TSTP Solution File: NUM386+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n014.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 11:47:32 EDT 2023

% Result   : Theorem 10.33s 2.28s
% Output   : Proof 13.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n014.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 15:06:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.60  ________       _____
% 0.21/0.60  ___  __ \_________(_)________________________________
% 0.21/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60  
% 0.21/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60  (2023-06-19)
% 0.21/0.60  
% 0.21/0.60  (c) Philipp Rümmer, 2009-2023
% 0.21/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60                Amanda Stjerna.
% 0.21/0.60  Free software under BSD-3-Clause.
% 0.21/0.60  
% 0.21/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60  
% 0.21/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62  Running up to 7 provers in parallel.
% 0.21/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.37/1.11  Prover 4: Preprocessing ...
% 2.37/1.11  Prover 1: Preprocessing ...
% 2.94/1.15  Prover 3: Preprocessing ...
% 2.94/1.15  Prover 5: Preprocessing ...
% 2.94/1.15  Prover 6: Preprocessing ...
% 2.94/1.15  Prover 2: Preprocessing ...
% 2.94/1.16  Prover 0: Preprocessing ...
% 4.40/1.53  Prover 1: Warning: ignoring some quantifiers
% 4.40/1.57  Prover 1: Constructing countermodel ...
% 4.40/1.58  Prover 5: Proving ...
% 5.40/1.60  Prover 4: Warning: ignoring some quantifiers
% 5.40/1.61  Prover 2: Proving ...
% 5.40/1.63  Prover 3: Warning: ignoring some quantifiers
% 6.41/1.64  Prover 4: Constructing countermodel ...
% 6.41/1.65  Prover 3: Constructing countermodel ...
% 6.41/1.66  Prover 6: Proving ...
% 6.88/1.72  Prover 0: Proving ...
% 8.35/1.92  Prover 3: gave up
% 8.63/1.93  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.66/1.98  Prover 1: gave up
% 8.66/1.99  Prover 7: Preprocessing ...
% 8.66/1.99  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.16/2.04  Prover 8: Preprocessing ...
% 9.61/2.11  Prover 7: Warning: ignoring some quantifiers
% 9.61/2.12  Prover 7: Constructing countermodel ...
% 10.33/2.22  Prover 8: Warning: ignoring some quantifiers
% 10.33/2.23  Prover 8: Constructing countermodel ...
% 10.33/2.28  Prover 0: proved (1655ms)
% 10.33/2.28  
% 10.33/2.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.33/2.28  
% 10.33/2.29  Prover 6: stopped
% 10.33/2.30  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.33/2.30  Prover 2: stopped
% 10.33/2.30  Prover 5: stopped
% 10.33/2.31  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.33/2.31  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.33/2.31  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.33/2.34  Prover 11: Preprocessing ...
% 10.91/2.34  Prover 10: Preprocessing ...
% 10.91/2.35  Prover 13: Preprocessing ...
% 10.91/2.36  Prover 16: Preprocessing ...
% 12.02/2.42  Prover 13: Warning: ignoring some quantifiers
% 12.02/2.44  Prover 13: Constructing countermodel ...
% 12.02/2.44  Prover 8: gave up
% 12.02/2.44  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.02/2.47  Prover 16: Warning: ignoring some quantifiers
% 12.02/2.47  Prover 19: Preprocessing ...
% 12.02/2.47  Prover 10: Warning: ignoring some quantifiers
% 12.02/2.48  Prover 10: Constructing countermodel ...
% 12.02/2.49  Prover 7: Found proof (size 35)
% 12.02/2.49  Prover 7: proved (555ms)
% 12.02/2.49  Prover 10: stopped
% 12.02/2.49  Prover 13: stopped
% 12.02/2.49  Prover 4: stopped
% 12.02/2.49  Prover 16: Constructing countermodel ...
% 12.02/2.50  Prover 16: stopped
% 12.63/2.51  Prover 11: Warning: ignoring some quantifiers
% 12.63/2.52  Prover 11: Constructing countermodel ...
% 12.63/2.53  Prover 11: stopped
% 12.63/2.56  Prover 19: Warning: ignoring some quantifiers
% 12.63/2.57  Prover 19: Constructing countermodel ...
% 12.63/2.58  Prover 19: stopped
% 12.63/2.58  
% 12.63/2.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.63/2.58  
% 12.63/2.59  % SZS output start Proof for theBenchmark
% 12.63/2.59  Assumptions after simplification:
% 12.63/2.59  ---------------------------------
% 12.63/2.59  
% 12.63/2.59    (commutativity_k2_xboole_0)
% 13.07/2.61     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) |  ~
% 13.07/2.61      $i(v1) |  ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) &  ! [v0: $i] :  !
% 13.07/2.61    [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 13.07/2.61      | (set_union2(v1, v0) = v2 & $i(v2)))
% 13.07/2.61  
% 13.07/2.61    (d1_ordinal1)
% 13.07/2.62     ! [v0: $i] :  ! [v1: $i] : ( ~ (succ(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :
% 13.07/2.62      (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) &  ! [v0:
% 13.07/2.62      $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :
% 13.07/2.62      (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 13.07/2.62  
% 13.07/2.62    (d1_tarski)
% 13.07/2.62     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0) = v1) |
% 13.07/2.62       ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v2, v1)) &  ? [v0: $i] :  ! [v1:
% 13.07/2.62      $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ~ $i(v1) |  ~
% 13.07/2.62      $i(v0) |  ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 |
% 13.07/2.62          in(v3, v0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) | 
% 13.07/2.62      ~ $i(v1) |  ~ $i(v0) | in(v0, v1))
% 13.07/2.62  
% 13.07/2.62    (d2_xboole_0)
% 13.07/2.62     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_union2(v0,
% 13.07/2.62          v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v3,
% 13.07/2.62        v2) | in(v3, v1) | in(v3, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 13.07/2.62     ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 13.07/2.63      $i(v1) |  ~ $i(v0) |  ~ in(v3, v1) | in(v3, v2)) &  ! [v0: $i] :  ! [v1: $i]
% 13.07/2.63    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) |  ~ $i(v3) |  ~
% 13.07/2.63      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v3, v0) | in(v3, v2)) &  ? [v0: $i] :
% 13.07/2.63     ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~ (set_union2(v1, v2) =
% 13.07/2.63        v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: $i] : ($i(v4) & ( ~
% 13.07/2.63          in(v4, v0) | ( ~ in(v4, v2) &  ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 13.07/2.63          | in(v4, v0))))
% 13.07/2.63  
% 13.07/2.63    (idempotence_k2_xboole_0)
% 13.07/2.63     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1) |  ~
% 13.07/2.63      $i(v0))
% 13.07/2.63  
% 13.07/2.63    (t13_ordinal1)
% 13.07/2.63     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) &
% 13.07/2.63      $i(v0) & (( ~ (v1 = v0) & in(v0, v2) &  ~ in(v0, v1)) | ( ~ in(v0, v2) & (v1
% 13.07/2.63            = v0 | in(v0, v1)))))
% 13.07/2.63  
% 13.07/2.63  Further assumptions not needed in the proof:
% 13.07/2.63  --------------------------------------------
% 13.07/2.63  antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 13.07/2.63  existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1,
% 13.07/2.63  fc2_xboole_0, fc3_xboole_0, fc4_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0,
% 13.07/2.63  rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 13.07/2.63  rc5_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole
% 13.07/2.63  
% 13.07/2.63  Those formulas are unsatisfiable:
% 13.07/2.63  ---------------------------------
% 13.07/2.63  
% 13.07/2.63  Begin of proof
% 13.07/2.63  | 
% 13.07/2.63  | ALPHA: (commutativity_k2_xboole_0) implies:
% 13.07/2.63  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 13.07/2.63  |          |  ~ $i(v1) |  ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 13.07/2.63  | 
% 13.07/2.63  | ALPHA: (d1_ordinal1) implies:
% 13.07/2.63  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (succ(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 13.07/2.63  |            $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 13.07/2.63  |            $i(v1)))
% 13.07/2.63  | 
% 13.07/2.63  | ALPHA: (d1_tarski) implies:
% 13.07/2.63  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) |  ~ $i(v1) |  ~
% 13.07/2.63  |          $i(v0) | in(v0, v1))
% 13.07/2.63  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0)
% 13.07/2.63  |            = v1) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v2, v1))
% 13.07/2.63  | 
% 13.07/2.63  | ALPHA: (d2_xboole_0) implies:
% 13.07/2.63  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 13.07/2.63  |          (set_union2(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 13.07/2.63  |          $i(v0) |  ~ in(v3, v0) | in(v3, v2))
% 13.07/2.63  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 13.07/2.63  |          (set_union2(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 13.07/2.63  |          $i(v0) |  ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 13.07/2.63  | 
% 13.07/2.64  | DELTA: instantiating (t13_ordinal1) with fresh symbols all_46_0, all_46_1,
% 13.07/2.64  |        all_46_2 gives:
% 13.07/2.64  |   (7)  succ(all_46_1) = all_46_0 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2)
% 13.07/2.64  |        & (( ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) &  ~ in(all_46_2,
% 13.07/2.64  |              all_46_1)) | ( ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 |
% 13.07/2.64  |              in(all_46_2, all_46_1))))
% 13.07/2.64  | 
% 13.07/2.64  | ALPHA: (7) implies:
% 13.07/2.64  |   (8)  $i(all_46_2)
% 13.07/2.64  |   (9)  $i(all_46_1)
% 13.07/2.64  |   (10)  succ(all_46_1) = all_46_0
% 13.07/2.64  |   (11)  ( ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) &  ~ in(all_46_2,
% 13.07/2.64  |             all_46_1)) | ( ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 |
% 13.07/2.64  |             in(all_46_2, all_46_1)))
% 13.07/2.64  | 
% 13.07/2.64  | GROUND_INST: instantiating (2) with all_46_1, all_46_0, simplifying with (9),
% 13.07/2.64  |              (10) gives:
% 13.07/2.64  |   (12)   ? [v0: $i] : (singleton(all_46_1) = v0 & set_union2(all_46_1, v0) =
% 13.07/2.64  |           all_46_0 & $i(v0) & $i(all_46_0))
% 13.07/2.64  | 
% 13.07/2.64  | DELTA: instantiating (12) with fresh symbol all_60_0 gives:
% 13.07/2.64  |   (13)  singleton(all_46_1) = all_60_0 & set_union2(all_46_1, all_60_0) =
% 13.07/2.64  |         all_46_0 & $i(all_60_0) & $i(all_46_0)
% 13.07/2.64  | 
% 13.07/2.64  | ALPHA: (13) implies:
% 13.07/2.64  |   (14)  $i(all_60_0)
% 13.07/2.64  |   (15)  set_union2(all_46_1, all_60_0) = all_46_0
% 13.07/2.64  |   (16)  singleton(all_46_1) = all_60_0
% 13.07/2.64  | 
% 13.07/2.64  | GROUND_INST: instantiating (idempotence_k2_xboole_0) with all_46_1, all_46_0,
% 13.07/2.64  |              simplifying with (9) gives:
% 13.07/2.64  |   (17)  all_46_0 = all_46_1 |  ~ (set_union2(all_46_1, all_46_1) = all_46_0)
% 13.07/2.64  | 
% 13.07/2.64  | GROUND_INST: instantiating (1) with all_60_0, all_46_1, all_46_0, simplifying
% 13.07/2.64  |              with (9), (14), (15) gives:
% 13.07/2.64  |   (18)  set_union2(all_60_0, all_46_1) = all_46_0 & $i(all_46_0)
% 13.07/2.64  | 
% 13.07/2.64  | ALPHA: (18) implies:
% 13.07/2.64  |   (19)  $i(all_46_0)
% 13.07/2.64  |   (20)  set_union2(all_60_0, all_46_1) = all_46_0
% 13.07/2.64  | 
% 13.07/2.64  | GROUND_INST: instantiating (3) with all_46_1, all_60_0, simplifying with (9),
% 13.07/2.64  |              (14), (16) gives:
% 13.07/2.64  |   (21)  in(all_46_1, all_60_0)
% 13.07/2.64  | 
% 13.07/2.64  | GROUND_INST: instantiating (5) with all_60_0, all_46_1, all_46_0, all_46_1,
% 13.07/2.64  |              simplifying with (9), (14), (19), (20), (21) gives:
% 13.07/2.64  |   (22)  in(all_46_1, all_46_0)
% 13.07/2.64  | 
% 13.07/2.64  | BETA: splitting (11) gives:
% 13.07/2.64  | 
% 13.07/2.64  | Case 1:
% 13.07/2.64  | | 
% 13.07/2.64  | |   (23)   ~ (all_46_1 = all_46_2) & in(all_46_2, all_46_0) &  ~ in(all_46_2,
% 13.07/2.64  | |           all_46_1)
% 13.07/2.64  | | 
% 13.07/2.64  | | ALPHA: (23) implies:
% 13.07/2.64  | |   (24)   ~ (all_46_1 = all_46_2)
% 13.07/2.64  | |   (25)   ~ in(all_46_2, all_46_1)
% 13.07/2.64  | |   (26)  in(all_46_2, all_46_0)
% 13.07/2.64  | | 
% 13.07/2.64  | | PRED_UNIFY: (25), (26) imply:
% 13.07/2.64  | |   (27)   ~ (all_46_0 = all_46_1)
% 13.07/2.64  | | 
% 13.07/2.64  | | BETA: splitting (17) gives:
% 13.07/2.64  | | 
% 13.07/2.64  | | Case 1:
% 13.07/2.64  | | | 
% 13.07/2.64  | | | 
% 13.07/2.64  | | | GROUND_INST: instantiating (6) with all_46_1, all_60_0, all_46_0,
% 13.07/2.64  | | |              all_46_2, simplifying with (8), (9), (14), (15), (19), (25),
% 13.07/2.64  | | |              (26) gives:
% 13.07/2.64  | | |   (28)  in(all_46_2, all_60_0)
% 13.07/2.64  | | | 
% 13.07/2.65  | | | GROUND_INST: instantiating (4) with all_46_1, all_60_0, all_46_2,
% 13.07/2.65  | | |              simplifying with (8), (9), (14), (16), (28) gives:
% 13.07/2.65  | | |   (29)  all_46_1 = all_46_2
% 13.07/2.65  | | | 
% 13.07/2.65  | | | REDUCE: (24), (29) imply:
% 13.07/2.65  | | |   (30)  $false
% 13.07/2.65  | | | 
% 13.07/2.65  | | | CLOSE: (30) is inconsistent.
% 13.07/2.65  | | | 
% 13.07/2.65  | | Case 2:
% 13.07/2.65  | | | 
% 13.07/2.65  | | |   (31)  all_46_0 = all_46_1
% 13.07/2.65  | | | 
% 13.07/2.65  | | | REDUCE: (27), (31) imply:
% 13.07/2.65  | | |   (32)  $false
% 13.07/2.65  | | | 
% 13.07/2.65  | | | CLOSE: (32) is inconsistent.
% 13.07/2.65  | | | 
% 13.07/2.65  | | End of split
% 13.07/2.65  | | 
% 13.07/2.65  | Case 2:
% 13.07/2.65  | | 
% 13.07/2.65  | |   (33)   ~ in(all_46_2, all_46_0) & (all_46_1 = all_46_2 | in(all_46_2,
% 13.07/2.65  | |             all_46_1))
% 13.07/2.65  | | 
% 13.07/2.65  | | ALPHA: (33) implies:
% 13.07/2.65  | |   (34)   ~ in(all_46_2, all_46_0)
% 13.07/2.65  | |   (35)  all_46_1 = all_46_2 | in(all_46_2, all_46_1)
% 13.07/2.65  | | 
% 13.07/2.65  | | PRED_UNIFY: (22), (34) imply:
% 13.07/2.65  | |   (36)   ~ (all_46_1 = all_46_2)
% 13.07/2.65  | | 
% 13.07/2.65  | | BETA: splitting (35) gives:
% 13.07/2.65  | | 
% 13.07/2.65  | | Case 1:
% 13.07/2.65  | | | 
% 13.07/2.65  | | |   (37)  in(all_46_2, all_46_1)
% 13.07/2.65  | | | 
% 13.07/2.65  | | | GROUND_INST: instantiating (5) with all_46_1, all_60_0, all_46_0,
% 13.07/2.65  | | |              all_46_2, simplifying with (8), (9), (14), (15), (19), (34),
% 13.07/2.65  | | |              (37) gives:
% 13.07/2.65  | | |   (38)  $false
% 13.07/2.65  | | | 
% 13.07/2.65  | | | CLOSE: (38) is inconsistent.
% 13.07/2.65  | | | 
% 13.07/2.65  | | Case 2:
% 13.07/2.65  | | | 
% 13.07/2.65  | | |   (39)  all_46_1 = all_46_2
% 13.07/2.65  | | | 
% 13.07/2.65  | | | REDUCE: (36), (39) imply:
% 13.07/2.65  | | |   (40)  $false
% 13.07/2.65  | | | 
% 13.07/2.65  | | | CLOSE: (40) is inconsistent.
% 13.07/2.65  | | | 
% 13.07/2.65  | | End of split
% 13.07/2.65  | | 
% 13.07/2.65  | End of split
% 13.07/2.65  | 
% 13.07/2.65  End of proof
% 13.07/2.65  % SZS output end Proof for theBenchmark
% 13.07/2.65  
% 13.07/2.65  2045ms
%------------------------------------------------------------------------------