        v2) | root_occ(v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~
% 19.49/3.41      $i(v0) |  ~ root_occ(v0, v1) |  ? [v2: $i] : ($i(v2) &
% 19.49/3.41        subactivity_occurrence(v0, v1) & root(v0, v2) & occurrence_of(v1, v2)))
% 19.49/3.41  
% 19.49/3.41    (sos_18)
% 19.49/3.41     ! [v0: $i] : ( ~ $i(v0) |  ~ activity_occurrence(v0) |  ? [v1: $i] : ($i(v1)
% 19.49/3.41        & activity(v1) & occurrence_of(v0, v1)))
% 19.49/3.41  
% 19.49/3.41    (sos_22)
% 19.49/3.41     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ $i(v2) |  ~ $i(v1) | 
% 19.49/3.41      ~ $i(v0) |  ~ occurrence_of(v0, v2) |  ~ occurrence_of(v0, v1))
% 19.49/3.41  
% 19.49/3.41    (sos_29)
% 19.49/3.41     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ occurrence_of(v1, v0)
% 19.49/3.41      | activity(v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 19.49/3.41      occurrence_of(v1, v0) | activity_occurrence(v1))
% 19.49/3.41  
% 19.49/3.41    (sos_30)
% 19.49/3.41     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ occurrence_of(v1, v0)
% 19.49/3.41      | atomic(v0) |  ? [v2: $i] : ($i(v2) & subactivity_occurrence(v2, v1) &
% 19.49/3.41        root(v2, v0)))
% 19.49/3.41  
% 19.49/3.41    (sos_32)
% 19.49/3.41    $i(tptp1) & $i(tptp2) & $i(tptp4) & $i(tptp3) & $i(tptp0) &  ! [v0: $i] : ( ~
% 19.49/3.41      $i(v0) |  ~ occurrence_of(v0, tptp0) |  ? [v1: $i] :  ? [v2: $i] :  ? [v3:
% 19.49/3.41        $i] : ($i(v3) & $i(v2) & $i(v1) & root_occ(v1, v0) & occurrence_of(v2,
% 19.49/3.41          tptp4) & occurrence_of(v1, tptp3) & min_precedes(v2, v3, tptp0) &
% 19.49/3.41        min_precedes(v1, v2, tptp0) &  ! [v4: $i] : (v4 = v3 | v4 = v2 |  ~ $i(v4)
% 19.49/3.41          |  ~ min_precedes(v1, v4, tptp0)) & (occurrence_of(v3, tptp1) |
% 19.49/3.41          occurrence_of(v3, tptp2))))
% 19.49/3.41  
% 19.49/3.41    (sos_34)
% 19.49/3.41    $i(tptp0) &  ~ atomic(tptp0)
% 19.49/3.41  
% 19.49/3.41    (sos_35)
% 19.49/3.41    $i(tptp4) & atomic(tptp4)
% 19.49/3.41  
% 19.49/3.41  Further assumptions not needed in the proof:
% 19.49/3.41  --------------------------------------------
% 19.49/3.41  sos_01, sos_03, sos_04, sos_05, sos_06, sos_07, sos_08, sos_09, sos_11, sos_12,
% 19.49/3.41  sos_13, sos_14, sos_15, sos_16, sos_17, sos_19, sos_20, sos_21, sos_23, sos_24,
% 19.49/3.41  sos_25, sos_26, sos_27, sos_28, sos_31, sos_33, sos_36, sos_37, sos_38, sos_39,
% 19.49/3.41  sos_40, sos_41, sos_42, sos_43, sos_44
% 19.49/3.41  
% 19.49/3.41  Those formulas are unsatisfiable:
% 19.49/3.41  ---------------------------------
% 19.49/3.41  
% 19.49/3.41  Begin of proof
% 19.49/3.41  | 
% 19.49/3.42  | ALPHA: (goals) implies:
% 19.49/3.42  |   (1)   ? [v0: $i] : ($i(v0) & occurrence_of(v0, tptp0) &  ! [v1: $i] :  !
% 19.49/3.42  |          [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ root_occ(v1, v0) |  ~
% 19.49/3.42  |            occurrence_of(v2, tptp1) |  ~ occurrence_of(v1, tptp3) |  ~
% 19.49/3.42  |            min_precedes(v1, v2, tptp0)) &  ! [v1: $i] :  ! [v2: $i] : ( ~
% 19.49/3.42  |            $i(v2) |  ~ $i(v1) |  ~ root_occ(v1, v0) |  ~ occurrence_of(v2,
% 19.49/3.42  |              tptp2) |  ~ occurrence_of(v1, tptp3) |  ~ min_precedes(v1, v2,
% 19.49/3.42  |              tptp0)))
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (sos_35) implies:
% 19.49/3.42  |   (2)  atomic(tptp4)
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (sos_34) implies:
% 19.49/3.42  |   (3)   ~ atomic(tptp0)
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (sos_32) implies:
% 19.49/3.42  |   (4)  $i(tptp0)
% 19.49/3.42  |   (5)  $i(tptp4)
% 19.49/3.42  |   (6)   ! [v0: $i] : ( ~ $i(v0) |  ~ occurrence_of(v0, tptp0) |  ? [v1: $i] : 
% 19.49/3.42  |          ? [v2: $i] :  ? [v3: $i] : ($i(v3) & $i(v2) & $i(v1) & root_occ(v1,
% 19.49/3.42  |              v0) & occurrence_of(v2, tptp4) & occurrence_of(v1, tptp3) &
% 19.49/3.42  |            min_precedes(v2, v3, tptp0) & min_precedes(v1, v2, tptp0) &  ! [v4:
% 19.49/3.42  |              $i] : (v4 = v3 | v4 = v2 |  ~ $i(v4) |  ~ min_precedes(v1, v4,
% 19.49/3.42  |                tptp0)) & (occurrence_of(v3, tptp1) | occurrence_of(v3,
% 19.49/3.42  |                tptp2))))
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (sos_29) implies:
% 19.49/3.42  |   (7)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 19.49/3.42  |          occurrence_of(v1, v0) | activity_occurrence(v1))
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (sos_10) implies:
% 19.49/3.42  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 19.49/3.42  |          $i(v0) |  ~ subactivity_occurrence(v0, v1) |  ~ root(v0, v2) |  ~
% 19.49/3.42  |          occurrence_of(v1, v2) | root_occ(v0, v1))
% 19.49/3.42  | 
% 19.49/3.42  | DELTA: instantiating (1) with fresh symbol all_36_0 gives:
% 19.49/3.42  |   (9)  $i(all_36_0) & occurrence_of(all_36_0, tptp0) &  ! [v0: $i] :  ! [v1:
% 19.49/3.42  |          $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ root_occ(v0, all_36_0) |  ~
% 19.49/3.42  |          occurrence_of(v1, tptp1) |  ~ occurrence_of(v0, tptp3) |  ~
% 19.49/3.42  |          min_precedes(v0, v1, tptp0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1)
% 19.49/3.42  |          |  ~ $i(v0) |  ~ root_occ(v0, all_36_0) |  ~ occurrence_of(v1, tptp2)
% 19.49/3.42  |          |  ~ occurrence_of(v0, tptp3) |  ~ min_precedes(v0, v1, tptp0))
% 19.49/3.42  | 
% 19.49/3.42  | ALPHA: (9) implies:
% 19.49/3.42  |   (10)  occurrence_of(all_36_0, tptp0)
% 19.49/3.42  |   (11)  $i(all_36_0)
% 19.49/3.42  |   (12)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ root_occ(v0,
% 19.49/3.42  |             all_36_0) |  ~ occurrence_of(v1, tptp2) |  ~ occurrence_of(v0,
% 19.49/3.42  |             tptp3) |  ~ min_precedes(v0, v1, tptp0))
% 19.49/3.42  |   (13)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ root_occ(v0,
% 19.49/3.42  |             all_36_0) |  ~ occurrence_of(v1, tptp1) |  ~ occurrence_of(v0,
% 19.49/3.42  |             tptp3) |  ~ min_precedes(v0, v1, tptp0))
% 19.49/3.42  | 
% 19.49/3.43  | PRED_UNIFY: (2), (3) imply:
% 19.49/3.43  |   (14)   ~ (tptp4 = tptp0)
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (6) with all_36_0, simplifying with (10), (11)
% 19.49/3.43  |              gives:
% 19.49/3.43  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 19.49/3.43  |           root_occ(v0, all_36_0) & occurrence_of(v1, tptp4) &
% 19.49/3.43  |           occurrence_of(v0, tptp3) & min_precedes(v1, v2, tptp0) &
% 19.49/3.43  |           min_precedes(v0, v1, tptp0) &  ! [v3: $i] : (v3 = v2 | v3 = v1 |  ~
% 19.49/3.43  |             $i(v3) |  ~ min_precedes(v0, v3, tptp0)) & (occurrence_of(v2,
% 19.49/3.43  |               tptp1) | occurrence_of(v2, tptp2)))
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (7) with tptp0, all_36_0, simplifying with (4),
% 19.49/3.43  |              (10), (11) gives:
% 19.49/3.43  |   (16)  activity_occurrence(all_36_0)
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (sos_30) with tptp0, all_36_0, simplifying with
% 19.49/3.43  |              (3), (4), (10), (11) gives:
% 19.49/3.43  |   (17)   ? [v0: $i] : ($i(v0) & subactivity_occurrence(v0, all_36_0) &
% 19.49/3.43  |           root(v0, tptp0))
% 19.49/3.43  | 
% 19.49/3.43  | DELTA: instantiating (17) with fresh symbol all_49_0 gives:
% 19.49/3.43  |   (18)  $i(all_49_0) & subactivity_occurrence(all_49_0, all_36_0) &
% 19.49/3.43  |         root(all_49_0, tptp0)
% 19.49/3.43  | 
% 19.49/3.43  | ALPHA: (18) implies:
% 19.49/3.43  |   (19)  root(all_49_0, tptp0)
% 19.49/3.43  |   (20)  subactivity_occurrence(all_49_0, all_36_0)
% 19.49/3.43  |   (21)  $i(all_49_0)
% 19.49/3.43  | 
% 19.49/3.43  | DELTA: instantiating (15) with fresh symbols all_51_0, all_51_1, all_51_2
% 19.49/3.43  |        gives:
% 19.49/3.43  |   (22)  $i(all_51_0) & $i(all_51_1) & $i(all_51_2) & root_occ(all_51_2,
% 19.49/3.43  |           all_36_0) & occurrence_of(all_51_1, tptp4) & occurrence_of(all_51_2,
% 19.49/3.43  |           tptp3) & min_precedes(all_51_1, all_51_0, tptp0) &
% 19.49/3.43  |         min_precedes(all_51_2, all_51_1, tptp0) &  ! [v0: any] : (v0 =
% 19.49/3.43  |           all_51_0 | v0 = all_51_1 |  ~ $i(v0) |  ~ min_precedes(all_51_2, v0,
% 19.49/3.43  |             tptp0)) & (occurrence_of(all_51_0, tptp1) |
% 19.49/3.43  |           occurrence_of(all_51_0, tptp2))
% 19.49/3.43  | 
% 19.49/3.43  | ALPHA: (22) implies:
% 19.49/3.43  |   (23)  min_precedes(all_51_2, all_51_1, tptp0)
% 19.49/3.43  |   (24)  min_precedes(all_51_1, all_51_0, tptp0)
% 19.49/3.43  |   (25)  occurrence_of(all_51_2, tptp3)
% 19.49/3.43  |   (26)  root_occ(all_51_2, all_36_0)
% 19.49/3.43  |   (27)  $i(all_51_2)
% 19.49/3.43  |   (28)  $i(all_51_1)
% 19.49/3.43  |   (29)  $i(all_51_0)
% 19.49/3.43  |   (30)  occurrence_of(all_51_0, tptp1) | occurrence_of(all_51_0, tptp2)
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (sos) with all_51_2, all_51_1, all_51_0, tptp0,
% 19.49/3.43  |              simplifying with (4), (23), (24), (27), (28), (29) gives:
% 19.49/3.43  |   (31)  min_precedes(all_51_2, all_51_0, tptp0)
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (sos_22) with all_36_0, tptp0, tptp4, simplifying
% 19.49/3.43  |              with (4), (5), (10), (11) gives:
% 19.49/3.43  |   (32)  tptp4 = tptp0 |  ~ occurrence_of(all_36_0, tptp4)
% 19.49/3.43  | 
% 19.49/3.43  | GROUND_INST: instantiating (8) with all_49_0, all_36_0, tptp0, simplifying
% 19.49/3.43  |              with (4), (10), (11), (19), (20), (21) gives:
% 19.49/3.43  |   (33)  root_occ(all_49_0, all_36_0)
% 19.49/3.43  | 
% 19.49/3.44  | GROUND_INST: instantiating (sos_18) with all_36_0, simplifying with (11), (16)
% 19.49/3.44  |              gives:
% 19.49/3.44  |   (34)   ? [v0: $i] : ($i(v0) & activity(v0) & occurrence_of(all_36_0, v0))
% 19.49/3.44  | 
% 19.49/3.44  | DELTA: instantiating (34) with fresh symbol all_62_0 gives:
% 19.49/3.44  |   (35)  $i(all_62_0) & activity(all_62_0) & occurrence_of(all_36_0, all_62_0)
% 19.49/3.44  | 
% 19.49/3.44  | ALPHA: (35) implies:
% 19.49/3.44  |   (36)  occurrence_of(all_36_0, all_62_0)
% 19.49/3.44  |   (37)  $i(all_62_0)
% 19.49/3.44  | 
% 19.49/3.44  | BETA: splitting (32) gives:
% 19.49/3.44  | 
% 19.49/3.44  | Case 1:
% 19.49/3.44  | | 
% 19.49/3.44  | | 
% 19.49/3.44  | | GROUND_INST: instantiating (sos_02) with all_51_2, all_49_0, all_36_0,
% 19.49/3.44  | |              all_62_0, simplifying with (11), (21), (26), (27), (33), (36),
% 19.49/3.44  | |              (37) gives:
% 19.49/3.44  | |   (38)  all_51_2 = all_49_0
% 19.49/3.44  | | 
% 19.49/3.44  | | REDUCE: (25), (38) imply:
% 19.49/3.44  | |   (39)  occurrence_of(all_49_0, tptp3)
% 19.49/3.44  | | 
% 19.49/3.44  | | REDUCE: (31), (38) imply:
% 19.49/3.44  | |   (40)  min_precedes(all_49_0, all_51_0, tptp0)
% 19.49/3.44  | | 
% 19.49/3.44  | | GROUND_INST: instantiating (13) with all_49_0, all_51_0, simplifying with
% 19.49/3.44  | |              (21), (29), (33), (39), (40) gives:
% 19.49/3.44  | |   (41)   ~ occurrence_of(all_51_0, tptp1)
% 19.49/3.44  | | 
% 19.49/3.44  | | GROUND_INST: instantiating (12) with all_49_0, all_51_0, simplifying with
% 19.49/3.44  | |              (21), (29), (33), (39), (40) gives:
% 19.49/3.44  | |   (42)   ~ occurrence_of(all_51_0, tptp2)
% 19.49/3.44  | | 
% 19.49/3.44  | | BETA: splitting (30) gives:
% 19.49/3.44  | | 
% 19.49/3.44  | | Case 1:
% 19.49/3.44  | | | 
% 19.49/3.44  | | |   (43)  occurrence_of(all_51_0, tptp1)
% 19.49/3.44  | | | 
% 19.49/3.44  | | | PRED_UNIFY: (41), (43) imply:
% 19.49/3.44  | | |   (44)  $false
% 19.49/3.44  | | | 
% 19.49/3.44  | | | CLOSE: (44) is inconsistent.
% 19.49/3.44  | | | 
% 19.49/3.44  | | Case 2:
% 19.49/3.44  | | | 
% 19.49/3.44  | | |   (45)  occurrence_of(all_51_0, tptp2)
% 19.49/3.44  | | | 
% 19.49/3.44  | | | PRED_UNIFY: (42), (45) imply:
% 19.49/3.44  | | |   (46)  $false
% 19.49/3.44  | | | 
% 19.49/3.44  | | | CLOSE: (46) is inconsistent.
% 19.49/3.44  | | | 
% 19.49/3.44  | | End of split
% 19.49/3.44  | | 
% 19.49/3.44  | Case 2:
% 19.49/3.44  | | 
% 19.49/3.44  | |   (47)  tptp4 = tptp0
% 19.49/3.44  | | 
% 19.49/3.44  | | REDUCE: (14), (47) imply:
% 19.49/3.44  | |   (48)  $false
% 19.49/3.44  | | 
% 19.49/3.44  | | CLOSE: (48) is inconsistent.
% 19.49/3.44  | | 
% 19.49/3.44  | End of split
% 19.49/3.44  | 
% 19.49/3.44  End of proof
% 19.49/3.44  % SZS output end Proof for theBenchmark
% 19.49/3.44  
% 19.49/3.44  2828ms
%------------------------------------------------------------------------------