TSTP Solution File: SET882+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET882+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 : n020.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 15:26:54 EDT 2023

% Result   : Theorem 4.82s 1.49s
% Output   : Proof 6.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 16:13:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.96/1.02  Prover 1: Preprocessing ...
% 1.96/1.02  Prover 4: Preprocessing ...
% 1.96/1.06  Prover 5: Preprocessing ...
% 1.96/1.06  Prover 3: Preprocessing ...
% 1.96/1.06  Prover 2: Preprocessing ...
% 1.96/1.06  Prover 6: Preprocessing ...
% 1.96/1.06  Prover 0: Preprocessing ...
% 3.58/1.23  Prover 4: Warning: ignoring some quantifiers
% 3.58/1.23  Prover 1: Warning: ignoring some quantifiers
% 3.58/1.24  Prover 3: Warning: ignoring some quantifiers
% 3.58/1.25  Prover 3: Constructing countermodel ...
% 3.58/1.25  Prover 1: Constructing countermodel ...
% 3.58/1.25  Prover 6: Proving ...
% 3.58/1.25  Prover 4: Constructing countermodel ...
% 3.58/1.27  Prover 5: Proving ...
% 3.58/1.27  Prover 0: Proving ...
% 4.07/1.30  Prover 2: Proving ...
% 4.82/1.49  Prover 5: proved (834ms)
% 4.82/1.49  
% 4.82/1.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.82/1.49  
% 4.82/1.49  Prover 6: stopped
% 4.82/1.50  Prover 2: stopped
% 4.82/1.51  Prover 3: stopped
% 4.82/1.51  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.82/1.51  Prover 0: stopped
% 4.82/1.51  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.82/1.51  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.82/1.51  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.82/1.51  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.82/1.53  Prover 13: Preprocessing ...
% 4.82/1.54  Prover 7: Preprocessing ...
% 4.82/1.54  Prover 10: Preprocessing ...
% 5.56/1.55  Prover 11: Preprocessing ...
% 5.56/1.55  Prover 8: Preprocessing ...
% 5.81/1.58  Prover 7: Warning: ignoring some quantifiers
% 5.81/1.59  Prover 7: Constructing countermodel ...
% 5.81/1.59  Prover 1: Found proof (size 35)
% 5.81/1.59  Prover 1: proved (950ms)
% 5.81/1.59  Prover 4: stopped
% 5.81/1.59  Prover 10: Warning: ignoring some quantifiers
% 5.81/1.59  Prover 7: stopped
% 5.81/1.60  Prover 10: Constructing countermodel ...
% 5.81/1.60  Prover 10: stopped
% 5.81/1.60  Prover 8: Warning: ignoring some quantifiers
% 5.81/1.61  Prover 11: Warning: ignoring some quantifiers
% 5.81/1.61  Prover 8: Constructing countermodel ...
% 5.81/1.61  Prover 11: Constructing countermodel ...
% 5.81/1.62  Prover 11: stopped
% 5.81/1.62  Prover 8: stopped
% 5.81/1.62  Prover 13: Warning: ignoring some quantifiers
% 5.81/1.63  Prover 13: Constructing countermodel ...
% 5.81/1.63  Prover 13: stopped
% 5.81/1.63  
% 5.81/1.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.81/1.63  
% 6.35/1.64  % SZS output start Proof for theBenchmark
% 6.35/1.65  Assumptions after simplification:
% 6.35/1.65  ---------------------------------
% 6.35/1.65  
% 6.35/1.65    (d1_tarski)
% 6.55/1.68     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v1) = v2) |
% 6.55/1.68       ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] : (in(v3, v0) = v4 &
% 6.55/1.68        $i(v3) & ( ~ (v4 = 0) |  ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) &  ! [v0: $i]
% 6.55/1.68    :  ! [v1: $i] : ( ~ (singleton(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v2:
% 6.55/1.68          $i] : (v2 = v0 |  ~ (in(v2, v1) = 0) |  ~ $i(v2)) &  ! [v2: int] : (v2 =
% 6.55/1.68          0 |  ~ (in(v0, v1) = v2))))
% 6.55/1.68  
% 6.55/1.68    (l39_zfmisc_1)
% 6.55/1.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 6.55/1.69      (set_difference(v3, v2) = v4) |  ~ (unordered_pair(v0, v1) = v3) |  ~ $i(v2)
% 6.55/1.69      |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :  ? [v7: $i] :
% 6.55/1.69      (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 & $i(v7) & (v7 = v4
% 6.55/1.69          | v5 = 0 | ( ~ (v6 = 0) &  ~ (v1 = v0))))) &  ! [v0: $i] :  ! [v1: $i] :
% 6.55/1.69     ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ (set_difference(v3, v2) = v4) | 
% 6.55/1.69      ~ (unordered_pair(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 6.55/1.69      [v5: $i] :  ? [v6: any] :  ? [v7: any] : (singleton(v0) = v5 & in(v1, v2) =
% 6.55/1.69        v7 & in(v0, v2) = v6 & $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 |
% 6.55/1.69              v1 = v0)))))
% 6.55/1.69  
% 6.55/1.69    (t23_zfmisc_1)
% 6.55/1.69     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 6.55/1.69      $i] : ( ~ (v5 = v4) &  ~ (v1 = v0) & set_difference(v2, v3) = v4 &
% 6.55/1.69      singleton(v1) = v3 & singleton(v0) = v5 & unordered_pair(v0, v1) = v2 &
% 6.55/1.69      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.55/1.69  
% 6.55/1.69    (function-axioms)
% 6.55/1.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.55/1.70      (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0:
% 6.55/1.70      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.55/1.70      (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0:
% 6.55/1.70      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 6.55/1.70    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 6.55/1.70      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 6.55/1.70      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 6.55/1.70    [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 6.55/1.70  
% 6.55/1.70  Further assumptions not needed in the proof:
% 6.55/1.70  --------------------------------------------
% 6.55/1.70  antisymmetry_r2_hidden, commutativity_k2_tarski, rc1_xboole_0, rc2_xboole_0
% 6.55/1.70  
% 6.55/1.70  Those formulas are unsatisfiable:
% 6.55/1.70  ---------------------------------
% 6.55/1.70  
% 6.55/1.70  Begin of proof
% 6.55/1.70  | 
% 6.55/1.70  | ALPHA: (d1_tarski) implies:
% 6.55/1.70  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) |  ~ $i(v1) |  ~
% 6.55/1.70  |          $i(v0) | ( ! [v2: $i] : (v2 = v0 |  ~ (in(v2, v1) = 0) |  ~ $i(v2)) &
% 6.55/1.70  |             ! [v2: int] : (v2 = 0 |  ~ (in(v0, v1) = v2))))
% 6.55/1.70  | 
% 6.55/1.70  | ALPHA: (l39_zfmisc_1) implies:
% 6.55/1.71  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (
% 6.55/1.71  |          ~ (set_difference(v3, v2) = v4) |  ~ (unordered_pair(v0, v1) = v3) | 
% 6.55/1.71  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: any] :  ?
% 6.55/1.71  |          [v7: any] : (singleton(v0) = v5 & in(v1, v2) = v7 & in(v0, v2) = v6 &
% 6.55/1.71  |            $i(v5) & ( ~ (v5 = v4) | ( ~ (v6 = 0) & (v7 = 0 | v1 = v0)))))
% 6.55/1.71  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (
% 6.55/1.71  |          ~ (set_difference(v3, v2) = v4) |  ~ (unordered_pair(v0, v1) = v3) | 
% 6.55/1.71  |          ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :  ?
% 6.55/1.71  |          [v7: $i] : (singleton(v0) = v7 & in(v1, v2) = v6 & in(v0, v2) = v5 &
% 6.55/1.71  |            $i(v7) & (v7 = v4 | v5 = 0 | ( ~ (v6 = 0) &  ~ (v1 = v0)))))
% 6.55/1.71  | 
% 6.55/1.71  | ALPHA: (function-axioms) implies:
% 6.55/1.71  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2)
% 6.55/1.71  |            = v1) |  ~ (singleton(v2) = v0))
% 6.55/1.71  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.55/1.71  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.55/1.71  | 
% 6.55/1.71  | DELTA: instantiating (t23_zfmisc_1) with fresh symbols all_13_0, all_13_1,
% 6.55/1.71  |        all_13_2, all_13_3, all_13_4, all_13_5 gives:
% 6.55/1.71  |   (6)   ~ (all_13_0 = all_13_1) &  ~ (all_13_4 = all_13_5) &
% 6.55/1.71  |        set_difference(all_13_3, all_13_2) = all_13_1 & singleton(all_13_4) =
% 6.55/1.71  |        all_13_2 & singleton(all_13_5) = all_13_0 & unordered_pair(all_13_5,
% 6.55/1.71  |          all_13_4) = all_13_3 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) &
% 6.55/1.71  |        $i(all_13_3) & $i(all_13_4) & $i(all_13_5)
% 6.55/1.71  | 
% 6.55/1.71  | ALPHA: (6) implies:
% 6.55/1.72  |   (7)   ~ (all_13_4 = all_13_5)
% 6.55/1.72  |   (8)   ~ (all_13_0 = all_13_1)
% 6.55/1.72  |   (9)  $i(all_13_5)
% 6.55/1.72  |   (10)  $i(all_13_4)
% 6.55/1.72  |   (11)  $i(all_13_2)
% 6.55/1.72  |   (12)  unordered_pair(all_13_5, all_13_4) = all_13_3
% 6.55/1.72  |   (13)  singleton(all_13_5) = all_13_0
% 6.55/1.72  |   (14)  singleton(all_13_4) = all_13_2
% 6.55/1.72  |   (15)  set_difference(all_13_3, all_13_2) = all_13_1
% 6.55/1.72  | 
% 6.55/1.72  | GROUND_INST: instantiating (1) with all_13_4, all_13_2, simplifying with (10),
% 6.55/1.72  |              (11), (14) gives:
% 6.55/1.72  |   (16)   ! [v0: any] : (v0 = all_13_4 |  ~ (in(v0, all_13_2) = 0) |  ~ $i(v0))
% 6.55/1.72  |         &  ! [v0: int] : (v0 = 0 |  ~ (in(all_13_4, all_13_2) = v0))
% 6.55/1.72  | 
% 6.55/1.72  | ALPHA: (16) implies:
% 6.55/1.72  |   (17)   ! [v0: int] : (v0 = 0 |  ~ (in(all_13_4, all_13_2) = v0))
% 6.55/1.72  |   (18)   ! [v0: any] : (v0 = all_13_4 |  ~ (in(v0, all_13_2) = 0) |  ~ $i(v0))
% 6.55/1.72  | 
% 6.55/1.72  | GROUND_INST: instantiating (3) with all_13_5, all_13_4, all_13_2, all_13_3,
% 6.55/1.72  |              all_13_1, simplifying with (9), (10), (11), (12), (15) gives:
% 6.55/1.72  |   (19)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (singleton(all_13_5) = v2
% 6.55/1.72  |           & in(all_13_4, all_13_2) = v1 & in(all_13_5, all_13_2) = v0 & $i(v2)
% 6.55/1.72  |           & (v2 = all_13_1 | v0 = 0 | ( ~ (v1 = 0) &  ~ (all_13_4 =
% 6.55/1.72  |                 all_13_5))))
% 6.55/1.72  | 
% 6.55/1.72  | GROUND_INST: instantiating (2) with all_13_5, all_13_4, all_13_2, all_13_3,
% 6.55/1.72  |              all_13_1, simplifying with (9), (10), (11), (12), (15) gives:
% 6.55/1.73  |   (20)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (singleton(all_13_5) = v0
% 6.55/1.73  |           & in(all_13_4, all_13_2) = v2 & in(all_13_5, all_13_2) = v1 & $i(v0)
% 6.55/1.73  |           & ( ~ (v0 = all_13_1) | ( ~ (v1 = 0) & (v2 = 0 | all_13_4 =
% 6.55/1.73  |                 all_13_5))))
% 6.55/1.73  | 
% 6.55/1.73  | DELTA: instantiating (19) with fresh symbols all_23_0, all_23_1, all_23_2
% 6.55/1.73  |        gives:
% 6.55/1.73  |   (21)  singleton(all_13_5) = all_23_0 & in(all_13_4, all_13_2) = all_23_1 &
% 6.55/1.73  |         in(all_13_5, all_13_2) = all_23_2 & $i(all_23_0) & (all_23_0 =
% 6.55/1.73  |           all_13_1 | all_23_2 = 0 | ( ~ (all_23_1 = 0) &  ~ (all_13_4 =
% 6.55/1.73  |               all_13_5)))
% 6.55/1.73  | 
% 6.55/1.73  | ALPHA: (21) implies:
% 6.55/1.73  |   (22)  in(all_13_5, all_13_2) = all_23_2
% 6.55/1.73  |   (23)  in(all_13_4, all_13_2) = all_23_1
% 6.55/1.73  |   (24)  singleton(all_13_5) = all_23_0
% 6.55/1.73  |   (25)  all_23_0 = all_13_1 | all_23_2 = 0 | ( ~ (all_23_1 = 0) &  ~ (all_13_4
% 6.55/1.73  |             = all_13_5))
% 6.55/1.73  | 
% 6.55/1.73  | DELTA: instantiating (20) with fresh symbols all_25_0, all_25_1, all_25_2
% 6.55/1.73  |        gives:
% 6.55/1.73  |   (26)  singleton(all_13_5) = all_25_2 & in(all_13_4, all_13_2) = all_25_0 &
% 6.55/1.73  |         in(all_13_5, all_13_2) = all_25_1 & $i(all_25_2) & ( ~ (all_25_2 =
% 6.55/1.73  |             all_13_1) | ( ~ (all_25_1 = 0) & (all_25_0 = 0 | all_13_4 =
% 6.55/1.73  |               all_13_5)))
% 6.55/1.73  | 
% 6.55/1.73  | ALPHA: (26) implies:
% 6.55/1.73  |   (27)  in(all_13_5, all_13_2) = all_25_1
% 6.55/1.73  |   (28)  in(all_13_4, all_13_2) = all_25_0
% 6.55/1.73  |   (29)  singleton(all_13_5) = all_25_2
% 6.55/1.73  | 
% 6.55/1.73  | GROUND_INST: instantiating (5) with all_23_2, all_25_1, all_13_2, all_13_5,
% 6.55/1.73  |              simplifying with (22), (27) gives:
% 6.55/1.73  |   (30)  all_25_1 = all_23_2
% 6.55/1.73  | 
% 6.55/1.73  | GROUND_INST: instantiating (5) with all_23_1, all_25_0, all_13_2, all_13_4,
% 6.55/1.73  |              simplifying with (23), (28) gives:
% 6.55/1.73  |   (31)  all_25_0 = all_23_1
% 6.55/1.73  | 
% 6.55/1.73  | GROUND_INST: instantiating (17) with all_25_0, simplifying with (28) gives:
% 6.55/1.73  |   (32)  all_25_0 = 0
% 6.55/1.73  | 
% 6.55/1.73  | GROUND_INST: instantiating (4) with all_13_0, all_25_2, all_13_5, simplifying
% 6.55/1.73  |              with (13), (29) gives:
% 6.55/1.73  |   (33)  all_25_2 = all_13_0
% 6.55/1.73  | 
% 6.55/1.73  | GROUND_INST: instantiating (4) with all_23_0, all_25_2, all_13_5, simplifying
% 6.55/1.73  |              with (24), (29) gives:
% 6.55/1.73  |   (34)  all_25_2 = all_23_0
% 6.55/1.73  | 
% 6.55/1.73  | COMBINE_EQS: (31), (32) imply:
% 6.55/1.73  |   (35)  all_23_1 = 0
% 6.55/1.73  | 
% 6.55/1.73  | SIMP: (35) implies:
% 6.55/1.73  |   (36)  all_23_1 = 0
% 6.55/1.73  | 
% 6.55/1.73  | COMBINE_EQS: (33), (34) imply:
% 6.55/1.73  |   (37)  all_23_0 = all_13_0
% 6.55/1.73  | 
% 6.55/1.73  | SIMP: (37) implies:
% 6.55/1.73  |   (38)  all_23_0 = all_13_0
% 6.55/1.73  | 
% 6.55/1.73  | BETA: splitting (25) gives:
% 6.55/1.73  | 
% 6.55/1.73  | Case 1:
% 6.55/1.73  | | 
% 6.55/1.73  | |   (39)  all_23_2 = 0
% 6.55/1.73  | | 
% 6.55/1.73  | | REDUCE: (22), (39) imply:
% 6.55/1.74  | |   (40)  in(all_13_5, all_13_2) = 0
% 6.55/1.74  | | 
% 6.55/1.74  | | GROUND_INST: instantiating (18) with all_13_5, simplifying with (9), (40)
% 6.55/1.74  | |              gives:
% 6.55/1.74  | |   (41)  all_13_4 = all_13_5
% 6.55/1.74  | | 
% 6.55/1.74  | | REDUCE: (7), (41) imply:
% 6.84/1.74  | |   (42)  $false
% 6.84/1.74  | | 
% 6.84/1.74  | | CLOSE: (42) is inconsistent.
% 6.84/1.74  | | 
% 6.84/1.74  | Case 2:
% 6.84/1.74  | | 
% 6.84/1.74  | |   (43)  all_23_0 = all_13_1 | ( ~ (all_23_1 = 0) &  ~ (all_13_4 = all_13_5))
% 6.84/1.74  | | 
% 6.84/1.74  | | BETA: splitting (43) gives:
% 6.84/1.74  | | 
% 6.84/1.74  | | Case 1:
% 6.84/1.74  | | | 
% 6.84/1.74  | | |   (44)  all_23_0 = all_13_1
% 6.84/1.74  | | | 
% 6.84/1.74  | | | COMBINE_EQS: (38), (44) imply:
% 6.84/1.74  | | |   (45)  all_13_0 = all_13_1
% 6.84/1.74  | | | 
% 6.84/1.74  | | | REDUCE: (8), (45) imply:
% 6.84/1.74  | | |   (46)  $false
% 6.84/1.74  | | | 
% 6.84/1.74  | | | CLOSE: (46) is inconsistent.
% 6.84/1.74  | | | 
% 6.84/1.74  | | Case 2:
% 6.84/1.74  | | | 
% 6.84/1.74  | | |   (47)   ~ (all_23_1 = 0) &  ~ (all_13_4 = all_13_5)
% 6.84/1.74  | | | 
% 6.84/1.74  | | | ALPHA: (47) implies:
% 6.84/1.74  | | |   (48)   ~ (all_23_1 = 0)
% 6.84/1.74  | | | 
% 6.84/1.74  | | | REDUCE: (36), (48) imply:
% 6.84/1.74  | | |   (49)  $false
% 6.84/1.74  | | | 
% 6.84/1.74  | | | CLOSE: (49) is inconsistent.
% 6.84/1.74  | | | 
% 6.84/1.74  | | End of split
% 6.84/1.74  | | 
% 6.84/1.74  | End of split
% 6.84/1.74  | 
% 6.84/1.74  End of proof
% 6.84/1.74  % SZS output end Proof for theBenchmark
% 6.84/1.74  
% 6.84/1.74  1117ms
%------------------------------------------------------------------------------