TSTP Solution File: SET347+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET347+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n032.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 15:24:41 EDT 2023

% Result   : Theorem 6.51s 1.55s
% Output   : Proof 7.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET347+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.30  % Computer : n032.cluster.edu
% 0.13/0.30  % Model    : x86_64 x86_64
% 0.13/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30  % Memory   : 8042.1875MB
% 0.13/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30  % CPULimit : 300
% 0.13/0.30  % WCLimit  : 300
% 0.13/0.30  % DateTime : Sat Aug 26 15:09:59 EDT 2023
% 0.13/0.30  % CPUTime  : 
% 0.15/0.52  ________       _____
% 0.15/0.52  ___  __ \_________(_)________________________________
% 0.15/0.52  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.15/0.52  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.15/0.52  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.15/0.52  
% 0.15/0.52  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.52  (2023-06-19)
% 0.15/0.52  
% 0.15/0.52  (c) Philipp Rümmer, 2009-2023
% 0.15/0.52  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.52                Amanda Stjerna.
% 0.15/0.52  Free software under BSD-3-Clause.
% 0.15/0.52  
% 0.15/0.52  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.52  
% 0.15/0.52  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.54  Running up to 7 provers in parallel.
% 0.15/0.55  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.55  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.55  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.55  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.55  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.55  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.01/0.91  Prover 1: Preprocessing ...
% 2.01/0.92  Prover 4: Preprocessing ...
% 2.01/0.95  Prover 0: Preprocessing ...
% 2.01/0.95  Prover 2: Preprocessing ...
% 2.01/0.95  Prover 3: Preprocessing ...
% 2.01/0.95  Prover 5: Preprocessing ...
% 2.01/0.95  Prover 6: Preprocessing ...
% 4.96/1.33  Prover 1: Constructing countermodel ...
% 4.96/1.34  Prover 3: Constructing countermodel ...
% 4.96/1.35  Prover 6: Proving ...
% 4.96/1.35  Prover 5: Proving ...
% 4.96/1.36  Prover 2: Proving ...
% 4.96/1.38  Prover 0: Proving ...
% 4.96/1.38  Prover 4: Constructing countermodel ...
% 6.51/1.55  Prover 3: proved (1002ms)
% 6.51/1.55  
% 6.51/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.51/1.55  
% 6.51/1.56  Prover 6: stopped
% 6.51/1.56  Prover 0: stopped
% 6.51/1.56  Prover 2: stopped
% 6.51/1.56  Prover 5: stopped
% 6.51/1.56  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.51/1.56  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.51/1.56  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.51/1.56  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.51/1.56  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.86/1.60  Prover 8: Preprocessing ...
% 6.86/1.60  Prover 7: Preprocessing ...
% 6.86/1.60  Prover 13: Preprocessing ...
% 6.86/1.61  Prover 11: Preprocessing ...
% 6.86/1.61  Prover 10: Preprocessing ...
% 6.86/1.62  Prover 1: Found proof (size 33)
% 6.86/1.62  Prover 1: proved (1079ms)
% 6.86/1.62  Prover 4: stopped
% 6.86/1.63  Prover 7: stopped
% 6.86/1.64  Prover 13: stopped
% 6.86/1.64  Prover 10: stopped
% 6.86/1.64  Prover 11: stopped
% 7.41/1.69  Prover 8: Warning: ignoring some quantifiers
% 7.41/1.70  Prover 8: Constructing countermodel ...
% 7.41/1.70  Prover 8: stopped
% 7.41/1.70  
% 7.41/1.71  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.41/1.71  
% 7.64/1.71  % SZS output start Proof for theBenchmark
% 7.64/1.72  Assumptions after simplification:
% 7.64/1.72  ---------------------------------
% 7.64/1.72  
% 7.64/1.72    (empty_set)
% 7.64/1.74    $i(empty_set) &  ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) |  ~ $i(v0))
% 7.64/1.74  
% 7.64/1.74    (equal_set)
% 7.80/1.74     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0, v1) =
% 7.80/1.74        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (subset(v1,
% 7.80/1.74          v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0:
% 7.80/1.74      $i] :  ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 7.80/1.74      (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.80/1.74  
% 7.80/1.74    (subset)
% 7.80/1.75     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 7.80/1.75      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 7.80/1.75        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 7.80/1.75    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 7.80/1.75        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 7.80/1.75  
% 7.80/1.75    (sum)
% 7.80/1.75     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (sum(v1)
% 7.80/1.75        = v2) |  ~ (member(v0, v2) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ! [v4: $i] : (
% 7.80/1.75        ~ (member(v0, v4) = 0) |  ~ $i(v4) |  ? [v5: int] : ( ~ (v5 = 0) &
% 7.80/1.75          member(v4, v1) = v5))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 7.80/1.75      (sum(v1) = v2) |  ~ (member(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 7.80/1.75        $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 7.80/1.75  
% 7.80/1.75    (thI38)
% 7.80/1.75    $i(empty_set) &  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & sum(empty_set) =
% 7.80/1.75      v0 & equal_set(v0, empty_set) = v1 & $i(v0))
% 7.80/1.75  
% 7.80/1.75  Further assumptions not needed in the proof:
% 7.80/1.75  --------------------------------------------
% 7.80/1.75  difference, intersection, power_set, product, singleton, union, unordered_pair
% 7.80/1.75  
% 7.80/1.75  Those formulas are unsatisfiable:
% 7.80/1.75  ---------------------------------
% 7.80/1.75  
% 7.80/1.75  Begin of proof
% 7.80/1.76  | 
% 7.80/1.76  | ALPHA: (subset) implies:
% 7.80/1.76  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 7.80/1.76  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 7.80/1.76  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.80/1.76  | 
% 7.80/1.76  | ALPHA: (equal_set) implies:
% 7.80/1.76  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0,
% 7.80/1.76  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 7.80/1.76  |          (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 7.80/1.76  |                0))))
% 7.80/1.76  | 
% 7.80/1.76  | ALPHA: (empty_set) implies:
% 7.80/1.76  |   (3)   ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) |  ~ $i(v0))
% 7.80/1.76  | 
% 7.80/1.76  | ALPHA: (sum) implies:
% 7.80/1.76  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sum(v1) = v2) |  ~
% 7.80/1.76  |          (member(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :
% 7.80/1.76  |          (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 7.80/1.76  | 
% 7.80/1.76  | ALPHA: (thI38) implies:
% 7.80/1.76  |   (5)  $i(empty_set)
% 7.80/1.76  |   (6)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & sum(empty_set) = v0 &
% 7.80/1.76  |          equal_set(v0, empty_set) = v1 & $i(v0))
% 7.80/1.76  | 
% 7.80/1.76  | DELTA: instantiating (6) with fresh symbols all_15_0, all_15_1 gives:
% 7.80/1.77  |   (7)   ~ (all_15_0 = 0) & sum(empty_set) = all_15_1 & equal_set(all_15_1,
% 7.80/1.77  |          empty_set) = all_15_0 & $i(all_15_1)
% 7.80/1.77  | 
% 7.80/1.77  | ALPHA: (7) implies:
% 7.80/1.77  |   (8)   ~ (all_15_0 = 0)
% 7.80/1.77  |   (9)  $i(all_15_1)
% 7.80/1.77  |   (10)  equal_set(all_15_1, empty_set) = all_15_0
% 7.80/1.77  |   (11)  sum(empty_set) = all_15_1
% 7.80/1.77  | 
% 7.80/1.77  | GROUND_INST: instantiating (2) with all_15_1, empty_set, all_15_0, simplifying
% 7.80/1.77  |              with (5), (9), (10) gives:
% 7.80/1.77  |   (12)  all_15_0 = 0 |  ? [v0: any] :  ? [v1: any] : (subset(all_15_1,
% 7.80/1.77  |             empty_set) = v0 & subset(empty_set, all_15_1) = v1 & ( ~ (v1 = 0)
% 7.80/1.77  |             |  ~ (v0 = 0)))
% 7.80/1.77  | 
% 7.80/1.77  | BETA: splitting (12) gives:
% 7.80/1.77  | 
% 7.80/1.77  | Case 1:
% 7.80/1.77  | | 
% 7.80/1.77  | |   (13)  all_15_0 = 0
% 7.80/1.77  | | 
% 7.80/1.77  | | REDUCE: (8), (13) imply:
% 7.80/1.77  | |   (14)  $false
% 7.80/1.77  | | 
% 7.80/1.77  | | CLOSE: (14) is inconsistent.
% 7.80/1.77  | | 
% 7.80/1.77  | Case 2:
% 7.80/1.77  | | 
% 7.80/1.77  | |   (15)   ? [v0: any] :  ? [v1: any] : (subset(all_15_1, empty_set) = v0 &
% 7.80/1.77  | |           subset(empty_set, all_15_1) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 7.80/1.77  | | 
% 7.80/1.77  | | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives:
% 7.80/1.77  | |   (16)  subset(all_15_1, empty_set) = all_24_1 & subset(empty_set, all_15_1)
% 7.80/1.77  | |         = all_24_0 & ( ~ (all_24_0 = 0) |  ~ (all_24_1 = 0))
% 7.80/1.77  | | 
% 7.80/1.77  | | ALPHA: (16) implies:
% 7.80/1.77  | |   (17)  subset(empty_set, all_15_1) = all_24_0
% 7.80/1.77  | |   (18)  subset(all_15_1, empty_set) = all_24_1
% 7.80/1.77  | |   (19)   ~ (all_24_0 = 0) |  ~ (all_24_1 = 0)
% 7.80/1.77  | | 
% 7.80/1.77  | | GROUND_INST: instantiating (1) with empty_set, all_15_1, all_24_0,
% 7.80/1.77  | |              simplifying with (5), (9), (17) gives:
% 7.80/1.77  | |   (20)  all_24_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 7.80/1.77  | |           member(v0, all_15_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 7.80/1.77  | | 
% 7.80/1.78  | | GROUND_INST: instantiating (1) with all_15_1, empty_set, all_24_1,
% 7.80/1.78  | |              simplifying with (5), (9), (18) gives:
% 7.80/1.78  | |   (21)  all_24_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 7.80/1.78  | |           member(v0, all_15_1) = 0 & member(v0, empty_set) = v1 & $i(v0))
% 7.80/1.78  | | 
% 7.80/1.78  | | BETA: splitting (19) gives:
% 7.80/1.78  | | 
% 7.80/1.78  | | Case 1:
% 7.80/1.78  | | | 
% 7.80/1.78  | | |   (22)   ~ (all_24_0 = 0)
% 7.80/1.78  | | | 
% 7.80/1.78  | | | BETA: splitting (20) gives:
% 7.80/1.78  | | | 
% 7.80/1.78  | | | Case 1:
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | |   (23)  all_24_0 = 0
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | REDUCE: (22), (23) imply:
% 7.80/1.78  | | | |   (24)  $false
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | CLOSE: (24) is inconsistent.
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | Case 2:
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | |   (25)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 7.80/1.78  | | | |           = v1 & member(v0, empty_set) = 0 & $i(v0))
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | DELTA: instantiating (25) with fresh symbols all_37_0, all_37_1 gives:
% 7.80/1.78  | | | |   (26)   ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 7.80/1.78  | | | |         member(all_37_1, empty_set) = 0 & $i(all_37_1)
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | ALPHA: (26) implies:
% 7.80/1.78  | | | |   (27)  $i(all_37_1)
% 7.80/1.78  | | | |   (28)  member(all_37_1, empty_set) = 0
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | GROUND_INST: instantiating (3) with all_37_1, simplifying with (27),
% 7.80/1.78  | | | |              (28) gives:
% 7.80/1.78  | | | |   (29)  $false
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | CLOSE: (29) is inconsistent.
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | End of split
% 7.80/1.78  | | | 
% 7.80/1.78  | | Case 2:
% 7.80/1.78  | | | 
% 7.80/1.78  | | |   (30)   ~ (all_24_1 = 0)
% 7.80/1.78  | | | 
% 7.80/1.78  | | | BETA: splitting (21) gives:
% 7.80/1.78  | | | 
% 7.80/1.78  | | | Case 1:
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | |   (31)  all_24_1 = 0
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | REDUCE: (30), (31) imply:
% 7.80/1.78  | | | |   (32)  $false
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | CLOSE: (32) is inconsistent.
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | Case 2:
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | |   (33)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 7.80/1.78  | | | |           = 0 & member(v0, empty_set) = v1 & $i(v0))
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | DELTA: instantiating (33) with fresh symbols all_37_0, all_37_1 gives:
% 7.80/1.78  | | | |   (34)   ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 7.80/1.78  | | | |         member(all_37_1, empty_set) = all_37_0 & $i(all_37_1)
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | ALPHA: (34) implies:
% 7.80/1.78  | | | |   (35)  $i(all_37_1)
% 7.80/1.78  | | | |   (36)  member(all_37_1, all_15_1) = 0
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | GROUND_INST: instantiating (4) with all_37_1, empty_set, all_15_1,
% 7.80/1.78  | | | |              simplifying with (5), (11), (35), (36) gives:
% 7.80/1.78  | | | |   (37)   ? [v0: $i] : (member(v0, empty_set) = 0 & member(all_37_1, v0)
% 7.80/1.78  | | | |           = 0 & $i(v0))
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | DELTA: instantiating (37) with fresh symbol all_45_0 gives:
% 7.80/1.78  | | | |   (38)  member(all_45_0, empty_set) = 0 & member(all_37_1, all_45_0) = 0
% 7.80/1.78  | | | |         & $i(all_45_0)
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | ALPHA: (38) implies:
% 7.80/1.78  | | | |   (39)  $i(all_45_0)
% 7.80/1.78  | | | |   (40)  member(all_45_0, empty_set) = 0
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | GROUND_INST: instantiating (3) with all_45_0, simplifying with (39),
% 7.80/1.78  | | | |              (40) gives:
% 7.80/1.78  | | | |   (41)  $false
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | | CLOSE: (41) is inconsistent.
% 7.80/1.78  | | | | 
% 7.80/1.78  | | | End of split
% 7.80/1.78  | | | 
% 7.80/1.78  | | End of split
% 7.80/1.78  | | 
% 7.80/1.78  | End of split
% 7.80/1.78  | 
% 7.80/1.78  End of proof
% 7.80/1.78  % SZS output end Proof for theBenchmark
% 7.80/1.78  
% 7.80/1.78  1259ms
%------------------------------------------------------------------------------