TSTP Solution File: SET762+4 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.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 15:26:20 EDT 2023

% Result   : Theorem 11.12s 2.20s
% Output   : Proof 13.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.03/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 10:54:50 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.53/0.62  ________       _____
% 0.53/0.62  ___  __ \_________(_)________________________________
% 0.53/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.53/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.53/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.53/0.62  
% 0.53/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.62  (2023-06-19)
% 0.53/0.62  
% 0.53/0.62  (c) Philipp Rümmer, 2009-2023
% 0.53/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.62                Amanda Stjerna.
% 0.53/0.62  Free software under BSD-3-Clause.
% 0.53/0.62  
% 0.53/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.62  
% 0.53/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.64  Running up to 7 provers in parallel.
% 0.69/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.53/1.17  Prover 4: Preprocessing ...
% 3.53/1.17  Prover 1: Preprocessing ...
% 3.78/1.21  Prover 6: Preprocessing ...
% 3.78/1.21  Prover 2: Preprocessing ...
% 3.78/1.21  Prover 3: Preprocessing ...
% 3.78/1.21  Prover 0: Preprocessing ...
% 3.78/1.21  Prover 5: Preprocessing ...
% 8.75/1.86  Prover 5: Proving ...
% 8.75/1.88  Prover 2: Proving ...
% 9.32/1.93  Prover 6: Proving ...
% 9.79/2.03  Prover 1: Constructing countermodel ...
% 9.79/2.04  Prover 3: Constructing countermodel ...
% 11.12/2.19  Prover 3: proved (1549ms)
% 11.12/2.20  
% 11.12/2.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.12/2.20  
% 11.12/2.20  Prover 2: stopped
% 11.12/2.20  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.12/2.21  Prover 6: stopped
% 11.12/2.21  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.12/2.21  Prover 5: stopped
% 11.12/2.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.70/2.22  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.70/2.25  Prover 7: Preprocessing ...
% 11.70/2.27  Prover 8: Preprocessing ...
% 11.70/2.28  Prover 10: Preprocessing ...
% 12.15/2.29  Prover 11: Preprocessing ...
% 12.15/2.32  Prover 1: Found proof (size 33)
% 12.15/2.32  Prover 1: proved (1674ms)
% 12.15/2.32  Prover 7: stopped
% 12.15/2.32  Prover 10: stopped
% 12.83/2.39  Prover 4: Constructing countermodel ...
% 12.83/2.40  Prover 11: stopped
% 12.83/2.41  Prover 0: Proving ...
% 12.83/2.41  Prover 0: stopped
% 13.14/2.42  Prover 4: stopped
% 13.26/2.50  Prover 8: Warning: ignoring some quantifiers
% 13.26/2.52  Prover 8: Constructing countermodel ...
% 13.68/2.52  Prover 8: stopped
% 13.68/2.52  
% 13.68/2.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.68/2.52  
% 13.68/2.53  % SZS output start Proof for theBenchmark
% 13.68/2.53  Assumptions after simplification:
% 13.68/2.53  ---------------------------------
% 13.68/2.53  
% 13.68/2.53    (empty_set)
% 13.68/2.56    $i(empty_set) &  ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) |  ~ $i(v0))
% 13.68/2.56  
% 13.68/2.56    (equal_set)
% 13.68/2.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0, v1) =
% 13.68/2.56        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] : (subset(v1,
% 13.68/2.56          v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0:
% 13.68/2.56      $i] :  ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 13.68/2.56      (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.68/2.56  
% 13.68/2.56    (image2)
% 13.68/2.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 13.68/2.56      |  ~ (image2(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ~ $i(v2) |  ~
% 13.68/2.56      $i(v1) |  ~ $i(v0) |  ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) |  ~ $i(v5) |
% 13.68/2.56         ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) &  ! [v0: $i] :  !
% 13.68/2.56    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (image2(v0, v1) = v3) |  ~
% 13.68/2.56      (member(v2, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: $i] :
% 13.68/2.56      (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4)))
% 13.68/2.56  
% 13.68/2.56    (subset)
% 13.68/2.57     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 13.68/2.57      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) &
% 13.68/2.57        member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  !
% 13.68/2.57    [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : (
% 13.68/2.57        ~ (member(v2, v0) = 0) |  ~ $i(v2) | member(v2, v1) = 0))
% 13.68/2.57  
% 13.68/2.57    (thIIa12)
% 13.68/2.57    $i(empty_set) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ?
% 13.68/2.57    [v4: int] : ( ~ (v4 = 0) & image2(v0, empty_set) = v3 & maps(v0, v1, v2) = 0 &
% 13.68/2.57      equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.68/2.57  
% 13.68/2.57  Further assumptions not needed in the proof:
% 13.68/2.57  --------------------------------------------
% 13.68/2.57  compose_function, compose_predicate, decreasing_function, difference,
% 13.68/2.57  equal_maps, identity, image3, increasing_function, injective, intersection,
% 13.68/2.57  inverse_function, inverse_image2, inverse_image3, inverse_predicate,
% 13.68/2.57  isomorphism, maps, one_to_one, power_set, product, singleton, sum, surjective,
% 13.68/2.57  union, unordered_pair
% 13.68/2.57  
% 13.68/2.57  Those formulas are unsatisfiable:
% 13.68/2.57  ---------------------------------
% 13.68/2.57  
% 13.68/2.57  Begin of proof
% 13.68/2.57  | 
% 13.68/2.57  | ALPHA: (subset) implies:
% 13.68/2.57  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 13.68/2.57  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 13.68/2.57  |            (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.68/2.57  | 
% 13.68/2.57  | ALPHA: (equal_set) implies:
% 13.68/2.57  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equal_set(v0,
% 13.68/2.57  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 13.68/2.57  |          (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 13.68/2.57  |                0))))
% 13.68/2.57  | 
% 13.68/2.57  | ALPHA: (empty_set) implies:
% 13.68/2.58  |   (3)   ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) |  ~ $i(v0))
% 13.68/2.58  | 
% 13.68/2.58  | ALPHA: (image2) implies:
% 13.68/2.58  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (image2(v0,
% 13.68/2.58  |              v1) = v3) |  ~ (member(v2, v3) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 13.68/2.58  |          $i(v0) |  ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 &
% 13.68/2.58  |            $i(v4)))
% 13.68/2.58  | 
% 13.68/2.58  | ALPHA: (thIIa12) implies:
% 13.68/2.58  |   (5)  $i(empty_set)
% 13.68/2.58  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] :
% 13.68/2.58  |        ( ~ (v4 = 0) & image2(v0, empty_set) = v3 & maps(v0, v1, v2) = 0 &
% 13.68/2.58  |          equal_set(v3, empty_set) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.68/2.58  | 
% 13.68/2.58  | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2,
% 13.68/2.58  |        all_32_3, all_32_4 gives:
% 13.68/2.58  |   (7)   ~ (all_32_0 = 0) & image2(all_32_4, empty_set) = all_32_1 &
% 13.68/2.58  |        maps(all_32_4, all_32_3, all_32_2) = 0 & equal_set(all_32_1, empty_set)
% 13.68/2.58  |        = all_32_0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4)
% 13.68/2.58  | 
% 13.68/2.58  | ALPHA: (7) implies:
% 13.68/2.58  |   (8)   ~ (all_32_0 = 0)
% 13.68/2.58  |   (9)  $i(all_32_4)
% 13.68/2.58  |   (10)  $i(all_32_1)
% 13.98/2.58  |   (11)  equal_set(all_32_1, empty_set) = all_32_0
% 13.98/2.58  |   (12)  image2(all_32_4, empty_set) = all_32_1
% 13.98/2.58  | 
% 13.98/2.58  | GROUND_INST: instantiating (2) with all_32_1, empty_set, all_32_0, simplifying
% 13.98/2.58  |              with (5), (10), (11) gives:
% 13.98/2.58  |   (13)  all_32_0 = 0 |  ? [v0: any] :  ? [v1: any] : (subset(all_32_1,
% 13.98/2.58  |             empty_set) = v0 & subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0)
% 13.98/2.58  |             |  ~ (v0 = 0)))
% 13.98/2.58  | 
% 13.98/2.58  | BETA: splitting (13) gives:
% 13.98/2.58  | 
% 13.98/2.58  | Case 1:
% 13.98/2.58  | | 
% 13.98/2.58  | |   (14)  all_32_0 = 0
% 13.98/2.58  | | 
% 13.98/2.58  | | REDUCE: (8), (14) imply:
% 13.98/2.58  | |   (15)  $false
% 13.98/2.58  | | 
% 13.98/2.58  | | CLOSE: (15) is inconsistent.
% 13.98/2.58  | | 
% 13.98/2.58  | Case 2:
% 13.98/2.58  | | 
% 13.98/2.58  | |   (16)   ? [v0: any] :  ? [v1: any] : (subset(all_32_1, empty_set) = v0 &
% 13.98/2.58  | |           subset(empty_set, all_32_1) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 13.98/2.58  | | 
% 13.98/2.58  | | DELTA: instantiating (16) with fresh symbols all_44_0, all_44_1 gives:
% 13.98/2.59  | |   (17)  subset(all_32_1, empty_set) = all_44_1 & subset(empty_set, all_32_1)
% 13.98/2.59  | |         = all_44_0 & ( ~ (all_44_0 = 0) |  ~ (all_44_1 = 0))
% 13.98/2.59  | | 
% 13.98/2.59  | | ALPHA: (17) implies:
% 13.98/2.59  | |   (18)  subset(empty_set, all_32_1) = all_44_0
% 13.98/2.59  | |   (19)  subset(all_32_1, empty_set) = all_44_1
% 13.98/2.59  | |   (20)   ~ (all_44_0 = 0) |  ~ (all_44_1 = 0)
% 13.98/2.59  | | 
% 13.98/2.59  | | GROUND_INST: instantiating (1) with empty_set, all_32_1, all_44_0,
% 13.98/2.59  | |              simplifying with (5), (10), (18) gives:
% 13.98/2.59  | |   (21)  all_44_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 13.98/2.59  | |           member(v0, all_32_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.98/2.59  | | 
% 13.98/2.59  | | GROUND_INST: instantiating (1) with all_32_1, empty_set, all_44_1,
% 13.98/2.59  | |              simplifying with (5), (10), (19) gives:
% 13.98/2.59  | |   (22)  all_44_1 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) &
% 13.98/2.59  | |           member(v0, all_32_1) = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.98/2.59  | | 
% 13.98/2.59  | | BETA: splitting (20) gives:
% 13.98/2.59  | | 
% 13.98/2.59  | | Case 1:
% 13.98/2.59  | | | 
% 13.98/2.59  | | |   (23)   ~ (all_44_0 = 0)
% 13.98/2.59  | | | 
% 13.98/2.59  | | | BETA: splitting (21) gives:
% 13.98/2.59  | | | 
% 13.98/2.59  | | | Case 1:
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | |   (24)  all_44_0 = 0
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | REDUCE: (23), (24) imply:
% 13.98/2.59  | | | |   (25)  $false
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | CLOSE: (25) is inconsistent.
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | Case 2:
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | |   (26)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.98/2.59  | | | |           = v1 & member(v0, empty_set) = 0 & $i(v0))
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | DELTA: instantiating (26) with fresh symbols all_57_0, all_57_1 gives:
% 13.98/2.59  | | | |   (27)   ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = all_57_0 &
% 13.98/2.59  | | | |         member(all_57_1, empty_set) = 0 & $i(all_57_1)
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | ALPHA: (27) implies:
% 13.98/2.59  | | | |   (28)  $i(all_57_1)
% 13.98/2.59  | | | |   (29)  member(all_57_1, empty_set) = 0
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | GROUND_INST: instantiating (3) with all_57_1, simplifying with (28),
% 13.98/2.59  | | | |              (29) gives:
% 13.98/2.59  | | | |   (30)  $false
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | CLOSE: (30) is inconsistent.
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | End of split
% 13.98/2.59  | | | 
% 13.98/2.59  | | Case 2:
% 13.98/2.59  | | | 
% 13.98/2.59  | | |   (31)   ~ (all_44_1 = 0)
% 13.98/2.59  | | | 
% 13.98/2.59  | | | BETA: splitting (22) gives:
% 13.98/2.59  | | | 
% 13.98/2.59  | | | Case 1:
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | |   (32)  all_44_1 = 0
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | REDUCE: (31), (32) imply:
% 13.98/2.59  | | | |   (33)  $false
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | CLOSE: (33) is inconsistent.
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | Case 2:
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | |   (34)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 13.98/2.59  | | | |           = 0 & member(v0, empty_set) = v1 & $i(v0))
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | DELTA: instantiating (34) with fresh symbols all_57_0, all_57_1 gives:
% 13.98/2.59  | | | |   (35)   ~ (all_57_0 = 0) & member(all_57_1, all_32_1) = 0 &
% 13.98/2.59  | | | |         member(all_57_1, empty_set) = all_57_0 & $i(all_57_1)
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | ALPHA: (35) implies:
% 13.98/2.59  | | | |   (36)  $i(all_57_1)
% 13.98/2.59  | | | |   (37)  member(all_57_1, all_32_1) = 0
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | GROUND_INST: instantiating (4) with all_32_4, empty_set, all_57_1,
% 13.98/2.59  | | | |              all_32_1, simplifying with (5), (9), (12), (36), (37)
% 13.98/2.59  | | | |              gives:
% 13.98/2.59  | | | |   (38)   ? [v0: $i] : (apply(all_32_4, v0, all_57_1) = 0 & member(v0,
% 13.98/2.59  | | | |             empty_set) = 0 & $i(v0))
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | DELTA: instantiating (38) with fresh symbol all_65_0 gives:
% 13.98/2.59  | | | |   (39)  apply(all_32_4, all_65_0, all_57_1) = 0 & member(all_65_0,
% 13.98/2.59  | | | |           empty_set) = 0 & $i(all_65_0)
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | ALPHA: (39) implies:
% 13.98/2.59  | | | |   (40)  $i(all_65_0)
% 13.98/2.59  | | | |   (41)  member(all_65_0, empty_set) = 0
% 13.98/2.59  | | | | 
% 13.98/2.59  | | | | GROUND_INST: instantiating (3) with all_65_0, simplifying with (40),
% 13.98/2.59  | | | |              (41) gives:
% 13.98/2.60  | | | |   (42)  $false
% 13.98/2.60  | | | | 
% 13.98/2.60  | | | | CLOSE: (42) is inconsistent.
% 13.98/2.60  | | | | 
% 13.98/2.60  | | | End of split
% 13.98/2.60  | | | 
% 13.98/2.60  | | End of split
% 13.98/2.60  | | 
% 13.98/2.60  | End of split
% 13.98/2.60  | 
% 13.98/2.60  End of proof
% 13.98/2.60  % SZS output end Proof for theBenchmark
% 13.98/2.60  
% 13.98/2.60  1970ms
%------------------------------------------------------------------------------